From 669bfb399125ec3c08ce9d7e24a4eb590ee68402 Mon Sep 17 00:00:00 2001 From: John Maddock Date: Mon, 7 Apr 2008 15:58:51 +0000 Subject: [PATCH] Merged changes from sandbox to Trunk: New special functions for truncation and rounding, plus exponential integrals and zeta. New non central distributions. Updated equation png's so that they are all consistent. 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100644 test/test_nc_t.cpp create mode 100644 test/test_ncbeta_hooks.hpp create mode 100644 test/test_nccs_hooks.hpp create mode 100644 test/test_round.cpp create mode 100644 test/test_zeta.cpp create mode 100644 test/test_zeta_hooks.hpp create mode 100644 test/zeta_1_below_data.ipp create mode 100644 test/zeta_1_up_data.ipp create mode 100644 test/zeta_data.ipp create mode 100644 test/zeta_neg_data.ipp create mode 100644 tools/expint_data.cpp create mode 100644 tools/expint_i_data.cpp create mode 100644 tools/zeta_data.cpp diff --git a/doc/sf_and_dist/Jamfile.v2 b/doc/sf_and_dist/Jamfile.v2 index 809b96ea2..852f2e3ae 100644 --- a/doc/sf_and_dist/Jamfile.v2 +++ b/doc/sf_and_dist/Jamfile.v2 @@ -40,7 +40,7 @@ boostbook standalone # PDF Options: # TOC Generation: this is needed for FOP-0.9 and later: - # fop1.extensions=1 + fop1.extensions=0 pdf:xep.extensions=1 # TOC generation: this is needed for FOP 0.2, but must not be set to zero for FOP-0.9! pdf:fop.extensions=0 diff --git a/doc/sf_and_dist/bessel_ik.qbk b/doc/sf_and_dist/bessel_ik.qbk index 9c246323c..aad74dd44 100644 --- a/doc/sf_and_dist/bessel_ik.qbk +++ b/doc/sf_and_dist/bessel_ik.qbk @@ -44,11 +44,11 @@ when `x <= 0`. The following graph illustrates the exponential behaviour of I[sub v]. -[$../graphs/bessel_i.png] +[graph cyl_bessel_i] The following graph illustrates the exponential decay of K[sub v]. -[$../graphs/bessel_k.png] +[graph cyl_bessel_k] [h4 Testing] diff --git a/doc/sf_and_dist/bessel_jy.qbk b/doc/sf_and_dist/bessel_jy.qbk index 04a6a5115..a970e09ea 100644 --- a/doc/sf_and_dist/bessel_jy.qbk +++ b/doc/sf_and_dist/bessel_jy.qbk @@ -44,12 +44,12 @@ when `x <= 0`. The following graph illustrates the cyclic nature of J[sub v]: -[$../graphs/bessel_jn.png] +[graph cyl_bessel_j] The following graph shows the behaviour of Y[sub v]: this is also cyclic for large /x/, but tends to -[infin][space] for small /x/: -[$../graphs/bessel_yv.png] +[graph cyl_neumann] [h4 Testing] diff --git a/doc/sf_and_dist/bessel_spherical.qbk b/doc/sf_and_dist/bessel_spherical.qbk index 7be51d8a2..6f5175583 100644 --- a/doc/sf_and_dist/bessel_spherical.qbk +++ b/doc/sf_and_dist/bessel_spherical.qbk @@ -39,12 +39,12 @@ undefined or complex: this occurs when `x < 0`. The j[sub v][space] function is cyclic like J[sub v][space] but differs in its behaviour at the origin: -[$../graphs/sph_bessel_j.png] +[graph sph_bessel] Likewise y[sub v][space] is also cyclic for large x, but tends to -[infin][space] for small /x/: -[$../graphs/sph_bessel_y.png] +[graph sph_neumann] [h4 Testing] diff --git a/doc/sf_and_dist/beta.qbk b/doc/sf_and_dist/beta.qbk index 8ec6ecc65..c9b0589bc 100644 --- a/doc/sf_and_dist/beta.qbk +++ b/doc/sf_and_dist/beta.qbk @@ -22,7 +22,7 @@ The beta function is defined by: [equation beta1] -[$../graphs/beta.png] +[graph beta] [optional_policy] diff --git a/doc/sf_and_dist/concepts.qbk b/doc/sf_and_dist/concepts.qbk index 5396241d2..3345006c7 100644 --- a/doc/sf_and_dist/concepts.qbk +++ b/doc/sf_and_dist/concepts.qbk @@ -174,13 +174,25 @@ In the following table /r/ is an object of type `RealType`, [[`asin(cr1)`][RealType]] [[`tan(cr1)`][RealType]] [[`atan(cr1)`][RealType]] +[[`fmod(cr1)`][RealType]] +[[`round(cr1)`][RealType]] +[[`iround(cr1)`][int]] +[[`trunc(cr1)`][RealType]] +[[`itrunc(cr1)`][int]] ] Note that the table above lists only those standard library functions known to be used (or likely to be used in the near future) by this library. -The following functions: `acos`, `atan2`, `fmod`, `cosh`, `sinh`, `tanh`, `modf` and `log10` +The following functions: `acos`, `atan2`, `fmod`, `cosh`, `sinh`, `tanh`, `log10`, +`lround`, `llround`, ltrunc`, `lltrunc` and `modf` are not currently used, but may be if further special functions are added. +Note that the `round`, `trunc` and `modf` functions are not part of the +current C++ standard: they are part of the additions added to C99 which will +likely be in the next C++ standard. There are Boost versions of these provided +as a backup, and the functions are always called unqualified so that +argument-dependent-lookup can take place. + In addition, for efficient and accurate results, a __lanczos is highly desirable. You may be able to adapt an existing approximation from [@../../../../../boost/math/special_functions/lanczos.hpp diff --git a/doc/sf_and_dist/credits.qbk b/doc/sf_and_dist/credits.qbk index 8faca7fa6..1fafc36b7 100644 --- a/doc/sf_and_dist/credits.qbk +++ b/doc/sf_and_dist/credits.qbk @@ -33,6 +33,17 @@ his program used to generate the html and pdf versions of this document, adding several new features en route. +Plots of the functions and distributions were prepared in +[@http://www.w3.org/ W3C] standard +[@http://www.svg.org/ Scalable Vector Graphic (SVG)] format +using a program created by Jacob Voytko during a Google 'Summer of Code'. +Since browser support for rendering SVG is still not universal +(Microsoft Internet Explorer, even IE 8 beta, still lacks native SVG support +but can be made to work with +[@http://www.adobe.com/svg/viewer/install/ Adobe's free SVG viewer] plugin), +so the SVG files were batch converted to JPEG using +[@http://www.inkscape.org/ Inkscape]. + We are also indebted to Matthias Schabel for managing the formal Boost-review of this library, and to all the reviewers - including Guillaume Melquiond, Arnaldur Gylfason, John Phillips, Stephan Tolksdorf and Jeff Garland @@ -41,7 +52,7 @@ Arnaldur Gylfason, John Phillips, Stephan Tolksdorf and Jeff Garland [endsect][/section:roadmap Roadmap] [/ - Copyright 2006 John Maddock and Paul A. Bristow. + Copyright 2006 - 2008 John Maddock and Paul A. Bristow. Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt). diff --git a/doc/sf_and_dist/digamma.qbk b/doc/sf_and_dist/digamma.qbk index c460c63b7..cf3b9c232 100644 --- a/doc/sf_and_dist/digamma.qbk +++ b/doc/sf_and_dist/digamma.qbk @@ -23,7 +23,7 @@ derivative of the gamma function: [equation digamma1] -[$../graphs/digamma.png] +[graph digamma] [optional_policy] diff --git a/doc/sf_and_dist/dist_reference.qbk b/doc/sf_and_dist/dist_reference.qbk index 100bafee0..ecb4e1260 100644 --- a/doc/sf_and_dist/dist_reference.qbk +++ b/doc/sf_and_dist/dist_reference.qbk @@ -15,6 +15,10 @@ [include distributions/gamma.qbk] [include distributions/lognormal.qbk] [include distributions/negative_binomial.qbk] +[include distributions/nc_beta.qbk] +[include distributions/nc_chi_squared.qbk] +[include distributions/nc_f.qbk] +[include distributions/nc_t.qbk] [include distributions/normal.qbk] [include distributions/pareto.qbk] [include distributions/poisson.qbk] diff --git a/doc/sf_and_dist/dist_tutorial.qbk b/doc/sf_and_dist/dist_tutorial.qbk index c687b127e..f09d9b521 100644 --- a/doc/sf_and_dist/dist_tutorial.qbk +++ b/doc/sf_and_dist/dist_tutorial.qbk @@ -158,13 +158,32 @@ example, we would write: `pdf(binomial_distribution(n, p), k);` -The distribution (effectively the random variate) is said to be 'supported' over a range that is +The ranges of random variate values that are permitted and are supported can be +tested by using two functions `range` and `support`. + +The distribution (effectively the random variate) is said to be 'supported' +over a range that is [@http://en.wikipedia.org/wiki/Probability_distribution "the smallest closed set whose complement has probability zero"]. MathWorld uses the word 'defined' for this range. Non-mathematicians might say it means the 'interesting' smallest range of random variate x that has the cdf going from zero to unity. Outside are uninteresting zones where the pdf is zero, and the cdf zero or unity. + +For most distributions, with probability distribution functions one might describe +as 'well-behaved', we have decided that it is most useful for the supported range +to exclude random variate values like exact zero *if the end point is discontinuous*. +For example, the Weibull (scale 1, shape 1) distribution smoothly heads for unity +as the random variate x declines towards zero. +But at x = zero, the value of the pdf is suddenly exactly zero, by definition. +If you are plotting the PDF, or otherwise calculating, +zero is not the most useful value for the lower limit of supported, as we discovered. +So for this, and similar distributions, +we have decided it is most numerically useful to use +the closest value to zero, min_value, for the limit of the supported range. +(The `range` remains from zero, so you will still get `pdf(weibull, 0) == 0`). +(Exponential and gamma distributions have similarly discontinuous functions). + Mathematically, the functions may make sense with an (+ or -) infinite value, but except for a few special cases (in the Normal and Cauchy distributions) this implementation limits random variates to finite values from the `max` @@ -172,8 +191,6 @@ to `min` for the `RealType`. (See [link math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity Handling of Floating-Point Infinity] for rationale). -The range of random variate values that is permitted and supported can be -tested by using two functions `range` and `support`. [note @@ -365,6 +382,7 @@ Now that you have the basics, the next section looks at some worked examples. [include distributions/binomial_example.qbk] [include distributions/negative_binomial_example.qbk] [include distributions/normal_example.qbk] +[include distributions/nc_chi_squared_example.qbk] [include distributions/error_handling_example.qbk] [include distributions/find_location_and_scale.qbk] [include distributions/nag_library.qbk] diff --git a/doc/sf_and_dist/distributions/bernoulli.qbk b/doc/sf_and_dist/distributions/bernoulli.qbk index 17200fb41..d22af07a1 100644 --- a/doc/sf_and_dist/distributions/bernoulli.qbk +++ b/doc/sf_and_dist/distributions/bernoulli.qbk @@ -42,11 +42,11 @@ The following graph illustrates how the [@http://en.wikipedia.org/wiki/Probability_density_function probability density function pdf] varies with the outcome of the single trial: -[$../graphs/bernoulli_pdf.png] +[graph bernoulli_pdf] and the [@http://en.wikipedia.org/wiki/Cumulative_Distribution_Function Cumulative distribution function] -[$../graphs/bernoulli_cdf.png] +[graph bernoulli_cdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/beta.qbk b/doc/sf_and_dist/distributions/beta.qbk index 6686ea73c..3a88f925b 100644 --- a/doc/sf_and_dist/distributions/beta.qbk +++ b/doc/sf_and_dist/distributions/beta.qbk @@ -84,7 +84,7 @@ of the shape parameters. Note the [alpha] = [beta] = 2 (blue line) is dome-shaped, and might be approximated by a symmetrical triangular distribution. -[$../graphs/beta_dist.png] +[graph beta_pdf] If [alpha] = [beta] = 1, then it is a __space [@http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29 uniform distribution], diff --git a/doc/sf_and_dist/distributions/binomial.qbk b/doc/sf_and_dist/distributions/binomial.qbk index cad52611d..d790e1708 100644 --- a/doc/sf_and_dist/distributions/binomial.qbk +++ b/doc/sf_and_dist/distributions/binomial.qbk @@ -76,12 +76,12 @@ The following two graphs illustrate how the PDF changes depending upon the distributions parameters, first we'll keep the success fraction /p/ fixed at 0.5, and vary the sample size: -[$../graphs/binomial_pdf_1.png] +[graph binomial_pdf_1] Alternatively, we can keep the sample size fixed at N=20 and vary the success fraction /p/: -[$../graphs/binomial_pdf_2.png] +[graph binomial_pdf_2] [discrete_quantile_warning Binomial] diff --git a/doc/sf_and_dist/distributions/cauchy.qbk b/doc/sf_and_dist/distributions/cauchy.qbk index 34ff68dd1..f56fcbea0 100644 --- a/doc/sf_and_dist/distributions/cauchy.qbk +++ b/doc/sf_and_dist/distributions/cauchy.qbk @@ -44,12 +44,12 @@ of spectral lines. The following graph shows how the distributions moves as the location parameter changes: -[$../graphs/cauchy1.png] +[graph cauchy_pdf1] While the following graph shows how the shape (scale) parameter alters the distribution: -[$../graphs/cauchy2.png] +[graph cauchy_pdf2] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/chi_squared.qbk b/doc/sf_and_dist/distributions/chi_squared.qbk index c4ff4c278..ed4f208a9 100644 --- a/doc/sf_and_dist/distributions/chi_squared.qbk +++ b/doc/sf_and_dist/distributions/chi_squared.qbk @@ -49,7 +49,7 @@ and has a single parameter [nu][space] that specifies the number of degrees of freedom. The following graph illustrates how the distribution changes for different values of [nu]: -[$../graphs/chi_square.png] +[graph chi_squared_pdf] [h4 Member Functions] @@ -105,6 +105,11 @@ See also section on Sample sizes required in All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] that are generic to all distributions are supported: __usual_accessors. +(We have followed the usual restriction of the mode to degrees of freedom >= 2, +but note that the maximum of the pdf is actually zero for degrees of freedom from 2 down to 0, +and provide an extended definition that would avoid a discontinuity in the mode +as alternative code in a comment). + The domain of the random variable is \[0, +[infin]\]. [h4 Examples] diff --git a/doc/sf_and_dist/distributions/exponential.qbk b/doc/sf_and_dist/distributions/exponential.qbk index 93286dfe9..17d923a90 100644 --- a/doc/sf_and_dist/distributions/exponential.qbk +++ b/doc/sf_and_dist/distributions/exponential.qbk @@ -33,7 +33,7 @@ events that happen at a constant average rate. The following graph shows how the distribution changes for different values of the rate parameter lambda: -[$../graphs/exponential_dist.png] +[graph exponential_pdf] [h4 Member Functions] @@ -90,6 +90,13 @@ In the following table [lambda] is the parameter lambda of the distribution, * [@http://www.itl.nist.gov/div898/handbook/eda/section3/eda3667.htm NIST Exploratory Data Analysis] * [@http://en.wikipedia.org/wiki/Exponential_distribution Wikipedia Exponential distribution] +(See also the reference documentation for the related __extreme_distrib.) + +* +[@http://www.worldscibooks.com/mathematics/p191.html Extreme Value Distributions, Theory and Applications +Samuel Kotz & Saralees Nadarajah] +discuss the relationship of the types of extreme value distributions. + [endsect][/section:exp_dist Exponential] [/ exponential.qbk diff --git a/doc/sf_and_dist/distributions/extreme_value.qbk b/doc/sf_and_dist/distributions/extreme_value.qbk index 66c184088..5e81eb51e 100644 --- a/doc/sf_and_dist/distributions/extreme_value.qbk +++ b/doc/sf_and_dist/distributions/extreme_value.qbk @@ -36,6 +36,11 @@ More information can be found on the and [@http://en.wikipedia.org/wiki/Extreme_value_theory Extreme value theory] websites. +The relationship of the types of extreme value distributions, of which this is but one, is +discussed by +[@http://www.worldscibooks.com/mathematics/p191.html Extreme Value Distributions, Theory and Applications +Samuel Kotz & Saralees Nadarajah]. + The distribution has a PDF given by: f(x) = (1/scale) e[super -(x-location)/scale] e[super -e[super -(x-location)/scale]] @@ -46,11 +51,11 @@ f(x) = e[super -x]e[super -e[super -x]] The following graph illustrates how the PDF varies with the location parameter: -[$../graphs/extreme_val_dist.png] +[graph extreme_value_pdf1] And this graph illustrates how the PDF varies with the shape parameter: -[$../graphs/extreme_val_dist2.png] +[graph extreme_value_pdf2] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/fisher.qbk b/doc/sf_and_dist/distributions/fisher.qbk index 7887e2f94..3a4905ca4 100644 --- a/doc/sf_and_dist/distributions/fisher.qbk +++ b/doc/sf_and_dist/distributions/fisher.qbk @@ -41,7 +41,7 @@ has the PDF: The following graph illustrates how the PDF varies depending on the two degrees of freedom parameters. -[$../graphs/fisher_f.png] +[graph fisher_f_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/gamma.qbk b/doc/sf_and_dist/distributions/gamma.qbk index 1bc233351..9a84c7cb6 100644 --- a/doc/sf_and_dist/distributions/gamma.qbk +++ b/doc/sf_and_dist/distributions/gamma.qbk @@ -61,9 +61,9 @@ parameter], you should pass the reciprocal of the rate as the scale parameter. The following two graphs illustrate how the PDF of the gamma distribution varies as the parameters vary: -[$../graphs/gamma_dist1.png] +[graph gamma1_pdf] -[$../graphs/gamma_dist2.png] +[graph gamma2_pdf] The [*Erlang Distribution] is the same as the Gamma, but with the shape parameter an integer. It is often expressed using a /rate/ rather than a /scale/ as the diff --git a/doc/sf_and_dist/distributions/lognormal.qbk b/doc/sf_and_dist/distributions/lognormal.qbk index 33ac076d6..621da172a 100644 --- a/doc/sf_and_dist/distributions/lognormal.qbk +++ b/doc/sf_and_dist/distributions/lognormal.qbk @@ -43,11 +43,11 @@ parameter on the PDF, note that the range of the random variable remains \[0,+[infin]\] irrespective of the value of the location parameter: -[$../graphs/lognormal1.png] +[graph lognormal_pdf1] The next graph illustrates the effect of the scale parameter on the PDF: -[$../graphs/lognormal2.png] +[graph lognormal_pdf2] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/nc_beta.qbk b/doc/sf_and_dist/distributions/nc_beta.qbk new file mode 100644 index 000000000..6f973fb5c --- /dev/null +++ b/doc/sf_and_dist/distributions/nc_beta.qbk @@ -0,0 +1,211 @@ +[section:nc_beta_dist Noncentral Beta Distribution] + +``#include `` + + namespace boost{ namespace math{ + + template + class non_central_beta_distribution; + + typedef non_central_beta_distribution<> non_central_beta; + + template + class non_central_beta_distribution + { + public: + typedef RealType value_type; + typedef Policy policy_type; + + // Constructor: + non_central_beta_distribution(RealType alpha, RealType beta, RealType lambda); + + // Accessor to shape parameters: + RealType alpha()const; + RealType beta()const; + + // Accessor to non-centrality parameter lambda: + RealType non_centrality()const; + }; + + }} // namespaces + +The noncentral beta distribution is a generalization of the __beta_distrib. + +It is defined as the ratio +X = [chi][sub m][super 2]([lambda]) \/ ([chi][sub m][super 2]([lambda]) ++ [chi][sub n][super 2]) +where [chi][sub m][super 2]([lambda]) is a noncentral [chi][super 2] +random variable with /m/ degrees of freedom, and [chi][sub n][super 2] +is a central [chi][super 2] random variable with /n/ degrees of freedom. + +This gives a PDF that can be expressed as a Poisson mixture +of beta distribution PDFs: + +[equation nc_beta_ref1] + +where P(i;[lambda]\/2) is the discrete Poisson probablity at /i/, with mean +[lambda]\/2, and I[sub x][super ']([alpha], [beta]) is the derivative of +the incomplete beta function. This leads to the usual form of the CDF +as: + +[equation nc_beta_ref2] + +The following graph illustrates how the distribution changes +for different values of [lambda]: + +[graph nc_beta_pdf] + +[h4 Member Functions] + + non_central_beta_distribution(RealType a, RealType b, RealType lambda); + +Constructs a noncentral beta distribution with shape parameters /a/ and /b/ +and non-centrality parameter /lambda/. + +Requires a > 0, b > 0 and lambda >= 0, otherwise calls __domain_error. + + RealType alpha()const; + +Returns the parameter /a/ from which this object was constructed. + + RealType beta()const; + +Returns the parameter /b/ from which this object was constructed. + + RealType non_centrality()const; + +Returns the parameter /lambda/ from which this object was constructed. + +[h4 Non-member Accessors] + +Most of the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] +are supported: __cdf, __pdf, __quantile, +__median, __mode, __hazard, __chf, __range and __support. + +However, the following are not currently implemented: +__mean, __variance, __sd, __skewness, + __kurtosis and __kurtosis_excess. + +The domain of the random variable is \[0, 1\]. + +[h4 Accuracy] + +The following table shows the peak errors +(in units of [@http://en.wikipedia.org/wiki/Machine_epsilon epsilon]) +found on various platforms with various floating point types. +No comparison to the [@http://www.r-project.org/ R-2.5.1 Math library], +or to the FORTRAN implementations of AS226 or AS310 are given since these appear +to only guarantee absolute error: this would causes our test harness +to assign an /"infinite"/ error to these libraries for some of our +test values when measuring /relative error/. +Unless otherwise specified any floating-point type that is narrower +than the one shown will have __zero_error. + +[table Errors In CDF of the Noncentral Beta +[[Significand Size] [Platform and Compiler] [[alpha], [beta],[lambda] < 200] [[alpha],[beta],[lambda] > 200]] +[[53] [Win32, Visual C++ 8] [Peak=620 Mean=22] [Peak=8670 Mean=1040]] +[[64] [RedHat Linux IA32, gcc-4.1.1] [Peak=825 Mean=50] [Peak=2.5x10[super 4] Mean=4000]] + +[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=825 Mean=30] [Peak=1.7x10[super 4] Mean=2500]] + +[[113] [HPUX IA64, aCC A.06.06] [Peak=420 Mean=50] [Peak=9200 Mean=1200]] +] + +Error rates for the PDF, the complement of the CDF and for the quantile +functions are broadly similar. + +[h4 Tests] + +There are two sets of test data used to verify this implementation: +firstly we can compare with a few sample values generated by the +[@http://www.r-project.org/ R library]. +Secondly, we have tables of test data, computed with this +implementation and using interval arithmetic - this data should +be accurate to at least 50 decimal digits - and is the used for +our accuracy tests. + +[h4 Implementation] + +The CDF and its complement are evaluated as follows: + +First we determine which of the two values (the CDF or its +complement) is likely to be the smaller, the crossover point +is taken to be the mean of the distribution: for this we use the +approximation due to: R. Chattamvelli and R. Shanmugam, +"Algorithm AS 310: Computing the Non-Central Beta Distribution Function", +Applied Statistics, Vol. 46, No. 1. (1997), pp. 146-156. + +[equation nc_beta_ref3] + +Then either the CDF or its complement is computed using the +relations: + +[equation nc_beta_ref4] + +The summation is performed by starting at i = [lambda]/2, and then recursing +in both directions, using the usual recurrence relations for the Poisson +PDF and incomplete beta functions. This is the "Method 2" described +by: + +Denise Benton and K. Krishnamoorthy, +"Computing discrete mixtures of continuous +distributions: noncentral chisquare, noncentral t +and the distribution of the square of the sample +multiple correlation coefficient", +Computational Statistics & Data Analysis 43 (2003) 249-267. + +Specific applications of the above formulae to the noncentral +beta distribution can be found in: + +Russell V. Lenth, +"Algorithm AS 226: Computing Noncentral Beta Probabilities", +Applied Statistics, Vol. 36, No. 2. (1987), pp. 241-244. + +H. Frick, +"Algorithm AS R84: A Remark on Algorithm AS 226: Computing Non-Central Beta +Probabilities", Applied Statistics, Vol. 39, No. 2. (1990), pp. 311-312. + +Ming Long Lam, +"Remark AS R95: A Remark on Algorithm AS 226: Computing Non-Central Beta +Probabilities", Applied Statistics, Vol. 44, No. 4. (1995), pp. 551-552. + +Harry O. Posten, +"An Effective Algorithm for the Noncentral Beta Distribution Function", +The American Statistician, Vol. 47, No. 2. (May, 1993), pp. 129-131. + +R. Chattamvelli, +"A Note on the Noncentral Beta Distribution Function", +The American Statistician, Vol. 49, No. 2. (May, 1995), pp. 231-234. + +Of these, the Posten reference provides the most complete overview, +and includes the modification starting iteration at [lambda]/2. + +The main difference between this implementation and the above +references is the direct computation of the complement when most +efficient to do so, and the accumulation of the sum to -1 rather +than subtracting the result from 1 at the end: this can substantially +reduce the number of iterations required when the result is near 1. + +The PDF is computed using the methodology of Benton and Krishnamoorthy +and the relation: + +[equation nc_beta_ref1] + +Quantiles are computed using a specially modified version of +[link math_toolkit.toolkit.internals1.roots2 bracket_and_solve_root], +starting the search for the root at the mean of the distribution. +(A Cornish-Fisher type expansion was also tried, but while this gets +quite close to the root in many cases, when it is wrong it tends to +introduce quite pathological behaviour: more investigation in this +area is probably warranted). + +[endsect][/section:nc_beta_dist] + +[/ nc_beta.qbk + Copyright 2008 John Maddock and Paul A. Bristow. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] + diff --git a/doc/sf_and_dist/distributions/nc_chi_squared.qbk b/doc/sf_and_dist/distributions/nc_chi_squared.qbk new file mode 100644 index 000000000..c83f84d1a --- /dev/null +++ b/doc/sf_and_dist/distributions/nc_chi_squared.qbk @@ -0,0 +1,280 @@ +[section:nc_chi_squared_dist Noncentral Chi-Squared Distribution] + +``#include `` + + namespace boost{ namespace math{ + + template + class non_central_chi_squared_distribution; + + typedef non_central_chi_squared_distribution<> non_central_chi_squared; + + template + class non_central_chi_squared_distribution + { + public: + typedef RealType value_type; + typedef Policy policy_type; + + // Constructor: + non_central_chi_squared_distribution(RealType v, RealType lambda); + + // Accessor to degrees of freedom parameter v: + RealType degrees_of_freedom()const; + + // Accessor to non centrality parameter lambda: + RealType non_centrality()const; + + // Parameter finders: + static RealType find_degrees_of_freedom(RealType lambda, RealType x, RealType p); + template + static RealType find_degrees_of_freedom(const complemented3_type& c); + + static RealType find_non_centrality(RealType v, RealType x, RealType p); + template + static RealType find_non_centrality(const complemented3_type& c); + }; + + }} // namespaces + +The noncentral chi-squared distribution is a generalization of the +__chi_squared_distrib. If X[sub i] are [nu] independent, normally +distributed random variables with means [mu][sub i] and variances +[sigma][sub i][super 2], then the random variable + +[equation nc_chi_squ_ref1] + +is distributed according to the noncentral chi-squared distribution. + +The noncentral chi-squared distribution has two parameters: +[nu] which specifies the number of degrees of freedom +(i.e. the number of X[sub i]), and [lambda] which is related to the +mean of the random variables X[sub i] by: + +[equation nc_chi_squ_ref2] + +(Note that some references define [lambda] as one half of the above sum). + +This leads to a PDF of: + +[equation nc_chi_squ_ref3] + +where ['f(x;k)] is the central chi-squared distribution PDF, and +['I[sub v](x)] is a modified Bessel function of the first kind. + +The following graph illustrates how the distribution changes +for different values of [lambda]: + +[graph nccs_pdf] + +[h4 Member Functions] + + non_central_chi_squared_distribution(RealType v, RealType lambda); + +Constructs a Chi-Squared distribution with /v/ degrees of freedom +and non-centrality parameter /lambda/. + +Requires v > 0 and lambda >= 0, otherwise calls __domain_error. + + RealType degrees_of_freedom()const; + +Returns the parameter /v/ from which this object was constructed. + + RealType non_centrality()const; + +Returns the parameter /lambda/ from which this object was constructed. + + + static RealType find_degrees_of_freedom(RealType lambda, RealType x, RealType p); + +This function returns the number of degrees of freedom /v/ such that: +`cdf(non_central_chi_squared(v, lambda), x) == p` + + template + static RealType find_degrees_of_freedom(const complemented3_type& c); + +When called with argument `boost::math::complement(lambda, x, q)` +this function returns the number of degrees of freedom /v/ such that: + +`cdf(complement(non_central_chi_squared(v, lambda), x)) == q`. + + static RealType find_non_centrality(RealType v, RealType x, RealType p); + +This function returns the non centrality parameter /lambda/ such that: + +`cdf(non_central_chi_squared(v, lambda), x) == p` + + template + static RealType find_non_centrality(const complemented3_type& c); + +When called with argument `boost::math::complement(v, x, q)` +this function returns the non centrality parameter /lambda/ such that: + +`cdf(complement(non_central_chi_squared(v, lambda), x)) == q`. + +[h4 Non-member Accessors] + +All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] +that are generic to all distributions are supported: __usual_accessors. + +The domain of the random variable is \[0, +[infin]\]. + +[h4 Examples] + +There is a +[link math_toolkit.dist.stat_tut.weg.nccs_eg worked example] +for the noncentral chi-squared distribution. + +[h4 Accuracy] + +The following table shows the peak errors +(in units of [@http://en.wikipedia.org/wiki/Machine_epsilon epsilon]) +found on various platforms with various floating-point types, +along with comparisons to the [@http://www.r-project.org/ R-2.5.1 Math library]. +Unless otherwise specified, any floating-point type that is narrower +than the one shown will have __zero_error. + +[table Errors In CDF of the Noncentral Chi-Squared +[[Significand Size] [Platform and Compiler] [[nu],[lambda] < 200] [[nu],[lambda] > 200]] +[[53] [Win32, Visual C++ 8] [Peak=50 Mean=9.9 + +R Peak=685 Mean=109 +] [Peak=9780 Mean=718 + +R Peak=3x10[super 8] Mean=2x10[super 7] ] ] +[[64] [RedHat Linux IA32, gcc-4.1.1] [Peak=270 Mean=27] [Peak=7900 Mean=900]] + +[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=107 Mean=17] [Peak=5000 Mean=630]] + +[[113] [HPUX IA64, aCC A.06.06] [Peak=270 Mean=20] [Peak=4600 Mean=560]] +] + +Error rates for the complement of the CDF and for the quantile +functions are broadly similar. Special mention should go to +the `mode` function: there is no closed form for this function, +so it is evaluated numerically by finding the maxima of the PDF: +in principal this can not produce an accuracy greater than the +square root of the machine epsilon. + +[h4 Tests] + +There are two sets of test data used to verify this implementation: +firstly we can compare with published data, for example with +Table 6 of "Self-Validating Computations of Probabilities for +Selected Central and Noncentral Univariate Probability Functions", +Morgan C. Wang and William J. Kennedy, +Journal of the American Statistical Association, +Vol. 89, No. 427. (Sep., 1994), pp. 878-887. +Secondly, we have tables of test data, computed with this +implementation and using interval arithmetic - this data should +be accurate to at least 50 decimal digits - and is the used for +our accuracy tests. + +[h4 Implementation] + +The CDF and its complement are evaluated as follows: + +First we determine which of the two values (the CDF or its +complement) is likely to be the smaller: for this we can use the +relation due to Temme (see "Asymptotic and Numerical Aspects of the +Noncentral Chi-Square Distribution", N. M. Temme, Computers Math. Applic. +Vol 25, No. 5, 55-63, 1993) that: + +F([nu],[lambda];[nu]+[lambda]) [asymp] 0.5 + +and so compute the CDF when the random variable is less than +[nu]+[lambda], and its complement when the random variable is +greater than [nu]+[lambda]. If necessary the computed result +is then subtracted from 1 to give the desired result (the CDF or its +complement). + +For small values of the non centrality parameter, the CDF is computed +using the method of Ding (see "Algorithm AS 275: Computing the Non-Central +#2 Distribution Function", Cherng G. Ding, Applied Statistics, Vol. 41, +No. 2. (1992), pp. 478-482). This uses the following series representation: + +[equation nc_chi_squ_ref4] + +which requires just one call to __gamma_p_derivative with the subsequent +terms being computed by recursion as shown above. + +For larger values of the non-centrality parameter, Ding's method can take +an unreasonable number of terms before convergence is achieved. Furthermore, +the largest term is not the first term, so in extreme cases the first term may +be zero, leading to a zero result, even though the true value may be non-zero. + +Therefore, when the non-centrality parameter is greater than 200, the method due +to Krishnamoorthy (see "Computing discrete mixtures of continuous distributions: +noncentral chisquare, noncentral t and the distribution of the +square of the sample multiple correlation coefficient", +Denise Benton and K. Krishnamoorthy, Computational Statistics & +Data Analysis, 43, (2003), 249-267) is used. + +This method uses the well known sum: + +[equation nc_chi_squ_ref5] + +Where P[sub a](x) is the incomplete gamma function. + +The method starts at the [lambda]th term, which is where the Poisson weighting +function achieves its maximum value, although this is not necessarily +the largest overall term. Subsequent terms are calculated via the normal +recurrence relations for the incomplete gamma function, and iteration proceeds +both forwards and backwards until sufficient precision has been achieved. It +should be noted that recurrence in the forwards direction of P[sub a](x) is +numerically unstable. However, since we always start /after/ the largest +term in the series, numeric instability is introduced more slowly than the +series converges. + +Computation of the complement of the CDF uses an extension of Krishnamoorthy's +method, given that: + +[equation nc_chi_squ_ref6] + +we can again start at the [lambda]'th term and proceed in both directions from +there until the required precision is achieved. This time it is backwards +recursion on the incomplete gamma function Q[sub a](x) which is unstable. +However, as long as we start well /before/ the largest term, this is not an +issue in practice. + +The PDF is computed directly using the relation: + +[equation nc_chi_squ_ref3] + +Where ['f(x; v)] is the PDF of the central __chi_squared_distrib and +['I[sub v](x)] is a modified Bessel function, see __cyl_bessel_i. +For small values of the +non-centrality parameter the relation in terms of __cyl_bessel_i +is used. However, this method fails for large values of the +non-centrality parameter, so in that case the infinite sum is +evaluated using the method of Benton and Krishnamoorthy, and +the usual recurrence relations for successive terms. + +The quantile functions are computed by numeric inversion of the CDF. + +There is no [@http://en.wikipedia.org/wiki/Closed_form closed form] +for the mode of the noncentral chi-squared +distribution: it is computed numerically by finding the maximum +of the PDF. Likewise, the median is computed numerically via +the quantile. + +The remaining non-member functions use the following formulas: + +[equation nc_chi_squ_ref7] + +Some analytic properties of noncentral distributions +(particularly unimodality, and monotonicity of their modes) +are surveyed and summarized by: + +Andrea van Aubel & Wolfgang Gawronski, Applied Mathematics and Computation, 141 (2003) 3-12. + +[endsect] [/section:nc_chi_squared_dist] + +[/ nc_chi_squared.qbk + Copyright 2008 John Maddock and Paul A. Bristow. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] + diff --git a/doc/sf_and_dist/distributions/nc_chi_squared_example.qbk b/doc/sf_and_dist/distributions/nc_chi_squared_example.qbk new file mode 100644 index 000000000..7d958cf75 --- /dev/null +++ b/doc/sf_and_dist/distributions/nc_chi_squared_example.qbk @@ -0,0 +1,20 @@ +[section:nccs_eg Non Central Chi Squared Example] + +(See also the reference documentation for the __non_central_chi_squared_distrib.) + +[section:nccs_power_eg Tables of the power function of the [chi][super 2] test.] + +[import ../../../example/nc_chi_sq_example.cpp] +[nccs_eg] + +[endsect] [/nccs_power_eg Tables of the power function of the [chi][super 2] test.] + +[endsect] [/section:nccs_eg Non Central Chi Squared Example] + +[/ + Copyright 2006 John Maddock and Paul A. Bristow. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] + diff --git a/doc/sf_and_dist/distributions/nc_f.qbk b/doc/sf_and_dist/distributions/nc_f.qbk new file mode 100644 index 000000000..6da627c73 --- /dev/null +++ b/doc/sf_and_dist/distributions/nc_f.qbk @@ -0,0 +1,193 @@ +[section:nc_f_dist Noncentral F Distribution] + +``#include `` + + namespace boost{ namespace math{ + + template + class non_central_f_distribution; + + typedef non_central_f_distribution<> non_central_f; + + template + class non_central_f_distribution + { + public: + typedef RealType value_type; + typedef Policy policy_type; + + // Constructor: + non_central_f_distribution(RealType v1, RealType v2, RealType lambda); + + // Accessor to degrees_of_freedom parameters v1 & v2: + RealType degrees_of_freedom1()const; + RealType degrees_of_freedom2()const; + + // Accessor to non-centrality parameter lambda: + RealType non_centrality()const; + }; + + }} // namespaces + +The noncentral F distribution is a generalization of the __F_distrib. +It is defined as the ratio + + F = (X/v1) / (Y/v2) + +where X is a noncentral [chi][super 2] +random variable with /v1/ degrees of freedom and non-centrality parameter [lambda], +and Y is a central [chi][super 2] random variable with /v2/ degrees of freedom. + +This gives the following PDF: + +[equation nc_f_ref1] + +where L[sub a][super b](c) is a generalised Laguerre polynomial and B(a,b) is the +__beta function, or + +[equation nc_f_ref2] + +The following graph illustrates how the distribution changes +for different values of [lambda]: + +[graph nc_f_pdf] + +[h4 Member Functions] + + non_central_f_distribution(RealType v1, RealType v2, RealType lambda); + +Constructs a non-central beta distribution with parameters /v1/ and /v2/ +and non-centrality parameter /lambda/. + +Requires v1 > 0, v2 > 0 and lambda >= 0, otherwise calls __domain_error. + + RealType degrees_of_freedom1()const; + +Returns the parameter /v1/ from which this object was constructed. + + RealType degrees_of_freedom2()const; + +Returns the parameter /v2/ from which this object was constructed. + + RealType non_centrality()const; + +Returns the non-centrality parameter /lambda/ from which this object was constructed. + +[h4 Non-member Accessors] + +All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] +that are generic to all distributions are supported: __usual_accessors. + +The domain of the random variable is \[0, +[infin]\]. + +[h4 Accuracy] + +This distribution is implemented in terms of the +__non_central_beta_distrib: refer to that distribution for accuracy data. + +[h4 Tests] + +Since this distribution is implemented by adapting another distribution, +the tests consist of basic sanity checks computed by the +[@http://www.r-project.org/ R-2.5.1 Math library statistical +package] and its pbeta and dbeta functions. + +[h4 Implementation] + +In the following table /v1/ and /v2/ are the first and second +degrees of freedom parameters of the distribution, [lambda] +is the non-centrality parameter, +/x/ is the random variate, /p/ is the probability, and /q = 1-p/. + +[table +[[Function][Implementation Notes]] +[[pdf][Implemented in terms of the non-central beta PDF using the relation: + +f(x;v1,v2;[lambda]) = (v1\/v2) / ((1+y)*(1+y)) * g(y\/(1+y);v1\/2,v2\/2;[lambda]) + +where g(x; a, b; [lambda]) is the non central beta PDF, and: + +y = x * v1 \/ v2 +]] +[[cdf][Using the relation: + +p = B[sub y](v1\/2, v2\/2; [lambda]) + +where B[sub x](a, b; [lambda]) is the noncentral beta distribution CDF and + +y = x * v1 \/ v2 + +]] + +[[cdf complement][Using the relation: + +q = 1 - B[sub y](v1\/2, v2\/2; [lambda]) + +where 1 - B[sub x](a, b; [lambda]) is the complement of the +noncentral beta distribution CDF and + +y = x * v1 \/ v2 + +]] +[[quantile][Using the relation: + +x = (bx \/ (1-bx)) * (v1 \/ v2) + +where + +bx = Q[sub p][super -1](v1\/2, v2\/2; [lambda]) + +and + +Q[sub p][super -1](v1\/2, v2\/2; [lambda]) + +is the noncentral beta quantile. + +]] +[[quantile + +from the complement][ +Using the relation: + +x = (bx \/ (1-bx)) * (v1 \/ v2) + +where + +bx = QC[sub q][super -1](v1\/2, v2\/2; [lambda]) + +and + +QC[sub q][super -1](v1\/2, v2\/2; [lambda]) + +is the noncentral beta quantile from the complement.]] +[[mean][v2 * (v1 + l) \/ (v1 * (v2 - 2))]] +[[mode][By numeric maximalisation of the PDF.]] +[[variance][Refer to, [@http://mathworld.wolfram.com/NoncentralF-Distribution.html + Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource.] ]] +[[skewness][Refer to, [@http://mathworld.wolfram.com/NoncentralF-Distribution.html + Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource.], + and to the [@http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html + Mathematica documentation] ]] +[[kurtosis and kurtosis excess] + [Refer to, [@http://mathworld.wolfram.com/NoncentralF-Distribution.html + Weisstein, Eric W. "Noncentral F-Distribution." From MathWorld--A Wolfram Web Resource.], + and to the [@http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html + Mathematica documentation] ]] +] + +Some analytic properties of noncentral distributions +(particularly unimodality, and monotonicity of their modes) +are surveyed and summarized by: + +Andrea van Aubel & Wolfgang Gawronski, Applied Mathematics and Computation, 141 (2003) 3-12. + +[endsect] [/section:nc_f_dist] + +[/ nc_f.qbk + Copyright 2008 John Maddock and Paul A. Bristow. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] + diff --git a/doc/sf_and_dist/distributions/nc_t.qbk b/doc/sf_and_dist/distributions/nc_t.qbk new file mode 100644 index 000000000..cf7871be3 --- /dev/null +++ b/doc/sf_and_dist/distributions/nc_t.qbk @@ -0,0 +1,195 @@ +[section:nc_t_dist Noncentral T Distribution] + +``#include `` + + namespace boost{ namespace math{ + + template + class non_central_t_distribution; + + typedef non_central_t_distribution<> non_central_t; + + template + class non_central_t_distribution + { + public: + typedef RealType value_type; + typedef Policy policy_type; + + // Constructor: + non_central_t_distribution(RealType v, RealType delta); + + // Accessor to degrees_of_freedom parameter v: + RealType degrees_of_freedom()const; + + // Accessor to non-centrality parameter lambda: + RealType non_centrality()const; + }; + + }} // namespaces + +The noncentral T distribution is a generalization of the __students_t_distrib. +Let X have a normal distribution with mean [delta] and variance 1, and let +[nu] S[super 2] have +a chi-squared distribution with degrees of freedom [nu]. Assume that +X and S[super 2] are independent. The +distribution of t[sub [nu]]([delta])=X/S is called a +noncentral t distribution with degrees of freedom [nu] and noncentrality +parameter [delta]. + +This gives the following PDF: + +[equation nc_t_ref1] + +where [sub 1]F[sub 1](a;b;x) is a confluent hypergeometric function. + +The following graph illustrates how the distribution changes +for different values of [delta]: + +[graph nc_t_pdf] + +[h4 Member Functions] + + non_central_t_distribution(RealType v, RealType lambda); + +Constructs a non-central t distribution with degrees of freedom +parameter /v/ and non-centrality parameter /delta/. + +Requires v > 0 and finite delta, otherwise calls __domain_error. + + RealType degrees_of_freedom()const; + +Returns the parameter /v/ from which this object was constructed. + + RealType non_centrality()const; + +Returns the non-centrality parameter /delta/ from which this object was constructed. + +[h4 Non-member Accessors] + +All the [link math_toolkit.dist.dist_ref.nmp usual non-member accessor functions] +that are generic to all distributions are supported: __usual_accessors. + +The domain of the random variable is \[-[infin], +[infin]\]. + +[h4 Accuracy] + +The following table shows the peak errors +(in units of [@http://en.wikipedia.org/wiki/Machine_epsilon epsilon]) +found on various platforms with various floating-point types. +Unless otherwise specified, any floating-point type that is narrower +than the one shown will have __zero_error. + +[table Errors In CDF of the Noncentral T Distribution +[[Significand Size] [Platform and Compiler] [[nu],[delta] < 600]] +[[53] [Win32, Visual C++ 8] [Peak=120 Mean=26 ] ] +[[64] [RedHat Linux IA32, gcc-4.1.1] [Peak=121 Mean=26] ] + +[[64] [Redhat Linux IA64, gcc-3.4.4] [Peak=122 Mean=25] ] + +[[113] [HPUX IA64, aCC A.06.06] [Peak=115 Mean=24] ] +] + +[caution The complexity of the current algorithm is dependent upon +[delta][super 2]: consequently the time taken to evaluate the CDF +increases rapidly for [delta] > 500, likewise the accuracy decreases +rapidly for very large [delta].] + +Accuracy for the quantile and PDF functions should be broadly similar, +note however that the /mode/ is determined numerically and can not +in principal be more accurate than the square root of machine epsilon. + +[h4 Tests] + +There are two sets of tests of this distribution: basic sanity checks +compare this implementation to the test values given in +"Computing discrete mixtures of continuous +distributions: noncentral chisquare, noncentral t +and the distribution of the square of the sample +multiple correlation coefficient." +Denise Benton, K. Krishnamoorthy, +Computational Statistics & Data Analysis 43 (2003) 249-267. +While accuracy checks use test data computed with this +implementation and arbitary precision interval arithmetic: +this test data is believed to be accurate to at least 50 +decimal places. + + +[h4 Implementation] + +The CDF is computed using a modification of the method +described in +"Computing discrete mixtures of continuous +distributions: noncentral chisquare, noncentral t +and the distribution of the square of the sample +multiple correlation coefficient." +Denise Benton, K. Krishnamoorthy, +Computational Statistics & Data Analysis 43 (2003) 249-267. + +This uses the following formula for the CDF: + +[equation nc_t_ref2] + +Where I[sub x](a,b) is the incomplete beta function, and +[Phi](x) is the normal CDF at x. + +Iteration starts at the largest of the Poisson weighting terms +(at i = [delta][super 2] / 2) and then proceeds in both directions +as per Benton and Krishnamoorthy's paper. + +Alternatively, by considering what happens when t = [infin], we have +x = 1, and therefore I[sub x](a,b) = 1 and: + +[equation nc_t_ref3] + +From this we can easily show that: + +[equation nc_t_ref4] + +and therefore we have a means to compute either the probability or its +complement directly without the risk of cancellation error. The +crossover criterion for choosing whether to calculate the CDF or +it's complement is the same as for the +__non_central_beta_distrib. + +The PDF can be computed by a very similar method using: + +[equation nc_t_ref5] + +Where I[sub x][super '](a,b) is the derivative of the incomplete beta function. + +The quantile is calculated via the usual +[link math_toolkit.toolkit.internals1.roots2 +derivative-free root-finding techniques], +with the initial guess taken as the quantile of a normal approximation +to the noncentral T. + +There is no closed form for the mode, so this is computed via +functional maximisation of the PDF. + +The remaining functions (mean, variance etc) are implemented +using the formulas given in +Weisstein, Eric W. "Noncentral Student's t-Distribution." +From MathWorld--A Wolfram Web Resource. +[@http://mathworld.wolfram.com/NoncentralStudentst-Distribution.html +http://mathworld.wolfram.com/NoncentralStudentst-Distribution.html] +and in the +[@http://reference.wolfram.com/mathematica/ref/NoncentralStudentTDistribution.html +Mathematica documentation]. + +Some analytic properties of noncentral distributions +(particularly unimodality, and monotonicity of their modes) +are surveyed and summarized by: + +Andrea van Aubel & Wolfgang Gawronski, Applied Mathematics and Computation, 141 (2003) 3-12. + +[endsect] [/section:nc_t_dist] + +[/ nc_t.qbk + Copyright 2008 John Maddock and Paul A. Bristow. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] + diff --git a/doc/sf_and_dist/distributions/negative_binomial.qbk b/doc/sf_and_dist/distributions/negative_binomial.qbk index de27bbe7b..5377a4bcd 100644 --- a/doc/sf_and_dist/distributions/negative_binomial.qbk +++ b/doc/sf_and_dist/distributions/negative_binomial.qbk @@ -72,12 +72,12 @@ It has the PDF: The following graph illustrate how the PDF varies as the success fraction /p/ changes: -[$../graphs/neg_binomial_pdf1.png] +[graph negative_binomial_pdf_1] Alternatively, this graph shows how the shape of the PDF varies as the number of successes changes: -[$../graphs/neg_binomial_pdf2.png] +[graph negative_binomial_pdf_2] [h4 Related Distributions] diff --git a/doc/sf_and_dist/distributions/normal.qbk b/doc/sf_and_dist/distributions/normal.qbk index 1b057dd44..b33b5517b 100644 --- a/doc/sf_and_dist/distributions/normal.qbk +++ b/doc/sf_and_dist/distributions/normal.qbk @@ -40,7 +40,7 @@ Given mean [mu][space] and standard deviation [sigma][space] it has the PDF: The variation the PDF with its parameters is illustrated in the following graph: -[$../graphs/normal.png] +[graph normal_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/pareto.qbk b/doc/sf_and_dist/distributions/pareto.qbk index 040b3c622..82de7fc0e 100644 --- a/doc/sf_and_dist/distributions/pareto.qbk +++ b/doc/sf_and_dist/distributions/pareto.qbk @@ -37,11 +37,14 @@ The [@http://mathworld.wolfram.com/paretoDistribution.html Pareto distribution] often describes the larger compared to the smaller. A classic example is that 80% of the wealth is owned by 20% of the population. -The following graph illustrates how the PDF varies with the shape parameter [alpha]: +The following graph illustrates how the PDF varies with the location parameter [beta]: + +[graph pareto_pdf1] + +And this graph illustrates how the PDF varies with the shape parameter [alpha]: + +[graph pareto_pdf2] -[/$../graphs/paretoShape.png] -[/ TODO produce a graph as png or svg] -[@http://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Pareto_distributionPDF.png/325px-Pareto_distributionPDF.png Pareto pdf] [h4 Related distributions] diff --git a/doc/sf_and_dist/distributions/poisson.qbk b/doc/sf_and_dist/distributions/poisson.qbk index e65638a97..4e63eef98 100644 --- a/doc/sf_and_dist/distributions/poisson.qbk +++ b/doc/sf_and_dist/distributions/poisson.qbk @@ -41,7 +41,7 @@ for k events, with an expected number of events [lambda]. The following graph illustrates how the PDF varies with the parameter [lambda]: -[$../graphs/poisson.png] +[graph poisson_pdf_1] [discrete_quantile_warning Poisson] diff --git a/doc/sf_and_dist/distributions/rayleigh.qbk b/doc/sf_and_dist/distributions/rayleigh.qbk index 8fa768406..b4e79d700 100644 --- a/doc/sf_and_dist/distributions/rayleigh.qbk +++ b/doc/sf_and_dist/distributions/rayleigh.qbk @@ -40,11 +40,11 @@ or real and imaginary components may have absolute values that are Rayleigh dist The following graph illustrates how the Probability density Function(pdf) varies with the shape parameter [sigma]: -[$../graphs/rayleigh_pdf.png] +[graph rayleigh_pdf] and the Cumulative Distribution Function (cdf) -[$../graphs/rayleigh_cdf.png] +[graph rayleigh_cdf] [h4 Related distributions] diff --git a/doc/sf_and_dist/distributions/students_t.qbk b/doc/sf_and_dist/distributions/students_t.qbk index 25fcdf384..5a6b61032 100644 --- a/doc/sf_and_dist/distributions/students_t.qbk +++ b/doc/sf_and_dist/distributions/students_t.qbk @@ -55,7 +55,7 @@ As the number of degrees of freedom tends towards infinity, then this distribution approaches the normal-distribution. The following graph illustrates how the PDF varies with the degrees of freedom [nu]: -[$../graphs/students_t.png] +[graph students_t_pdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/triangular.qbk b/doc/sf_and_dist/distributions/triangular.qbk index eb04ee5a3..4b237f990 100644 --- a/doc/sf_and_dist/distributions/triangular.qbk +++ b/doc/sf_and_dist/distributions/triangular.qbk @@ -72,11 +72,11 @@ The following graph illustrates how the [@http://en.wikipedia.org/wiki/Probability_density_function probability density function PDF] varies with the various parameters: -[$../graphs/triangular_pdf.png] +[graph triangular_pdf] and cumulative distribution function -[$../graphs/triangular_cdf.png] +[graph triangular_cdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/uniform.qbk b/doc/sf_and_dist/distributions/uniform.qbk index 098a8d150..5eb664802 100644 --- a/doc/sf_and_dist/distributions/uniform.qbk +++ b/doc/sf_and_dist/distributions/uniform.qbk @@ -61,11 +61,11 @@ The following graph illustrates how the [@http://en.wikipedia.org/wiki/Probability_density_function probability density function PDF] varies with the shape parameter: -[$../graphs/uniform_pdf.png] +[graph uniform_pdf] Likewise for the CDF: -[$../graphs/uniform_cdf.png] +[graph uniform_cdf] [h4 Member Functions] diff --git a/doc/sf_and_dist/distributions/weibull.qbk b/doc/sf_and_dist/distributions/weibull.qbk index 140f13792..b0ed6680d 100644 --- a/doc/sf_and_dist/distributions/weibull.qbk +++ b/doc/sf_and_dist/distributions/weibull.qbk @@ -45,11 +45,11 @@ If the failure rate is: The following graph illustrates how the PDF varies with the shape parameter [alpha]: -[$../graphs/weibull.png] +[graph weibull_pdf1] While this graph illustrates how the PDF varies with the scale parameter [beta]: -[$../graphs/weibull2.png] +[graph weibull_pdf2] [h4 Related distributions] @@ -58,6 +58,11 @@ When [alpha][space] = 3, the [@http://en.wikipedia.org/wiki/Normal_distribution normal distribution]. When [alpha][space] = 1, the Weibull distribution reduces to the [@http://en.wikipedia.org/wiki/Exponential_distribution exponential distribution]. +The relationship of the types of extreme value distributions, of which the Weibull is but one, is +discussed by +[@http://www.worldscibooks.com/mathematics/p191.html Extreme Value Distributions, Theory and Applications +Samuel Kotz & Saralees Nadarajah]. + [h4 Member Functions] diff --git a/doc/sf_and_dist/ellint_carlson.qbk b/doc/sf_and_dist/ellint_carlson.qbk index de09a536d..512c4d416 100644 --- a/doc/sf_and_dist/ellint_carlson.qbk +++ b/doc/sf_and_dist/ellint_carlson.qbk @@ -76,7 +76,7 @@ These functions return Carlson's symmetrical elliptic integrals, the functions have complicated behavior over all their possible domains, but the following graph gives an idea of their behavior: -[$../graphs/ellint_c.png] +[graph ellint_carlson] The return type of these functions is computed using the __arg_pomotion_rules when the arguments are of different types: otherwise the return is the same type diff --git a/doc/sf_and_dist/ellint_legendre.qbk b/doc/sf_and_dist/ellint_legendre.qbk index a14afcbdf..220b5e73e 100644 --- a/doc/sf_and_dist/ellint_legendre.qbk +++ b/doc/sf_and_dist/ellint_legendre.qbk @@ -35,7 +35,7 @@ LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) These two functions evaluate the incomplete elliptic integral of the first kind ['F([phi], k)] and its complete counterpart ['K(k) = F([pi]/2, k)]. -[$../graphs/ellint_1.png] +[graph ellint_1] The return type of these functions is computed using the __arg_pomotion_rules when T1 and T2 are different types: when they are the same type then the result @@ -135,7 +135,7 @@ and These two functions evaluate the incomplete elliptic integral of the second kind ['E([phi], k)] and its complete counterpart ['E(k) = E([pi]/2, k)]. -[$../graphs/ellint_2.png] +[graph ellint_2] The return type of these functions is computed using the __arg_pomotion_rules when T1 and T2 are different types: when they are the same type then the result @@ -235,7 +235,7 @@ and These two functions evaluate the incomplete elliptic integral of the third kind ['[Pi](n, [phi], k)] and its complete counterpart ['[Pi](n, k) = E(n, [pi]/2, k)]. -[$../graphs/ellint_3.png] +[graph ellint_3] The return type of these functions is computed using the __arg_pomotion_rules when the arguments are of different types: when they are the same type then the result diff --git a/doc/sf_and_dist/equations/expint_i_1.mml b/doc/sf_and_dist/equations/expint_i_1.mml new file mode 100644 index 000000000..f42d338ca --- /dev/null +++ b/doc/sf_and_dist/equations/expint_i_1.mml @@ -0,0 +1,46 @@ + + + E + i + + + x + + + = + − + + E + 1 + + + + − + x + + + = + + ∫ + + − + x + + ∞ + + + + + e + + − + t + + + d + t + + t + + + \ No newline at end of file diff --git a/doc/sf_and_dist/equations/expint_i_1.png b/doc/sf_and_dist/equations/expint_i_1.png new file mode 100644 index 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+ +Ï‚(s)=C+R(s−n)+1s−1 \ No newline at end of file diff --git a/doc/sf_and_dist/erf.qbk b/doc/sf_and_dist/erf.qbk index 046346336..f6c3fede6 100644 --- a/doc/sf_and_dist/erf.qbk +++ b/doc/sf_and_dist/erf.qbk @@ -40,7 +40,7 @@ Returns the [@http://en.wikipedia.org/wiki/Error_function error function] [equation erf1] -[$../graphs/erf1.png] +[graph erf] template ``__sf_result`` erfc(T z); @@ -52,7 +52,7 @@ Returns the complement of the [@http://functions.wolfram.com/GammaBetaErf/Erfc/ [equation erf2] -[$../graphs/erf2.png] +[graph erfc] [h4 Accuracy] diff --git a/doc/sf_and_dist/erf_inv.qbk b/doc/sf_and_dist/erf_inv.qbk index fe79369e2..79d3ddca5 100644 --- a/doc/sf_and_dist/erf_inv.qbk +++ b/doc/sf_and_dist/erf_inv.qbk @@ -40,7 +40,7 @@ of z, that is a value x such that: p = erf(x); -[$../graphs/erf_inv.png] +[graph erf_inv] template ``__sf_result`` erfc_inv(T z); @@ -53,7 +53,7 @@ value x such that: p = erfc(x); -[$../graphs/erfc_inv.png] +[graph erfc_inv] [h4 Accuracy] diff --git a/doc/sf_and_dist/error_handling.qbk b/doc/sf_and_dist/error_handling.qbk index eca907b6b..0efe0de59 100644 --- a/doc/sf_and_dist/error_handling.qbk +++ b/doc/sf_and_dist/error_handling.qbk @@ -26,6 +26,9 @@ The kinds of errors that can be raised are: to be represented by any other value in the type being returned by the function.]] [[Denormalisation Error][Occurs when the returned result would be a denormalised value.]] +[[Rounding Error][Occurs when the argument to one of the rounding functions __trunc, + __round and __modf can not be represented as an integer type, is is + outide the range of the result type.]] [[Evaluation Error][Occurs when an internal error occured that prevented the result from being evaluated: this should never occur, but if it does, then it's likely to be due to an iterative method not converging fast enough.]] @@ -100,6 +103,16 @@ with the default action for each error shown in bold: this function must be defined by the user].]] ] +[table Possible Actions for Rounding Errors +[[Action] [Behaviour]] +[[throw_on_error][Throws `boost::math::rounding_error`]] +[[errno_on_error][Sets `::errno` to `ERANGE` and returns an unspecified value.]] +[[ignore_error][[*Returns the an unspecified value.]]] +[[user_error][Returns the result of `boost::math::policies::user_rounding_error`: + [link math_toolkit.policy.pol_tutorial.user_def_err_pol + this function must be defined by the user].]] +] + [table Possible Actions for Internal Evaluation Errors [[Action] [Behaviour]] [[throw_on_error][[*Throws `boost::math::evaluation_error`]]] @@ -291,6 +304,33 @@ For example if `Message` contains a "%1%" then it is replaced by the value of `val` to the full precision of T, where as "%.3g" would contain the value of `val` to 3 digits. See the __format documentation for more details. +[heading [#rounding_error]Rounding Errors] + +When one of the rounding functions __round, __trunc or __modf is +called with an argument that has no integer representation, or +is too large to be represented in the result type then the +value returned is the result of a call to: + + boost::math::policies::raise_rounding_error(FunctionName, Message, Val, __Policy); + +Where +`T` is the floating point type passed to the function, `FunctionName` is the +name of the function, `Message` is an error message describing the problem, +`Val` is the erroneous argument, +and __Policy is the current policy +in use for the called function. + +The default behaviour of this function is to throw a `boost::math::rounding_error`. + +Note that in order to support information rich error messages when throwing +exceptions, `Message` must contain +a __format recognised format specifier: the argument `val` is inserted into +the error message according to the specifier used. + +For example if `Message` contains a "%1%" then it is replaced by the value of +`val` to the full precision of T, where as "%.3g" would contain the value of +`val` to 3 digits. See the __format documentation for more details. + [heading [#checked_narrowing_cast]Errors from typecasts] Many special functions evaluate their results at a higher precision diff --git a/doc/sf_and_dist/expint.qbk b/doc/sf_and_dist/expint.qbk new file mode 100644 index 000000000..441d527fb --- /dev/null +++ b/doc/sf_and_dist/expint.qbk @@ -0,0 +1,240 @@ +[section:expint Exponential Integrals] + +[section:expint_n Exponential Integral En] + +[h4 Synopsis] + +`` +#include +`` + + namespace boost{ namespace math{ + + template + ``__sf_result`` expint(unsigned n, T z); + + template + ``__sf_result`` expint(unsigned n, T z, const ``__Policy``&); + + }} // namespaces + +The return type of these functions is computed using the __arg_pomotion_rules: +the return type is `double` if T is an integer type, and T otherwise. + +[optional_policy] + +[h4 Description] + + template + ``__sf_result`` expint(unsigned n, T z); + + template + ``__sf_result`` expint(unsigned n, T z, const ``__Policy``&); + +Returns the [@http://mathworld.wolfram.com/En-Function.html exponential integral En] +of z: + +[equation expint_n_1] + +[graph expint2] + +[h4 Accuracy] + +The following table shows the peak errors (in units of epsilon) +found on various platforms with various floating point types, +along with comparisons to the __cephes library. +Unless otherwise specified any floating point type that is narrower +than the one shown will have __zero_error. + +[table Errors In the Function expint(n, z) +[[Significand Size] [Platform and Compiler] [En][E1]] +[[53] [Win32, Visual C++ 8] [Peak=7.1 Mean=1.8 + +__cephes Peak=5.1 Mean=1.3 +] +[Peak=0.99 Mean=0.5 + +__cephes Peak=3.1 Mean=1.1]] +[[64] [RedHat Linux IA_EM64, gcc-4.1] [Peak=9.9 Mean=2.1] [Peak=0.97 Mean=0.4]] +[[64] [Redhat Linux IA64, gcc-4.1] [Peak=9.9 Mean=2.1] [Peak=0.97 Mean=0.4]] +[[113] [HPUX IA64, aCC A.06.06] [Peak=23.3 Mean=3.7] [Peak=1.6 Mean=0.5]] +] + +[h4 Testing] + +The tests for these functions come in two parts: +basic sanity checks use spot values calculated using +[@http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=ExpIntegralE Mathworld's online evaluator], +while accuracy checks use high-precision test values calculated at 1000-bit precision with +[@http://shoup.net/ntl/doc/RR.txt NTL::RR] and this implementation. +Note that the generic and type-specific +versions of these functions use differing implementations internally, so this +gives us reasonably independent test data. Using our test data to test other +"known good" implementations also provides an additional sanity check. + +[h4 Implementation] + +The generic version of this function uses the continued fraction: + +[equation expint_n_3] + +for large /x/ and the infinite series: + +[equation expint_n_2] + +for small /x/. + +Where the precision of /x/ is known at compile time and is 113 bits or fewer +in precision, then rational approximations [jm_rationals] are used for the +`n == 1` case. + +For `x < 1` the approximating form is a minimax approximation: + +[equation expint_n_4] + +and for `x > 1` a Chebyshev interpolated approximation of the form: + +[equation expint_n_5] + +is used. + + +[endsect] + +[section:expint_i Exponential Integral Ei] + +[h4 Synopsis] + +`` +#include +`` + + namespace boost{ namespace math{ + + template + ``__sf_result`` expint(T z); + + template + ``__sf_result`` expint(T z, const ``__Policy``&); + + }} // namespaces + +The return type of these functions is computed using the __arg_pomotion_rules: +the return type is `double` if T is an integer type, and T otherwise. + +[optional_policy] + +[h4 Description] + + template + ``__sf_result`` expint(T z); + + template + ``__sf_result`` expint(T z, const ``__Policy``&); + +Returns the [@http://mathworld.wolfram.com/ExponentialIntegral.html exponential integral] +of z: + +[equation expint_i_1] + +[graph expint_i] + +[h4 Accuracy] + +The following table shows the peak errors (in units of epsilon) +found on various platforms with various floating point types, +along with comparisons to Cody's SPECFUN implementation and the __gsl library. +Unless otherwise specified any floating point type that is narrower +than the one shown will have __zero_error. + +[table Errors In the Function expint(z) +[[Significand Size] [Platform and Compiler] [Error]] +[[53] [Win32, Visual C++ 8] [Peak=2.4 Mean=0.6 + +GSL Peak=8.9 Mean=0.7 + +SPECFUN (Cody) Peak=2.5 Mean=0.6 +]] +[[64] [RedHat Linux IA_EM64, gcc-4.1] [Peak=5.1 Mean=0.8]] +[[64] [Redhat Linux IA64, gcc-4.1] [Peak=5.0 Mean=0.8] ] +[[113] [HPUX IA64, aCC A.06.06] [Peak=1.9 Mean=0.63]] +] + +It should be noted that all three libraries tested above +offer sub-epsilon precision over most of their range. + +GSL has the greatest difficulty near the positive root of En, while +Cody's SPECFUN along with this implementation increase their +error rates very slightly over the range \[4,6\]. + +[h4 Testing] + +The tests for these functions come in two parts: +basic sanity checks use spot values calculated using +[@http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=ExpIntegralEi Mathworld's online evaluator], +while accuracy checks use high-precision test values calculated at 1000-bit precision with +[@http://shoup.net/ntl/doc/RR.txt NTL::RR] and this implementation. +Note that the generic and type-specific +versions of these functions use differing implementations internally, so this +gives us reasonably independent test data. Using our test data to test other +"known good" implementations also provides an additional sanity check. + +[h4 Implementation] + +For x < 0 this function just calls __expint_n(1, -x): which in turn is implemented +in terms of rational approximations when the type of x has 113 or fewer bits of +precision. + +For x > 0 the generic version is implemented using the infinte series: + +[equation expint_i_2] + +However, when the precision of the argument type is known at compile time +and is 113 bits or less, then rational approximations [jm_rationals] are used. + +For 0 < z < 6 a root-preserving approximation of the form: + +[equation expint_i_3] + +is used, where z[sub 0] is the positive root of the function, and +R(z/3 - 1) is a minimax rational approximation rescaled so that +it is evaluated over \[-1,1\]. Note that while the rational approximation +over \[0,6\] converges rapidly to the minimax solution it is rather +ill-conditioned in practice. Cody and Thacher +[footnote W. J. Cody and H. C. Thacher, Jr., +Rational Chebyshev approximations for the exponential integral E[sub 1](x), +Math. Comp. 22 (1968), 641-649, +and W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for the +exponential integral Ei(x), Math. Comp. 23 (1969), 289-303.] +experienced the same issue and +converted the polynomials into Chebeshev form to ensure stable +computation. By experiment we found that the polynomials are just as stable +in polynomial as Chebyshev form, /provided/ they are computed +over the interval \[-1,1\]. + +Over the a series of intervals [a,b] and [b,INF] the rational approximation +takes the form: + +[equation expint_i_4] + +where /c/ is a constant, and R(t) is a minimax solution optimised for low +absolute error compared to /c/. Variable /t/ is `1/z` when the range in infinite +and `2z/(b-a) - (2a/(b-a) + 1)` otherwise: this has the effect of scaling z to the +interval \[-1,1\]. As before rational approximations over arbitrary intervals +were found to be ill-conditioned: Cody and Thacher solved this issue by +converting the polynomials to their J-Fraction equivalent. However, as long +as the interval of evaluation was \[-1,1\] and the number of terms carefully chosen, +it was found that the polynomials /could/ be evaluated to suitable precision: +error rates are typically 2 to 3 epsilon which is comparible to the error +rate that Cody and Thacher achieved using J-Fractions, but marginally more +efficient given that fewer divisions are involved. + +[endsect] +[endsect] + +[/ + Copyright 2006 John Maddock and Paul A. Bristow. + Distributed under the Boost Software License, Version 1.0. + (See accompanying file LICENSE_1_0.txt or copy at + http://www.boost.org/LICENSE_1_0.txt). +] diff --git a/doc/sf_and_dist/gamma_ratios.qbk b/doc/sf_and_dist/gamma_ratios.qbk index c459cee73..e7b289ba1 100644 --- a/doc/sf_and_dist/gamma_ratios.qbk +++ b/doc/sf_and_dist/gamma_ratios.qbk @@ -55,6 +55,8 @@ typically used when /a/ is large and /delta/ is very small. The return type of these functions is computed using the __arg_pomotion_rules when T1 and T2 are different types, otherwise the result type is simple T1. +[graph tgamma_delta_ratio] + [h4 Accuracy] The following table shows the peak errors (in units of epsilon) diff --git a/doc/sf_and_dist/graphs/acosh.png b/doc/sf_and_dist/graphs/acosh.png new file mode 100644 index 0000000000000000000000000000000000000000..4ee46e77504f87caae4a84d8c34cf510f336fa10 GIT binary patch literal 20544 zcmeAS@N?(olHy`uVBq!ia0y~yU}|7sU|h|?#=yW3;HT!zz`(##?Bp53!NI{%!;#X# zz`(#+;1OBOz`%C|gc+x5^GP!>Fi4iTMwA5SrEaktG3U+Q%80PkN5?)&N4m0ziv+mD6ddIZ2r53w8*^H9ZpV7rVcm)aN=#h~G*0~b_pczSEzo(&bml$x&zBaO zKHu})^7%2Q_m$_;z8-Tg_F-aRXgIoI;u7;?JX4$Z&b=7Pz`&5;W^Qa`n){7^JJ*8d zy>m|mGcYnR=r~y}W@cbuSWpoN=JK!#FfbfA6fhV#3pjLQb_B@RewjFF^5ot=CI;3; z3``D!GfcCmsrk)WaeBJGv@9zFmkT2c1H%Rb5eEha25x6YmViZfb`&~aym-;7^3#%a z@%!UeZ0zjp^z!u7EZBYKjE}5k(UW=G{yN9R%t=a0nlgEE@%d!ExIHU^m-}g&n}45o zoWY@R0RxkU;4@Qxdw1Qrb0=hHQEKS=xY+Y{zt<=!DSgVVesjZcYySN>QLT^(>({T>3SXy_pP&Et z$K(F;yWd}2T>SLSn>Djcvsd}ewbF{;w}*+D*|hlC8SB22Cr@5{KEGZsKR^HKia=*O zJG)guOS{B$B0eP4J1_*a(#v-F zx)a-TLqevkbnBH;%g)XYc5!jJ_bc=AvY9F~o0^;RPnW#9qIr4s`hBzVV_#oe>pRJ3 z-@bjzWUb4d{LVQu!%)q0*}uQP??0Z;#xTSE)>)p*((-2w3%Mj5Ixnn=G!9)8@p0SN zy1KfodwX^U1qX`?3s2tu@Adlq*Jc{0g96Mj`PdWbT;)!(nzr%s-{nBV@7LH^&Ho6}W2b8l_gsT;hv>g$)2>hte> z{2j3^XQoxjiwXI6i_hDtds-DfI&ybkErUjwhy#PFo0nHt*!sA&*W;>v9UUFHI5;M3 z-@g6O;lrw$_noKl%UCFQN*SeiH2(hkIO@QI2M?_4{vH4Ie_z@L|M_;4mYlcy?UTRv z>$E;u>$2;w1^&;TI`wMqYa3fzRZmV%PS!s5hDQ#JECEV6H#RtaeRcKn;(ohT{`P-E z9zJ}yY1_82$!fkKOTDJv-ezC+W`+tVPq4nT*3$C2RNr;u|F7h~D}$GR@`~G@clXO7 zZhZ}1UElZn|L>b+lDWuhs@BT<`}=Nf%?@9<&)nVJ-E-G+CQgQ6nhAC{7`B(CbE>d&7)HEnHU_y7B~+N$Kmf{TmY?_dAU#h}W_ zD$wxIEa%38J9lDutFw_|NQ*? 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zdp}>ec4y48npr+-^X+P@Qbp!BDmF~H#qD~4e`()}j}|=79R|HJ9eR5EmB@{VOi0J&i&0Xx^U9rG{ra?PmHs`&{|ta)QAI zPe#q7=iV$S-FW}~?MV*O5}kbD(c`1LZst5Q1C7e;i_vHG0F7WUc&xNKVVQdI@#DuY zU#^U0bnwd6O3(LFNoo$t+87bSe@)$uX+n^U-6FfXKQmtK|NZ;-k1`v%+d2(XlBO@c zeeHkrS(V>UPfveXP*GU;@ynN#$xN)PU-EcbuK#qh#`U6@@nOBNN2P8$OK*Ga?by3N z`&aQs5rw7Sl+yQyJk#zf+q7fy + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +5 +10 +0 +0 +5 +10 +0 +-5 +-10 + +digamma(z) + +z + + + + + + + + + + + + + + + + + +digamma + diff --git a/doc/sf_and_dist/graphs/dist_graphs.cpp b/doc/sf_and_dist/graphs/dist_graphs.cpp new file mode 100644 index 000000000..195d9401a --- /dev/null +++ b/doc/sf_and_dist/graphs/dist_graphs.cpp @@ -0,0 +1,583 @@ +// (C) Copyright John Maddock 2008. +// Copyright Paul A. Bristow 2008 +// Use, modification and distribution are subject to the +// Boost Software License, Version 1.0. (See accompanying file +// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) + +#ifdef _MSC_VER +# pragma warning (disable : 4180) // qualifier applied to function type has no meaning; ignored +# pragma warning (disable : 4503) // decorated name length exceeded, name was truncated +# pragma warning (disable : 4512) // assignment operator could not be generated +# pragma warning (disable : 4224) // nonstandard extension used : formal parameter 'function_ptr' was previously defined as a type +# pragma warning (disable : 4127) // conditional expression is constant +#endif + +#define BOOST_MATH_OVERFLOW_ERROR_POLICY ignore_error + +#include +#include +#include + +#include +#include +#include + +template +struct is_discrete_distribution + : public boost::mpl::false_{}; + +template +struct is_discrete_distribution > + : public boost::mpl::true_{}; +template +struct is_discrete_distribution > + : public boost::mpl::true_{}; +template +struct is_discrete_distribution > + : public boost::mpl::true_{}; +template +struct is_discrete_distribution > + : public boost::mpl::true_{}; + + +template +struct value_finder +{ + value_finder(Dist const& d, typename Dist::value_type v) + : m_dist(d), m_value(v) {} + + inline typename Dist::value_type operator()(const typename Dist::value_type& x) + { + return pdf(m_dist, x) - m_value; + } + +private: + Dist m_dist; + typename Dist::value_type m_value; +}; + +template +class distribution_plotter +{ +public: + distribution_plotter() : m_pdf(true), m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {} + distribution_plotter(bool pdf) : m_pdf(pdf), m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0) {} + + void add(const Dist& d, const std::string& name) + { + // + // Add to our list for later: + // + m_distributions.push_back(std::make_pair(name, d)); + // + // Get the extent: + // + double a, b; + std::tr1::tie(a, b) = support(d); + // + // PDF maximimum is at the mode: + // + double mod; + try + { + mod = mode(d); + } + catch(const std::domain_error& ) + { + mod = a; + } + if((mod <= a) && !is_discrete_distribution::value) + { + if((a != 0) && (fabs(a) > 1e-2)) + mod = a * (1 + 1e-2); + else + mod = 1e-2; + } + double peek_y = pdf(d, mod); + double min_y = peek_y / 20; + // + // If the extent is "infinite" then find out how large it + // has to be for the PDF to decay to min_y: + // + if(a <= -(std::numeric_limits::max)()) + { + boost::uintmax_t max_iter = 500; + double guess = mod; + if((pdf(d, 0) > min_y) || (guess == 0)) + guess = -1e-3; + a = boost::math::tools::bracket_and_solve_root( + value_finder(d, min_y), + guess, + 8.0, + true, + boost::math::tools::eps_tolerance(10), + max_iter).first; + } + if(b >= (std::numeric_limits::max)()) + { + boost::uintmax_t max_iter = 500; + double guess = mod; + if(a <= 0) + if((pdf(d, 0) > min_y) || (guess == 0)) + guess = 1e-3; + b = boost::math::tools::bracket_and_solve_root( + value_finder(d, min_y), + guess, + 8.0, + false, + boost::math::tools::eps_tolerance(10), + max_iter).first; + } + // + // Recalculate peek_y and location of mod so that + // it's not too close to one end of the graph: + // otherwise we may be shooting off to infinity. + // + if(!is_discrete_distribution::value) + { + if(mod <= a + (b-a)/50) + { + mod = a + (b-a)/50; + } + if(mod >= b - (b-a)/50) + { + mod = b - (b-a)/50; + } + peek_y = pdf(d, mod); + } + // + // Now set our limits: + // + if(peek_y > m_max_y) + m_max_y = peek_y; + if(m_max_x == m_min_x) + { + m_max_x = b; + m_min_x = a; + } + else + { + if(a < m_min_x) + m_min_x = a; + if(b > m_max_x) + m_max_x = b; + } + } + + void plot(const std::string& title, const std::string& file) + { + using namespace boost::svg; + + static const svg_color colors[5] = + { + darkblue, + darkred, + darkgreen, + darkorange, + chartreuse + }; + + if(m_pdf == false) + { + m_min_y = 0; + m_max_y = 1; + } + + svg_2d_plot plot; + plot.image_size(750, 400); + plot.coord_precision(4); // Avoids any visible steps. + plot.title_font_size(20); + plot.legend_title_font_size(15); + plot.title(title); + if((m_distributions.size() == 1) && (m_distributions.begin()->first == "")) + plot.legend_on(false); + else + plot.legend_on(true); + plot.title_on(true); + //plot.x_major_labels_on(true).y_major_labels_on(true); + //double x_delta = (m_max_x - m_min_x) / 10; + double y_delta = (m_max_y - m_min_y) / 10; + if(is_discrete_distribution::value) + plot.x_range(m_min_x - 0.5, m_max_x + 0.5) + .y_range(m_min_y, m_max_y + y_delta); + else + plot.x_range(m_min_x, m_max_x) + .y_range(m_min_y, m_max_y + y_delta); + plot.x_label_on(true).x_label("Random Variable"); + plot.y_label_on(true).y_label("Probability"); + plot.plot_border_color(lightslategray) + .background_border_color(lightslategray) + .legend_border_color(lightslategray) + .legend_background_color(white); + // + // Work out axis tick intervals: + // + double l = std::floor(std::log10((m_max_x - m_min_x) / 10) + 0.5); + double interval = std::pow(10.0, (int)l); + if(((m_max_x - m_min_x) / interval) > 10) + interval *= 5; + if(is_discrete_distribution::value) + { + interval = interval > 1 ? std::floor(interval) : 1; + plot.x_num_minor_ticks(0); + } + plot.x_major_interval(interval); + l = std::floor(std::log10((m_max_y - m_min_y) / 10) + 0.5); + interval = std::pow(10.0, (int)l); + if(((m_max_y - m_min_y) / interval) > 10) + interval *= 5; + plot.y_major_interval(interval); + + int color_index = 0; + + if(!is_discrete_distribution::value) + { + // + // Continuous distribution: + // + for(std::list >::const_iterator i = m_distributions.begin(); + i != m_distributions.end(); ++i) + { + double x = m_min_x; + double interval = (m_max_x - m_min_x) / 200; + std::map data; + while(x <= m_max_x) + { + data[x] = m_pdf ? pdf(i->second, x) : cdf(i->second, x); + x += interval; + } + plot.plot(data, i->first) + .line_on(true) + .line_color(colors[color_index]) + .line_width(1.) + .shape(none); + //.bezier_on(true) // Bezier can't cope with badly behaved like uniform & triangular. + ++color_index; + color_index = color_index % (sizeof(colors)/sizeof(colors[0])); + } + } + else + { + // + // Discrete distribution: + // + double x_width = 0.75 / m_distributions.size(); + double x_off = -0.5 * 0.75; + for(std::list >::const_iterator i = m_distributions.begin(); + i != m_distributions.end(); ++i) + { + double x = ceil(m_min_x); + double interval = 1; + std::map data; + while(x <= m_max_x) + { + double p; + try{ + p = m_pdf ? pdf(i->second, x) : cdf(i->second, x); + } + catch(const std::domain_error&) + { + p = 0; + } + data[x + x_off] = 0; + data[x + x_off + 0.00001] = p; + data[x + x_off + x_width] = p; + data[x + x_off + x_width + 0.00001] = 0; + x += interval; + } + x_off += x_width; + svg_2d_plot_series& s = plot.plot(data, i->first); + s.line_on(true) + .line_color(colors[color_index]) + .line_width(1.) + .shape(none) + .area_fill(colors[color_index]); + ++color_index; + color_index = color_index % (sizeof(colors)/sizeof(colors[0])); + } + } + plot.write(file); + } + +private: + bool m_pdf; + std::list > m_distributions; + double m_min_x, m_max_x, m_min_y, m_max_y; +}; + +int main() +{ + distribution_plotter > + gamma_plotter; + gamma_plotter.add(boost::math::gamma_distribution<>(1), "shape = 0.5"); + gamma_plotter.add(boost::math::gamma_distribution<>(2), "shape = 1"); + gamma_plotter.add(boost::math::gamma_distribution<>(4), "shape = 3"); + gamma_plotter.plot("Gamma Distribution PDF With Scale = 1", "gamma1_pdf.svg"); + + distribution_plotter > + gamma_plotter2; + gamma_plotter2.add(boost::math::gamma_distribution<>(2, 0.5), "scale = 2"); + gamma_plotter2.add(boost::math::gamma_distribution<>(2, 1), "scale = 0.5"); + gamma_plotter2.add(boost::math::gamma_distribution<>(2, 2), "scale = 2"); + gamma_plotter2.plot("Gamma Distribution PDF With Shape = 2", "gamma2_pdf.svg"); + + distribution_plotter + normal_plotter; + normal_plotter.add(boost::math::normal(0, 1), "μ = 0, σ = 1"); + normal_plotter.add(boost::math::normal(0, 0.5), "μ = 0, σ = 0.5"); + normal_plotter.add(boost::math::normal(0, 2), "μ = 0, σ = 2"); + normal_plotter.add(boost::math::normal(-1, 1), "μ = -1, σ = 1"); + normal_plotter.add(boost::math::normal(1, 1), "μ = 1, σ = 1"); + normal_plotter.plot("Normal Distribution PDF", "normal_pdf.svg"); + + distribution_plotter + nc_cs_plotter; + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 0), "v=20, λ=0"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 1), "v=20, λ=1"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 5), "v=20, λ=5"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 10), "v=20, λ=10"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 20), "v=20, λ=20"); + nc_cs_plotter.add(boost::math::non_central_chi_squared(20, 100), "v=20, λ=100"); + nc_cs_plotter.plot("Non Central Chi Squared PDF", "nccs_pdf.svg"); + + distribution_plotter + nc_beta_plotter; + nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 0), "α=10, β=15, δ=0"); + nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 1), "α=10, β=15, δ=1"); + nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 5), "α=10, β=15, δ=5"); + nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 10), "α=10, β=15, δ=10"); + nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 40), "α=10, β=15, δ=40"); + nc_beta_plotter.add(boost::math::non_central_beta(10, 15, 100), "α=10, β=15, δ=100"); + nc_beta_plotter.plot("Non Central Beta PDF", "nc_beta_pdf.svg"); + + distribution_plotter + nc_f_plotter; + nc_f_plotter.add(boost::math::non_central_f(10, 20, 0), "v1=10, v2=20, λ=0"); + nc_f_plotter.add(boost::math::non_central_f(10, 20, 1), "v1=10, v2=20, λ=1"); + nc_f_plotter.add(boost::math::non_central_f(10, 20, 5), "v1=10, v2=20, λ=5"); + nc_f_plotter.add(boost::math::non_central_f(10, 20, 10), "v1=10, v2=20, λ=10"); + nc_f_plotter.add(boost::math::non_central_f(10, 20, 40), "v1=10, v2=20, λ=40"); + nc_f_plotter.add(boost::math::non_central_f(10, 20, 100), "v1=10, v2=20, λ=100"); + nc_f_plotter.plot("Non Central F PDF", "nc_f_pdf.svg"); + + distribution_plotter + nc_t_plotter; + nc_t_plotter.add(boost::math::non_central_t(10, -10), "v=10, δ=-10"); + nc_t_plotter.add(boost::math::non_central_t(10, -5), "v=10, δ=-5"); + nc_t_plotter.add(boost::math::non_central_t(10, 0), "v=10, δ=0"); + nc_t_plotter.add(boost::math::non_central_t(10, 5), "v=10, δ=5"); + nc_t_plotter.add(boost::math::non_central_t(10, 10), "v=10, δ=10"); + nc_t_plotter.plot("Non Central T PDF", "nc_t_pdf.svg"); + + distribution_plotter > + beta_plotter; + beta_plotter.add(boost::math::beta_distribution<>(0.5, 0.5), "alpha=0.5, beta=0.5"); + beta_plotter.add(boost::math::beta_distribution<>(5, 1), "alpha=5, beta=1"); + beta_plotter.add(boost::math::beta_distribution<>(1, 3), "alpha=1, beta=3"); + beta_plotter.add(boost::math::beta_distribution<>(2, 2), "alpha=2, beta=2"); + beta_plotter.add(boost::math::beta_distribution<>(2, 5), "alpha=2, beta=5"); + beta_plotter.plot("Beta Distribution PDF", "beta_pdf.svg"); + + distribution_plotter > + cauchy_plotter; + cauchy_plotter.add(boost::math::cauchy_distribution<>(-5, 1), "location = -5"); + cauchy_plotter.add(boost::math::cauchy_distribution<>(0, 1), "location = 0"); + cauchy_plotter.add(boost::math::cauchy_distribution<>(5, 1), "location = 5"); + cauchy_plotter.plot("Cauchy Distribution PDF (scale = 1)", "cauchy_pdf1.svg"); + + distribution_plotter > + cauchy_plotter2; + cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 0.5), "scale = 0.5"); + cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 1), "scale = 1"); + cauchy_plotter2.add(boost::math::cauchy_distribution<>(0, 2), "scale = 2"); + cauchy_plotter2.plot("Cauchy Distribution PDF (location = 0)", "cauchy_pdf2.svg"); + + distribution_plotter > + chi_squared_plotter; + //chi_squared_plotter.add(boost::math::chi_squared_distribution<>(1), "v=1"); + chi_squared_plotter.add(boost::math::chi_squared_distribution<>(2), "v=2"); + chi_squared_plotter.add(boost::math::chi_squared_distribution<>(5), "v=5"); + chi_squared_plotter.add(boost::math::chi_squared_distribution<>(10), "v=10"); + chi_squared_plotter.plot("Chi Squared Distribution PDF", "chi_squared_pdf.svg"); + + distribution_plotter > + exponential_plotter; + exponential_plotter.add(boost::math::exponential_distribution<>(0.5), "λ=1"); + exponential_plotter.add(boost::math::exponential_distribution<>(1), "λ=2"); + exponential_plotter.add(boost::math::exponential_distribution<>(2), "λ=5"); + exponential_plotter.plot("Exponential Distribution PDF", "exponential_pdf.svg"); + + distribution_plotter > + extreme_value_plotter; + extreme_value_plotter.add(boost::math::extreme_value_distribution<>(-5), "location=1"); + extreme_value_plotter.add(boost::math::extreme_value_distribution<>(0), "location=2"); + extreme_value_plotter.add(boost::math::extreme_value_distribution<>(5), "location=5"); + extreme_value_plotter.plot("Extreme Value Distribution PDF (shape=1)", "extreme_value_pdf1.svg"); + + distribution_plotter > + extreme_value_plotter2; + extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 0.5), "shape=0.5"); + extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 1), "shape=1"); + extreme_value_plotter2.add(boost::math::extreme_value_distribution<>(0, 2), "shape=2"); + extreme_value_plotter2.plot("Extreme Value Distribution PDF (location=0)", "extreme_value_pdf2.svg"); + + distribution_plotter > + fisher_f_plotter; + fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 4), "n=4, m=4"); + fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 4), "n=10, m=4"); + fisher_f_plotter.add(boost::math::fisher_f_distribution<>(10, 10), "n=10, m=10"); + fisher_f_plotter.add(boost::math::fisher_f_distribution<>(4, 10), "n=4, m=10"); + fisher_f_plotter.plot("F Distribution PDF", "fisher_f_pdf.svg"); + + distribution_plotter > + lognormal_plotter; + lognormal_plotter.add(boost::math::lognormal_distribution<>(-1), "location=-1"); + lognormal_plotter.add(boost::math::lognormal_distribution<>(0), "location=0"); + lognormal_plotter.add(boost::math::lognormal_distribution<>(1), "location=1"); + lognormal_plotter.plot("Lognormal Distribution PDF (scale=1)", "lognormal_pdf1.svg"); + + distribution_plotter > + lognormal_plotter2; + lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 0.5), "scale=0.5"); + lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 1), "scale=1"); + lognormal_plotter2.add(boost::math::lognormal_distribution<>(0, 2), "scale=2"); + lognormal_plotter2.plot("Lognormal Distribution PDF (location=0)", "lognormal_pdf2.svg"); + + distribution_plotter > + pareto_plotter; + pareto_plotter.add(boost::math::pareto_distribution<>(1), "location=1"); + pareto_plotter.add(boost::math::pareto_distribution<>(2), "location=2"); + pareto_plotter.add(boost::math::pareto_distribution<>(3), "location=3"); + pareto_plotter.plot("Pareto Distribution PDF (scale=1)", "pareto_pdf1.svg"); + + distribution_plotter > + pareto_plotter2; + pareto_plotter2.add(boost::math::pareto_distribution<>(1, 0.5), "scale=0.5"); + pareto_plotter2.add(boost::math::pareto_distribution<>(1, 1), "scale=1"); + pareto_plotter2.add(boost::math::pareto_distribution<>(1, 2), "scale=2"); + pareto_plotter2.plot("Pareto Distribution PDF (location=1)", "pareto_pdf2.svg"); + + distribution_plotter > + rayleigh_plotter; + rayleigh_plotter.add(boost::math::rayleigh_distribution<>(0.5), "σ=0.5"); + rayleigh_plotter.add(boost::math::rayleigh_distribution<>(1), "σ=1"); + rayleigh_plotter.add(boost::math::rayleigh_distribution<>(2), "σ=2"); + rayleigh_plotter.add(boost::math::rayleigh_distribution<>(4), "σ=4"); + rayleigh_plotter.add(boost::math::rayleigh_distribution<>(10), "σ=10"); + rayleigh_plotter.plot("Rayleigh Distribution PDF", "rayleigh_pdf.svg"); + + distribution_plotter > + rayleigh_cdf_plotter(false); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(0.5), "σ=0.5"); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(1), "σ=1"); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(2), "σ=2"); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(4), "σ=4"); + rayleigh_cdf_plotter.add(boost::math::rayleigh_distribution<>(10), "σ=10"); + rayleigh_cdf_plotter.plot("Rayleigh Distribution CDF", "rayleigh_cdf.svg"); + + distribution_plotter > + triangular_plotter; + triangular_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}"); + triangular_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}"); + triangular_plotter.add(boost::math::triangular_distribution<>(0,1,3), "{0,1,3}"); + triangular_plotter.add(boost::math::triangular_distribution<>(0,0.5,1), "{0,0.5,1}"); + triangular_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}"); + triangular_plotter.plot("Triangular Distribution PDF", "triangular_pdf.svg"); + + distribution_plotter > + triangular_cdf_plotter(false); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-1,0,1), "{-1,0,1}"); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,1), "{0,1,1}"); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,1,3), "{0,1,3}"); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(0,0.5,1), "{0,0.5,1}"); + triangular_cdf_plotter.add(boost::math::triangular_distribution<>(-2,0,3), "{-2,0,3}"); + triangular_cdf_plotter.plot("Triangular Distribution CDF", "triangular_cdf.svg"); + + distribution_plotter > + students_t_plotter; + students_t_plotter.add(boost::math::students_t_distribution<>(1), "v=1"); + students_t_plotter.add(boost::math::students_t_distribution<>(5), "v=5"); + students_t_plotter.add(boost::math::students_t_distribution<>(30), "v=30"); + students_t_plotter.plot("Students T Distribution PDF", "students_t_pdf.svg"); + + distribution_plotter > + weibull_plotter; + weibull_plotter.add(boost::math::weibull_distribution<>(0.75), "shape=0.75"); + weibull_plotter.add(boost::math::weibull_distribution<>(1), "shape=1"); + weibull_plotter.add(boost::math::weibull_distribution<>(5), "shape=5"); + weibull_plotter.add(boost::math::weibull_distribution<>(10), "shape=10"); + weibull_plotter.plot("Weibull Distribution PDF (scale=1)", "weibull_pdf1.svg"); + + distribution_plotter > + weibull_plotter2; + weibull_plotter2.add(boost::math::weibull_distribution<>(3, 0.5), "scale=0.5"); + weibull_plotter2.add(boost::math::weibull_distribution<>(3, 1), "scale=1"); + weibull_plotter2.add(boost::math::weibull_distribution<>(3, 2), "scale=2"); + weibull_plotter2.plot("Weibull Distribution PDF (shape=3)", "weibull_pdf2.svg"); + + distribution_plotter > + uniform_plotter; + uniform_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}"); + uniform_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}"); + uniform_plotter.add(boost::math::uniform_distribution<>(-2, 3), "{-2,3}"); + uniform_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}"); + uniform_plotter.plot("Uniform Distribution PDF", "uniform_pdf.svg"); + + distribution_plotter > + uniform_cdf_plotter(false); + uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 1), "{0,1}"); + uniform_cdf_plotter.add(boost::math::uniform_distribution<>(0, 3), "{0,3}"); + uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-2, 3), "{-2,3}"); + uniform_cdf_plotter.add(boost::math::uniform_distribution<>(-1, 1), "{-1,1}"); + uniform_cdf_plotter.plot("Uniform Distribution CDF", "uniform_cdf.svg"); + + distribution_plotter > + bernoulli_plotter; + bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25"); + bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5"); + bernoulli_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75"); + bernoulli_plotter.plot("Bernoulli Distribution PDF", "bernoulli_pdf.svg"); + + distribution_plotter > + bernoulli_cdf_plotter(false); + bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.25), "p=0.25"); + bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.5), "p=0.5"); + bernoulli_cdf_plotter.add(boost::math::bernoulli_distribution<>(0.75), "p=0.75"); + bernoulli_cdf_plotter.plot("Bernoulli Distribution CDF", "bernoulli_cdf.svg"); + + distribution_plotter > + binomial_plotter; + binomial_plotter.add(boost::math::binomial_distribution<>(5, 0.5), "n=5 p=0.5"); + binomial_plotter.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5"); + binomial_plotter.add(boost::math::binomial_distribution<>(50, 0.5), "n=50 p=0.5"); + binomial_plotter.plot("Binomial Distribution PDF", "binomial_pdf_1.svg"); + + distribution_plotter > + binomial_plotter2; + binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.1), "n=20 p=0.1"); + binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.5), "n=20 p=0.5"); + binomial_plotter2.add(boost::math::binomial_distribution<>(20, 0.9), "n=20 p=0.9"); + binomial_plotter2.plot("Binomial Distribution PDF", "binomial_pdf_2.svg"); + + distribution_plotter > + negative_binomial_plotter; + negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.25), "n=20 p=0.25"); + negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=20 p=0.5"); + negative_binomial_plotter.add(boost::math::negative_binomial_distribution<>(20, 0.75), "n=20 p=0.75"); + negative_binomial_plotter.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_1.svg"); + + distribution_plotter > + negative_binomial_plotter2; + negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(10, 0.5), "n=10 p=0.5"); + negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(20, 0.5), "n=40 p=0.5"); + negative_binomial_plotter2.add(boost::math::negative_binomial_distribution<>(70, 0.5), "n=70 p=0.5"); + negative_binomial_plotter2.plot("Negative Binomial Distribution PDF", "negative_binomial_pdf_2.svg"); + + distribution_plotter > + poisson_plotter; + poisson_plotter.add(boost::math::poisson_distribution<>(5), "λ=1"); + poisson_plotter.add(boost::math::poisson_distribution<>(10), "λ=10"); + poisson_plotter.add(boost::math::poisson_distribution<>(20), "λ=50"); + poisson_plotter.plot("Poisson Distribution PDF", "poisson_pdf_1.svg"); + +} diff --git a/doc/sf_and_dist/graphs/ellint_1.png b/doc/sf_and_dist/graphs/ellint_1.png index f5e193b95186db1ff9fae9ee70f712537670eb00..1cb3bb95f1d091e5567d3b73f70896b5fa18ab1e 100644 GIT binary patch literal 29530 zcmeAS@N?(olHy`uVBq!ia0y~yU}|7sU|h|?#=yW3;HT!zz`(##?Bp53!NI{%!;#X# 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function_arity1_plotter() : m_min_x(0), m_max_x(0), m_min_y(0), m_max_y(0), m_has_legend(false) {} + + void add(boost::function f, double a, double b, const std::string& name) + { + if(name.size()) + m_has_legend = true; + // + // Now set our x-axis limits: + // + if(m_max_x == m_min_x) + { + m_max_x = b; + m_min_x = a; + } + else + { + if(a < m_min_x) + m_min_x = a; + if(b > m_max_x) + m_max_x = b; + } + m_points.push_back(std::pair >(name, std::map())); + std::map& points = m_points.rbegin()->second; + double interval = (b - a) / 200; + for(double x = a; x <= b; x += interval) + { + // + // Evaluate the function, set the Y axis limits + // if needed and then store the pair of points: + // + double y = f(x); + if((m_min_y == m_max_y) && (m_min_y == 0)) + m_min_y = m_max_y = y; + if(m_min_y > y) + m_min_y = y; + if(m_max_y < y) + m_max_y = y; + points[x] = y; + } + } + + void add(const std::map& m, const std::string& name) + { + if(name.size()) + m_has_legend = true; + m_points.push_back(std::pair >(name, m)); + std::map::const_iterator i = m.begin(); + + while(i != m.end()) + { + if((m_min_x == m_min_y) && (m_min_y == 0)) + { + m_min_x = m_max_x = i->first; + } + if(i->first < m_min_x) + { + m_min_x = i->first; + } + if(i->first > m_max_x) + { + m_max_x = i->first; + } + + if((m_min_y == m_max_y) && (m_min_y == 0)) + { + m_min_y = m_max_y = i->second; + } + if(i->second < m_min_y) + { + m_min_y = i->second; + } + if(i->second > m_max_y) + { + m_max_y = i->second; + } + + ++i; + } + } + + void plot(const std::string& title, const std::string& file, + const std::string& x_lable = std::string(), + const std::string& y_lable = std::string()) + { + using namespace boost::svg; + + static const svg_color colors[5] = + { + darkblue, + darkred, + darkgreen, + darkorange, + chartreuse + }; + + svg_2d_plot plot; + plot.image_size(600, 400); + plot.copyright_holder("John Maddock").copyright_date("2008").boost_license_on(true); + plot.coord_precision(4); // Could be 3 for smaller plots? + plot.title(title).title_font_size(20).title_on(true); + plot.legend_on(m_has_legend); + + double x_delta = (m_max_x - m_min_x) / 50; + double y_delta = (m_max_y - m_min_y) / 50; + plot.x_range(m_min_x, m_max_x + x_delta) + .y_range(m_min_y, m_max_y + y_delta); + plot.x_label_on(true).x_label(x_lable); + plot.y_label_on(true).y_label(y_lable); + plot.y_major_grid_on(false).x_major_grid_on(false); + plot.x_num_minor_ticks(3); + plot.y_num_minor_ticks(3); + // + // Work out axis tick intervals: + // + double l = std::floor(std::log10((m_max_x - m_min_x) / 10) + 0.5); + double interval = std::pow(10.0, (int)l); + if(((m_max_x - m_min_x) / interval) > 10) + interval *= 5; + plot.x_major_interval(interval); + l = std::floor(std::log10((m_max_y - m_min_y) / 10) + 0.5); + interval = std::pow(10.0, (int)l); + if(((m_max_y - m_min_y) / interval) > 10) + interval *= 5; + plot.y_major_interval(interval); + plot.plot_window_on(true); + plot.plot_border_color(lightslategray) + .background_border_color(lightslategray) + .legend_border_color(lightslategray) + .legend_background_color(white); + + int color_index = 0; + + for(std::list > >::const_iterator i = m_points.begin(); + i != m_points.end(); ++i) + { + plot.plot(i->second, i->first) + .line_on(true) + .line_color(colors[color_index]) + .line_width(1.) + .shape(none); + if(i->first.size()) + ++color_index; + color_index = color_index % (sizeof(colors)/sizeof(colors[0])); + } + plot.write(file); + } + + void clear() + { + m_points.clear(); + m_min_x = m_min_y = m_max_x = m_max_y = 0; + m_has_legend = false; + } + +private: + std::list > > m_points; + double m_min_x, m_max_x, m_min_y, m_max_y; + bool m_has_legend; +}; + +template +struct location_finder +{ + location_finder(F _f, double t, double x0) : f(_f), target(t), x_off(x0){} + + double operator()(double x) + { + try + { + return f(x + x_off) - target; + } + catch(const std::overflow_error&) + { + return boost::math::tools::max_value(); + } + catch(const std::domain_error&) + { + if(x + x_off == x_off) + return f(x_off + boost::math::tools::epsilon() * x_off); + throw; + } + } + +private: + F f; + double target; + double x_off; +}; + +template +double find_end_point(F f, double x0, double target, bool rising, double x_off = 0) +{ + boost::math::tools::eps_tolerance tol(50); + boost::uintmax_t max_iter = 1000; + return boost::math::tools::bracket_and_solve_root( + location_finder(f, target, x_off), + x0, + double(1.5), + rising, + tol, + max_iter).first; +} + +double sqrt1pm1(double x) +{ + return boost::math::sqrt1pm1(x); +} + +double lbeta(double a, double b) +{ + return std::log(boost::math::beta(a, b)); +} + +int main() +{ + function_arity1_plotter plot; + double (*f)(double); + double (*f2)(double, double); + double (*f2u)(unsigned, double); + double (*f2i)(int, double); + double (*f3)(double, double, double); + double (*f4)(double, double, double, double); + + f = boost::math::zeta; + plot.add(f, 1 + find_end_point(f, 0.1, 40.0, false, 1.0), 10, ""); + plot.add(f, -20, 1 + find_end_point(f, -0.1, -40.0, false, 1.0), ""); + plot.plot("Zeta Function Over [-20,10]", "zeta1.svg", "z", "zeta(z)"); + + plot.clear(); + plot.add(f, -14, 0, ""); + plot.plot("Zeta Function Over [-14,0]", "zeta2.svg", "z", "zeta(z)"); + + f = boost::math::tgamma; + double max_val = f(6); + plot.clear(); + plot.add(f, find_end_point(f, 0.1, max_val, false), 6, ""); + plot.add(f, -1 + find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, -max_val, false), ""); + plot.add(f, -2 + find_end_point(f, 0.1, max_val, false, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, -3 + find_end_point(f, 0.1, -max_val, true, -3), -2 + find_end_point(f, -0.1, -max_val, false, -2), ""); + plot.add(f, -4 + find_end_point(f, 0.1, max_val, false, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); + plot.plot("tgamma", "tgamma.svg", "z", "tgamma(z)"); + + f = boost::math::lgamma; + max_val = f(10); + plot.clear(); + plot.add(f, find_end_point(f, 0.1, max_val, false), 10, ""); + plot.add(f, -1 + find_end_point(f, 0.1, max_val, false, -1), find_end_point(f, -0.1, max_val, true), ""); + plot.add(f, -2 + find_end_point(f, 0.1, max_val, false, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, -3 + find_end_point(f, 0.1, max_val, false, -3), -2 + find_end_point(f, -0.1, max_val, true, -2), ""); + plot.add(f, -4 + find_end_point(f, 0.1, max_val, false, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); + plot.add(f, -5 + find_end_point(f, 0.1, max_val, false, -5), -4 + find_end_point(f, -0.1, max_val, true, -4), ""); + plot.plot("lgamma", "lgamma.svg", "z", "lgamma(z)"); + + f = boost::math::digamma; + max_val = 10; + plot.clear(); + plot.add(f, find_end_point(f, 0.1, -max_val, true), 10, ""); + plot.add(f, -1 + find_end_point(f, 0.1, -max_val, true, -1), find_end_point(f, -0.1, max_val, true), ""); + plot.add(f, -2 + find_end_point(f, 0.1, -max_val, true, -2), -1 + find_end_point(f, -0.1, max_val, true, -1), ""); + plot.add(f, -3 + find_end_point(f, 0.1, -max_val, true, -3), -2 + find_end_point(f, -0.1, max_val, true, -2), ""); + plot.add(f, -4 + find_end_point(f, 0.1, -max_val, true, -4), -3 + find_end_point(f, -0.1, max_val, true, -3), ""); + plot.plot("digamma", "digamma.svg", "z", "digamma(z)"); + + f = boost::math::erf; + plot.clear(); + plot.add(f, -3, 3, ""); + plot.plot("erf", "erf.svg", "z", "erf(z)"); + f = boost::math::erfc; + plot.clear(); + plot.add(f, -3, 3, ""); + plot.plot("erfc", "erfc.svg", "z", "erfc(z)"); + + f = boost::math::erf_inv; + plot.clear(); + plot.add(f, -1 + find_end_point(f, 0.1, -3, true, -1), 1 + find_end_point(f, -0.1, 3, true, 1), ""); + plot.plot("erf_inv", "erf_inv.svg", "z", "erf_inv(z)"); + f = boost::math::erfc_inv; + plot.clear(); + plot.add(f, find_end_point(f, 0.1, 3, false), 2 + find_end_point(f, -0.1, -3, false, 2), ""); + plot.plot("erfc_inv", "erfc_inv.svg", "z", "erfc_inv(z)"); + + f = boost::math::log1p; + plot.clear(); + plot.add(f, -1 + find_end_point(f, 0.1, -10, true, -1), 10, ""); + plot.plot("log1p", "log1p.svg", "z", "log1p(z)"); + + f = boost::math::expm1; + plot.clear(); + plot.add(f, -4, 2, ""); + plot.plot("expm1", "expm1.svg", "z", "expm1(z)"); + + f = boost::math::cbrt; + plot.clear(); + plot.add(f, -10, 10, ""); + plot.plot("cbrt", "cbrt.svg", "z", "cbrt(z)"); + + f = sqrt1pm1; + plot.clear(); + plot.add(f, -1 + find_end_point(f, 0.1, -10, true, -1), 5, ""); + plot.plot("sqrt1pm1", "sqrt1pm1.svg", "z", "sqrt1pm1(z)"); + + f2 = boost::math::powm1; + plot.clear(); + plot.add(boost::bind(f2, 0.0001, _1), find_end_point(boost::bind(f2, 0.0001, _1), -1, 10, false), 5, "a=0.0001"); + plot.add(boost::bind(f2, 0.001, _1), find_end_point(boost::bind(f2, 0.001, _1), -1, 10, false), 5, "a=0.001"); + plot.add(boost::bind(f2, 0.01, _1), find_end_point(boost::bind(f2, 0.01, _1), -1, 10, false), 5, "a=0.01"); + plot.add(boost::bind(f2, 0.1, _1), find_end_point(boost::bind(f2, 0.1, _1), -1, 10, false), 5, "a=0.1"); + plot.add(boost::bind(f2, 0.75, _1), -5, 5, "a=0.75"); + plot.add(boost::bind(f2, 1.25, _1), -5, 5, "a=1.25"); + plot.plot("powm1", "powm1.svg", "z", "powm1(a, z)"); + + f = boost::math::sinc_pi; + plot.clear(); + plot.add(f, -10, 10, ""); + plot.plot("sinc_pi", "sinc_pi.svg", "z", "sinc_pi(z)"); + + f = boost::math::sinhc_pi; + plot.clear(); + plot.add(f, -5, 5, ""); + plot.plot("sinhc_pi", "sinhc_pi.svg", "z", "sinhc_pi(z)"); + + f = boost::math::acosh; + plot.clear(); + plot.add(f, 1, 10, ""); + plot.plot("acosh", "acosh.svg", "z", "acosh(z)"); + + f = boost::math::asinh; + plot.clear(); + plot.add(f, -10, 10, ""); + plot.plot("asinh", "asinh.svg", "z", "asinh(z)"); + + f = boost::math::atanh; + plot.clear(); + plot.add(f, -1 + find_end_point(f, 0.1, -5, true, -1), 1 + find_end_point(f, -0.1, 5, true, 1), ""); + plot.plot("atanh", "atanh.svg", "z", "atanh(z)"); + + f2 = boost::math::tgamma_delta_ratio; + plot.clear(); + plot.add(boost::bind(f2, _1, -0.5), 1, 40, "delta = -0.5"); + plot.add(boost::bind(f2, _1, -0.2), 1, 40, "delta = -0.2"); + plot.add(boost::bind(f2, _1, -0.1), 1, 40, "delta = -0.1"); + plot.add(boost::bind(f2, _1, 0.1), 1, 40, "delta = 0.1"); + plot.add(boost::bind(f2, _1, 0.2), 1, 40, "delta = 0.2"); + plot.add(boost::bind(f2, _1, 0.5), 1, 40, "delta = 0.5"); + plot.add(boost::bind(f2, _1, 1.0), 1, 40, "delta = 1.0"); + plot.plot("tgamma_delta_ratio", "tgamma_delta_ratio.svg", "z", "tgamma_delta_ratio(delta, z)"); + + f2 = boost::math::gamma_p; + plot.clear(); + plot.add(boost::bind(f2, 0.5, _1), 0, 20, "a = 0.5"); + plot.add(boost::bind(f2, 1.0, _1), 0, 20, "a = 1.0"); + plot.add(boost::bind(f2, 5.0, _1), 0, 20, "a = 5.0"); + plot.add(boost::bind(f2, 10.0, _1), 0, 20, "a = 10.0"); + plot.plot("gamma_p", "gamma_p.svg", "z", "gamma_p(a, z)"); + + f2 = boost::math::gamma_q; + plot.clear(); + plot.add(boost::bind(f2, 0.5, _1), 0, 20, "a = 0.5"); + plot.add(boost::bind(f2, 1.0, _1), 0, 20, "a = 1.0"); + plot.add(boost::bind(f2, 5.0, _1), 0, 20, "a = 5.0"); + plot.add(boost::bind(f2, 10.0, _1), 0, 20, "a = 10.0"); + plot.plot("gamma_q", "gamma_q.svg", "z", "gamma_q(a, z)"); + + f2 = lbeta; + plot.clear(); + plot.add(boost::bind(f2, 0.5, _1), 0.00001, 5, "a = 0.5"); + plot.add(boost::bind(f2, 1.0, _1), 0.00001, 5, "a = 1.0"); + plot.add(boost::bind(f2, 5.0, _1), 0.00001, 5, "a = 5.0"); + plot.add(boost::bind(f2, 10.0, _1), 0.00001, 5, "a = 10.0"); + plot.plot("beta", "beta.svg", "z", "log(beta(a, z))"); + + f = boost::math::expint; + max_val = f(4); + plot.clear(); + plot.add(f, find_end_point(f, 0.1, -max_val, true), 4, ""); + plot.add(f, -3, find_end_point(f, -0.1, -max_val, false), ""); + plot.plot("Exponential Integral Ei", "expint_i.svg", "z", "expint(z)"); + + f2u = boost::math::expint; + max_val = 1; + plot.clear(); + plot.add(boost::bind(f2u, 1, _1), find_end_point(boost::bind(f2u, 1, _1), 0.1, max_val, false), 2, "n = 1 "); + plot.add(boost::bind(f2u, 2, _1), find_end_point(boost::bind(f2u, 2, _1), 0.1, max_val, false), 2, "n = 2 "); + plot.add(boost::bind(f2u, 3, _1), 0, 2, "n = 3 "); + plot.add(boost::bind(f2u, 4, _1), 0, 2, "n = 4 "); + plot.plot("Exponential Integral En", "expint2.svg", "z", "expint(n, z)"); + + f3 = boost::math::ibeta; + plot.clear(); + plot.add(boost::bind(f3, 9, 1, _1), 0, 1, "a = 9, b = 1"); + plot.add(boost::bind(f3, 7, 2, _1), 0, 1, "a = 7, b = 2"); + plot.add(boost::bind(f3, 5, 5, _1), 0, 1, "a = 1, b = 1"); + plot.add(boost::bind(f3, 2, 7, _1), 0, 1, "a = 2, b = 7"); + plot.add(boost::bind(f3, 1, 9, _1), 0, 1, "a = 1, b = 9"); + plot.plot("ibeta", "ibeta.svg", "z", "ibeta(a, b, z)"); + + f2i = boost::math::legendre_p; + plot.clear(); + plot.add(boost::bind(f2i, 1, _1), -1, 1, "l = 1"); + plot.add(boost::bind(f2i, 2, _1), -1, 1, "l = 2"); + plot.add(boost::bind(f2i, 3, _1), -1, 1, "l = 3"); + plot.add(boost::bind(f2i, 4, _1), -1, 1, "l = 4"); + plot.add(boost::bind(f2i, 5, _1), -1, 1, "l = 5"); + plot.plot("Legendre Polynomials", "legendre_p.svg", "x", "legendre_p(l, x)"); + + f2u = boost::math::legendre_q; + plot.clear(); + plot.add(boost::bind(f2u, 1, _1), -0.95, 0.95, "l = 1"); + plot.add(boost::bind(f2u, 2, _1), -0.95, 0.95, "l = 2"); + plot.add(boost::bind(f2u, 3, _1), -0.95, 0.95, "l = 3"); + plot.add(boost::bind(f2u, 4, _1), -0.95, 0.95, "l = 4"); + plot.add(boost::bind(f2u, 5, _1), -0.95, 0.95, "l = 5"); + plot.plot("Legendre Polynomials of the Second Kind", "legendre_q.svg", "x", "legendre_q(l, x)"); + + f2u = boost::math::laguerre; + plot.clear(); + plot.add(boost::bind(f2u, 0, _1), -5, 10, "n = 0"); + plot.add(boost::bind(f2u, 1, _1), -5, 10, "n = 1"); + plot.add(boost::bind(f2u, 2, _1), + find_end_point(boost::bind(f2u, 2, _1), -2, 20, false), + find_end_point(boost::bind(f2u, 2, _1), 4, 20, true), + "n = 2"); + plot.add(boost::bind(f2u, 3, _1), + find_end_point(boost::bind(f2u, 3, _1), -2, 20, false), + 8 + find_end_point(boost::bind(f2u, 3, _1), 1, 20, false, 8), + "n = 3"); + plot.add(boost::bind(f2u, 4, _1), + find_end_point(boost::bind(f2u, 4, _1), -2, 20, false), + 8 + find_end_point(boost::bind(f2u, 4, _1), 1, 20, true, 8), + "n = 4"); + plot.add(boost::bind(f2u, 5, _1), + find_end_point(boost::bind(f2u, 5, _1), -2, 20, false), + 8 + find_end_point(boost::bind(f2u, 5, _1), 1, 20, true, 8), + "n = 5"); + plot.plot("Laguerre Polynomials", "laguerre.svg", "x", "laguerre(n, x)"); + + f2u = boost::math::hermite; + plot.clear(); + plot.add(boost::bind(f2u, 0, _1), -1.8, 1.8, "n = 0"); + plot.add(boost::bind(f2u, 1, _1), -1.8, 1.8, "n = 1"); + plot.add(boost::bind(f2u, 2, _1), -1.8, 1.8, "n = 2"); + plot.add(boost::bind(f2u, 3, _1), -1.8, 1.8, "n = 3"); + plot.add(boost::bind(f2u, 4, _1), -1.8, 1.8, "n = 4"); + plot.plot("Hermite Polynomials", "hermite.svg", "x", "hermite(n, x)"); + + f2 = boost::math::cyl_bessel_j; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), -20, 20, "v = 0"); + plot.add(boost::bind(f2, 1, _1), -20, 20, "v = 1"); + plot.add(boost::bind(f2, 2, _1), -20, 20, "v = 2"); + plot.add(boost::bind(f2, 3, _1), -20, 20, "v = 3"); + plot.add(boost::bind(f2, 4, _1), -20, 20, "v = 4"); + plot.plot("Bessel J", "cyl_bessel_j.svg", "x", "cyl_bessel_j(v, x)"); + + f2 = boost::math::cyl_neumann; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), find_end_point(boost::bind(f2, 0, _1), 0.1, -5, true), 20, "v = 0"); + plot.add(boost::bind(f2, 1, _1), find_end_point(boost::bind(f2, 1, _1), 0.1, -5, true), 20, "v = 1"); + plot.add(boost::bind(f2, 2, _1), find_end_point(boost::bind(f2, 2, _1), 0.1, -5, true), 20, "v = 2"); + plot.add(boost::bind(f2, 3, _1), find_end_point(boost::bind(f2, 3, _1), 0.1, -5, true), 20, "v = 3"); + plot.add(boost::bind(f2, 4, _1), find_end_point(boost::bind(f2, 4, _1), 0.1, -5, true), 20, "v = 4"); + plot.plot("Bessel Y", "cyl_neumann.svg", "x", "cyl_neumann(v, x)"); + + f2 = boost::math::cyl_bessel_i; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), find_end_point(boost::bind(f2, 0, _1), -0.1, 20, false), find_end_point(boost::bind(f2, 0, _1), 0.1, 20, true), "v = 0"); + plot.add(boost::bind(f2, 2, _1), find_end_point(boost::bind(f2, 2, _1), -0.1, 20, false), find_end_point(boost::bind(f2, 2, _1), 0.1, 20, true), "v = 2"); + plot.add(boost::bind(f2, 5, _1), find_end_point(boost::bind(f2, 5, _1), -0.1, -20, true), find_end_point(boost::bind(f2, 5, _1), 0.1, 20, true), "v = 5"); + plot.add(boost::bind(f2, 7, _1), find_end_point(boost::bind(f2, 7, _1), -0.1, -20, true), find_end_point(boost::bind(f2, 7, _1), 0.1, 20, true), "v = 7"); + plot.add(boost::bind(f2, 10, _1), find_end_point(boost::bind(f2, 10, _1), -0.1, 20, false), find_end_point(boost::bind(f2, 10, _1), 0.1, 20, true), "v = 10"); + plot.plot("Bessel I", "cyl_bessel_i.svg", "x", "cyl_bessel_i(v, x)"); + + f2 = boost::math::cyl_bessel_k; + plot.clear(); + plot.add(boost::bind(f2, 0, _1), find_end_point(boost::bind(f2, 0, _1), 0.1, 10, false), 10, "v = 0"); + plot.add(boost::bind(f2, 2, _1), find_end_point(boost::bind(f2, 2, _1), 0.1, 10, false), 10, "v = 2"); + plot.add(boost::bind(f2, 5, _1), find_end_point(boost::bind(f2, 5, _1), 0.1, 10, false), 10, "v = 5"); + plot.add(boost::bind(f2, 7, _1), find_end_point(boost::bind(f2, 7, _1), 0.1, 10, false), 10, "v = 7"); + plot.add(boost::bind(f2, 10, _1), find_end_point(boost::bind(f2, 10, _1), 0.1, 10, false), 10, "v = 10"); + plot.plot("Bessel K", "cyl_bessel_k.svg", "x", "cyl_bessel_k(v, x)"); + + f2u = boost::math::sph_bessel; + plot.clear(); + plot.add(boost::bind(f2u, 0, _1), 0, 20, "v = 0"); + plot.add(boost::bind(f2u, 2, _1), 0, 20, "v = 2"); + plot.add(boost::bind(f2u, 5, _1), 0, 20, "v = 5"); + plot.add(boost::bind(f2u, 7, _1), 0, 20, "v = 7"); + plot.add(boost::bind(f2u, 10, _1), 0, 20, "v = 10"); + plot.plot("Bessel j", "sph_bessel.svg", "x", "sph_bessel(v, x)"); + + f2u = boost::math::sph_neumann; + plot.clear(); + plot.add(boost::bind(f2u, 0, _1), find_end_point(boost::bind(f2u, 0, _1), 0.1, -5, true), 20, "v = 0"); + plot.add(boost::bind(f2u, 2, _1), find_end_point(boost::bind(f2u, 2, _1), 0.1, -5, true), 20, "v = 2"); + plot.add(boost::bind(f2u, 5, _1), find_end_point(boost::bind(f2u, 5, _1), 0.1, -5, true), 20, "v = 5"); + plot.add(boost::bind(f2u, 7, _1), find_end_point(boost::bind(f2u, 7, _1), 0.1, -5, true), 20, "v = 7"); + plot.add(boost::bind(f2u, 10, _1), find_end_point(boost::bind(f2u, 10, _1), 0.1, -5, true), 20, "v = 10"); + plot.plot("Bessel y", "sph_neumann.svg", "x", "sph_neumann(v, x)"); + + f4 = boost::math::ellint_rj; + plot.clear(); + plot.add(boost::bind(f4, _1, _1, _1, _1), find_end_point(boost::bind(f4, _1, _1, _1, _1), 0.1, 10, false), 4, "RJ"); + f3 = boost::math::ellint_rf; + plot.add(boost::bind(f3, _1, _1, _1), find_end_point(boost::bind(f3, _1, _1, _1), 0.1, 10, false), 4, "RF"); + plot.plot("Elliptic Integrals", "ellint_carlson.svg", "x", ""); + + f2 = boost::math::ellint_1; + plot.clear(); + plot.add(boost::bind(f2, _1, 0.5), -0.9, 0.9, "φ=0.5"); + plot.add(boost::bind(f2, _1, 0.75), -0.9, 0.9, "φ=0.75"); + plot.add(boost::bind(f2, _1, 1.25), -0.9, 0.9, "φ=1.25"); + plot.add(boost::bind(f2, _1, boost::math::constants::pi() / 2), -0.9, 0.9, "φ=π/2"); + plot.plot("Elliptic Of the First Kind", "ellint_1.svg", "k", "ellint_1(k, phi)"); + + f2 = boost::math::ellint_2; + plot.clear(); + plot.add(boost::bind(f2, _1, 0.5), -1, 1, "φ=0.5"); + plot.add(boost::bind(f2, _1, 0.75), -1, 1, "φ=0.75"); + plot.add(boost::bind(f2, _1, 1.25), -1, 1, "φ=1.25"); + plot.add(boost::bind(f2, _1, boost::math::constants::pi() / 2), -1, 1, "φ=π/2"); + plot.plot("Elliptic Of the Second Kind", "ellint_2.svg", "k", "ellint_2(k, phi)"); + + f3 = boost::math::ellint_3; + plot.clear(); + plot.add(boost::bind(f3, _1, 0, 1.25), -1, 1, "n=0 φ=1.25"); + plot.add(boost::bind(f3, _1, 0.5, 1.25), -1, 1, "n=0.5 φ=1.25"); + plot.add(boost::bind(f3, _1, 0.25, boost::math::constants::pi() / 2), + find_end_point( + boost::bind(f3, _1, 0.25, boost::math::constants::pi() / 2), + 0.5, 4, false, -1) - 1, + find_end_point( + boost::bind(f3, _1, 0.25, boost::math::constants::pi() / 2), + -0.5, 4, true, 1) + 1, "n=0.25 φ=π/2"); + plot.add(boost::bind(f3, _1, 0.75, boost::math::constants::pi() / 2), + find_end_point( + boost::bind(f3, _1, 0.75, boost::math::constants::pi() / 2), + 0.5, 4, false, -1) - 1, + find_end_point( + boost::bind(f3, _1, 0.75, boost::math::constants::pi() / 2), + -0.5, 4, true, 1) + 1, "n=0.75 φ=π/2"); + plot.plot("Elliptic Of the Third Kind", "ellint_3.svg", "k", "ellint_3(k, n, phi)"); + + return 0; +} + diff --git a/doc/sf_and_dist/graphs/sinc_pi.png b/doc/sf_and_dist/graphs/sinc_pi.png new file mode 100644 index 0000000000000000000000000000000000000000..7c38a90510390c465d7b9de474a8c9dc75576d2b GIT binary patch literal 22485 zcmeAS@N?(olHy`uVBq!ia0y~yU}|7sU|h|?#=yW3;HT!zz`(##?Bp53!NI{%!;#X# 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a/doc/sf_and_dist/graphs/zeta2.svg b/doc/sf_and_dist/graphs/zeta2.svg new file mode 100644 index 000000000..1cd600c64 --- /dev/null +++ b/doc/sf_and_dist/graphs/zeta2.svg @@ -0,0 +1,57 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +0 +0 +-5 +-10 +0 +0 +-0.1 +-0.2 +-0.3 +-0.4 + +zeta(z) + +z + + + + + + + + + +Zeta Function Over [-14,0] + diff --git a/doc/sf_and_dist/hermite.qbk b/doc/sf_and_dist/hermite.qbk index c19c1f2b3..1819379ce 100644 --- a/doc/sf_and_dist/hermite.qbk +++ b/doc/sf_and_dist/hermite.qbk @@ -40,7 +40,7 @@ Returns the value of the Hermite Polynomial of order /n/ at point /x/: The following graph illustrates the behaviour of the first few Hermite Polynomials: -[$../graphs/hermite.png] +[graph hermite] template ``__sf_result`` hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1); diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 3a9f88262..e30d9a8ae 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -36,11 +36,14 @@

    Xiaogang Zhang

    +

    +Bruno Lalande +

    -

    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    -

    +

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    @@ -93,6 +96,8 @@ Binomial Distribution Examples
    Normal Distribution Examples
    +
    Non Central + Chi Squared Example
    Error Handling Example
    Find Location @@ -132,6 +137,14 @@ Log Normal Distribution
    Negative Binomial Distribution
    +
    Noncentral + Beta Distribution
    +
    + Noncentral Chi-Squared Distribution
    +
    Noncentral + F Distribution
    +
    Noncentral + T Distribution
    Normal (Gaussian) Distribution
    Pareto @@ -233,6 +246,15 @@
    Elliptic Integrals of the Third Kind - Legendre Form
    +
    Zeta Functions
    +
    Riemann Zeta Function
    +
    Exponential Integrals
    +
    +
    Exponential + Integral En
    +
    Exponential + Integral Ei
    +
    Logs, Powers, Roots and Exponentials
    @@ -242,6 +264,8 @@
    sqrt1pm1
    powm1
    hypot
    +
    Compile Time Power + of a Runtime Base
    Sinus Cardinal and Hyperbolic Sinus Cardinal Functions
    @@ -259,6 +283,14 @@
    asinh
    atanh
    +
    Rounding Truncation and + Integer Conversion
    +
    +
    Rounding Functions
    +
    Truncation Functions
    +
    Integer and Fractional + Part Splitting (modf)
    +
    Floating Point Classification: Infinities and NaN's
    @@ -291,7 +323,7 @@ Profiling, and Generating Test Data for Special Functions -
    Use with User Defined Floating-Point +
    Use with User-Defined Floating-Point Types
    Using With NTL - a High-Precision @@ -390,7 +422,7 @@

    - +

    Last revised: March 15, 2008 at 13:34:43 GMT

    Last revised: April 06, 2008 at 17:06:52 GMT
    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders.html b/doc/sf_and_dist/html/math_toolkit/backgrounders.html index 1055d463c..570f2d350 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders.html @@ -38,8 +38,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html index c3df1627c..48fc2f961 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html @@ -33,7 +33,7 @@ and reflect more the general implementation philosophy used.

    - + Implemention philosophy
    @@ -85,7 +85,7 @@ These could still provide sufficient accuracy for some speed-critical applications.

    - + Accuracy and Representation of Test Values
    @@ -130,7 +130,7 @@ binary value).

    - + Tolerance of Tests
    @@ -156,7 +156,7 @@ first that the suffix L is present, and then that the tolerance is big enough.

    - + Handling Unsuitable Arguments
    @@ -242,7 +242,7 @@

    - + Handling of Functions that are Not Mathematically defined
    @@ -276,7 +276,7 @@

    - + Median of distributions
    @@ -309,7 +309,7 @@ Basic Statistics. give more detail, in particular for discrete distributions.

    - + Handling of Floating-Point Infinity
    @@ -336,6 +336,12 @@ have permitted argument(s) to be infinity, provided infinity is implemented for the realType on that implementation.

    +

    + Users who require special handling of infinity (or other specific value) + can, of course, always intercept this before calling a distribution or function + and return their own choice of value, or other behavior. This will often + be simpler than trying to handle the aftermath of the error policy. +

    Overflow, underflow, denorm can be handled using error handling policies. @@ -347,7 +353,7 @@ handling policies.

    - + Scale, Shape and Location
    @@ -374,7 +380,7 @@ functions, they can be added if required.

    - + Notes on Implementation of Specific Functions & Distributions
    @@ -386,7 +392,7 @@ 0 and upper = 1 would be more suitable.
    - + Rational Approximations Used
    @@ -429,7 +435,7 @@ to the "true" minimax solution.

    - + Representation of Mathematical Constants
    @@ -490,7 +496,7 @@ double p = boost::math::constants::pi(); // Context does not allow for disambiguation of overloaded function
    - + Thread safety
    @@ -515,7 +521,7 @@ the right thing here at some point.

    - + Sources of Test Data
    @@ -559,7 +565,7 @@ the underlying special function is known to be difficult to implement.

    - + Creating and Managing the Equations
    @@ -620,6 +626,15 @@ and a command such as: 

    java -jar 'C:\download\open\batik-1.7\batik-rasterizer.jar' -dpi 120 *.svg
    +

    + Or using Inkscape and a command such as: +

    +
    for file in *.svg; do 
+  /cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file); 
+done
    +

    + Currently Inkscape seems to generate the better looking png's. +

    The PDF is generated into \pdf\math.pdf using a command from a shell or command window with current directory \math_toolkit\libs\math\doc\sf_and_dist, typically: @@ -711,7 +726,7 @@ HTML: this needs further investigation.

    - + Producing Graphs
    @@ -732,8 +747,8 @@ -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html index daa9d9a2f..44d2eb057 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html @@ -27,7 +27,7 @@ The Lanczos Approximation
    - + Motivation

    @@ -98,7 +98,7 @@ functions divided by large powers into single (simpler) expressions.

    - + The Approximation
    @@ -160,7 +160,7 @@

    - + Computing the Coefficients
    @@ -204,7 +204,7 @@ multiplied by F as the last step.

    - + Choosing the Right Parameters
    @@ -228,7 +228,7 @@ computing to float precision with double precision arithmetic.

    -

    Table 45. Optimal choices for N and g when computing with +

    Table 52. Optimal choices for N and g when computing with guard digits (source: Pugh)

    @@ -371,7 +371,7 @@ exactly matches the machine epsilon for the type in question.

    -

    Table 46. Optimum value for N and g when computing at fixed +

    Table 53. Optimum value for N and g when computing at fixed precision

    @@ -536,7 +536,7 @@ is exact, and so isn't used for the gamma function.

    - + References
      @@ -561,8 +561,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html index ee563aac0..2f0702154 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html @@ -27,7 +27,7 @@ References
    - + General references
    @@ -74,9 +74,15 @@ (Paperback) by N.A.J. Hastings, Brian Peacock, Merran Evans, ISBN: 0471371246, Wiley 2000.

    +

    + EXTREME VALUE + DISTRIBUTIONS, Theory and Applications Samuel Kotz & Saralees + Nadarajah, ISBN 978-1-86094-224-2 & 1-86094-224-5 Oct 2000, Chapter 1.2 + discusses the various extreme value distributions. +

    pugh.pdf - (application/pdf Object) Pugh Msc Thesis on the Lanczzos approximation + (application/pdf Object) Pugh Msc Thesis on the Lanczos approximation to the gamma function.

    @@ -85,7 +91,7 @@ Library (version 2), Walter E. Brown

    - + Calculators* that we found (and used to cross-check - as far as their widely-varying accuracy allowed). @@ -95,7 +101,7 @@ Binomial Probability Distribution Calculator.

    - + Other Libraries

    @@ -155,8 +161,8 @@ -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html index 5385be5d8..924cf8989 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/relative_error.html @@ -81,7 +81,7 @@

    - + The Impossibility of Zero Error
    @@ -109,8 +109,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html index bf357d04a..4c28b39f5 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html @@ -94,7 +94,7 @@ are located!

    - + The Remez Method
    @@ -174,7 +174,7 @@
    - + Remez Step 1
    @@ -205,7 +205,7 @@ to 5.6x10-4.

    - + Remez Step 2
    @@ -234,7 +234,7 @@ In our example we perform multi-point exchange.

    - + Iteration

    @@ -250,7 +250,7 @@ remez-4

    - + Rational Approximations
    @@ -299,7 +299,7 @@ number of terms overall.

    - + Practical Considerations
    @@ -407,7 +407,7 @@ desired minimax solution (5x10-4).

    - + Remez Method Checklist
    @@ -461,7 +461,7 @@
    - + References

    @@ -527,8 +527,8 @@ -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist.html b/doc/sf_and_dist/html/math_toolkit/dist.html index 1a3a97686..b11951ded 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist.html @@ -93,6 +93,10 @@ Distribution Examples
    Some Miscellaneous Examples of the Normal (Gaussian) Distribution
    +
    Non Central + Chi Squared Example
    +
    + Tables of the power function of the χ2 test.
    Error Handling Example
    Find Location @@ -140,6 +144,14 @@ Log Normal Distribution
    Negative Binomial Distribution
    +
    Noncentral + Beta Distribution
    +
    + Noncentral Chi-Squared Distribution
    +
    Noncentral + F Distribution
    +
    Noncentral + T Distribution
    Normal (Gaussian) Distribution
    Pareto @@ -165,8 +177,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html index 3a6446325..1e4668fdd 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref.html @@ -52,6 +52,14 @@ Log Normal Distribution
    Negative Binomial Distribution
    +
    Noncentral + Beta Distribution
    +
    + Noncentral Chi-Squared Distribution
    +
    Noncentral + F Distribution
    +
    Noncentral + T Distribution
    Normal (Gaussian) Distribution
    Pareto @@ -75,8 +83,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html index 1e405328e..265e3242c 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dist_algorithms.html @@ -28,7 +28,7 @@ Algorithms
    - + Finding the Location and Scale for Normal and similar distributions
    @@ -50,7 +50,7 @@ using boost::math::complement; // Will be needed by users who want to use complements.
    - + find_location function
    @@ -80,7 +80,7 @@ }} // namespaces
    - + find_scale function
    @@ -130,8 +130,8 @@ -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html index 91452f3c3..14bcd41af 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists.html @@ -48,6 +48,14 @@ Log Normal Distribution
    Negative Binomial Distribution
    +
    Noncentral + Beta Distribution
    +
    + Noncentral Chi-Squared Distribution
    +
    Noncentral + F Distribution
    +
    Noncentral + T Distribution
    Normal (Gaussian) Distribution
    Pareto @@ -68,8 +76,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html index ceea048ab..07366f66b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/bernoulli_dist.html @@ -77,17 +77,17 @@ density function pdf varies with the outcome of the single trial:

    - bernoulli_pdf +

    and the Cumulative distribution function

    - bernoulli_cdf +

    - + Member Functions
    @@ -103,7 +103,7 @@ Returns the success_fraction parameter of this distribution.

    - + Non-member Accessors
    @@ -128,7 +128,7 @@ exception and make an error message available.

    - + Accuracy

    @@ -136,7 +136,7 @@ and so should have errors within an epsilon or two.

    - + Implementation

    @@ -327,7 +327,7 @@

    - + References
      @@ -339,8 +339,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html index 7301ff403..31d3269ef 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/beta_dist.html @@ -122,7 +122,7 @@ might be approximated by a symmetrical triangular distribution.

    - beta_dist +

    If α = β = 1, then it is a ​ @@ -133,12 +133,12 @@ from the centre (where x = half).

    - + Member Functions
    - + Constructor 
    beta_distribution(RealType alpha, RealType beta);
@@ -165,7 +165,7 @@
             yellow in the graph above).
           
    
 
    
-
+
             Parameter
             Accessors
           
    
@@ -189,7 +189,7 @@
 assert(mybeta.beta() == 5.);   // mybeta.beta()  returns 5
    - + Parameter Estimators
    @@ -242,7 +242,7 @@ from presumed-known mean and variance. Returns the value of β that gives: cdf(beta_distribution<RealType>(alpha, beta), x) == probability.

    - + Non-member Accessor Functions
    @@ -264,7 +264,7 @@ from presumed-known mean and variance. Mathworld.

    - + Applications

    @@ -277,7 +277,7 @@ from presumed-known mean and variance. statistical inference.

    - + Related distributions
    @@ -303,7 +303,7 @@ from presumed-known mean and variance. Distribution with its p parameter set to x.

    - + Accuracy

    @@ -315,7 +315,7 @@ from presumed-known mean and variance. please refer to these functions for information on accuracy.

    - + Implementation

    @@ -597,7 +597,7 @@ from presumed-known mean and variance.

    - + References

    @@ -615,8 +615,8 @@ from presumed-known mean and variance. -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html index 84b956d13..1135899af 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/binomial_dist.html @@ -118,14 +118,14 @@ p fixed at 0.5, and vary the sample size:

    - binomial_pdf_1 +

    Alternatively, we can keep the sample size fixed at N=20 and vary the success fraction p:

    - binomial_pdf_2 +

    @@ -167,12 +167,12 @@

    - + Member Functions
    - + Construct 
    binomial_distribution(RealType n, RealType p);
@@ -189,7 +189,7 @@
             otherwise calls domain_error.
           
    
 
    
-
+
             Accessors
           
    
 
    RealType success_fraction() const;
@@ -205,7 +205,7 @@
             was constructed.
           
    
 
    
-
+
             Lower
             Bound on the Success Fraction
           
    
@@ -311,7 +311,7 @@
             limits illustrated in the case of the binomial. Biometrika 26 404-413.
           
    
 
    
-
+
             Upper
             Bound on the Success Fraction
           
    
@@ -389,7 +389,7 @@

    - + Estimating the Number of Trials Required for a Certain Number of Successes
    @@ -431,7 +431,7 @@ of seeing 10 events that occur with frequency one half.

    - + Estimating the Maximum Number of Trials to Ensure no more than a Certain Number of Successes @@ -479,7 +479,7 @@ Worked Example.

    - + Non-member Accessors
    @@ -504,7 +504,7 @@ in the context of this distribution:

    -

    Table 9. Meaning of the non-member accessors

    +

    Table 10. Meaning of the non-member accessors

    @@ -627,7 +627,7 @@

    - + Examples

    @@ -635,7 +635,7 @@ examples are available illustrating the use of the binomial distribution.

    - + Accuracy

    @@ -645,7 +645,7 @@ please refer to these functions for information on accuracy.

    - + Implementation

    @@ -886,7 +886,7 @@

    - + References
      @@ -907,8 +907,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html index a841d5d0b..ef30da17d 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/cauchy_dist.html @@ -78,17 +78,17 @@ parameter changes:

    - cauchy1 +

    While the following graph shows how the shape (scale) parameter alters the distribution:

    - cauchy2 +

    - + Member Functions
    @@ -114,7 +114,7 @@ Returns the scale parameter of the distribution.

    - + Non-member Accessors
    @@ -151,7 +151,7 @@ The domain of the random variable is [-[max_value], +[min_value]].

    - + Accuracy

    @@ -160,7 +160,7 @@ have very low error rates.

    - + Implementation

    @@ -276,7 +276,7 @@

    - + References
      @@ -291,8 +291,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html index 85338a37b..d45a03557 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/chi_squared_dist.html @@ -84,10 +84,10 @@ independent, normally distributed random values of ν:

    - chi_square +

    - + Member Functions
    @@ -170,7 +170,7 @@ independent, normally distributed random NIST Engineering Statistics Handbook, Section 7.2.3.2.

    - + Non-member Accessors
    @@ -186,11 +186,17 @@ independent, normally distributed random kurtosis, kurtosis_excess, range and support.

    +

    + (We have followed the usual restriction of the mode to degrees of freedom + >= 2, but note that the maximum of the pdf is actually zero for degrees + of freedom from 2 down to 0, and provide an extended definition that + would avoid a discontinuity in the mode as alternative code in a comment). +

    The domain of the random variable is [0, +∞].

    - + Examples

    @@ -198,7 +204,7 @@ independent, normally distributed random are available illustrating the use of the Chi Squared Distribution.

    - + Accuracy

    @@ -206,7 +212,7 @@ independent, normally distributed random gamma functions: please refer to the accuracy data for those functions.

    - + Implementation

    @@ -373,7 +379,7 @@ independent, normally distributed random

    - + References
      @@ -388,8 +394,8 @@ independent, normally distributed random
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html index e9e7ff94a..5d2907617 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/exp_dist.html @@ -68,10 +68,10 @@ values of the rate parameter lambda:

    - exponential_dist +

    - + Member Functions
    @@ -91,7 +91,7 @@ Accessor function returns the lambda parameter of the distribution.

    - + Non-member Accessors
    @@ -111,7 +111,7 @@ The domain of the random variable is [0, +∞].

    - + Accuracy

    @@ -122,7 +122,7 @@ should have very low error rates.

    - + Implementation

    @@ -283,7 +283,7 @@

    - + references
    +

    + (See also the reference documentation for the related Extreme + Distributions.) +

    +
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html index ca11178a6..e3b091e0e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/extreme_dist.html @@ -68,6 +68,12 @@ and Extreme value theory websites.

    +

    + The relationship of the types of extreme value distributions, of which + this is but one, is discussed by Extreme + Value Distributions, Theory and Applications Samuel Kotz & Saralees + Nadarajah. +

    The distribution has a PDF given by:

    @@ -85,16 +91,16 @@ parameter:

    - extreme_val_dist +

    And this graph illustrates how the PDF varies with the shape parameter:

    - extreme_val_dist2 +

    - + Member Functions
    @@ -119,7 +125,7 @@ Returns the scale parameter of the distribution.

    - + Non-member Accessors
    @@ -139,7 +145,7 @@ The domain of the random parameter is [-∞, +∞].

    - + Accuracy

    @@ -148,7 +154,7 @@ very low error rates.

    - + Implementation

    @@ -314,8 +320,8 @@

    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html index e551811e3..8f827964f 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/f_dist.html @@ -77,10 +77,10 @@ degrees of freedom parameters.

    - fisher_f +

    - + Member Functions
    @@ -106,7 +106,7 @@ Returns the denominator degrees of freedom parameter of the distribution.

    - + Non-member Accessors
    @@ -126,7 +126,7 @@ The domain of the random variable is [0, +∞].

    - + Examples

    @@ -134,7 +134,7 @@ are available illustrating the use of the F Distribution.

    - + Accuracy

    @@ -143,7 +143,7 @@ refer to those functions for accuracy data.

    - + Implementation

    @@ -423,8 +423,8 @@

    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html index 84f55f90f..937cceb9a 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/gamma_dist.html @@ -118,10 +118,10 @@ varies as the parameters vary:

    - gamma_dist1 +

    - gamma_dist2 +

    The Erlang Distribution is the same @@ -137,7 +137,7 @@ than a dedicated Erlang Distribution.

    - + Member Functions
    @@ -162,7 +162,7 @@ Returns the scale parameter of this distribution.

    - + Non-member Accessors
    @@ -182,7 +182,7 @@ The domain of the random variable is [0,+∞].

    - + Accuracy

    @@ -194,7 +194,7 @@ refer to the accuracy data for those functions for more information.

    - + Implementation

    @@ -363,8 +363,8 @@

    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html index d49ccdf5b..bb7b94231 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/lognormal_dist.html @@ -79,16 +79,16 @@ irrespective of the value of the location parameter:

    - lognormal1 +

    The next graph illustrates the effect of the scale parameter on the PDF:

    - lognormal2 +

    - + Member Functions
    @@ -121,7 +121,7 @@ Returns the scale parameter of this distribution.

    - + Non-member Accessors
    @@ -141,7 +141,7 @@ The domain of the random variable is [0,+∞].

    - + Accuracy

    @@ -150,7 +150,7 @@ function, and as such should have very low error rates.

    - + Implementation

    @@ -318,8 +318,8 @@

    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html index 64fe8c6a2..1c5a55425 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/negative_binomial_dist.html @@ -7,7 +7,7 @@ - + @@ -20,7 +20,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    @@ -113,17 +113,17 @@ p changes:

    - neg_binomial_pdf1 +

    Alternatively, this graph shows how the shape of the PDF varies as the number of successes changes:

    - neg_binomial_pdf2 +

    - + Related Distributions
    @@ -200,12 +200,12 @@

    - + Member Functions
    - + Construct 
    negative_binomial_distribution(RealType r, RealType p);
@@ -221,7 +221,7 @@
             <= 1.
           
    
 
    
-
+
             Accessors
           
    
 
    RealType success_fraction() const; // successes / trials (0 <= p <= 1)
@@ -237,7 +237,7 @@
             was constructed.
           
    
 
    
-
+
             Lower
             Bound on Parameter p
           
    
@@ -298,7 +298,7 @@
             vol. 48, no3, 605-621.
           
    
 
    
-
+
             Upper
             Bound on Parameter p
           
    
@@ -358,7 +358,7 @@
             vol. 48, no3, 605-621.
           
    
 
    
-
+
             Estimating
             Number of Trials to Ensure at Least a Certain Number of Failures
           
    
@@ -409,7 +409,7 @@
             probability of observing k failures or fewer.
           
    
 
    
-
+
             Estimating
             Number of Trials to Ensure a Maximum Number of Failures or Less
           
    
@@ -457,7 +457,7 @@
             probability of observing more than k failures.
           
    
 
    
-
+
             Non-member
             Accessors
           
    
@@ -478,7 +478,7 @@
             in the context of this distribution:
           
    
 
    
-
    Table 10. Meaning of the non-member accessors.
    
+
    Table 11. Meaning of the non-member accessors.
    
 
    @@ -603,7 +603,7 @@
 
    
 
 

    
 
    
 
    
-
+
             Accuracy
           
    
 
    
@@ -613,7 +613,7 @@
             please refer to these functions for information on accuracy.
           
    
 
    
-
+
             Implementation
           
    
 
    
@@ -894,8 +894,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    @@ -903,7 +903,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html index 9e1d8c3c9..e542b1b79 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/normal_dist.html @@ -6,7 +6,7 @@ - + @@ -20,7 +20,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    @@ -76,10 +76,10 @@ graph:

    - normal +

    - + Member Functions
    @@ -109,7 +109,7 @@ be used generically).

    - + Non-member Accessors
    @@ -131,7 +131,7 @@ and complement cdf -∞ = 1 and +∞ = 0, if RealType permits.

    - + Accuracy

    @@ -139,7 +139,7 @@ function, and as such should have very low error rates.

    - + Implementation

    @@ -289,8 +289,8 @@

    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    @@ -298,7 +298,7 @@
    -PrevUpHomeNext +PrevUpHomeNext
    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html index f99ad99b1..3a44ab2f4 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/pareto.html @@ -72,20 +72,26 @@ A classic example is that 80% of the wealth is owned by 20% of the population.

    - The following graph illustrates how the PDF varies with the shape parameter + The following graph illustrates how the PDF varies with the location + parameter β: +

    +

    + +

    +

    + And this graph illustrates how the PDF varies with the shape parameter α:

    - Pareto - pdf +

    - + Related distributions
    - + Member Functions
    @@ -111,7 +117,7 @@ Returns the shape parameter of this distribution.

    - + Non-member Accessors
    @@ -131,7 +137,7 @@ The supported domain of the random variable is [location, ∞].

    - + Accuracy

    @@ -141,7 +147,7 @@ to unity.

    - + Implementation

    @@ -309,7 +315,7 @@

    - + References
      @@ -322,8 +328,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html index e9c3c6614..94afdd6c2 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/poisson_dist.html @@ -80,7 +80,7 @@ λ:

    - poisson +

    @@ -122,7 +122,7 @@

    - + Member Functions
    @@ -137,7 +137,7 @@ Returns the mean of this distribution.

    - + Non-member Accessors
    @@ -157,7 +157,7 @@ The domain of the random variable is [0, ∞].

    - + Accuracy

    @@ -171,7 +171,7 @@ using an iterative method with a lower tolerance to avoid excessive computation.

    - + Implementation

    @@ -326,8 +326,8 @@

    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html index a0ddd0000..bbfa1d6fa 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/rayleigh.html @@ -77,16 +77,16 @@ varies with the shape parameter σ:

    - rayleigh_pdf +

    and the Cumulative Distribution Function (cdf)

    - rayleigh_cdf +

    - + Related distributions
    @@ -102,7 +102,7 @@ distribution.

    - + Member Functions
    @@ -121,7 +121,7 @@ Returns the sigma parameter of this distribution.

    - + Non-member Accessors
    @@ -141,7 +141,7 @@ The domain of the random variable is [0, max_value].

    - + Accuracy

    @@ -151,7 +151,7 @@ using NTL RR type with 150-bit accuracy, about 50 decimal digits.

    - + Implementation

    @@ -320,7 +320,7 @@

    - + References
      @@ -332,8 +332,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html index a3bc33df0..95510c1a5 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/students_t_dist.html @@ -94,10 +94,10 @@ the PDF varies with the degrees of freedom ν:

    - students_t +

    - + Member Functions
    @@ -174,7 +174,7 @@ Engineering Statistics Handbook.

    - + Non-member Accessors
    @@ -194,7 +194,7 @@ The domain of the random variable is [-∞, +∞].

    - + Examples

    @@ -202,7 +202,7 @@ are available illustrating the use of the Student's t distribution.

    - + Accuracy

    @@ -211,7 +211,7 @@ inverses, refer to accuracy data on those functions for more information.

    - + Implementation

    @@ -408,8 +408,8 @@

    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html index 06c846734..400ed5eed 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/triangular_dist.html @@ -119,16 +119,16 @@ density function PDF varies with the various parameters:

    - triangular_pdf +

    and cumulative distribution function

    - triangular_cdf +

    - + Member Functions
    @@ -163,7 +163,7 @@ (default+1).

    - + Non-member Accessors
    @@ -184,7 +184,7 @@ range is lower <= x <= upper.

    - + Accuracy

    @@ -193,7 +193,7 @@ with arguments nearing the extremes of zero and unity.

    - + Implementation

    @@ -378,7 +378,7 @@ Calculate and plot probability distributions

    - + References
      @@ -404,8 +404,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html index fab50b7d5..b33bc58c1 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/uniform_dist.html @@ -108,16 +108,16 @@ density function PDF varies with the shape parameter:

    - uniform_pdf +

    Likewise for the CDF:

    - uniform_cdf +

    - + Member Functions
    @@ -144,7 +144,7 @@ Returns the upper parameter of this distribution.

    - + Non-member Accessors
    @@ -165,7 +165,7 @@ range is only lower <= x <= upper.

    - + Accuracy

    @@ -173,7 +173,7 @@ and so should have errors within an epsilon or two.

    - + Implementation

    @@ -337,7 +337,7 @@

    - + References
      @@ -351,8 +351,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html index d71627051..bf1376fc8 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/weibull.html @@ -90,17 +90,17 @@ α:

    - weibull +

    While this graph illustrates how the PDF varies with the scale parameter β:

    - weibull2 +

    - + Related distributions
    @@ -109,10 +109,12 @@ distribution appears similar to the normal distribution. When α = 1, the Weibull distribution reduces to the exponential - distribution. + distribution. The relationship of the types of extreme value + distributions, of which the Weibull is but one, is discussed by Extreme Value + Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah.

    - + Member Functions
    @@ -138,7 +140,7 @@ Returns the scale parameter of this distribution.

    - + Non-member Accessors
    @@ -158,7 +160,7 @@ The domain of the random variable is [0, ∞].

    - + Accuracy

    @@ -168,7 +170,7 @@ as such should have very low error rates.

    - + Implementation

    @@ -335,7 +337,7 @@

    - + References
      @@ -349,8 +351,8 @@
    -
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin - and Xiaogang Zhang

    +

    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert + Holin, Xiaogang Zhang and Bruno Lalande

    Distributed under the Boost Software License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html index ee9e0250f..1becda47e 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/nmp.html @@ -37,7 +37,7 @@ the function you want if you already know its name.

    - + Function Index
    @@ -93,7 +93,7 @@
    - + Conceptual Index
    @@ -174,7 +174,7 @@
    - + Cumulative Distribution Function
    @@ -198,7 +198,7 @@ cdf

    - + Complement of the Cumulative Distribution Function
    @@ -239,7 +239,7 @@ complement is useful and when it should be used.

    - + Hazard Function 
    template <class RealType, class Policy>
@@ -267,7 +267,7 @@
    - + Cumulative Hazard Function
    @@ -295,7 +295,7 @@

    - + mean 
    template<class RealType, class Policy>
@@ -310,7 +310,7 @@
           distribution).
         
    
 
    
-
+
           median
         
    
 
    template<class RealType, class Policy>
@@ -320,7 +320,7 @@
           Returns the median of the distribution dist.
         
    
 
    
-
+
           mode
         
    
 
    template<class RealType, Policy>
@@ -334,7 +334,7 @@
           if the distribution does not have a defined mode.
         
    
 
    
-
+
           Probability
           Density Function
         
    
@@ -363,7 +363,7 @@
           pdf
         
    
 
    
-
+
           range
         
    
 
    template<class RealType, class Policy>
@@ -373,7 +373,7 @@
           Returns the valid range of the random variable over distribution dist.
         
    
 
    
-
+
           Quantile
         
    
 
    template <class RealType, class Policy>
@@ -402,7 +402,7 @@
           quantile
         
    
 
    
-
+
           Quantile
           from the complement of the probability.
         
    
@@ -448,7 +448,7 @@
           survival_inv
         
    
 
    
-
+
           Standard
           Deviation
         
    
@@ -463,7 +463,7 @@
           if the distribution does not have a defined standard deviation.
         
    
 
    
-
+
           support
         
    
 
    template<class RealType, class Policy>
@@ -480,7 +480,7 @@
           where the pdf is zero, and the cdf zero or unity.
         
    
 
    
-
+
           Variance
         
    
 
    template <class RealType, class Policy>
@@ -494,7 +494,7 @@
           if the distribution does not have a defined variance.
         
    
 
    
-
+
           Skewness
         
    
 
    template <class RealType, class Policy>
@@ -508,7 +508,7 @@
           if the distribution does not have a defined skewness.
         
    
 
    
-
+
           Kurtosis
         
    
 
    template <class RealType, class Policy>
@@ -550,7 +550,7 @@
           'Proper' kurtosis can have a value from zero to + infinity.
         
    
 
    
-
+
           Kurtosis
           excess
         
    
@@ -585,7 +585,7 @@
           The kurtosis excess of a normal distribution is zero.
         
    
 
    
-
+
           P and Q
         
    
 
    
@@ -595,7 +595,7 @@
           returned by these functions.
         
    
 
    
-
+
           Percent
           Point Function
         
    
@@ -604,7 +604,7 @@
           the Quantile.
         
    
 
    
-
+
           Inverse
           CDF Function.
         
    
@@ -613,7 +613,7 @@
           Quantile.
         
    
 
    
-
+
           Inverse
           Survival Function.
         
    
@@ -621,7 +621,7 @@
           The inverse of the survival function, is the same as computing the quantile from the complement of the probability.
         
    
 
    
-
+
           Probability
           Mass Function
         
    
@@ -635,7 +635,7 @@
           applies to continuous distributions.
         
    
 
    
-
+
           Lower
           Critical Value.
         
    
@@ -645,7 +645,7 @@
           the Quantile.
         
    
 
    
-
+
           Upper
           Critical Value.
         
    
@@ -656,7 +656,7 @@
           complement of the probability.
         
    
 
    
-
+
           Survival
           Function
         
    
@@ -667,8 +667,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/future.html b/doc/sf_and_dist/html/math_toolkit/dist/future.html
index 8c08d2df1..6f212ffe4 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/future.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/future.html
@@ -27,7 +27,7 @@
  Extras/Future Directions
 
    
 
    
-
+
         Adding
         Additional Location and Scale Parameters
       
    
@@ -55,7 +55,7 @@
         functions.
       
    
 
    
-
+
         An
         "any_distribution" class
       
    
@@ -84,7 +84,7 @@
         use case: this needs more investigation.
       
    
 
    
-
+
         Higher
         Level Hypothesis Tests
       
    
@@ -104,7 +104,7 @@
         expected_mean.
       
    
 
    
-
+
         Integration
         With Statistical Accumulators
       
    
@@ -126,8 +126,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html
index 943964d7f..f28cf7bdd 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut.html
@@ -91,6 +91,10 @@
           Distribution Examples
 
    
             Some Miscellaneous Examples of the Normal (Gaussian) Distribution
    
+
     Non Central
+          Chi Squared Example
    
+
    
+            Tables of the power function of the χ2 test.
    
 
     Error Handling
           Example
    
 
     Find Location
@@ -119,8 +123,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html
index 6abcf796d..fc32007af 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/dist_params.html
@@ -83,8 +83,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html
index 60ba736c7..87aecdd75 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview.html
@@ -27,7 +27,7 @@
  Overview
 
    
 
    
-
+
           Headers
           and Namespaces
         
    
@@ -44,7 +44,7 @@
           or <boost/math/distributions.hpp>
         
    
 
    
-
+
           Distributions
           are Objects
         
    
@@ -131,7 +131,7 @@
           and quantiles etc for these distributions.
         
    
 
    
-
+
           Generic
           operations common to all distributions are non-member functions
         
    
@@ -229,6 +229,11 @@
 
    
           pdf(binomial_distribution<RealType>(n, p), k);
         
    
+
    
+          The ranges of random variate values that are permitted and are supported
+          can be tested by using two functions range
+          and support.
+        
    
 
    
           The distribution (effectively the random variate) is said to be 'supported'
           over a range that is "the
@@ -236,17 +241,31 @@
           MathWorld uses the word 'defined' for this range. Non-mathematicians might
           say it means the 'interesting' smallest range of random variate x that
           has the cdf going from zero to unity. Outside are uninteresting zones where
-          the pdf is zero, and the cdf zero or unity. Mathematically, the functions
-          may make sense with an (+ or -) infinite value, but except for a few special
-          cases (in the Normal and Cauchy distributions) this implementation limits
-          random variates to finite values from the max
-          to min for the RealType. (See Handling
-          of Floating-Point Infinity for rationale).
+          the pdf is zero, and the cdf zero or unity.
         
    
 
    
-          The range of random variate values that is permitted and supported can
-          be tested by using two functions range
-          and support.
+          For most distributions, with probability distribution functions one might
+          describe as 'well-behaved', we have decided that it is most useful for
+          the supported range to exclude random variate values like exact zero if the end point is discontinuous. For example,
+          the Weibull (scale 1, shape 1) distribution smoothly heads for unity as
+          the random variate x declines towards zero. But at x = zero, the value
+          of the pdf is suddenly exactly zero, by definition. If you are plotting
+          the PDF, or otherwise calculating, zero is not the most useful value for
+          the lower limit of supported, as we discovered. So for this, and similar
+          distributions, we have decided it is most numerically useful to use the
+          closest value to zero, min_value, for the limit of the supported range.
+          (The range remains from
+          zero, so you will still get pdf(weibull, 0)
+          == 0).
+          (Exponential and gamma distributions have similarly discontinuous functions).
+        
    
+
    
+          Mathematically, the functions may make sense with an (+ or -) infinite
+          value, but except for a few special cases (in the Normal and Cauchy distributions)
+          this implementation limits random variates to finite values from the max to min
+          for the RealType. (See
+          Handling
+          of Floating-Point Infinity for rationale).
         
    
 
    
@@ -307,7 +326,7 @@
 
    
         
    
-
+
           Complements
           are supported too
         
    
@@ -442,7 +461,7 @@
 
    
 
    
 
    
 
    
 
    
-
+
           Parameters
           can be calculated
         
    
@@ -473,7 +492,7 @@
           sample size.
         
    
 
    
-
+
           Summary
         
    
 
      
@@ -507,8 +526,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html
index dcaa21b3c..45e334a43 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/variates.html
@@ -59,8 +59,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html
index c84014e58..6efb36056 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg.html
@@ -87,6 +87,10 @@
           Distribution Examples
 
    
             Some Miscellaneous Examples of the Normal (Gaussian) Distribution
    
+
     Non Central
+          Chi Squared Example
    
+
    
+            Tables of the power function of the χ2 test.
    
 
     Error Handling
           Example
    
 
     Find Location
@@ -109,8 +113,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html
index 3e0871c5e..767995728 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg.html
@@ -45,8 +45,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html
index 42b89eb8d..b3f127c3b 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_conf.html
@@ -227,8 +227,8 @@ _______________________________________________________________________
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html
index a6d236f16..8e30351de 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binom_size_eg.html
@@ -143,8 +143,8 @@ ____________________________
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html
index d3086da6f..6147086ac 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_coinflip_example.html
@@ -391,8 +391,8 @@ Probability of getting upto (<) heads
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html
index d687afd10..4dec16513 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/binom_eg/binomial_quiz_example.html
@@ -497,7 +497,7 @@ Probability of getting between 4 and 4 answers right by guessing is 0.2252
               
               
    
 
    
-
+
                 Using
                 Binomial distribution moments
               
    
@@ -534,7 +534,7 @@ Skewness is 0.2887
               
               
    
 
    
-
+
                 Quantiles
               
    
 
    
@@ -726,8 +726,8 @@ If guessing then percentiles 1 to 99% will get 0 to 7.788 right.
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html
index f75b88463..f7558c182 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg.html
@@ -39,8 +39,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html
index a82698e9d..60ee4398e 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_intervals.html
@@ -139,7 +139,7 @@ _____________________________________________
               is between 0.00551 and 0.00729.
             
    
 
    
-
+
               Confidence
               intervals as a function of the number of observations
             
    
@@ -220,8 +220,8 @@ ________________________________________
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html
index 9cee9d189..c81392f00 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_size.html
@@ -166,8 +166,8 @@ _______________________________________________________________
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html
index 7b510357e..ccfd9ded9 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/cs_eg/chi_sq_test.html
@@ -280,8 +280,8 @@ Standard Deviation  > 10.000            ACCEPTED
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html
index af2dd2e5a..834cd4b82 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/dist_construct_eg.html
@@ -332,7 +332,7 @@ error C3861: 'mybetad0': identifier not found
             
             
    
 
    
-
+
               Default
               arguments to distribution constructors.
             
    
@@ -396,8 +396,8 @@ error C3861: 'mybetad0': identifier not found
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html
index 237b7f5f3..8d8f11c01 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/error_eg.html
@@ -6,7 +6,7 @@
 
 
 
-
+
 
 
 
@@ -20,7 +20,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -250,8 +250,8 @@ errno is set to: 33
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
@@ -259,7 +259,7 @@ errno is set to: 33
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html
index adbaaff16..eadec18d4 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/f_eg.html
@@ -315,8 +315,8 @@ Standard deviation 1 is greater than standard deviation 2 ACCEPTED
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html
index 42f80810d..886872e5c 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg.html
@@ -38,8 +38,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html
index a50869414..c4a41f471 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_location_eg.html
@@ -175,7 +175,7 @@ Normal distribution with mean = 1.09023 has fraction > -2, p = 0.999
               
               
    
 
    
-
+
                 Controlling
                 Error Handling from find_location
               
    
@@ -266,8 +266,8 @@ Normal distribution with mean = 0.355146 has fraction > 2 = 0.05
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
index 652c57c57..a5717e755 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_mean_and_sd_eg.html
@@ -62,7 +62,7 @@
               
               
    
 
    
-
+
                 Using
                 find_location and find_scale to meet dispensing and measurement specifications
               
    
@@ -246,7 +246,7 @@
               
               
    
 
    
-
+
                 Using
                 Cauchy-Lorentz instead of normal distribution
               
    
@@ -397,7 +397,7 @@
               
               
    
 
    
-
+
                 Changing
                 the scale or standard deviation
               
    
@@ -711,8 +711,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html
index 6d77f01f4..d2cf03cf0 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/find_eg/find_scale_eg.html
@@ -179,7 +179,7 @@ Normal distribution with mean = 0 has fraction > -2, p = 0.999
               
               
    
 
    
-
+
                 Controlling
                 how Errors from find_scale are handled
               
    
@@ -291,8 +291,8 @@ Normal distribution with mean = 0.946339 has fraction > -2 = 0.999
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html
index a5db0b3e9..01ce4d954 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/nag_library.html
@@ -99,8 +99,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html
index 40245e536..a2b269392 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg.html
@@ -45,8 +45,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
index 53acf0bcd..69b2eaa1c 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_conf.html
@@ -251,8 +251,8 @@ ___________________________________________
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
index e2b0960bf..f827b06af 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/neg_binom_size_eg.html
@@ -233,8 +233,8 @@ ____________________________
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
index 91cac1274..a22975bd5 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example1.html
@@ -791,8 +791,8 @@ If confidence of meeting quota is 0.95, then finishing house is 21
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
index 8c1f1cc84..67e9b3e71 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/neg_binom_eg/negative_binomial_example2.html
@@ -135,8 +135,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html
index 05e90abd5..0cb008689 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example.html
@@ -36,8 +36,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html
index 1dca13da9..89e6e1124 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/normal_example/normal_misc.html
@@ -7,7 +7,7 @@
 
 
 
-
+
 
 
 
@@ -20,7 +20,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -32,7 +32,7 @@
               illustrates their use.
             
    
 
    
-
+
               Traditional
               Tables
             
    
@@ -278,7 +278,7 @@
 
    
             
    
 
    
-
+
               Standard
               deviations either side of the Mean
             
    
@@ -346,12 +346,12 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
    
             
    
 
    
-
+
               Some
               simple examples
             
    
 
    
-
+
               Life
               of light bulbs
             
    
@@ -435,7 +435,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
    
             
    
 
    
-
+
               How
               many onions?
             
    
@@ -494,7 +494,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
    
             
    
 
    
-
+
               Packing
               beef
             
    
@@ -703,7 +703,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
    
             
    
 
    
-
+
               Length
               of bolts
             
    
@@ -744,8 +744,8 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
@@ -753,7 +753,7 @@ Fraction 3 standard deviations within either side of mean is 0.997300203936740
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html
index b6db8925b..9d89537d0 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg.html
@@ -43,8 +43,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html
index 123ff4428..3f37f404b 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/paired_st.html
@@ -64,8 +64,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html
index a1f47d8e3..b5fc17e71 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_intervals.html
@@ -253,8 +253,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html
index 644cd6b13..afcb46bcf 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_size.html
@@ -165,8 +165,8 @@ _______________________________________________________________
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html
index 70782f38d..9ce0790de 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/tut_mean_test.html
@@ -319,8 +319,8 @@ Mean  > 38.900            REJECTED
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html
index 5548fbb3c..77924cec6 100644
--- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html
+++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/st_eg/two_sample_students_t.html
@@ -343,8 +343,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview.html
index 4ce3da8a8..5e850fc44 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview.html
@@ -52,8 +52,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html
index 9a4702453..07cd96068 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/compilers_overview.html
@@ -37,7 +37,7 @@
 
    
         
    
 
    
-
    Table 7. Supported/Tested Compilers
    
+
    Table 8. Supported/Tested Compilers
    
 
    @@ -539,7 +539,7 @@
 

     
    
-
    Table 8. Unsupported Compilers
    
+
    Table 9. Unsupported Compilers
    
 
    
 
 

 
 
    @@ -613,8 +613,8 @@
 
    
 
 

 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html b/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html
index 4aeb13d4d..019dff789 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/contact.html
@@ -47,8 +47,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html
index 595d58076..635dd03bb 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/directories.html
@@ -28,7 +28,7 @@
       File Structure
 
    
 
    
-
+
         boost/math
       
    
 
    
@@ -73,7 +73,7 @@
 
 
    
 
    
-
+
         boost/libs
       
    
 
    
@@ -109,8 +109,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html
index 909e75dd1..4219e870b 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/error_handling.html
@@ -27,7 +27,7 @@
  Error Handling
 
    
 
    
-
+
         Quick
         Reference
       
    
@@ -75,6 +75,14 @@
 
    
             Occurs when the returned result would be a denormalised value.
           
    
+
    Rounding Error
    
+
    
+            Occurs when the argument to one of the rounding functions trunc,
+            round and
+            modf can not
+            be represented as an integer type, is is outide the range of the result
+            type.
+          
    
 
    Evaluation Error
    
 
    
             Occurs when an internal error occured that prevented the result from
@@ -121,7 +129,7 @@
         the default action for each error shown in bold:
       
    
 
    
-
    Table 1. Possible Actions for Domain Errors
    
+
    Table 1. Possible Actions for Domain Errors
    
 
    @@ -196,7 +204,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 2. Possible Actions for Pole Errors
    
+
    Table 2. Possible Actions for Pole Errors
    
 
    @@ -271,7 +279,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 3. Possible Actions for Overflow Errors
    
+
    Table 3. Possible Actions for Overflow Errors
    
 
    @@ -346,7 +354,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 4. Possible Actions for Underflow Errors
    
+
    Table 4. Possible Actions for Underflow Errors
    
 
    @@ -421,7 +429,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 5. Possible Actions for Denorm Errors
    
+
    Table 5. Possible Actions for Denorm Errors
    
 
    @@ -496,7 +504,82 @@
 
    
 
 

    
 
    
 
    
-
    Table 6. Possible Actions for Internal Evaluation
+
    Table 6. Possible Actions for Rounding Errors
    
+
    
++++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    



    
+            
    
+              Action
+            
    
+                		
+            
    
+              Behaviour
+            
    
+            
    
+            
    
+              throw_on_error
+            
    
+                		
+            
    
+              Throws boost::math::rounding_error
+            
    
+            
    
+            
    
+              errno_on_error
+            
    
+                		
+            
    
+              Sets ::errno
+              to ERANGE and returns
+              an unspecified value.
+            
    
+            
    
+            
    
+              ignore_error
+            
    
+                		
+            
    
+              Returns the an unspecified value.
+            
    
+            
    
+            
    
+              user_error
+            
    
+                		
+            
    
+              Returns the result of boost::math::policies::user_rounding_error:
+              this
+              function must be defined by the user.
+            
    
+            
    
+
    
+
    
+
    Table 7. Possible Actions for Internal Evaluation
       Errors
    
 
    
@@ -573,7 +656,7 @@
 
    
 
    
 
    
-
+
         Rationale
       
    
 
    
@@ -592,7 +675,7 @@
         
 
 
    
-
+
         Finding
         More Information
       
    
@@ -614,7 +697,7 @@
         The various kind of errors are described in more detail below.
       
    
 
    
-
+
         Domain
         Errors
       
    
@@ -707,7 +790,7 @@
         for more details.
       
    
 
    
-
+
         Evaluation
         at a pole
       
    
@@ -746,7 +829,7 @@
         for more details.
       
    
 
    
-
+
         Numeric
         Overflow
       
    
@@ -771,7 +854,7 @@
         doesn't support infinities, the maximum value for the type is returned.
       
    
 
    
-
+
         Numeric
         Underflow
       
    
@@ -794,7 +877,7 @@
         an std::underflow_error C++ exception.
       
    
 
    
-
+
         Denormalisation
         Errors
       
    
@@ -817,7 +900,7 @@
         throws an std::underflow_error C++ exception.
       
    
 
    
-
+
         Evaluation
         Errors
       
    
@@ -853,8 +936,47 @@
         Boost.Format documentation
         for more details.
       
    
+
    
+
+        Rounding
+        Errors
+      
    
+
    
+        When one of the rounding functions round,
+        trunc or modf is called with an
+        argument that has no integer representation, or is too large to be represented
+        in the result type then the value returned is the result of a call to:
+      
    
+
    boost::math::policies::raise_rounding_error<T>(FunctionName, Message, Val, Policy);
+
    
+
    
+        Where T is the floating point
+        type passed to the function, FunctionName
+        is the name of the function, Message
+        is an error message describing the problem, Val
+        is the erroneous argument, and Policy
+        is the current policy in use for the called function.
+      
    
+
    
+        The default behaviour of this function is to throw a boost::math::rounding_error.
+      
    
+
    
+        Note that in order to support information rich error messages when throwing
+        exceptions, Message must
+        contain a Boost.Format
+        recognised format specifier: the argument val
+        is inserted into the error message according to the specifier used.
+      
    
+
    
+        For example if Message contains
+        a "%1%" then it is replaced by the value of val
+        to the full precision of T, where as "%.3g" would contain the value
+        of val to 3 digits. See the
+        Boost.Format documentation
+        for more details.
+      
    
 
    
-
+
         Errors
         from typecasts
       
    
@@ -877,8 +999,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html
index be43b26bb..bb0f9da9a 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/history1.html
@@ -31,7 +31,7 @@
         
         
    
 
    
-
+
           Milestone
           5: Post Review First Official Release
         
    
@@ -68,7 +68,7 @@
         
         
    
 
    
-
+
           Milestone
           4: Second Review Candidate (1st March 2007)
         
    
@@ -87,7 +87,7 @@
         
         
    
 
    
-
+
           Milestone
           3: First Review Candidate (31st Dec 2006)
         
    
@@ -120,7 +120,7 @@
         
         
    
 
    
-
+
           Milestone
           2: Released September 10th 2006
         
    
@@ -161,7 +161,7 @@
         
         
    
 
    
-
+
           Milestone
           1: Released March 31st 2006
         
    
@@ -203,8 +203,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html
index 53d00f0b2..f60ddadf3 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/intro.html
@@ -30,7 +30,7 @@
         This library is divided into three interconnected parts:
       
    
 
    
-
+
         Statistical
         Distributions
       
    
@@ -56,7 +56,7 @@
         tests.
       
    
 
    
-
+
         Mathematical
         Special Functions
       
    
@@ -83,7 +83,7 @@
         double.
       
    
 
    
-
+
         Implementation
         Toolkit
       
    
@@ -119,8 +119,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html b/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html
index ff820d70d..ef2ebe544 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/namespaces.html
@@ -59,8 +59,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html
index 7c70a1e00..3609dd685 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/navigation.html
@@ -31,7 +31,7 @@
         as handy shortcuts for common navigation tasks.
       
    
 
    
-
+
         Shortcuts
       
    
 
    
@@ -139,8 +139,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html b/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html
index 7a8b0a8ec..f74a48f9f 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/perf_over.html
@@ -78,8 +78,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html b/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html
index 69c93b8da..f548821ea 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/pol_overview.html
@@ -121,8 +121,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html b/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html
index a1509cc61..329673f08 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/result_type.html
@@ -133,8 +133,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html b/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html
index 740684f25..8d979b05f 100644
--- a/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html
+++ b/doc/sf_and_dist/html/math_toolkit/main_overview/threads.html
@@ -54,8 +54,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/perf.html b/doc/sf_and_dist/html/math_toolkit/perf.html
index 6d9e2d6b6..53d1272a3 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf.html
@@ -41,8 +41,8 @@
 
    
 
-
@@ -284,13 +284,13 @@
               
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html b/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html
index 012168d42..161a95bd1 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/comp_compilers.html
@@ -35,7 +35,7 @@
         in this respect).
       
    
 
    
-
    Table 40. Performance Comparison of Various Windows Compilers
    
+
    Table 47. Performance Comparison of Various Windows Compilers
    
 
    @@ -362,8 +362,8 @@
 
    
 
 

 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html
index 353746a7d..217d9a187 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html
@@ -46,7 +46,7 @@
         
    
 
    
 
    
-
+
         Comparison
         to GSL-1.9 and Cephes
       
    
@@ -213,7 +213,7 @@
 
    		
               
    
                 +INF
-                [1]
+                [1]
               
    
                   		
 
    
 
 
    [1] 
+
    [1] 
                     Cephes gets stuck in an infinite loop while trying to execute
                     our test cases.
                   
    
 
    
 
    
-
+
         Comparison
         to the R Statistical Library on Windows
       
    
@@ -301,7 +301,7 @@
         appears not to be buildable with Visual C++).
       
    
 
    
-
    Table 43. A Comparison to the R Statistical Library on Windows
+
    Table 50. A Comparison to the R Statistical Library on Windows
       XP
    
 
    
@@ -374,7 +374,7 @@
             
    
               
    74.66
-              [1]
+              [1]
               
     
    (4.905e-004s)
    
@@ -792,7 +792,7 @@
             
    
               
    53.59
-              [2]
+              [2]
               
     
    (5.145e-004s)
    
@@ -1010,12 +1010,12 @@
 
    
 
 
 
 
 
 
 
 
    
-
    [1] 
+
    [1] 
                   There are a small number of our test cases where the R library
                   fails to converge on a result: these tend to dominate the performance
                   result.
                 
    
-
    [2] 
+
    [2] 
                   The R library appears to use a linear-search strategy, that can
                   perform very badly in a small number of pathological cases, but
                   may or may not be more efficient in "typical" cases
@@ -1024,7 +1024,7 @@
 
    
 
    
 
    
-
+
         Comparison
         to the R Statistical Library on Linux
       
    
@@ -1033,7 +1033,7 @@
         Linux machine, with the test program and R-2.5.0 compiled with GNU G++ 4.2.0.
       
    
 
    
-
    Table 44. A Comparison to the R Statistical Library on Linux
    
+
    Table 51. A Comparison to the R Statistical Library on Linux
    
 
    @@ -1104,7 +1104,7 @@
             
    
               
    44.06
-              [1]
+              [1]
               
     
    (5.701e-004s)
    
@@ -1522,7 +1522,7 @@
             
    
               
    30.07
-              [2]
+              [2]
               
     
    (5.490e-004s)
    
@@ -1740,12 +1740,12 @@
 
    
 
 

 
 
 
 
 
 
 
 
    
-
    [1] 
+
    [1] 
                   There are a small number of our test cases where the R library
                   fails to converge on a result: these tend to dominate the performance
                   result.
                 
    
-
    [2] 
+
    [2] 
                   The R library appears to use a linear-search strategy, that can
                   perform very badly in a small number of pathological cases, but
                   may or may not be more efficient in "typical" cases
@@ -1757,8 +1757,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html
index 46512e70e..00e39118e 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/getting_best.html
@@ -33,7 +33,7 @@
         penalty for using the library in debug mode can be quite large.
       
    
 
    
-
    Table 39. Performance Comparison of Release and Debug Settings
    
+
    Table 46. Performance Comparison of Release and Debug Settings
    
 
    @@ -279,8 +279,8 @@
 
    
 
 

 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/interp.html b/doc/sf_and_dist/html/math_toolkit/perf/interp.html
index 68e657ba2..efa8e24b7 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/interp.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/interp.html
@@ -55,8 +55,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html b/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html
index 451ce1d3c..84b549f75 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/perf_over.html
@@ -78,8 +78,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html b/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html
index d79c3261f..dcabfcf48 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/perf_test_app.html
@@ -48,8 +48,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html
index f93b8b6d9..6b4df8033 100644
--- a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html
+++ b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html
@@ -234,7 +234,7 @@
         highly vectorisable processors in the future.
       
    
 
    
-
    Table 41. A Comparison of Polynomial Evaluation Methods
    
+
    Table 48. A Comparison of Polynomial Evaluation Methods
    
 
    @@ -634,7 +634,7 @@
         tutorial.
       
    
-
    Table 42. Performance Comparison with and Without Internal
+
    Table 49. Performance Comparison with and Without Internal
       Promotion to long double
    
 
    
 
 

 
    
@@ -882,8 +882,8 @@
 
 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy.html b/doc/sf_and_dist/html/math_toolkit/policy.html
index b22513fa5..53f2ff514 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy.html
@@ -76,8 +76,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html
index ffe95d9f0..607cd42c9 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_overview.html
@@ -120,8 +120,8 @@
 
    
 
-
+
+
+
+
+
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html
index ae0d48440..493ae7b4b 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref.html
@@ -49,8 +49,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html
index 3a6a90403..a4f55426d 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/assert_undefined.html
@@ -74,8 +74,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html
index ea7e0f3b1..943b7cf49 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/discrete_quant_ref.html
@@ -55,7 +55,7 @@
           can take have the following meanings:
         
    
 
    
-
+
           real
         
    
 
    
@@ -93,7 +93,7 @@
           = 68.1584.
         
    
 
    
-
+
           integer_round_outwards
         
    
 
    
@@ -151,7 +151,7 @@
           in each tail.
         
    
 
    
-
+
           integer_round_inwards
         
    
 
    
@@ -214,7 +214,7 @@
           in each tail.
         
    
 
    
-
+
           integer_round_down
         
    
 
    
@@ -222,7 +222,7 @@
           or a lower quantile.
         
    
 
    
-
+
           integer_round_up
         
    
 
    
@@ -230,7 +230,7 @@
           a lower quantile.
         
    
 
    
-
+
           integer_round_nearest
         
    
 
    
@@ -275,8 +275,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html
index 164936c0b..7e5dcd32f 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/error_handling_policies.html
@@ -39,7 +39,7 @@
           
 
    
 
    
-
+
           Available
           Actions When an Error is Raised
         
    
@@ -62,7 +62,7 @@
           The various enumerated values have the following meanings:
         
    
 
    
-
+
           throw_on_error
         
    
 
    
@@ -162,7 +162,7 @@
 
    
 
    
 
    
-
+
           errno_on_error
         
    
 
    
@@ -263,7 +263,7 @@
 
    
 
    
 
    
-
+
           ignore_error
         
    
 
    
@@ -364,7 +364,7 @@
 
    
 
    
 
    
-
+
           user_error
         
    
 
    
@@ -388,6 +388,9 @@
 template <class T>
 T user_denorm_error(const char* function, const char* message, const T& val);
 
+template <class T>
+T user_rounding_error(const char* function, const char* message, const T& val);
+
 template <class T>
 T user_evaluation_error(const char* function, const char* message, const T& val);
 
@@ -407,7 +410,7 @@
           here.
         
    
 
    
-
+
           Kinds
           of Error Raised
         
    
@@ -564,6 +567,34 @@
                     		
 
    
 
    
+                
    
+                  Rounding Error
+                
    
+                    		
+                
    
+                  boost::math::policies::rounding_error<action>
+                
    
+                    		
+                
    
+                  Raised When one of the rounding functions round,
+                  trunc
+                  or modf
+                  is called with an argument that has no integer representation,
+                  or is too large to be represented in the result type
+                
    
+                
    
+                  Defaults to boost::math::policies::rounding_error<throw_on_error>
+                
    
+                
    
+                  When the action is throw_on_error then throws
+                  boost::math::rounding_error
+                
    
+                
    
 
                 
    
                   Evaluation Error
@@ -593,7 +624,7 @@
 
    
 
    
 
    
-
+
           Examples
         
    
 
    
@@ -668,8 +699,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html
index a3efce173..0ac4604b2 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/internal_promotion.html
@@ -84,7 +84,7 @@
 
    
 
    
 
    
-
+
           Examples
         
    
 
    
@@ -151,8 +151,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html
index 2ef146ed0..9b81636a0 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/iteration_pol.html
@@ -51,8 +51,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html
index e74705bb8..10f6d076e 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/namespace_pol.html
@@ -151,8 +151,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html
index 2c86cbb48..6737301d6 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/pol_ref_ref.html
@@ -60,6 +60,7 @@
    typedef computed-from-template-arguments overflow_error_type;
    typedef computed-from-template-arguments underflow_error_type;
    typedef computed-from-template-arguments denorm_error_type;
+   typedef computed-from-template-arguments rounding_error_type;
    typedef computed-from-template-arguments evaluation_error_type;
    typedef computed-from-template-arguments precision_type;
    typedef computed-from-template-arguments promote_float_type;
@@ -133,6 +134,14 @@
           one of the error_policy_type
           enumerated values.
         
    
+
    policy<...>::rounding_error_type
+
    
+
    
+          Specifies how rounding errors are handled, will be an instance of boost::math::policies::rounding_error<>
+          with the template argument to rounding_error
+          one of the error_policy_type
+          enumerated values.
+        
    
 
    policy<...>::evaluation_error_type
 
    
 
    
@@ -220,8 +229,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html
index 5f366c072..487881e7b 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/policy_defaults.html
@@ -61,7 +61,7 @@
           then you can do so by defining various macros in boost/math/tools/user.hpp.
         
    
 
    
-
+
           BOOST_MATH_DOMAIN_ERROR_POLICY
         
    
 
    
@@ -71,7 +71,7 @@
           ignore_error or user_error.
         
    
 
    
-
+
           BOOST_MATH_POLE_ERROR_POLICY
         
    
 
    
@@ -81,7 +81,7 @@
           ignore_error or user_error.
         
    
 
    
-
+
           BOOST_MATH_OVERFLOW_ERROR_POLICY
         
    
 
    
@@ -90,8 +90,18 @@
           but can be set to any of the enumerated actions for error handing: throw_on_error, errno_on_error,
           ignore_error or user_error.
         
    
+
    
+
+          BOOST_MATH_ROUNDING_ERROR_POLICY
+        
    
+
    
+          Defines what happens when a rounding error occurs, if not defined then
+          defaults to throw_on_error,
+          but can be set to any of the enumerated actions for error handing: throw_on_error, errno_on_error,
+          ignore_error or user_error.
+        
    
 
    
-
+
           BOOST_MATH_EVALUATION_ERROR_POLICY
         
    
 
    
@@ -101,7 +111,7 @@
           ignore_error or user_error.
         
    
 
    
-
+
           BOOST_MATH_UNDERFLOW_ERROR_POLICY
         
    
 
    
@@ -111,7 +121,7 @@
           ignore_error or user_error.
         
    
 
    
-
+
           BOOST_MATH_DENORM_ERROR_POLICY
         
    
 
    
@@ -121,7 +131,7 @@
           ignore_error or user_error.
         
    
 
    
-
+
           BOOST_MATH_DIGITS10_POLICY
         
    
 
    
@@ -132,7 +142,7 @@
           recommended that you change this from the default.
         
    
 
    
-
+
           BOOST_MATH_PROMOTE_FLOAT_POLICY
         
    
 
    
@@ -144,7 +154,7 @@
           off.
         
    
 
    
-
+
           BOOST_MATH_PROMOTE_DOUBLE_POLICY
         
    
 
    
@@ -156,7 +166,7 @@
           off.
         
    
 
    
-
+
           BOOST_MATH_DISCRETE_QUANTILE_POLICY
         
    
 
    
@@ -167,7 +177,7 @@
           Defaults to integer_round_outwards.
         
    
 
    
-
+
           BOOST_MATH_ASSERT_UNDEFINED_POLICY
         
    
 
    
@@ -180,7 +190,7 @@
           whether or not a particular property is well defined.
         
    
 
    
-
+
           BOOST_MATH_MAX_SERIES_ITERATION_POLICY
         
    
 
    
@@ -189,7 +199,7 @@
           Defaults to 1000000.
         
    
 
    
-
+
           BOOST_MATH_MAX_ROOT_ITERATION_POLICY
         
    
 
    
@@ -198,7 +208,7 @@
           Defaults to 200.
         
    
 
    
-
+
           Example
         
    
 
    
@@ -223,8 +233,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html
index 135db155a..2df21a8fa 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_ref/precision_pol.html
@@ -122,8 +122,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html
index 43609ba39..8a1bd1a53 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial.html
@@ -49,8 +49,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html
index e6035a12e..7257842a7 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_dist_policies.html
@@ -93,8 +93,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html
index 5a8ee8ae8..10e9abf1e 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/ad_hoc_sf_policies.html
@@ -152,8 +152,8 @@ errno = 33
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html
index a08bd82a8..25c792971 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/changing_policy_defaults.html
@@ -316,8 +316,8 @@ errno is set to: 33
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html
index e2d1c4c83..1349d2f26 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/namespace_policies.html
@@ -448,8 +448,8 @@ Result of quantile(complement(binom, 0.05)) is: 8
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html
index 6f749b06b..17a2f646e 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_tut_defaults.html
@@ -55,6 +55,10 @@
 
    
               Ignores the fact that the result is denormalised, and returns it.
             
    
+
    Rounding Error
    
+
    
+              Throws a boost::math::rounding_error exception.
+            
    
 
    Internal Evaluation Error
    
 
    
               Throws a boost::math::evaluation_error exception.
@@ -114,8 +118,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html
index 01a41d9be..ae5f355e0 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/policy_usage.html
@@ -56,8 +56,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html
index 44d701cfb..3eeec624e 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/understand_dis_quant.html
@@ -177,7 +177,7 @@
           base your comparisons on CDF's instead.
         
    
 
    
-
+
           Other
           Rounding Policies are Available
         
    
@@ -418,8 +418,8 @@ Upper quantiles at p = 0.95.
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html
index b9bb8acfe..571658b91 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/user_def_err_pol.html
@@ -611,8 +611,8 @@ Result of tgamma(-190.5) is: 0
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html
index b7d6fb4a2..9ed20453a 100644
--- a/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html
+++ b/doc/sf_and_dist/html/math_toolkit/policy/pol_tutorial/what_is_a_policy.html
@@ -72,8 +72,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special.html b/doc/sf_and_dist/html/math_toolkit/special.html
index 35e5651f5..6f0c3ab06 100644
--- a/doc/sf_and_dist/html/math_toolkit/special.html
+++ b/doc/sf_and_dist/html/math_toolkit/special.html
@@ -104,6 +104,15 @@
 
     Elliptic Integrals
         of the Third Kind - Legendre Form
    
 
+
     Zeta Functions
    
+
     Riemann Zeta Function
    
+
     Exponential Integrals
    
+
    
+
     Exponential
+        Integral En
    
+
     Exponential
+        Integral Ei
    
+
    
 
     Logs, Powers, Roots and
       Exponentials
    
 
    
@@ -113,6 +122,8 @@
 
     sqrt1pm1
    
 
     powm1
    
 
     hypot
    
+
     Compile Time Power
+        of a Runtime Base
    
 
    
 
     Sinus Cardinal and Hyperbolic
       Sinus Cardinal Functions
    
@@ -130,14 +141,24 @@
 
     asinh
    
 
     atanh
    
 
+
     Rounding Truncation and
+      Integer Conversion
    
+
    
+
     Rounding Functions
    
+
     Truncation Functions
    
+
     Integer and Fractional
+        Part Splitting (modf)
    
+
    
 
     Floating Point Classification:
       Infinities and NaN's
    
 
    
+
    
+    
    
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel.html
index ead0709df..08b53777d 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel.html
@@ -47,8 +47,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html
index 46885d2b1..91b765392 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel.html
@@ -28,7 +28,7 @@
         of the First and Second Kinds
 
    
 
    
-
+
           Synopsis
         
    
 
    template <class T1, class T2>
@@ -44,7 +44,7 @@
 calculated-result-type cyl_neumann(T1 v, T2 x, const Policy&);
 
    
 
    
-
+
           Description
         
    
 
    
@@ -100,17 +100,17 @@
           The following graph illustrates the cyclic nature of Jv:
         
    
 
    
-          bessel_jn
+          
         
    
 
    
           The following graph shows the behaviour of Yv: this is also cyclic for
           large x, but tends to -∞ for small x:
         
    
 
    
-          bessel_yv
+          
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -119,7 +119,7 @@
           (with all the special case handling removed).
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -135,7 +135,7 @@
           zero error. All values are relative errors in units of epsilon.
         
    
 
    
-
    Table 31. Errors Rates in cyl_bessel_j
    
+
    Table 35. Errors Rates in cyl_bessel_j
    
 
    @@ -304,7 +304,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 32. Errors Rates in cyl_neumann
    
+
    Table 36. Errors Rates in cyl_neumann
    
 
    @@ -494,7 +494,7 @@
           were found.
         
    
-
+
           Implementation
         
    
@@ -657,8 +657,8 @@ are also computed by recursions (involving gamma functions), but
 
 
    
 
 

 
 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html
index e76448704..7a4f3d717 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/bessel_over.html
@@ -28,7 +28,7 @@
         Overview
 
    
 
    
-
+
           Ordinary
           Bessel Functions
         
    
@@ -103,7 +103,7 @@ and is known as either a Bessel
           
         
    
 
    
-
+
           Modified
           Bessel Functions
         
    
@@ -167,7 +167,7 @@ respectively:
           
         
    
 
    
-
+
           Spherical
           Bessel Functions
         
    
@@ -198,8 +198,8 @@ is also known as the
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html
index 28a6f0f9a..ca303a384 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/mbessel.html
@@ -28,7 +28,7 @@
         Functions of the First and Second Kinds
 
    
 
    
-
+
           Synopsis
         
    
 
    template <class T1, class T2>
@@ -44,7 +44,7 @@
 calculated-result-type cyl_bessel_k(T1 v, T2 x, const Policy&);
 
    
 
    
-
+
           Description
         
    
 
    
@@ -100,16 +100,16 @@
           The following graph illustrates the exponential behaviour of Iv.
         
    
 
    
-          bessel_i
+          
         
    
 
    
           The following graph illustrates the exponential decay of Kv.
         
    
 
    
-          bessel_k
+          
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -118,7 +118,7 @@
           (with all the special case handling removed).
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -129,7 +129,7 @@
           zero error. All values are relative errors in units of epsilon.
         
    
 
    
-
    Table 33. Errors Rates in cyl_bessel_i
    
+
    Table 37. Errors Rates in cyl_bessel_i
    
 
    @@ -226,7 +226,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 34. Errors Rates in cyl_bessel_k
    
+
    Table 38. Errors Rates in cyl_bessel_k
    
 
    @@ -326,7 +326,7 @@
 
    
 
 

    
 
    
 
    
-
+
           Implementation
         
    
 
    
@@ -469,8 +469,8 @@ are also computed by recursions (involving gamma functions), but
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html
index 3c37c97df..a6fcec8c8 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/bessel/sph_bessel.html
@@ -28,7 +28,7 @@
         Bessel Functions of the First and Second Kinds
 
    
 
    
-
+
           Synopsis
         
    
 
    template <class T1, class T2>
@@ -44,7 +44,7 @@
 calculated-result-type sph_neumann(unsigned v, T2 x, const Policy&);
 
    
 
    
-
+
           Description
         
    
 
    
@@ -87,17 +87,17 @@
           The jv function is cyclic like Jv but differs in its behaviour at the origin:
         
    
 
    
-          sph_bessel_j
+          
         
    
 
    
           Likewise yv is also cyclic for large x, but tends to -∞
 for small x:
         
    
 
    
-          sph_bessel_y
+          
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -106,7 +106,7 @@ for small x:
           implementation (with all the special case handling removed).
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -116,7 +116,7 @@ for small x:
           refer to these functions for accuracy data.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -146,8 +146,8 @@ for small x:
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint.html b/doc/sf_and_dist/html/math_toolkit/special/ellint.html
index fce070090..11b07b58d 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint.html
@@ -41,8 +41,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html
index a71546ce7..fee169e70 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_1.html
@@ -28,7 +28,7 @@
         of the First Kind - Legendre Form
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -55,7 +55,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -64,7 +64,7 @@
           = F(π/2, k).
         
    
 
    
-          ellint_1
+          
         
    
 
    
           The return type of these functions is computed using the result
@@ -123,7 +123,7 @@
 
    
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -134,7 +134,7 @@
           All values are relative errors in units of epsilon.
         
    
 
    
-
    Table 36. Errors Rates in the Elliptic Integrals of the
+
    Table 40. Errors Rates in the Elliptic Integrals of the
         First Kind
    
 
    
@@ -237,7 +237,7 @@
 
    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -247,7 +247,7 @@
           this implementation.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -266,8 +266,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html
index c0f5e0c18..75f9f2e05 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_2.html
@@ -28,7 +28,7 @@
         of the Second Kind - Legendre Form
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -55,7 +55,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -64,7 +64,7 @@
           = E(π/2, k).
         
    
 
    
-          ellint_2
+          
         
    
 
    
           The return type of these functions is computed using the result
@@ -123,7 +123,7 @@
 
    
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -134,7 +134,7 @@
           All values are relative errors in units of epsilon.
         
    
 
    
-
    Table 37. Errors Rates in the Elliptic Integrals of the
+
    Table 41. Errors Rates in the Elliptic Integrals of the
         Second Kind
    
 
    
@@ -237,7 +237,7 @@
 
    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -247,7 +247,7 @@
           this implementation.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -266,8 +266,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html
index 9e19fbe5e..1eb8ed585 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_3.html
@@ -7,7 +7,7 @@
 
 
 
-
+
 
 
 
@@ -20,7 +20,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -28,7 +28,7 @@
         of the Third Kind - Legendre Form
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -55,7 +55,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -64,7 +64,7 @@
           k) = E(n, π/2, k).
         
    
 
    
-          ellint_3
+          
         
    
 
    
           The return type of these functions is computed using the result
@@ -135,7 +135,7 @@
           [opitonal_policy]
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -146,7 +146,7 @@
           All values are relative errors in units of epsilon.
         
    
 
    
-
    Table 38. Errors Rates in the Elliptic Integrals of the
+
    Table 42. Errors Rates in the Elliptic Integrals of the
         Third Kind
    
 
    
@@ -249,7 +249,7 @@
 
    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -259,7 +259,7 @@
           this implementation.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -320,8 +320,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
@@ -329,7 +329,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html
index 595d991c2..1348aa2db 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_carlson.html
@@ -28,7 +28,7 @@
         Integrals - Carlson Form
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -100,7 +100,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -109,7 +109,7 @@
           graph gives an idea of their behavior:
         
    
 
    
-          ellint_c
+          
         
    
 
    
           The return type of these functions is computed using the result
@@ -236,7 +236,7 @@
           
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -265,7 +265,7 @@
           to verify their correctness: see the above Carlson paper for details.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -276,7 +276,7 @@
           All values are relative errors in units of epsilon.
         
    
 
    
-
    Table 35. Errors Rates in the Carlson Elliptic Integrals
    
+
    Table 39. Errors Rates in the Carlson Elliptic Integrals
    
 
    @@ -419,7 +419,7 @@
 
    
 
 

    
 
    
 
    
-
+
           Implementation
         
    
 
    
@@ -457,8 +457,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html
index e8e6ec400..3974506ec 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/ellint/ellint_intro.html
@@ -61,14 +61,14 @@
           Elliptic integral.
         
    
 
    
-
+
           Notation
         
    
 
    
           All variables are real numbers unless otherwise noted.
         
    
 
    
-
+
           Definition
         
    
 
    
@@ -257,7 +257,7 @@
 
    
 
    
 
    
-
+
           Duplication
           Theorem
         
    
@@ -269,7 +269,7 @@
           
         
    
 
    
-
+
           Carlson's
           Formulas
         
    
@@ -287,7 +287,7 @@
           
         
    
 
    
-
+
           Numerical
           Algorithms
         
    
@@ -301,7 +301,7 @@
           integrals with satisfactory precisions.
         
    
 
    
-
+
           References
         
    
 
    
@@ -408,8 +408,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials.html b/doc/sf_and_dist/html/math_toolkit/special/factorials.html
index cf9dc56a3..d41c6acef 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials.html
@@ -41,8 +41,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html
index 7ba293705..2cfa3309e 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_binomial.html
@@ -65,7 +65,7 @@
           if the result is too large to represent in type T.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -74,14 +74,14 @@
           function for larger arguments.
         
    
 
    
-
+
           Testing
         
    
 
    
           The spot tests for the binomial coefficients use data generated by functions.wolfram.com.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -108,8 +108,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html
index 155ba4892..16d6abe67 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_double_factorial.html
@@ -64,7 +64,7 @@
           of i! is possible.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -72,14 +72,14 @@
           so error rates should be no more than a couple of epsilon higher.
         
    
 
    
-
+
           Testing
         
    
 
    
           The spot tests for the double factorial use data generated by functions.wolfram.com.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -101,8 +101,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html
index 666d0109f..f01b9f1f3 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_factorial.html
@@ -27,7 +27,7 @@
  Factorial
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -54,7 +54,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    template <class T>
@@ -112,7 +112,7 @@
           the size of further tables that depend on the factorials.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -121,7 +121,7 @@
           will be the same as for tgamma.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -130,7 +130,7 @@
           function handle those cases already.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -141,8 +141,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html
index cdc9db59d..4bb49dad0 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_falling_factorial.html
@@ -76,7 +76,7 @@
           the type of the result is T.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -84,14 +84,14 @@
           function.
         
    
 
    
-
+
           Testing
         
    
 
    
           The spot tests for the falling factorials use data generated by functions.wolfram.com.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -103,8 +103,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html
index 83c119934..546ec4e4a 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/factorials/sf_rising_factorial.html
@@ -80,7 +80,7 @@
           the type of the result is T.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -88,14 +88,14 @@
           function.
         
    
 
    
-
+
           Testing
         
    
 
    
           The spot tests for the rising factorials use data generated by functions.wolfram.com.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -107,8 +107,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/fpclass.html b/doc/sf_and_dist/html/math_toolkit/special/fpclass.html
index 13104ac1a..208b2e180 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/fpclass.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/fpclass.html
@@ -6,7 +6,7 @@
 
 
 
-
+
 
 
 
@@ -20,7 +20,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -28,7 +28,7 @@
       Infinities and NaN's
 
    
 
    
-
+
         Synopsis
       
    
 
    #define FP_ZERO        /* implementation specific value */
@@ -53,7 +53,7 @@
 bool isnormal(T t);
 
    
 
    
-
+
         Description
       
    
 
    
@@ -205,8 +205,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
@@ -214,7 +214,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html
index 61336029e..ec273d531 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper.html
@@ -36,8 +36,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html
index 9c549652b..d7fa8d56e 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/acosh.html
@@ -65,11 +65,14 @@
           
    
 
    
         
    
+
    
+          
+        
    
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html
index 339e22ede..b778866e7 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/asinh.html
@@ -49,6 +49,9 @@
           type calculation rules: the return type is double when T is an integer type, and T
           otherwise.
         
    
+
    
+          
+        
    
 
    
           
    
 
    
@@ -62,8 +65,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html
index bf88328aa..225974755 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/atanh.html
@@ -7,7 +7,7 @@
 
 
 
-
+
 
 
 
@@ -20,7 +20,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -73,11 +73,14 @@ denoting
           type calculation rules: the return type is double when T is an integer type, and T
           otherwise.
         
    
+
    
+          
+        
    
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
@@ -85,7 +88,7 @@ denoting
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html
index 48f1dca23..becc33cfa 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/inv_hyper/inv_hyper_over.html
@@ -148,8 +148,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers.html b/doc/sf_and_dist/html/math_toolkit/special/powers.html
index 914fbb86e..5cddd82ce 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers.html
@@ -6,7 +6,7 @@
 
 
 
-
+
 
 
 
@@ -20,7 +20,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
@@ -47,7 +49,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html
index b34eb0ff2..1920a5fa3 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers/cbrt.html
@@ -64,8 +64,14 @@
 
    
           Implemented using Halley iteration.
         
    
+
    
+          The following graph illustrates the behaviour of cbrt:
+        
    
+
    
+          
+        
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -73,7 +79,7 @@
           should have approximately 2 epsilon accuracy.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -83,8 +89,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html
index 81aeb34d4..fdc714d8e 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers/expm1.html
@@ -73,8 +73,14 @@
           specializations of this template simply forward to the platform's native
           (POSIX) implementation of this function.
         
    
+
    
+          The following graph illustrates the behaviour of expm1:
+        
    
+
    
+          
+        
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -82,7 +88,7 @@
           should have approximately 1 epsilon accuracy.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -92,8 +98,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html
index d2a71e440..bb9a8a7ad 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers/hypot.html
@@ -7,7 +7,7 @@
 
 
 
-
+
 
 
 
@@ -20,7 +20,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -58,7 +58,7 @@ in such a
           representable.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -78,8 +78,8 @@ in such a
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
@@ -87,7 +87,7 @@ in such a
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html
index cf1b64c08..828a3f0fb 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers/log1p.html
@@ -86,8 +86,14 @@
           specializations of this template simply forward to the platform's native
           (POSIX) implementation of this function.
         
    
+
    
+          The following graph illustrates the behaviour of log1p:
+        
    
+
    
+          
+        
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -95,7 +101,7 @@
           should have approximately 1 epsilon accuracy.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -105,8 +111,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html
index 5056ebc07..437dc82c2 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers/powm1.html
@@ -67,15 +67,21 @@
 
    
           Implemented in terms of expm1.
         
    
+
    
+          The following graph illustrates the behaviour of powm1:
+        
    
+
    
+          
+        
    
 
    
-
+
           Accuracy
         
    
 
    
           Should have approximately 2-3 epsilon accuracy.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -85,8 +91,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html
index ede597b3a..f2e0561c1 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/powers/sqrt1pm1.html
@@ -69,8 +69,14 @@
           Implemented in terms of log1p
           and expm1.
         
    
+
    
+          The following graph illustrates the behaviour of sqrt1pm1:
+        
    
+
    
+          
+        
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -78,7 +84,7 @@
           should have approximately 3 epsilon accuracy.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -88,8 +94,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html
index dcef98c2c..01e4ca313 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta.html
@@ -38,8 +38,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html
index dd8468d83..18ef172dd 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_derivative.html
@@ -28,7 +28,7 @@
         of the Incomplete Beta Function
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -49,7 +49,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -76,14 +76,14 @@
 
    
         
    
 
    
-
+
           Accuracy
         
    
 
    
           Almost identical to the incomplete beta function ibeta.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -94,8 +94,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html
index 8bbe4e91f..bc8d277d1 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/beta_function.html
@@ -27,7 +27,7 @@
  Beta
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -48,7 +48,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -58,7 +58,7 @@
           
         
    
 
    
-          beta
+          
         
    
 
    
           
    
@@ -86,7 +86,7 @@
           type calculation rules when T1 and T2 are different types.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -98,7 +98,7 @@
           zero error.
         
    
 
    
-
    Table 17. Peak Errors In the Beta Function
    
+
    Table 21. Peak Errors In the Beta Function
    
 
    @@ -244,7 +244,7 @@
           very small.
         
    
-
+
           Testing
         
    
@@ -253,7 +253,7 @@
           at 1000-bit precision.
         
    
-
+
           Implementation
         
    
@@ -319,8 +319,8 @@
 
 
    
 
 

 
 
 
 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html
index 6f8f64562..a20555b5e 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_function.html
@@ -28,7 +28,7 @@
         Beta Functions
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -67,7 +67,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -111,7 +111,7 @@
           
         
    
 
    
-          ibeta
+          
         
    
 
    template <class T1, class T2, class T3>
 calculated-result-type ibetac(T1 a, T2 b, T3 x);
@@ -153,7 +153,7 @@
           
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -172,7 +172,7 @@
           with the wider exponent range of the long double types.
         
    
 
    
-
    Table 18. Errors In the Function ibeta(a,b,x)
    
+
    Table 22. Errors In the Function ibeta(a,b,x)
    
 
    @@ -359,7 +359,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 19. Errors In the Function ibetac(a,b,x)
    
+
    Table 23. Errors In the Function ibetac(a,b,x)
    
 
    @@ -526,7 +526,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 20. Errors In the Function beta(a, b, x)
    
+
    Table 24. Errors In the Function beta(a, b, x)
    
 
    @@ -693,7 +693,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 21. Errors In the Function betac(a,b,x)
    
+
    Table 25. Errors In the Function betac(a,b,x)
    
 
    @@ -860,7 +860,7 @@
 
    
 
 

    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -878,7 +878,7 @@
           have test data that is fully independent of the code.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -961,8 +961,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html
index 3b7016e6f..ee6b1f89d 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_beta/ibeta_inv_function.html
@@ -87,7 +87,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -323,7 +323,7 @@
 
    
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -335,7 +335,7 @@
           or 1.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -359,7 +359,7 @@
           
 
    
 
    
-
+
           Implementation
           of ibeta_inv and ibetac_inv
         
    
@@ -527,7 +527,7 @@
           rapidly converges on the true value.
         
    
 
    
-
+
           Implementation
           of inverses on the a and b parameters
         
    
@@ -554,8 +554,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html
index 651bd0697..447f0bf03 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf.html
@@ -35,8 +35,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html
index 43011c37c..bf58b5576 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_function.html
@@ -28,7 +28,7 @@
         Functions
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -69,7 +69,7 @@
 
    
         
    
 
    
-
+
           Description
         
    
 
    template <class T>
@@ -87,7 +87,7 @@
           
         
    
 
    
-          erf1
+          
         
    
 
    template <class T>
 calculated-result-type erfc(T z);
@@ -103,10 +103,10 @@
           
         
    
 
    
-          erf2
+          
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -119,7 +119,7 @@
           the one shown will have effectively zero error.
         
    
 
    
-
    Table 22. Errors In the Function erf(z)
    
+
    Table 26. Errors In the Function erf(z)
    
 
    @@ -325,7 +325,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 23. Errors In the Function erfc(z)
    
+
    Table 27. Errors In the Function erfc(z)
    
 
    @@ -531,7 +531,7 @@
 
    
 
 

    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -546,7 +546,7 @@
           check.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -618,8 +618,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html
index c77c0cb7a..d7abca854 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_erf/error_inv.html
@@ -28,7 +28,7 @@
         Inverses
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -69,7 +69,7 @@
 
    
         
    
 
    
-
+
           Description
         
    
 
    template <class T>
@@ -85,7 +85,7 @@
 
    p = erf(x);
 
    
 
    
-          erf_inv
+          
         
    
 
    template <class T>
 calculated-result-type erfc_inv(T z);
@@ -100,10 +100,10 @@
 
    p = erfc(x);
 
    
 
    
-          erfc_inv
+          
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -113,7 +113,7 @@
           error functions.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -135,7 +135,7 @@
           
 
 
    
-
+
           Implementation
         
    
 
    
@@ -195,8 +195,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html
index 4bdc5cf58..32b075fe9 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma.html
@@ -42,8 +42,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html
index ba4dea451..b4388898f 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/digamma.html
@@ -27,7 +27,7 @@
  Digamma
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -48,7 +48,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -59,7 +59,7 @@
           
         
    
 
    
-          digamma
+          
         
    
 
    
           
    
@@ -82,7 +82,7 @@
           T otherwise.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -270,7 +270,7 @@
           absolute error will remain very low.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -280,7 +280,7 @@
           see below).
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -379,8 +379,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html
index 17a69dea5..78aae771d 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_derivatives.html
@@ -28,7 +28,7 @@
         of the Incomplete Gamma Function
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -49,7 +49,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -80,7 +80,7 @@
           otherwise the return type is simply T1.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -88,7 +88,7 @@
           refer to the documentation for that function for more information.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -99,8 +99,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html
index 8f3975583..f8f4c3760 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/gamma_ratios.html
@@ -51,7 +51,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    template <class T1, class T2> 
@@ -113,8 +113,11 @@
           type calculation rules when T1 and T2 are different types,
           otherwise the result type is simple T1.
         
    
+
    
+          
+        
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -124,7 +127,7 @@
           effectively zero error.
         
    
 
    
-
    Table 11. Errors In the Function tgamma_delta_ratio(a, delta)
    
+
    Table 15. Errors In the Function tgamma_delta_ratio(a, delta)
    
 
    @@ -227,7 +230,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 12. Errors In the Function tgamma_ratio(a,
+
    Table 16. Errors In the Function tgamma_ratio(a,
         b)
    
 
    
@@ -326,7 +329,7 @@
 
    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -335,7 +338,7 @@
           a deliberately naive calculation of Γ(x)/Γ(y).
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -352,8 +355,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
index 0bb02cf26..28903c090 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma.html
@@ -28,7 +28,7 @@
         Functions
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -67,7 +67,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -113,7 +113,7 @@
           This function changes rapidly from 0 to 1 around the point z == a:
         
    
 
    
-          gamma_p
+          
         
    
 
    template <class T1, class T2>
 calculated-result-type gamma_q(T1 a, T2 z);
@@ -131,7 +131,7 @@
           This function changes rapidly from 1 to 0 around the point z == a:
         
    
 
    
-          gamma_q
+          
         
    
 
    template <class T1, class T2>
 calculated-result-type tgamma_lower(T1 a, T2 z);
@@ -160,7 +160,7 @@
           
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -185,7 +185,7 @@
           All values are in units of epsilon.
         
    
 
    
-
    Table 13. Errors In the Function gamma_p(a,z)
    
+
    Table 17. Errors In the Function gamma_p(a,z)
    
 
    @@ -372,7 +372,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 14. Errors In the Function gamma_q(a,z)
    
+
    Table 18. Errors In the Function gamma_q(a,z)
    
 
    @@ -558,7 +558,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 15. Errors In the Function tgamma_lower(a,z)
    
+
    Table 19. Errors In the Function tgamma_lower(a,z)
    
 
    @@ -693,7 +693,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 16. Errors In the Function tgamma(a,z)
    
+
    Table 20. Errors In the Function tgamma(a,z)
    
 
    @@ -828,7 +828,7 @@
 
    
 
 

    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -844,7 +844,7 @@
           fraction (see below) is unstable for small a and z.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -1013,7 +1013,7 @@
           by Temme (see references below).
         
    
 
    
-
+
           References
         
    
 
      
@@ -1039,8 +1039,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html
index 17d4650b1..50b6c6166 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/igamma_inv.html
@@ -28,7 +28,7 @@
         Gamma Function Inverses
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -67,7 +67,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -173,7 +173,7 @@
           0.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -187,7 +187,7 @@
           functions.
         
    
 
    
-
+
           Testing
         
    
 
    
@@ -210,7 +210,7 @@
           
 
 
    
-
+
           Implementation
         
    
 
    
@@ -249,8 +249,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html
index 2ee36945b..eff9e6234 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/lgamma.html
@@ -27,7 +27,7 @@
  Log Gamma
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -54,7 +54,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -79,7 +79,7 @@
 
    
         
    
 
    
-          lgamma
+          
         
    
 
    
           There are effectively two versions of this function internally: a fully
@@ -98,7 +98,7 @@
           T otherwise.
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -349,7 +349,7 @@
 
    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -360,7 +360,7 @@
           Random tests in key problem areas are also used.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -472,8 +472,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html
index 9e2b6ead4..9909020be 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_gamma/tgamma.html
@@ -27,7 +27,7 @@
  Gamma
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -54,7 +54,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    template <class T>
@@ -70,7 +70,7 @@
           
         
    
 
    
-          gamma
+          
         
    
 
    
           
    
@@ -129,7 +129,7 @@
 
    
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -384,7 +384,7 @@
 
    
 
    
 
    
-
+
           Testing
         
    
 
    
@@ -399,7 +399,7 @@
           a lanczos approximation accurate to around 100 decimal digits.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -464,8 +464,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html
index 4d4798db0..ee941c797 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly.html
@@ -37,8 +37,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html
index 76e04bb8e..9cdeb71c9 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/hermite.html
@@ -27,7 +27,7 @@
  Hermite Polynomials
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -51,7 +51,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -88,7 +88,7 @@
           Polynomials:
         
    
 
    
-          hermite
+          
         
    
 
    template <class T1, class T2, class T3>
 calculated-result-type hermite_next(unsigned n, T1 x, T2 Hn, T3 Hnm1);
@@ -136,7 +136,7 @@
 
 
 
    
-
+
           Accuracy
         
    
 
    
@@ -146,7 +146,7 @@
           zero error.
         
    
 
    
-
    Table 29. Peak Errors In the Hermite Polynomial
    
+
    Table 33. Peak Errors In the Hermite Polynomial
    
 
    @@ -253,7 +253,7 @@
           is very close to a root.
         
    
-
+
           Testing
         
    
@@ -263,7 +263,7 @@
           precision.
         
    
-
+
           Implementation
         
    
@@ -274,8 +274,8 @@
 
 
    
 
 

 
 
 
 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html
index 033e7d739..f288d7c6e 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/laguerre.html
@@ -28,7 +28,7 @@
         Associated) Polynomials
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -62,7 +62,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -99,7 +99,7 @@
           Polynomials:
         
    
 
    
-          laguerre
+          
         
    
 
    template <class T>
 calculated-result-type laguerre(unsigned n, unsigned m, T x);
@@ -210,7 +210,7 @@
 
 
 
    
-
+
           Accuracy
         
    
 
    
@@ -220,7 +220,7 @@
           zero error.
         
    
 
    
-
    Table 27. Peak Errors In the Laguerre Polynomial
    
+
    Table 31. Peak Errors In the Laguerre Polynomial
    
 
    @@ -320,7 +320,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 28. Peak Errors In the Associated Laguerre
+
    Table 32. Peak Errors In the Associated Laguerre
         Polynomial
    
 
    
@@ -429,7 +429,7 @@
           is very close to a root.
         
    
-
+
           Testing
         
    
@@ -439,7 +439,7 @@
           precision.
         
    
-
+
           Implementation
         
    
@@ -450,8 +450,8 @@
 
 
    
 
 
 
 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html
index b927f4a5b..d9790a239 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/legendre.html
@@ -28,7 +28,7 @@
         Associated) Polynomials
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -84,7 +84,7 @@
 
    
         
    
 
    
-
+
           Description
         
    
 
    template <class T>
@@ -113,7 +113,7 @@
           Polynomials:
         
    
 
    
-          legendre_p1
+          
         
    
 
    template <class T>
 calculated-result-type legendre_p(int l, int m, T x);
@@ -192,7 +192,7 @@
           second kind:
         
    
 
    
-          legendre_q
+          
         
    
 
    template <class T1, class T2, class T3>
 calculated-result-type legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1);
@@ -292,7 +292,7 @@
 
 
 
    
-
+
           Accuracy
         
    
 
    
@@ -302,7 +302,7 @@
           zero error.
         
    
 
    
-
    Table 24. Peak Errors In the Legendre P Function
    
+
    Table 28. Peak Errors In the Legendre P Function
    
 
    @@ -431,7 +431,7 @@
 
    
 
 

    
 
    
 
    
-
    Table 25. Peak Errors In the Associated Legendre
+
    Table 29. Peak Errors In the Associated Legendre
         P Function
    
 
    
@@ -533,7 +533,7 @@
 
    
 
    
 
    
-
    Table 26. Peak Errors In the Legendre Q Function
    
+
    Table 30. Peak Errors In the Legendre Q Function
    
 
    @@ -675,7 +675,7 @@
           given here.
         
    
-
+
           Testing
         
    
@@ -685,7 +685,7 @@
           precision.
         
    
-
+
           Implementation
         
    
@@ -696,8 +696,8 @@
 
 
    
 
 

 
 
 
 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html
index dafd2e11f..d71dd35b1 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sf_poly/sph_harm.html
@@ -27,7 +27,7 @@
  Spherical Harmonics
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -60,7 +60,7 @@
 }} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -155,7 +155,7 @@
           
         
    
 
    
-
+
           Accuracy
         
    
 
    
@@ -170,7 +170,7 @@
           All values are in units of epsilon.
         
    
 
    
-
    Table 30. Peak Errors In the Sperical Harmonic Functions
    
+
    Table 34. Peak Errors In the Sperical Harmonic Functions
    
 
    @@ -276,7 +276,7 @@
           arbitrarily large when the function is very close to a root.
         
    
-
+
           Testing
         
    
@@ -286,7 +286,7 @@
           precision.
         
    
-
+
           Implementation
         
    
@@ -301,8 +301,8 @@
 
 
    
 
 

 
 
 
 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc.html b/doc/sf_and_dist/html/math_toolkit/special/sinc.html
index 6488344a4..2094cde8b 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sinc.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sinc.html
@@ -6,7 +6,7 @@
 
 
 
-
+
 
 
 
@@ -20,7 +20,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
    
 
    
@@ -36,8 +36,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
@@ -45,7 +45,7 @@
 
    
 
    
 
    
-PrevUpHomeNext
+PrevUpHomeNext
 
    
 
 
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html
index d54e0db3d..495bc629c 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_overview.html
@@ -30,13 +30,21 @@
 
    
           The Sinus Cardinal
           family of functions (indexed by the family of indices a
-          > 0) is defined by ;
+          > 0) is defined by
+        
    
+
    
+          
+        
    
+
    
           it sees heavy use in signal processing tasks.
         
    
 
    
           By analogy, the Hyperbolic
           Sinus Cardinal family of functions (also indexed by the family
-          of indices a > 0) is defined by .
+          of indices a > 0) is defined by
+        
    
+
    
+          
         
    
 
    
           These two families of functions are composed of entire functions.
@@ -70,8 +78,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html
index fb49f0265..a33511f61 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinc_pi.html
@@ -55,6 +55,9 @@
           The second form is for complex numbers, quaternions, octonions etc. Taylor
           series are used at the origin to ensure accuracy.
         
    
+
    
+          
+        
    
 
    
           
    
 
    
@@ -68,8 +71,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html
index d08c90926..23c5beb69 100644
--- a/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html
+++ b/doc/sf_and_dist/html/math_toolkit/special/sinc/sinhc_pi.html
@@ -69,11 +69,14 @@
           
    
 
    
         
    
+
    
+          
+        
    
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/status.html b/doc/sf_and_dist/html/math_toolkit/status.html
index 5ed6130ce..283ed3fa8 100644
--- a/doc/sf_and_dist/html/math_toolkit/status.html
+++ b/doc/sf_and_dist/html/math_toolkit/status.html
@@ -35,8 +35,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/status/compilers.html b/doc/sf_and_dist/html/math_toolkit/status/compilers.html
index a965551f3..fff7c117d 100644
--- a/doc/sf_and_dist/html/math_toolkit/status/compilers.html
+++ b/doc/sf_and_dist/html/math_toolkit/status/compilers.html
@@ -37,7 +37,7 @@
 
    
         
    
 
    
-
    Table 47. Supported/Tested Compilers
    
+
    Table 54. Supported/Tested Compilers
    
 
    @@ -539,7 +539,7 @@
 

     
    
-
    Table 48. Unsupported Compilers
    
+
    Table 55. Unsupported Compilers
    
 
    
 
 

 
 
    @@ -613,8 +613,8 @@
 
    
 
 

 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/status/credits.html b/doc/sf_and_dist/html/math_toolkit/status/credits.html
index 229158650..10174d9bf 100644
--- a/doc/sf_and_dist/html/math_toolkit/status/credits.html
+++ b/doc/sf_and_dist/html/math_toolkit/status/credits.html
@@ -60,6 +60,16 @@
         program used to generate the html and pdf versions of this document, adding
         several new features en route.
       
    
+
    
+        Plots of the functions and distributions were prepared in W3C
+        standard Scalable Vector Graphic (SVG)
+        format using a program created by Jacob Voytko during a Google 'Summer of
+        Code'. Since browser support for rendering SVG is still not universal (Microsoft
+        Internet Explorer, even IE 8 beta, still lacks native SVG support but can
+        be made to work with Adobe's
+        free SVG viewer plugin), so the SVG files were batch converted to
+        JPEG using Inkscape.
+      
    
 
    
         We are also indebted to Matthias Schabel for managing the formal Boost-review
         of this library, and to all the reviewers - including Guillaume Melquiond,
@@ -69,8 +79,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/status/history1.html b/doc/sf_and_dist/html/math_toolkit/status/history1.html
index 4db4d1537..5e355ae85 100644
--- a/doc/sf_and_dist/html/math_toolkit/status/history1.html
+++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html
@@ -30,7 +30,7 @@
         
         
    
 
    
-
+
           Milestone
           5: Post Review First Official Release
         
    
@@ -67,7 +67,7 @@
         
         
    
 
    
-
+
           Milestone
           4: Second Review Candidate (1st March 2007)
         
    
@@ -86,7 +86,7 @@
         
         
    
 
    
-
+
           Milestone
           3: First Review Candidate (31st Dec 2006)
         
    
@@ -119,7 +119,7 @@
         
         
    
 
    
-
+
           Milestone
           2: Released September 10th 2006
         
    
@@ -160,7 +160,7 @@
         
         
    
 
    
-
+
           Milestone
           1: Released March 31st 2006
         
    
@@ -202,8 +202,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/status/issues.html b/doc/sf_and_dist/html/math_toolkit/status/issues.html
index 5b2da6255..1b790723d 100644
--- a/doc/sf_and_dist/html/math_toolkit/status/issues.html
+++ b/doc/sf_and_dist/html/math_toolkit/status/issues.html
@@ -43,7 +43,7 @@
         with it.
       
    
 
    
-
+
         tgamma
       
    
 
    • 
@@ -51,7 +51,7 @@
           be optimized any further? (low priority)
         
    
 
    
-
+
         Incomplete Beta
       
    
 
    • 
@@ -59,7 +59,7 @@
           (medium priority).
         
    
 
    
-
+
         Inverse Gamma
       
    
 
    • 
@@ -67,7 +67,7 @@
           is good enough (Medium Priority).
         
    
 
    
-
+
         Polynomials
       
    
 
    • 
@@ -77,7 +77,7 @@
           not (Low Priority).
         
    
 
    
-
+
         Elliptic Integrals
       
    
 
      
@@ -127,7 +127,7 @@
         
 
    
 
    
-
+
         Inverse
         Hyperbolic Functions
       
    
@@ -137,7 +137,7 @@
           is probably only an issue for very high precision types (Low Priority).
         
    
 
    
-
+
         Statistical
         distributions
       
    
@@ -145,11 +145,1312 @@
           Student's t Perhaps switch to normal distribution as a better approximation
           for very large degrees of freedom?
         
+
    
+
+        Feature Requests
+      
    
+
    
+        The following table lists distributions that are found in other packages
+        but which are not yet present here, the more frequently the distribution
+        is found, the higher the priority for implementing it:
+      
    
+
    
++++++++
+
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+
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+
    







    
+              
    
+                Distribution
+              
    
+                  		
+              
    
+                R
+              
    
+                  		
+              
    
+                Mathematica 6
+              
    
+                  		
+              
    
+                NIST
+              
    
+                  		
+              
    
+                Regress+
+              
    
+                  		
+              
    
+                Matlab
+              
    
+              
    
+              
    
+                Non-central Chi Squared
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Non-central F
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Non-central T
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Logistic
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Log Logistic
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Hypergeometric
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Geometric
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Multinomial
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Tukey (Studentized range)
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Tukey Lambda
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Wilcoxon rank sum
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Wincoxon signed rank
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Non-central Beta
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Half Normal / Folded Normal
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Inverse Gausian / Inverse Normal
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Laplace
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Maxwell
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Chi
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Gumbel
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Geometric
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Beta-Binomial
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Beta-negative Binomial
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Discrete Uniform
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Zipf
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Log Series
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Birnbaum-Saunders / Fatigue Life
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Double Exponential
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Power Normal
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Power Lognormal
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Cosine
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Double Gamma
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Double Weibul
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Hyperbolic Secant
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Laplace
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Semicircular
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Bradford
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Birr / Fisk
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
+              
    
+                Nakagami (generalised Chi)
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                X
+              
    
+              
    
+              
    
+                Reciprocal
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                -
+              
    
+                  		
+              
    
+                X
+              
    
+                  		
+              
    
+                -
+              
    
+              
    
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit.html b/doc/sf_and_dist/html/math_toolkit/toolkit.html
index 18a614c46..b52ff8042 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit.html
@@ -57,8 +57,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html
index 88e8fa88f..e90bf7b3c 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1.html
@@ -43,8 +43,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html
index c38f82faf..bb461a19e 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/cf.html
@@ -28,7 +28,7 @@
         Evaluation
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -59,7 +59,7 @@
 }}} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -157,7 +157,7 @@
           a continued fraction for convergence.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -167,7 +167,7 @@
           Lentz, W.J. 1976, Applied Optics, vol. 15, pp. 668-671.
         
    
 
    
-
+
           Examples
         
    
 
    
@@ -250,8 +250,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html
index 135f074ca..e32ad039e 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/minima.html
@@ -28,7 +28,7 @@
         Minima
 
    
 
    
-
+
           synopsis
         
    
 
    
@@ -45,7 +45,7 @@
 std::pair<T, T> brent_find_minima(F f, T min, T max, int bits, boost::uintmax_t& max_iter);
 
 
    
-
+
           Description
         
    
 
    
@@ -88,7 +88,7 @@
           the abscissa at the minima and the value of f(x) at the minima.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -111,8 +111,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html
index 7824e45cb..6c5c6500c 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/rational.html
@@ -28,7 +28,7 @@
         and Rational Function Evaluation
 
    
 
    
-
+
           synopsis
         
    
 
    
@@ -79,7 +79,7 @@
 V evaluate_rational(const T* num, const U* denom, V z, unsigned count);
 
 
    
-
+
           Description
         
    
 
    
@@ -193,7 +193,7 @@
           evaluation with compile-time array sizes may offer slightly better performance.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -222,8 +222,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html
index f4a27dd50..f30ac9437 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots.html
@@ -28,7 +28,7 @@
         With Derivatives
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -61,7 +61,7 @@
 }}} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -176,7 +176,7 @@
 
    
         
    
 
    
-
+
           Newton
           Raphson Method
         
    
@@ -196,7 +196,7 @@
 
    
         
    
 
    
-
+
           Halley's
           Method
         
    
@@ -220,7 +220,7 @@
 
    
         
    
 
    
-
+
           Schroeder's
           Method
         
    
@@ -244,7 +244,7 @@
           iteration.
         
    
 
    
-
+
           Example
         
    
 
    
@@ -369,8 +369,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html
index addd6b49c..03d6314ea 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/roots2.html
@@ -28,7 +28,7 @@
         Without Derivatives
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -141,7 +141,7 @@
 }}} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -559,7 +559,7 @@
           as soon as both ends of the interval round to the same nearest integer.
         
    
 
    
-
+
           Implementation
         
    
 
    
@@ -577,8 +577,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html
index fd5e020e7..790bf23ce 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/series_evaluation.html
@@ -28,7 +28,7 @@
         Series Evaluation
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -61,7 +61,7 @@
 }}} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -117,7 +117,7 @@
           summation in this way.
         
    
 
    
-
+
           Example
         
    
 
    
@@ -175,8 +175,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html
index 025891348..25d08dc2c 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html
@@ -38,8 +38,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html
index 50d067688..abcd46727 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/error_test.html
@@ -28,7 +28,7 @@
         Error and Testing
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -45,7 +45,7 @@
 test_result<see-below> test(const A& a, F1 test_func, F2 expect_func);
 
 
    
-
+
           Description
         
    
 
    template <class T>
@@ -165,7 +165,7 @@
           is mainly a debugging/development aid (and a good place for a breakpoint).
         
    
 
    
-
+
           Example
         
    
 
    
@@ -220,8 +220,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
index cc1e2ab73..aa130bae4 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/minimax.html
@@ -176,18 +176,29 @@
 
    x-offset val
    
 
    
               Sets the x-offset to val: the approximation will
-              be generated for f(x + X) + Y where X is
-              the x-offset and Y is the y-offset. Defaults to
-              zero. To avoid rounding errors, take care to specify a value that can
-              be exactly represented as a floating point number.
+              be generated for f(S * (x + X)) + Y
+              where X is the x-offset, S
+              is the x-scale and Y is the y-offset. Defaults
+              to zero. To avoid rounding errors, take care to specify a value that
+              can be exactly represented as a floating point number.
+            
    
+
    x-scale val
    
+
    
+              Sets the x-scale to val: the approximation will
+              be generated for f(S * (x + X)) + Y
+              where S is the x-scale, X
+              is the x-offset and Y is the y-offset. Defaults
+              to one. To avoid rounding errors, take care to specify a value that
+              can be exactly represented as a floating point number.
             
    
 
    y-offset val
    
 
    
               Sets the y-offset to val: the approximation will
-              be generated for f(x + X) + Y where X is
-              the x-offset and Y is the y-offset. Defaults to
-              zero. To avoid rounding errors, take care to specify a value that can
-              be exactly represented as a floating point number.
+              be generated for f(S * (x + X)) + Y
+              where X is the x-offset, S
+              is the x-scale and Y is the y-offset. Defaults
+              to zero. To avoid rounding errors, take care to specify a value that
+              can be exactly represented as a floating point number.
             
    
 
    y-offset auto
    
 
    
@@ -256,8 +267,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html
index ab71be83d..1d6b0c31e 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/polynomials.html
@@ -27,7 +27,7 @@
  Polynomials
 
    
 
    
-
+
           Synopsis
         
    
 
    
@@ -103,7 +103,7 @@
 }}} // namespaces
 
 
    
-
+
           Description
         
    
 
    
@@ -122,8 +122,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html
index 1991f3edc..8838f84e1 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2/test_data.html
@@ -7,7 +7,7 @@
 
 
 
-
+
 
 
 
@@ -46,7 +46,7 @@
           
    
-
+
           Synopsis
         
    namespace boost{ namespace math{ namespace tools{
@@ -147,7 +147,7 @@
 }}} // namespaces
 
    
-
+
           Description
         
    
@@ -177,7 +177,7 @@
           
 
 
    
-
+
           Example
           1: Output Data for Graph Plotting
         
    
@@ -208,10 +208,10 @@
           Which, when plotted, results in:
         
    
-          lgamma
+          
         
    
-
+
           Example
           2: Creating Test Data
         
    
@@ -375,7 +375,7 @@
           used by default as it's rather hard on the compiler when the table is large.
         
    
-
+
           Example
           3: Profiling a Continued Fraction for Convergence and Accuracy
         
    
@@ -481,7 +481,7 @@
           of a and z.
         
    
-
+
           reference
         
    
@@ -534,8 +534,8 @@
 
 
    
 
 
 
 
 
 
 
 
 
 
    
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html
index f5a2d4994..2cc2494ba 100644
--- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html
+++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals_overview.html
@@ -43,8 +43,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt.html b/doc/sf_and_dist/html/math_toolkit/using_udt.html
index e38016778..52089c74e 100644
--- a/doc/sf_and_dist/html/math_toolkit/using_udt.html
+++ b/doc/sf_and_dist/html/math_toolkit/using_udt.html
@@ -1,7 +1,7 @@
 
 
 
-Use with User Defined Floating-Point Types
+Use with User-Defined Floating-Point Types
 
 
 
@@ -24,7 +24,7 @@
 
    
 
    
 
    
 
    
@@ -40,8 +40,8 @@
 
    
 
-
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html b/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html
index c616a1eab..d8e921858 100644
--- a/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html
+++ b/doc/sf_and_dist/html/math_toolkit/using_udt/archetypes.html
@@ -5,7 +5,7 @@
 
 
 
-
+
 
 
 
@@ -163,8 +163,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html b/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html
index f043a7bd0..49a467d9b 100644
--- a/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html
+++ b/doc/sf_and_dist/html/math_toolkit/using_udt/concepts.html
@@ -5,7 +5,7 @@
 
 
 
-
+
 
 
 
@@ -42,7 +42,7 @@
         behaves just like a built in floating point type.
       
    
 
    
-
+
         Basic
         Arithmetic Requirements
       
    
@@ -1034,7 +1034,7 @@
 
    
 
    
 
    
-
+
         Standard
         Library Support Requirements
       
    
@@ -1253,6 +1253,66 @@
               
    
                   		
 
    
+              
    
+                fmod(cr1)
+              
    
+                  		
+              
    
+                RealType
+              
    
+              
    
+              
    
+                round(cr1)
+              
    
+                  		
+              
    
+                RealType
+              
    
+              
    
+              
    
+                iround(cr1)
+              
    
+                  		
+              
    
+                int
+              
    
+              
    
+              
    
+                trunc(cr1)
+              
    
+                  		
+              
    
+                RealType
+              
    
+              
    
+              
    
+                itrunc(cr1)
+              
    
+                  		
+              
    
+                int
+              
    
+              
    
     
 
    
 
    
@@ -1261,9 +1321,17 @@
         following functions: acos,
         atan2, fmod,
         cosh, sinh,
-        tanh, modf
-        and log10 are not currently
-        used, but may be if further special functions are added.
+        tanh, log10,
+        lround, llround,
+        ltrunc, lltrunc and modf` are not currently used, but may
+        be if further special functions are added.
+      
    
+
    
+        Note that the round, trunc and modf
+        functions are not part of the current C++ standard: they are part of the
+        additions added to C99 which will likely be in the next C++ standard. There
+        are Boost versions of these provided as a backup, and the functions are always
+        called unqualified so that argument-dependent-lookup can take place.
       
    
 
    
         In addition, for efficient and accurate results, a Lanczos
@@ -1281,8 +1349,8 @@
 
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html b/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html
index 6eb83f1e1..0dd86e805 100644
--- a/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html
+++ b/doc/sf_and_dist/html/math_toolkit/using_udt/dist_concept.html
@@ -5,7 +5,7 @@
 
 
 
-
+
 
 
 
@@ -381,8 +381,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html b/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html
index 01f5eef15..493603678 100644
--- a/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html
+++ b/doc/sf_and_dist/html/math_toolkit/using_udt/use_ntl.html
@@ -5,8 +5,8 @@
 
 
 
-
-
+
+
 
 
 
@@ -53,8 +53,8 @@
 
    
 
-
    
 
    Copyright © 2006 -2007 John Maddock, Paul A. Bristow, Hubert Holin
-      and Xiaogang Zhang
    
+
    Copyright © 2006 , 2007, 2008 John Maddock, Paul A. Bristow, Hubert
+      Holin, Xiaogang Zhang and Bruno Lalande
    
         Distributed under the Boost Software License, Version 1.0. (See accompanying
         file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
       
    
diff --git a/doc/sf_and_dist/ibeta.qbk b/doc/sf_and_dist/ibeta.qbk
index 73a1eb330..fb94d983b 100644
--- a/doc/sf_and_dist/ibeta.qbk
+++ b/doc/sf_and_dist/ibeta.qbk
@@ -61,7 +61,7 @@ Returns the normalised incomplete beta function of a, b and x:
 
 [equation ibeta3]
 
-[$../graphs/ibeta.png]
+[graph ibeta]
 
    template 
    ``__sf_result`` ibetac(T1 a, T2 b, T3 x);
diff --git a/doc/sf_and_dist/igamma.qbk b/doc/sf_and_dist/igamma.qbk
index 9e0eac33b..ba5c69a6d 100644
--- a/doc/sf_and_dist/igamma.qbk
+++ b/doc/sf_and_dist/igamma.qbk
@@ -64,7 +64,7 @@ Returns the normalised lower incomplete gamma function of a and z:
 
 This function changes rapidly from 0 to 1 around the point z == a:
 
-[$../graphs/gamma_p.png]
+[graph gamma_p]
 
    template 
    ``__sf_result`` gamma_q(T1 a, T2 z);
@@ -78,7 +78,7 @@ Returns the normalised upper incomplete gamma function of a and z:
 
 This function changes rapidly from 1 to 0 around the point z == a:
 
-[$../graphs/gamma_q.png]
+[graph gamma_q]
 
    template 
    ``__sf_result`` tgamma_lower(T1 a, T2 z);
diff --git a/doc/sf_and_dist/implementation.qbk b/doc/sf_and_dist/implementation.qbk
index d3e8701c3..ac647f7f8 100644
--- a/doc/sf_and_dist/implementation.qbk
+++ b/doc/sf_and_dist/implementation.qbk
@@ -207,6 +207,11 @@ However in a few cases, for example normal, where we felt it obvious,
 we have permitted argument(s) to be infinity,
 provided infinity is implemented for the realType on that implementation.
 
+Users who require special handling of infinity (or other specific value) can, 
+of course, always intercept this before calling a distribution or function
+and return their own choice of value, or other behavior.
+This will often be simpler than trying to handle the aftermath of the error policy.
+
 Overflow, underflow, denorm can be handled using __error_policy.
 
 We have also tried to catch boundary cases where the mathematical specification
@@ -445,6 +450,14 @@ and a command such as:
 
 [pre java -jar 'C:\download\open\batik-1.7\batik-rasterizer.jar' -dpi 120 *.svg]
 
+Or using Inkscape and a command such as:
+
+[pre for file in *.svg; do 
+  /cygdrive/c/progra~1/Inkscape/inkscape -d 120 -e $(cygpath -a -w $(basename $file .svg).png) $(cygpath -a -w $file); 
+done]
+
+Currently Inkscape seems to generate the better looking png's.
+
 The PDF is generated into \pdf\math.pdf
 using a command from a shell or command window with current directory
 \math_toolkit\libs\math\doc\sf_and_dist, typically:
diff --git a/doc/sf_and_dist/inv_hyper.qbk b/doc/sf_and_dist/inv_hyper.qbk
index d353bb06a..05fc23a28 100644
--- a/doc/sf_and_dist/inv_hyper.qbk
+++ b/doc/sf_and_dist/inv_hyper.qbk
@@ -96,6 +96,8 @@ the return type is `double` when T is an integer type, and T otherwise.
 
 [optional_policy]
 
+[graph acosh]
+
 [endsect]
 
 [section:asinh asinh]
@@ -119,6 +121,8 @@ infinity to ensure accuracy.
 The return type of this function is computed using the __arg_pomotion_rules:
 the return type is `double` when T is an integer type, and T otherwise.
 
+[graph asinh]
+
 [optional_policy]
 
 [endsect]
@@ -164,6 +168,8 @@ numeric_limits::epsilon().
 The return type of this function is computed using the __arg_pomotion_rules:
 the return type is `double` when T is an integer type, and T otherwise.
 
+[graph atanh]
+
 [endsect]
 
 [endsect]
diff --git a/doc/sf_and_dist/issues.qbk b/doc/sf_and_dist/issues.qbk
index 5ff84c47f..1d7201ae0 100644
--- a/doc/sf_and_dist/issues.qbk
+++ b/doc/sf_and_dist/issues.qbk
@@ -80,6 +80,55 @@ for very high precision types (Low Priority).
 
 * Student's t Perhaps switch to normal distribution as a better approximation for very large degrees of freedom?
 
+[h4 Feature Requests]
+
+The following table lists distributions that are found in other packages
+but which are not yet present here, the more frequently the distribution
+is found, the higher the priority for implementing it:
+
+[table
+[[Distribution][R][Mathematica 6][NIST][Regress+][Matlab]]
+[[Non-central Chi Squared][X][X][-][-][X]]
+[[Non-central F][X][X][-][-][X]]
+[[Non-central T][X][X][-][-][X]]
+[[Logistic][X][X][-][X][X]]
+[[Log Logistic][-][-][-][-][X]]
+[[Hypergeometric][X][X][-][X][X]]
+[[Geometric][X][-][-][-][X]]
+[[Multinomial][X][-][-][-][X]]
+[[Tukey (Studentized range)][X][-][-][-][-]]
+[[Tukey Lambda][X][-][X][-][-]]
+[[Wilcoxon rank sum][X][-][-][-][-]]
+[[Wincoxon signed rank][X][-][-][-][-]]
+[[Non-central Beta][X][-][-][-][-]]
+[[Half Normal / Folded Normal][-][X][-][X][-]]
+[[Inverse Gausian / Inverse Normal][-][X][-][X][X]]
+[[Laplace][-][X][-][-][-]]
+[[Maxwell][-][X][-][-][-]]
+[[Chi][-][X][-][X][-]]
+[[Gumbel][-][X][-][X][-]]
+[[Geometric][-][X][-][-][-]]
+[[Beta-Binomial][-][X][-][-][-]]
+[[Beta-negative Binomial][-][X][-][-][-]]
+[[Discrete Uniform][-][X][-][-][X]]
+[[Zipf][-][X][-][-][-]]
+[[Log Series][-][X][-][X][-]]
+[[Birnbaum-Saunders / Fatigue Life][-][-][X][-][-]]
+[[Double Exponential][-][-][X][-][-]]
+[[Power Normal][-][-][X][-][-]]
+[[Power Lognormal][-][-][X][-][-]]
+[[Cosine][-][-][-][X][-]]
+[[Double Gamma][-][-][-][X][-]]
+[[Double Weibul][-][-][-][X][-]]
+[[Hyperbolic Secant][-][-][-][X][-]]
+[[Laplace][-][-][-][X][-]]
+[[Semicircular][-][-][-][X][-]]
+[[Bradford][-][-][-][X][-]]
+[[Birr / Fisk][-][-][-][X][-]]
+[[Nakagami (generalised Chi)][-][-][-][X][X]]
+[[Reciprocal][-][-][-][X][-]]
+]
+
 [endsect][/section:issues Known Issues, and Todo List]
 
 [/ 
diff --git a/doc/sf_and_dist/laguerre.qbk b/doc/sf_and_dist/laguerre.qbk
index 6afc4af88..cbf52a357 100644
--- a/doc/sf_and_dist/laguerre.qbk
+++ b/doc/sf_and_dist/laguerre.qbk
@@ -50,7 +50,7 @@ Returns the value of the Laguerre Polynomial of order /n/ at point /x/:
 The following graph illustrates the behaviour of the first few 
 Laguerre Polynomials:
 
-[$../graphs/laguerre.png]
+[graph laguerre]
    
    template 
    ``__sf_result`` laguerre(unsigned n, unsigned m, T x);
diff --git a/doc/sf_and_dist/legendre.qbk b/doc/sf_and_dist/legendre.qbk
index c7935689f..b88594324 100644
--- a/doc/sf_and_dist/legendre.qbk
+++ b/doc/sf_and_dist/legendre.qbk
@@ -62,7 +62,7 @@ P[sub -l-1](x) = P[sub l](x)
 The following graph illustrates the behaviour of the first few 
 Legendre Polynomials:
 
-[$../graphs/legendre_p1.png]
+[graph legendre_p]
    
    template 
    ``__sf_result`` legendre_p(int l, int m, T x);
@@ -119,7 +119,7 @@ Requires -1 <= x <= 1, otherwise __domain_error is called.
 The following graph illustrates the first few Legendre functions of the
 second kind:
 
-[$../graphs/legendre_q.png]
+[graph legendre_q]
    
    template 
    ``__sf_result`` legendre_next(unsigned l, T1 x, T2 Pl, T3 Plm1);
diff --git a/doc/sf_and_dist/lgamma.qbk b/doc/sf_and_dist/lgamma.qbk
index b961d50b0..f373840c2 100644
--- a/doc/sf_and_dist/lgamma.qbk
+++ b/doc/sf_and_dist/lgamma.qbk
@@ -33,7 +33,7 @@ which if non-null is set on output to the sign of tgamma(z).
 
 [optional_policy]
 
-[$../graphs/lgamma.png]
+[graph lgamma]
 
 There are effectively two versions of this function internally: a fully
 generic version that is slow, but reasonably accurate, and a much more
diff --git a/doc/sf_and_dist/math.qbk b/doc/sf_and_dist/math.qbk
index afaa99421..b57eab2e2 100644
--- a/doc/sf_and_dist/math.qbk
+++ b/doc/sf_and_dist/math.qbk
@@ -1,13 +1,13 @@
 [article Math Toolkit
     [quickbook 1.4]
-    [copyright 2006-2007 John Maddock, Paul A. Bristow, Hubert Holin and Xiaogang Zhang]
+    [copyright 2006, 2007, 2008 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang and Bruno Lalande]
     [purpose ISBN 0-9504833-2-X  978-0-9504833-2-0, Classification 519.2-dc22]
     [license
         Distributed under the Boost Software License, Version 1.0.
         (See accompanying file LICENSE_1_0.txt or copy at
         [@http://www.boost.org/LICENSE_1_0.txt])
     ]
-    [authors [Maddock, John], [Bristow, Paul A.], [Holin, Hubert], [Zhang, Xiaogang]]
+    [authors [Maddock, John], [Bristow, Paul A.], [Holin, Hubert], [Zhang, Xiaogang], [Lalande, Bruno]]
     [category math]
     [purpose mathematics]
     [/last-revision $Date$]
@@ -22,9 +22,18 @@
 
 ''']
 
+[template graph[name]  '''
+
+
+
+
+
+
+''']
+
 [include html4_symbols.qbk] [/ just for testing]
 [/include latin1_symbols.qbk] [/ just for testing]
-[include common_overviews.qbk][/ overviews that appear in more than one place!]
+[include common_overviews.qbk] [/ overviews that appear in more than one place!]
 [include roadmap.qbk] [/ for history]
 
 [def __effects [*Effects: ]]
@@ -65,6 +74,7 @@
 [def __underflow_error [link underflow_error underflow_error]]
 [def __denorm_error [link denorm_error denorm_error]]
 [def __evaluation_error [link evaluation_error evaluation_error]]
+[def __rounding_error [link rounding_error rounding_error]]
 [def __checked_narrowing_cast [link checked_narrowing_cast checked_narrowing_cast]]
 
 [def __arg_pomotion_rules [link math_toolkit.main_overview.result_type ['result type calculation rules]]]
@@ -162,6 +172,22 @@ and use the function's name as the link text]
 [def __sqrt1pm1 [link math_toolkit.special.powers.sqrt1pm1 sqrt1pm1]]
 [def __powm1 [link math_toolkit.special.powers.powm1 powm1]]
 [def __hypot [link math_toolkit.special.powers.hypot hypot]]
+[def __pow [link math_toolkit.special.powers.ct_pow pow]]
+
+[/zeta]
+[def __zeta [link math_toolkit.special.zetas.zeta zeta]]
+
+[/expint]
+[def __expint_i [link math_toolkit.special.expint.expint_i zeta]]
+[def __expint_n [link math_toolkit.special.expint.expint_n zeta]]
+
+[/rounding]
+[def __round [link math_toolkit.special.rounding.round round]]
+[def __trunc [link math_toolkit.special.rounding.trunc trunc]]
+[def __modf [link math_toolkit.special.rounding.modf modf]]
+
+
+
 
 [/ distribution non-members]
 [def __cdf [link math.dist.cdf Cumulative Distribution Function]]
@@ -187,11 +213,15 @@ and use the function's name as the link text]
 [def __binomial_distrib [link math_toolkit.dist.dist_ref.dists.binomial_dist Binomial Distribution]]
 [def __cauchy_distrib [link math_toolkit.dist.dist_ref.dists.cauchy_dist Cauchy Distribution]]
 [def __chi_squared_distrib [link math_toolkit.dist.dist_ref.dists.chi_squared_dist Chi Squared Distribution]]
+[def __extreme_distrib [link math_toolkit.dist.dist_ref.dists.extreme_dist Extreme Distributions]]
 [def __exp_distrib [link math_toolkit.dist.dist_ref.dists.exp_dist Exponential Distribution]]
 [def __F_distrib [link math_toolkit.dist.dist_ref.dists.f_dist Fisher F Distribution]]
 [def __gamma_distrib [link math_toolkit.dist.dist_ref.dists.gamma_dist Gamma Distribution]]
 [def __lognormal_distrib [link math_toolkit.dist.dist_ref.dists.lognormal_dist Log-normal Distribution]]
 [def __negative_binomial_distrib [link math_toolkit.dist.dist_ref.dists.negative_binomial_dist Negative Binomial Distribution]]
+[def __non_central_chi_squared_distrib [link math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist Non Central Chi Squared]]
+[def __non_central_beta_distrib [link math_toolkit.dist.dist_ref.dists.nc_beta_dist noncentral beta distribution]]
+[def __non_central_F_distrib [link math_toolkit.dist.dist_ref.dists.nc_f_dist noncentral F distribution]]
 [def __normal_distrib [link math_toolkit.dist.dist_ref.dists.normal_dist Normal Distribution]]
 [def __poisson_distrib [link math_toolkit.dist.dist_ref.dists.poisson_dist Poisson Distribution]]
 [def __students_t_distrib [link math_toolkit.dist.dist_ref.dists.students_t_dist Students t Distribution]]
@@ -347,9 +377,16 @@ printer friendly PDF format].
 [include ellint_legendre.qbk]
 [endsect] [/section:ellint Elliptic Integrals]
 
+[section:zetas Zeta Functions]
+[include zeta.qbk]
+[endsect]
+
+[include expint.qbk]
+
 [include powers.qbk]
 [include sinc.qbk]
 [include inv_hyper.qbk]
+[include rounding_func.qbk]
 [include fpclassify.qbk]
 [endsect] [/section:special Special Functions]
 
@@ -375,7 +412,7 @@ printer friendly PDF format].
 
 [endsect] [/section:toolkit Toolkit]
 
-[section:using_udt Use with User Defined Floating-Point Types]
+[section:using_udt Use with User-Defined Floating-Point Types]
 [include concepts.qbk]
 [endsect] [/section:using_udt Use with User Defined Floating-Point Types]
 
@@ -406,7 +443,7 @@ printer friendly PDF format].
 [endsect] [/section:status Status and Roadmap] 
 
 [/ math.qbk
-  Copyright 2006 John Maddock and Paul A. Bristow.
+  Copyright 2008 John Maddock and Paul A. Bristow.
   Distributed under the Boost Software License, Version 1.0.
   (See accompanying file LICENSE_1_0.txt or copy at
   http://www.boost.org/LICENSE_1_0.txt).
diff --git a/doc/sf_and_dist/minimax.qbk b/doc/sf_and_dist/minimax.qbk
index 59b9a078d..4349210f5 100644
--- a/doc/sf_and_dist/minimax.qbk
+++ b/doc/sf_and_dist/minimax.qbk
@@ -94,12 +94,20 @@ Command line options for the program are as follows:
             try a higher value if an approximation won't converge,
             or a lower value to get speedier convergence.]]
 [[x-offset val][Sets the x-offset to /val/: the approximation will
-            be generated for `f(x + X) + Y` where /X/ is the x-offset
+            be generated for `f(S * (x + X)) + Y` where /X/ is the 
+            x-offset, /S/ is the x-scale
             and /Y/ is the y-offset.  Defaults to zero.  To avoid
             rounding errors, take care to specify a value that can
             be exactly represented as a floating point number.]]
+[[x-scale val][Sets the x-scale to /val/: the approximation will
+            be generated for `f(S * (x + X)) + Y` where /S/ is the 
+            x-scale, /X/ is the x-offset
+            and /Y/ is the y-offset.  Defaults to one.  To avoid
+            rounding errors, take care to specify a value that can
+            be exactly represented as a floating point number.]]
 [[y-offset val][Sets the y-offset to /val/: the approximation will
-            be generated for `f(x + X) + Y` where /X/ is the x-offset
+            be generated for `f(S * (x + X)) + Y` where /X/ 
+            is the x-offset, /S/ is the x-scale
             and /Y/ is the y-offset.  Defaults to zero.  To avoid
             rounding errors, take care to specify a value that can
             be exactly represented as a floating point number.]]
diff --git a/doc/sf_and_dist/policy.qbk b/doc/sf_and_dist/policy.qbk
index 88b9f5d52..17df239e7 100644
--- a/doc/sf_and_dist/policy.qbk
+++ b/doc/sf_and_dist/policy.qbk
@@ -99,6 +99,9 @@ must be provided by the user:
    template 
    T user_denorm_error(const char* function, const char* message, const T& val);
    
+   template 
+   T user_rounding_error(const char* function, const char* message, const T& val);
+   
    template 
    T user_evaluation_error(const char* function, const char* message, const T& val);
    
@@ -168,6 +171,15 @@ which are summarised in the following table:
       Defaults to `boost::math::policies::denorm_error`
 
       When the action is ['throw_on_error] then throws a `std::underflow_error`]]
+[[Rounding Error]
+   [boost::math::policies::rounding_error<['action]>]
+      [Raised When one of the rounding functions __round, __trunc or __modf is
+      called with an argument that has no integer representation, or
+      is too large to be represented in the result type
+
+      Defaults to `boost::math::policies::rounding_error`
+
+      When the action is ['throw_on_error] then throws `boost::math::rounding_error`]]
 [[Evaluation Error]
    [boost::math::policies::evaluation_error<['action]>]
       [Raised when the result of the function is well defined and
@@ -497,6 +509,13 @@ defaults to `throw_on_error`, but can be set to any of the enumerated
 actions for error handing: `throw_on_error`, `errno_on_error`, 
 `ignore_error` or `user_error`.
 
+[h5 BOOST_MATH_ROUNDING_ERROR_POLICY]
+
+Defines what happens when a rounding error occurs, if not defined then
+defaults to `throw_on_error`, but can be set to any of the enumerated
+actions for error handing: `throw_on_error`, `errno_on_error`, 
+`ignore_error` or `user_error`.
+
 [h5 BOOST_MATH_EVALUATION_ERROR_POLICY]
 
 Defines what happens when an internal evaluation error occurs, if not defined then
@@ -674,6 +693,7 @@ compile-time container for a collection of policies:
       typedef ``['computed-from-template-arguments]`` overflow_error_type;
       typedef ``['computed-from-template-arguments]`` underflow_error_type;
       typedef ``['computed-from-template-arguments]`` denorm_error_type;
+      typedef ``['computed-from-template-arguments]`` rounding_error_type;
       typedef ``['computed-from-template-arguments]`` evaluation_error_type;
       typedef ``['computed-from-template-arguments]`` precision_type;
       typedef ``['computed-from-template-arguments]`` promote_float_type;
@@ -735,6 +755,12 @@ Specifies how denorm errors are handled, will be an instance of
 `boost::math::policies::denorm_error<>` with the template argument to
 `denorm_error` one of the `error_policy_type` enumerated values.
 
+   policy<...>::rounding_error_type
+   
+Specifies how rounding errors are handled, will be an instance of
+`boost::math::policies::rounding_error<>` with the template argument to
+`rounding_error` one of the `error_policy_type` enumerated values.
+
    policy<...>::evaluation_error_type
    
 Specifies how evaluation errors are handled, will be an instance of
diff --git a/doc/sf_and_dist/policy_tutorial.qbk b/doc/sf_and_dist/policy_tutorial.qbk
index e0b4668a5..1fc7d1757 100644
--- a/doc/sf_and_dist/policy_tutorial.qbk
+++ b/doc/sf_and_dist/policy_tutorial.qbk
@@ -44,6 +44,7 @@ stop reading now!
 [[Overflow Error][Throws a `std::overflow_error` exception.]]
 [[Underflow][Ignores the underflow, and returns zero.]]
 [[Denormalised Result][Ignores the fact that the result is denormalised, and returns it.]]
+[[Rounding Error][Throws a `boost::math::rounding_error` exception.]]
 [[Internal Evaluation Error][Throws a `boost::math::evaluation_error` exception.]]
 [[Promotion of float to double][Does occur by default - gives full float precision results.]]
 [[Promotion of double to long double][Does occur by default if long double offers
diff --git a/doc/sf_and_dist/pow.qbk b/doc/sf_and_dist/pow.qbk
new file mode 100644
index 000000000..6f9b91314
--- /dev/null
+++ b/doc/sf_and_dist/pow.qbk
@@ -0,0 +1,144 @@
+[section:ct_pow Compile Time Power of a Runtime Base]
+
+The `pow` function effectively computes the compile-time integral 
+power of a run-time base.
+
+[h4 Synopsis]
+
+[@../../../../../boost/math/special_functions/pow.hpp `#include `]
+
+    namespace boost { namespace math {
+
+    template 
+    ``__sf_result`` pow(T base);
+
+    template 
+    ``__sf_result`` pow(T base, const Policy& policy);
+
+    }}
+
+[h4 Rationale and Usage]
+
+Computing the power of a number with an exponent that is known 
+at compile time is a common need for programmers. In such cases, 
+the usual method is to avoid the overhead implied by
+the `pow`, `powf` and `powl` C functions by hardcoding an expression
+such as:
+
+    // Hand-written 8th power of a 'base' variable
+    double result = base*base*base*base*base*base*base*base;
+
+However, this kind of expression is not really readable (knowing the 
+value of the exponent involves counting the number of occurrences of /base/), 
+error-prone (it's easy to forget an occurrence), syntactically bulky, and 
+non-optimal in terms of performance.
+
+The pow function of Boost.Math helps writing this kind expression along 
+with solving all the problems listed above:
+
+    // 8th power of a 'base' variable using math::pow
+    double result = pow<8>(base);
+
+The expression is now shorter, easier to read, safer, and even faster. 
+Indeed, `pow` will compute the expression such that only log2(N) 
+products are made for a power of N. For instance in the
+example above, the resulting expression will be the same as if we had 
+written this, with only one computation of each identical subexpression:
+
+    // Internal effect of pow<8>(base)
+    double result = ((base*base)*(base*base))*((base*base)*(base*base));
+
+Only 3 different products were actually computed.
+
+
+[h4 Return Type]
+
+The return type of these functions is computed using the __arg_pomotion_rules
+when T1 and T2 are different types.  For example:
+
+* If T is a `float`, the return type is a `float`.
+* If T is a `long double`, the return type is a `long double`.
+* Otherwise, the return type is a `double`.
+
+[h4 Policies]
+
+[optional_policy]
+
+[h4 Error Handling]
+
+In the case where `pow` is called with a null base and a negative exponent, 
+an error occurs since this operation is a division by 0 (it equals to 1/0). 
+The error raised is an __overflow_error following the 
+[@sf_and_dist/html/math_toolkit/main_overview/error_handling.html 
+general policies of error handling in Boost.Math].
+
+The default overflow error policy is `throw_on_error`. A call like `pow<-2>(0)` 
+will thus throw a `std::overflow_error` exception. As shown in the 
+link given above, other error handling policies can be used:
+
+* `errno_on_error`: Sets `::errno`  to `ERANGE` and returns `std::numeric_limits::infinity()`.
+* `ignore_error`: Returns `std::numeric_limits::infinity()`.
+* `user_error`: Returns the result of `boost::math::policies::user_overflow_error`: 
+   this function must be defined by the user.
+
+Here is an example of error handling customization where we want to 
+specify the result that has to be returned in case of error. We will 
+thus use the `user_error` policy, by passing as second argument an 
+instance of an overflow_error policy templated with `user_error`:
+
+    // First we open the boost::math::policies namespace and define the `user_overflow_error`
+    // by making it return the value we want in case of error (-1 here)
+
+    namespace boost { namespace math { namespace policies {
+    template 
+    T user_overflow_error(const char*, const char*, const T&)
+    { return -1; }
+    }}}
+
+
+    // Then we invoke pow and indicate that we want to use the user_error policy
+    using boost::math::policies;
+    double result = pow<-5>(base, policy >());
+
+    // We can now test the returned value and treat the special case if needed:
+    if (result == -1)
+    {
+        // there was an error, do something...
+    }
+
+Another way is to redefine the default `overflow_error` policy by using the
+BOOST_MATH_OVERFLOW_ERROR_POLICY macro. Once the `user_overflow_error` function 
+is defined as above, we can achieve the same result like this:
+
+    // Redefine the default error_overflow policy
+    #define BOOST_MATH_OVERFLOW_ERROR_POLICY user_error
+    #include 
+
+    // From this point, passing a policy in argument is no longer needed, a call like this one
+    // will return -1 in case of error:
+
+    double result = pow<-5>(base);
+
+
+[h4 Acknowledgements]
+
+Bruno Lalande submitted this addition to Boost.Math.
+
+'''
+Thanks to Joaquín López Muñoz and Scott McMurray for their help in
+improving the implementation.
+'''
+
+[h4 References]
+
+D.E. Knuth, ['The Art of Computer Programming, Vol. 2: Seminumerical Algorithms], 2nd ed., Addison-Wesley, Reading, MA, 1981
+
+[endsect]
+
+[/ 
+  Copyright 2008 Bruno Lalande.
+  Distributed under the Boost Software License, Version 1.0.
+  (See accompanying file LICENSE_1_0.txt or copy at
+  http://www.boost.org/LICENSE_1_0.txt).
+]
+
diff --git a/doc/sf_and_dist/powers.qbk b/doc/sf_and_dist/powers.qbk
index ea6cf7854..29e2fe8f8 100644
--- a/doc/sf_and_dist/powers.qbk
+++ b/doc/sf_and_dist/powers.qbk
@@ -44,6 +44,10 @@ Finally when BOOST_HAS_LOG1P is defined then the `float/double/long double`
 specializations of this template simply forward to the platform's 
 native (POSIX) implementation of this function.
 
+The following graph illustrates the behaviour of log1p:
+
+[graph log1p]
+
 [h4 Accuracy]
 
 For built in floating point types `log1p`
@@ -87,6 +91,10 @@ a series expansion when x is small (giving an accuracy of less than __te).
 Finally when BOOST_HAS_EXPM1 is defined then the `float/double/long double` 
 specializations of this template simply forward to the platform's 
 native (POSIX) implementation of this function.
+
+The following graph illustrates the behaviour of expm1:
+
+[graph expm1]
    
 [h4 Accuracy]
 
@@ -124,6 +132,10 @@ the return is `double` when /x/ is an integer type and T otherwise.
 [optional_policy]
 
 Implemented using Halley iteration.
+
+The following graph illustrates the behaviour of cbrt:
+
+[graph cbrt]
    
 [h4 Accuracy]
 
@@ -165,6 +177,10 @@ x is itself close to 1.
 
 Implemented in terms of `log1p` and `expm1`.
 
+The following graph illustrates the behaviour of sqrt1pm1:
+
+[graph sqrt1pm1]
+
 [h4 Accuracy]
 
 For built in floating-point types `sqrt1pm1`
@@ -205,6 +221,10 @@ x is close to 1.
 
 Implemented in terms of `expm1`.
 
+The following graph illustrates the behaviour of powm1:
+
+[graph powm1]
+
 [h4 Accuracy]
 
 Should have approximately 2-3 epsilon accuracy.
@@ -248,6 +268,8 @@ Otherwise the result is given by:
 
 [endsect]
 
+[include pow.qbk]
+
 
 [endsect][/section:powers Logs, Powers, Roots and Exponentials]
 
diff --git a/doc/sf_and_dist/references.qbk b/doc/sf_and_dist/references.qbk
index 7e7fb4d96..dccd93e84 100644
--- a/doc/sf_and_dist/references.qbk
+++ b/doc/sf_and_dist/references.qbk
@@ -31,8 +31,12 @@ The Wolfram Research Documentation Center is a collection of online reference ma
 Statistical Distributions (Wiley Series in Probability & Statistics) (Paperback)
 by N.A.J. Hastings, Brian Peacock, Merran Evans, ISBN: 0471371246, Wiley 2000.
 
+[@http://www.worldscibooks.com/mathematics/p191.html EXTREME VALUE DISTRIBUTIONS, Theory and Applications]
+Samuel Kotz & Saralees Nadarajah, ISBN 978-1-86094-224-2 & 1-86094-224-5 Oct 2000,
+Chapter 1.2 discusses the various extreme value distributions.
+
 [@http://bh0.physics.ubc.ca/People/matt/Doc/ThesesOthers/Phd/pugh.pdf pugh.pdf (application/pdf Object)]
-Pugh Msc Thesis on the Lanczzos approximation to the gamma function.
+Pugh Msc Thesis on the Lanczos approximation to the gamma function.
 
 [@http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2003 N1514, 03-0097, A Proposal to Add Mathematical Special Functions to the C++ Standard Library (version 2), Walter E. Brown]
 
diff --git a/doc/sf_and_dist/rounding_func.qbk b/doc/sf_and_dist/rounding_func.qbk
new file mode 100644
index 000000000..13cc1fb2a
--- /dev/null
+++ b/doc/sf_and_dist/rounding_func.qbk
@@ -0,0 +1,128 @@
+
+[section:rounding Rounding Truncation and Integer Conversion]
+
+[section:round Rounding Functions]
+
+``#include ``
+
+   template 
+   T round(const T& v);
+   
+   template 
+   T round(const T& v, const Policy&);
+   
+   template 
+   int iround(const T& v);
+
+   template 
+   int iround(const T& v, const Policy&);
+
+   template 
+   long lround(const T& v);
+
+   template 
+   long lround(const T& v, const Policy&);
+
+   template 
+   long long llround(const T& v);
+
+   template 
+   long long llround(const T& v, const Policy&);
+
+These functions return the closest integer to the argument /v/.
+
+Halfway cases are rounded away from zero, regardless of the current rounding
+direction.
+
+If the argument /v/ is either non-finite or else outside the range
+of the result type, then returns the result of __rounding_error: by
+default this throws an instance of boost::math::rounding_error.
+
+[endsect]
+
+[section:trunc Truncation Functions]
+
+``#include ``
+
+   template 
+   T trunc(const T& v);
+
+   template 
+   T trunc(const T& v, const Policy&);
+
+   template 
+   int itrunc(const T& v);
+
+   template 
+   int itrunc(const T& v, const Policy&);
+
+   template 
+   long ltrunc(const T& v);
+
+   template 
+   long ltrunc(const T& v, const Policy&);
+
+   template 
+   long long lltrunc(const T& v);
+
+   template 
+   long long lltrunc(const T& v, const Policy&);
+
+The trunc functions round their argument to the integer value,
+nearest to but no larger in magnitude than the argument.
+
+For example `itrunc(3.7)` would return `3` and `ltrunc(-4.6)` 
+would return `-4`.
+
+If the argument /v/ is either non-finite or else outside the range
+of the result type, then returns the result of __rounding_error: by
+default this throws an instance of boost::math::rounding_error.
+
+[endsect]
+
+[section:modf Integer and Fractional Part Splitting (modf)]
+
+``#include ``
+
+   template 
+   T modf(const T& v, T* ipart);
+
+   template 
+   T modf(const T& v, T* ipart, const Policy&);
+
+   template 
+   T modf(const T& v, int* ipart);
+
+   template 
+   T modf(const T& v, int* ipart, const Policy&);
+
+   template 
+   T modf(const T& v, long* ipart);
+
+   template 
+   T modf(const T& v, long* ipart, const Policy&);
+
+   template 
+   T modf(const T& v, long long* ipart);
+
+   template 
+   T modf(const T& v, long long* ipart, const Policy&);
+
+The `modf` functions store the integer part of /v/ in `*ipart` 
+and return the fractional part of /v/.
+
+If the argument /v/ is either non-finite or else outside the range
+of the result type, then returns the result of __rounding_error: by
+default this throws an instance of boost::math::rounding_error.
+
+[endsect]
+
+
+[endsect] [/section:rounding Rounding Truncation and Integer Conversion]
+
+[/ 
+  Copyright 2006 John Maddock and Paul A. Bristow.
+  Distributed under the Boost Software License, Version 1.0.
+  (See accompanying file LICENSE_1_0.txt or copy at
+  http://www.boost.org/LICENSE_1_0.txt).
+]
diff --git a/doc/sf_and_dist/sinc.qbk b/doc/sf_and_dist/sinc.qbk
index 3d7cfbf16..3c9e12e8e 100644
--- a/doc/sf_and_dist/sinc.qbk
+++ b/doc/sf_and_dist/sinc.qbk
@@ -12,14 +12,17 @@
 The [@http://mathworld.wolfram.com/SincFunction.html Sinus Cardinal family of functions]
 (indexed by the family of indices [^a > 0]) 
 is defined by 
-[equation special_functions_blurb20]; 
+
+[equation special_functions_blurb20]
+
 it sees heavy use in signal processing tasks.
 
 By analogy, the 
 [@http://mathworld.wolfram.com/SinhcFunction.htm Hyperbolic Sinus Cardinal]
 family of functions 
 (also indexed by the family of indices [^a > 0]) is defined by 
-[equation special_functions_blurb22].
+
+[equation special_functions_blurb22]
 
 These two families of functions are composed of entire functions.
 
@@ -61,6 +64,8 @@ The second form is for complex numbers,
 quaternions, octonions etc. Taylor series are used at the origin 
 to ensure accuracy.
 
+[graph sinc_pi]
+
 [optional_policy]
 
 [endsect]
@@ -98,6 +103,8 @@ when T is an integer type.
 
 [optional_policy]
 
+[graph sinhc_pi]
+
 [endsect]
 
 [endsect]
diff --git a/doc/sf_and_dist/test_data.qbk b/doc/sf_and_dist/test_data.qbk
index dcc0480fd..70879473a 100644
--- a/doc/sf_and_dist/test_data.qbk
+++ b/doc/sf_and_dist/test_data.qbk
@@ -149,7 +149,7 @@ one could do this like so:
    
 Which, when plotted, results in:
 
-[$../graphs/lgamma.png]
+[graph lgamma]
 
 [h5 Example 2: Creating Test Data]
 
diff --git a/doc/sf_and_dist/tgamma.qbk b/doc/sf_and_dist/tgamma.qbk
index a660eaf0a..3e5660683 100644
--- a/doc/sf_and_dist/tgamma.qbk
+++ b/doc/sf_and_dist/tgamma.qbk
@@ -34,7 +34,7 @@ Returns the "true gamma" (hence name tgamma) of value z:
 
 [equation gamm1]
 
-[$../graphs/gamma.png]
+[graph tgamma]
 
 [optional_policy]
 
diff --git a/doc/sf_and_dist/zeta.qbk b/doc/sf_and_dist/zeta.qbk
new file mode 100644
index 000000000..aeef3fa5c
--- /dev/null
+++ b/doc/sf_and_dist/zeta.qbk
@@ -0,0 +1,133 @@
+[section:zeta Riemann Zeta Function]
+
+[h4 Synopsis]
+
+``
+#include 
+``
+
+   namespace boost{ namespace math{
+   
+   template 
+   ``__sf_result`` zeta(T z);
+   
+   template 
+   ``__sf_result`` zeta(T z, const ``__Policy``&);
+   
+   }} // namespaces
+   
+The return type of these functions is computed using the __arg_pomotion_rules:
+the return type is `double` if T is an integer type, and T otherwise.
+
+[optional_policy]
+
+[h4 Description]
+
+   template 
+   ``__sf_result`` zeta(T z);
+   
+   template 
+   ``__sf_result`` zeta(T z, const ``__Policy``&);
+   
+Returns the [@http://mathworld.wolfram.com/RiemannZetaFunction.html zeta function]
+of z:
+
+[equation zeta1]
+
+[graph zeta1]
+
+[graph zeta2]
+
+[h4 Accuracy]
+
+The following table shows the peak errors (in units of epsilon) 
+found on various platforms with various floating point types, 
+along with comparisons to the __gsl and __cephes libraries.
+Unless otherwise specified any floating point type that is narrower
+than the one shown will have __zero_error.
+
+[table Errors In the Function zeta(z)
+[[Significand Size] [Platform and Compiler] [z > 0][z < 0]]
+[[53] [Win32, Visual C++ 8] [Peak=0.99 Mean=0.1
+
+GSL Peak=8.7 Mean=1.0 
+
+__cephes Peak=2.1 Mean=1.1
+]  [Peak=7.1 Mean=3.0 
+
+GSL Peak=137 Mean=14 
+
+__cephes Peak=5084 Mean=470
+]]
+[[64] [RedHat Linux IA_EM64, gcc-4.1] [Peak=0.99 Mean=0.5]  [Peak=570 Mean=60]]
+[[64] [Redhat Linux IA64, gcc-4.1] [Peak=0.99 Mean=0.5]  [Peak=559 Mean=56]]
+[[113] [HPUX IA64, aCC A.06.06] [Peak=1.0 Mean=0.4]  [Peak=1018 Mean=79]]
+]
+
+[h4 Testing]
+
+The tests for these functions come in two parts:
+basic sanity checks use spot values calculated using
+[@http://functions.wolfram.com/webMathematica/FunctionEvaluation.jsp?name=Zeta Mathworld's online evaluator],
+while accuracy checks use high-precision test values calculated at 1000-bit precision with
+[@http://shoup.net/ntl/doc/RR.txt NTL::RR] and this implementation. 
+Note that the generic and type-specific
+versions of these functions use differing implementations internally, so this
+gives us reasonably independent test data.  Using our test data to test other
+"known good" implementations also provides an additional sanity check. 
+
+[h4 Implementation]
+
+All versions of these functions first use the usual reflection formulas
+to make their arguments positive:
+
+[equation zeta3]
+
+The generic versions of these functions are implemented using the series:
+
+[equation zeta1]
+
+for large z, and using the globally convergent series:
+
+[equation zeta2]
+
+In all other cases.  The crossover point for these is chosen so that the first
+series is used only if it will converge reasonably quickly, the problem with this
+series is that convergence become slower the more terms you take, so we really do
+have to be certain of convergence before using this series, even though the 
+alternative is often quite slow.
+
+When the significand (mantissa) size is recognised
+(currently for 53, 64 and 113-bit reals, plus single-precision 24-bit handled via promotion to double)
+then a series of rational approximations [jm_rationals] are used.
+
+For 0 < z < 1 the approximating form is:
+
+[equation zeta4]
+
+For a rational approximation R(1-z) and a constant C.
+
+For 1 < z < 4 the approximating form is:
+
+[equation zeta5]
+
+For a rational approximation R(n-z) and a constant C and integer n.
+
+For z > 4 the approximating form is:
+
+[zeta](z) = 1 + e[super R(z - n)]
+
+For a rational approximation R(z-n) and integer n, note that the accuracy 
+required for R(z-n) is not full machine precision, but an absolute error
+of: [epsilon]/R(0).  This saves us quite a few digits when dealing with large 
+z, especially when [epsilon] is small.
+
+[endsect]
+[/ :error_function The Error Functions]
+
+[/ 
+  Copyright 2006 John Maddock and Paul A. Bristow.
+  Distributed under the Boost Software License, Version 1.0.
+  (See accompanying file LICENSE_1_0.txt or copy at
+  http://www.boost.org/LICENSE_1_0.txt).
+]
diff --git a/example/nc_chi_sq_example.cpp b/example/nc_chi_sq_example.cpp
new file mode 100644
index 000000000..73e5b95c5
--- /dev/null
+++ b/example/nc_chi_sq_example.cpp
@@ -0,0 +1,109 @@
+// Copyright John Maddock 2008
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+// Caution: this file contains Quickbook markup as well as code
+// and comments, don't change any of the special comment markups!
+
+//[nccs_eg
+
+/*`
+
+This example computes a table of the power of the [chi][super 2]
+test at the 5% significance level, for various degrees of freedom
+and non-centrality parameters.  The table is deliberately the same
+as Table 6 from "The Non-Central [chi][super 2] and F-Distributions and
+their applications.", P. B. Patnaik, Biometrika, Vol. 36, No. 1/2 (June 1949),
+202-232.
+
+First we need some includes to access the non-central chi squared distribution
+(and some basic std output of course).
+
+*/
+
+#include 
+#include 
+
+int main()
+{
+   /*`
+   Create a table of the power of the [chi][super 2] test at
+   5% significance level, start with a table header:
+   */
+   std::cout << "[table\n[[[nu]]";
+   for(int lam = 2; lam <= 20; lam += 2)
+   {
+      std::cout << "[[lambda]=" << lam << "]";
+   }
+   std::cout << "]\n";
+
+   /*`
+   (Note: the enclosing [] brackets are to format as a table in Boost.Quickbook).
+
+   Enumerate the rows and columns and print the power of the test
+   for each table cell:
+   */
+
+   for(int n = 2; n <= 20; ++n)
+   {
+      std::cout << "[[" << n << "]";
+      for(int lam = 2; lam <= 20; lam += 2)
+      {
+         /*`
+         Calculate the [chi][super 2] statistic for a 5% significance:
+         */
+         double cs = quantile(complement(boost::math::chi_squared(n), 0.05));
+         /*`
+         The power of the test is given by the complement of the CDF
+         of the non-central [chi][super 2] distribution:
+         */
+         double beta = cdf(complement(boost::math::non_central_chi_squared(n, lam), cs));
+         /*`
+         Then output the cell value:
+         */
+         std::cout << "[" << std::setprecision(3) << beta << "]";
+      }
+      std::cout << "]" << std::endl;
+   }
+   std::cout << "]" << std::endl;
+}
+
+/*`
+The output from this program is a table in Boost.Quickbook format as shown below.
+
+We can interpret this as follows - for example if [nu]=10 and [lambda]=10
+then the power of the test is 0.542 - so we have only a 54% chance of
+correctly detecting that our null hypothesis is false, and a 46% chance
+of incurring a type II error (failing to reject the null hypothesis when
+it is in fact false):
+
+[table
+[[[nu]][[lambda]=2][[lambda]=4][[lambda]=6][[lambda]=8][[lambda]=10][[lambda]=12][[lambda]=14][[lambda]=16][[lambda]=18][[lambda]=20]]
+[[2][0.226][0.415][0.584][0.718][0.815][0.883][0.928][0.957][0.974][0.985]]
+[[3][0.192][0.359][0.518][0.654][0.761][0.84][0.896][0.934][0.959][0.975]]
+[[4][0.171][0.32][0.47][0.605][0.716][0.802][0.866][0.912][0.943][0.964]]
+[[5][0.157][0.292][0.433][0.564][0.677][0.769][0.839][0.89][0.927][0.952]]
+[[6][0.146][0.27][0.403][0.531][0.644][0.738][0.813][0.869][0.911][0.94]]
+[[7][0.138][0.252][0.378][0.502][0.614][0.71][0.788][0.849][0.895][0.928]]
+[[8][0.131][0.238][0.357][0.477][0.588][0.685][0.765][0.829][0.879][0.915]]
+[[9][0.125][0.225][0.339][0.454][0.564][0.661][0.744][0.811][0.863][0.903]]
+[[10][0.121][0.215][0.323][0.435][0.542][0.64][0.723][0.793][0.848][0.891]]
+[[11][0.117][0.206][0.309][0.417][0.523][0.62][0.704][0.775][0.833][0.878]]
+[[12][0.113][0.198][0.297][0.402][0.505][0.601][0.686][0.759][0.818][0.866]]
+[[13][0.11][0.191][0.286][0.387][0.488][0.584][0.669][0.743][0.804][0.854]]
+[[14][0.108][0.185][0.276][0.374][0.473][0.567][0.653][0.728][0.791][0.842]]
+[[15][0.105][0.179][0.267][0.362][0.459][0.552][0.638][0.713][0.777][0.83]]
+[[16][0.103][0.174][0.259][0.351][0.446][0.538][0.623][0.699][0.764][0.819]]
+[[17][0.101][0.169][0.251][0.341][0.434][0.525][0.609][0.686][0.752][0.807]]
+[[18][0.0992][0.165][0.244][0.332][0.423][0.512][0.596][0.673][0.74][0.796]]
+[[19][0.0976][0.161][0.238][0.323][0.412][0.5][0.584][0.66][0.728][0.786]]
+[[20][0.0961][0.158][0.232][0.315][0.402][0.489][0.572][0.648][0.716][0.775]]
+]
+
+See [@../../../example/nc_chi_sq_example.cpp nc_chi_sq_example.cpp] for the full C++ source code.
+
+*/
+
+//]
diff --git a/include/boost/math/bindings/rr.hpp b/include/boost/math/bindings/rr.hpp
index 3708b068f..09b6eb625 100644
--- a/include/boost/math/bindings/rr.hpp
+++ b/include/boost/math/bindings/rr.hpp
@@ -697,6 +697,18 @@ namespace ntl{
       return x - factor * y;
    }
 
+   template 
+   inline int iround(RR const& x, const Policy& pol)
+   {
+      return tools::real_cast(round(x, pol));
+   }
+
+   template 
+   inline int itrunc(RR const& x, const Policy& pol)
+   {
+      return tools::real_cast(trunc(x, pol));
+   }
+
 } // namespace ntl
 
 } // namespace math
diff --git a/include/boost/math/concepts/real_concept.hpp b/include/boost/math/concepts/real_concept.hpp
index d79268ed7..25ebb508f 100644
--- a/include/boost/math/concepts/real_concept.hpp
+++ b/include/boost/math/concepts/real_concept.hpp
@@ -22,7 +22,9 @@
 
 #include 
 #include 
-#include 
+#include 
+#include 
+#include 
 #include 
 #include 
 #include 
@@ -38,6 +40,12 @@ namespace boost{ namespace math{
 namespace concepts
 {
 
+#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   typedef double real_concept_base_type;
+#else
+   typedef long double real_concept_base_type;
+#endif
+
 class real_concept
 {
 public:
@@ -56,11 +64,11 @@ public:
    real_concept(unsigned long c) : m_value(c){}
    real_concept(long c) : m_value(c){}
 #if defined(BOOST_HAS_LONG_LONG) || defined(__DECCXX) || defined(__SUNPRO_CC)
-   real_concept(unsigned long long c) : m_value(static_cast(c)){}
-   real_concept(long long c) : m_value(static_cast(c)){}
+   real_concept(unsigned long long c) : m_value(static_cast(c)){}
+   real_concept(long long c) : m_value(static_cast(c)){}
 #elif defined(BOOST_HAS_MS_INT64)
-   real_concept(unsigned __int64 c) : m_value(static_cast(c)){}
-   real_concept(__int64 c) : m_value(static_cast(c)){}
+   real_concept(unsigned __int64 c) : m_value(static_cast(c)){}
+   real_concept(__int64 c) : m_value(static_cast(c)){}
 #endif
    real_concept(float c) : m_value(c){}
    real_concept(double c) : m_value(c){}
@@ -80,15 +88,15 @@ public:
    real_concept& operator=(long c) { m_value = c; return *this; }
    real_concept& operator=(unsigned long c) { m_value = c; return *this; }
 #ifdef BOOST_HAS_LONG_LONG
-   real_concept& operator=(long long c) { m_value = static_cast(c); return *this; }
-   real_concept& operator=(unsigned long long c) { m_value = static_cast(c); return *this; }
+   real_concept& operator=(long long c) { m_value = static_cast(c); return *this; }
+   real_concept& operator=(unsigned long long c) { m_value = static_cast(c); return *this; }
 #endif
    real_concept& operator=(float c) { m_value = c; return *this; }
    real_concept& operator=(double c) { m_value = c; return *this; }
    real_concept& operator=(long double c) { m_value = c; return *this; }
 
    // Access:
-   long double value()const{ return m_value; }
+   real_concept_base_type value()const{ return m_value; }
 
    // Member arithmetic:
    real_concept& operator+=(const real_concept& other)
@@ -103,9 +111,13 @@ public:
    { return -m_value; }
    real_concept const& operator+()const
    { return *this; }
+   real_concept& operator++()
+   { ++m_value;  return *this; }
+   real_concept& operator--()
+   { --m_value;  return *this; }
 
 private:
-   long double m_value;
+   real_concept_base_type m_value;
 };
 
 // Non-member arithmetic:
@@ -148,40 +160,6 @@ inline bool operator > (const real_concept& a, const real_concept& b)
 inline bool operator >= (const real_concept& a, const real_concept& b)
 { return a.value() >= b.value(); }
 
-#if 0
-// Non-member mixed compare:
-template 
-inline bool operator == (const T& a, const real_concept& b)
-{
-   return a == b.value();
-}
-template 
-inline bool operator != (const T& a, const real_concept& b)
-{
-   return a != b.value();
-}
-template 
-inline bool operator < (const T& a, const real_concept& b)
-{
-   return a < b.value();
-}
-template 
-inline bool operator > (const T& a, const real_concept& b)
-{
-   return a > b.value();
-}
-template 
-inline bool operator <= (const T& a, const real_concept& b)
-{
-   return a <= b.value();
-}
-template 
-inline bool operator >= (const T& a, const real_concept& b)
-{
-   return a >= b.value();
-}
-#endif  // Non-member mixed compare:
-
 // Non-member functions:
 inline real_concept acos(real_concept a)
 { return std::acos(a.value()); }
@@ -196,6 +174,8 @@ inline real_concept atan2(real_concept a, real_concept b)
 inline real_concept ceil(real_concept a)
 { return std::ceil(a.value()); }
 #ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+// I've seen std::fmod(long double) crash on some platforms
+// so use fmodl instead:
 #ifdef _WIN32_WCE
 //
 // Ugly workaround for macro fmodl:
@@ -221,8 +201,8 @@ inline real_concept floor(real_concept a)
 { return std::floor(a.value()); }
 inline real_concept modf(real_concept a, real_concept* ipart)
 {
-   long double ip;
-   long double result = std::modf(a.value(), &ip);
+   real_concept_base_type ip;
+   real_concept_base_type result = std::modf(a.value(), &ip);
    *ipart = ip;
    return result;
 }
@@ -243,7 +223,7 @@ inline real_concept pow(real_concept a, int b)
 { return std::pow(a.value(), b); }
 #else
 inline real_concept pow(real_concept a, int b)
-{ return std::pow(a.value(), static_cast(b)); }
+{ return std::pow(a.value(), static_cast(b)); }
 #endif
 inline real_concept sin(real_concept a)
 { return std::sin(a.value()); }
@@ -274,13 +254,13 @@ inline std::basic_istream& operator>>(std::basic_istream> s;
    std::sscanf(s.c_str(), "%Lf", &d);
    a = d;
    return is;
 #else
-   long double v;
+   real_concept_base_type v;
    is >> v;
    a = v;
    return is;
@@ -291,86 +271,47 @@ inline std::basic_istream& operator>>(std::basic_istream
-inline unsigned int real_cast(concepts::real_concept r)
-{
-   return static_cast(r.value());
-}
-
-template <>
-inline int real_cast(concepts::real_concept r)
-{
-   return static_cast(r.value());
-}
-
-template <>
-inline long real_cast(concepts::real_concept r)
-{
-   return static_cast(r.value());
-}
-
-// Converts from T to narrower floating-point types, float, double & long double.
-
-template <>
-inline float real_cast(concepts::real_concept r)
-{
-   return static_cast(r.value());
-}
-template <>
-inline double real_cast(concepts::real_concept r)
-{
-   return static_cast(r.value());
-}
-template <>
-inline long double real_cast(concepts::real_concept r)
-{
-   return r.value();
-}
 
 template <>
 inline concepts::real_concept max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
 {
-   return max_value();
+   return max_value();
 }
 
 template <>
 inline concepts::real_concept min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
 {
-   return min_value();
+   return min_value();
 }
 
 template <>
 inline concepts::real_concept log_max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
 {
-   return log_max_value();
+   return log_max_value();
 }
 
 template <>
 inline concepts::real_concept log_min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
 {
-   return log_min_value();
+   return log_min_value();
 }
 
 template <>
 inline concepts::real_concept epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
 {
 #ifdef __SUNPRO_CC
-   return std::numeric_limits::epsilon();
+   return std::numeric_limits::epsilon();
 #else
-   return tools::epsilon();
+   return tools::epsilon();
 #endif
 }
 
 template <>
 inline int digits(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::real_concept))
 { 
-   // Assume number of significand bits is same as long double,
+   // Assume number of significand bits is same as real_concept_base_type,
    // unless std::numeric_limits::is_specialized to provide digits.
-   return tools::digits();
+   return tools::digits();
    // Note that if numeric_limits real concept is NOT specialized to provide digits10
    // (or max_digits10) then the default precision of 6 decimal digits will be used
    // by Boost test (giving misleading error messages like
@@ -380,6 +321,77 @@ inline int digits(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC
 
 } // namespace tools
 
+//
+// Conversion and truncation routines:
+//
+template 
+inline int iround(const concepts::real_concept& v, const Policy& pol)
+{
+   return iround(v.value(), pol);
+}
+inline int iround(const concepts::real_concept& v)
+{
+   return iround(v.value(), policies::policy<>());
+}
+
+template 
+inline long lround(const concepts::real_concept& v, const Policy& pol)
+{
+   return lround(v.value(), pol);
+}
+inline long lround(const concepts::real_concept& v)
+{
+   return lround(v.value(), policies::policy<>());
+}
+
+#ifdef BOOST_HAS_LONG_LONG
+
+template 
+inline long long llround(const concepts::real_concept& v, const Policy& pol)
+{
+   return llround(v.value(), pol);
+}
+inline long long llround(const concepts::real_concept& v)
+{
+   return llround(v.value(), policies::policy<>());
+}
+
+#endif
+
+template 
+inline int itrunc(const concepts::real_concept& v, const Policy& pol)
+{
+   return itrunc(v.value(), pol);
+}
+inline int itrunc(const concepts::real_concept& v)
+{
+   return itrunc(v.value(), policies::policy<>());
+}
+
+template 
+inline long ltrunc(const concepts::real_concept& v, const Policy& pol)
+{
+   return ltrunc(v.value(), pol);
+}
+inline long ltrunc(const concepts::real_concept& v)
+{
+   return ltrunc(v.value(), policies::policy<>());
+}
+
+#ifdef BOOST_HAS_LONG_LONG
+
+template 
+inline long long lltrunc(const concepts::real_concept& v, const Policy& pol)
+{
+   return lltrunc(v.value(), pol);
+}
+inline long long lltrunc(const concepts::real_concept& v)
+{
+   return lltrunc(v.value(), policies::policy<>());
+}
+
+#endif
+
 } // namespace math
 } // namespace boost
 
diff --git a/include/boost/math/concepts/std_real_concept.hpp b/include/boost/math/concepts/std_real_concept.hpp
index 329c35225..25408575b 100644
--- a/include/boost/math/concepts/std_real_concept.hpp
+++ b/include/boost/math/concepts/std_real_concept.hpp
@@ -18,9 +18,9 @@
 
 #include 
 #include 
-#include 
 #include 
 #include 
+#include 
 
 #include 
 #include 
@@ -35,6 +35,12 @@ namespace boost{ namespace math{
 namespace concepts
 {
 
+#ifdef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   typedef double std_real_concept_base_type;
+#else
+   typedef long double std_real_concept_base_type;
+#endif
+
 class std_real_concept
 {
 public:
@@ -53,8 +59,8 @@ public:
    std_real_concept(unsigned long c) : m_value(c){}
    std_real_concept(long c) : m_value(c){}
 #if defined(BOOST_HAS_LONG_LONG) || defined(__DECCXX) || defined(__SUNPRO_CC)
-   std_real_concept(unsigned long long c) : m_value(static_cast(c)){}
-   std_real_concept(long long c) : m_value(static_cast(c)){}
+   std_real_concept(unsigned long long c) : m_value(static_cast(c)){}
+   std_real_concept(long long c) : m_value(static_cast(c)){}
 #endif
    std_real_concept(float c) : m_value(c){}
    std_real_concept(double c) : m_value(c){}
@@ -74,15 +80,15 @@ public:
    std_real_concept& operator=(long c) { m_value = c; return *this; }
    std_real_concept& operator=(unsigned long c) { m_value = c; return *this; }
 #if defined(BOOST_HAS_LONG_LONG) || defined(__DECCXX) || defined(__SUNPRO_CC)
-   std_real_concept& operator=(long long c) { m_value = static_cast(c); return *this; }
-   std_real_concept& operator=(unsigned long long c) { m_value = static_cast(c); return *this; }
+   std_real_concept& operator=(long long c) { m_value = static_cast(c); return *this; }
+   std_real_concept& operator=(unsigned long long c) { m_value = static_cast(c); return *this; }
 #endif
    std_real_concept& operator=(float c) { m_value = c; return *this; }
    std_real_concept& operator=(double c) { m_value = c; return *this; }
    std_real_concept& operator=(long double c) { m_value = c; return *this; }
 
    // Access:
-   long double value()const{ return m_value; }
+   std_real_concept_base_type value()const{ return m_value; }
 
    // Member arithmetic:
    std_real_concept& operator+=(const std_real_concept& other)
@@ -99,7 +105,7 @@ public:
    { return *this; }
 
 private:
-   long double m_value;
+   std_real_concept_base_type m_value;
 };
 
 // Non-member arithmetic:
@@ -142,40 +148,6 @@ inline bool operator > (const std_real_concept& a, const std_real_concept& b)
 inline bool operator >= (const std_real_concept& a, const std_real_concept& b)
 { return a.value() >= b.value(); }
 
-#if 0
-// Non-member mixed compare:
-template 
-inline bool operator == (const T& a, const std_real_concept& b)
-{
-   return a == b.value();
-}
-template 
-inline bool operator != (const T& a, const std_real_concept& b)
-{
-   return a != b.value();
-}
-template 
-inline bool operator < (const T& a, const std_real_concept& b)
-{
-   return a < b.value();
-}
-template 
-inline bool operator > (const T& a, const std_real_concept& b)
-{
-   return a > b.value();
-}
-template 
-inline bool operator <= (const T& a, const std_real_concept& b)
-{
-   return a <= b.value();
-}
-template 
-inline bool operator >= (const T& a, const std_real_concept& b)
-{
-   return a >= b.value();
-}
-#endif  // Non-member mixed compare:
-
 } // namespace concepts
 } // namespace math
 } // namespace boost
@@ -214,8 +186,8 @@ inline boost::math::concepts::std_real_concept floor(boost::math::concepts::std_
 { return std::floor(a.value()); }
 inline boost::math::concepts::std_real_concept modf(boost::math::concepts::std_real_concept a, boost::math::concepts::std_real_concept* ipart)
 {
-   long double ip;
-   long double result = std::modf(a.value(), &ip);
+   boost::math::concepts::std_real_concept_base_type ip;
+   boost::math::concepts::std_real_concept_base_type result = std::modf(a.value(), &ip);
    *ipart = ip;
    return result;
 }
@@ -260,7 +232,7 @@ inline std::basic_ostream& operator<<(std::basic_ostream
 inline std::basic_istream& operator>>(std::basic_istream& is, std_real_concept& a)
 {
-   long double v;
+   std_real_concept_base_type v;
    is >> v;
    a = v;
    return is;
@@ -270,84 +242,117 @@ inline std::basic_istream& operator>>(std::basic_istream
-inline unsigned int real_cast(concepts::std_real_concept r)
-{
-   return static_cast(r.value());
-}
-
-template <>
-inline int real_cast(concepts::std_real_concept r)
-{
-   return static_cast(r.value());
-}
-
-template <>
-inline long real_cast(concepts::std_real_concept r)
-{
-   return static_cast(r.value());
-}
-
-// Converts from T to narrower floating-point types, float, double & long double.
-
-template <>
-inline float real_cast(concepts::std_real_concept r)
-{
-   return static_cast(r.value());
-}
-template <>
-inline double real_cast(concepts::std_real_concept r)
-{
-   return static_cast(r.value());
-}
-template <>
-inline long double real_cast(concepts::std_real_concept r)
-{
-   return r.value();
-}
 
 template <>
 inline concepts::std_real_concept max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
 {
-   return max_value();
+   return max_value();
 }
 
 template <>
 inline concepts::std_real_concept min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
 {
-   return min_value();
+   return min_value();
 }
 
 template <>
 inline concepts::std_real_concept log_max_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
 {
-   return log_max_value();
+   return log_max_value();
 }
 
 template <>
 inline concepts::std_real_concept log_min_value(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
 {
-   return log_min_value();
+   return log_min_value();
 }
 
 template <>
-inline concepts::std_real_concept epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
+inline concepts::std_real_concept epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
 {
-   return tools::epsilon();
+   return tools::epsilon();
 }
 
 template <>
 inline int digits(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(concepts::std_real_concept))
-{ // Assume number of significand bits is same as long double,
+{ // Assume number of significand bits is same as std_real_concept_base_type,
   // unless std::numeric_limits::is_specialized to provide digits.
-   return digits();
+   return digits();
 }
 
 } // namespace tools
+
+//
+// Conversion and truncation routines:
+//
+template 
+inline int iround(const concepts::std_real_concept& v, const Policy& pol)
+{
+   return iround(v.value(), pol);
+}
+inline int iround(const concepts::std_real_concept& v)
+{
+   return iround(v.value(), policies::policy<>());
+}
+
+template 
+inline long lround(const concepts::std_real_concept& v, const Policy& pol)
+{
+   return lround(v.value(), pol);
+}
+inline long lround(const concepts::std_real_concept& v)
+{
+   return lround(v.value(), policies::policy<>());
+}
+
+#ifdef BOOST_HAS_LONG_LONG
+
+template 
+inline long long llround(const concepts::std_real_concept& v, const Policy& pol)
+{
+   return llround(v.value(), pol);
+}
+inline long long llround(const concepts::std_real_concept& v)
+{
+   return llround(v.value(), policies::policy<>());
+}
+
+#endif
+
+template 
+inline int itrunc(const concepts::std_real_concept& v, const Policy& pol)
+{
+   return itrunc(v.value(), pol);
+}
+inline int itrunc(const concepts::std_real_concept& v)
+{
+   return itrunc(v.value(), policies::policy<>());
+}
+
+template 
+inline long ltrunc(const concepts::std_real_concept& v, const Policy& pol)
+{
+   return ltrunc(v.value(), pol);
+}
+inline long ltrunc(const concepts::std_real_concept& v)
+{
+   return ltrunc(v.value(), policies::policy<>());
+}
+
+#ifdef BOOST_HAS_LONG_LONG
+
+template 
+inline long long lltrunc(const concepts::std_real_concept& v, const Policy& pol)
+{
+   return lltrunc(v.value(), pol);
+}
+inline long long lltrunc(const concepts::std_real_concept& v)
+{
+   return lltrunc(v.value(), policies::policy<>());
+}
+
+#endif
+
 } // namespace math
 } // namespace boost
 
diff --git a/include/boost/math/distributions.hpp b/include/boost/math/distributions.hpp
index bf81c2689..dd6c02b75 100644
--- a/include/boost/math/distributions.hpp
+++ b/include/boost/math/distributions.hpp
@@ -24,6 +24,10 @@
 #include 
 #include 
 #include 
+#include 
+#include 
+#include 
+#include 
 #include 
 #include 
 #include 
@@ -32,11 +36,8 @@
 #include 
 #include 
 #include 
-// find location and shape for appropriate distributions,
-// normal, cauchy, lognormal, symmetric triangular
-// Disabled for now, these are still work in progress.
-//#include 
-//#include 
+#include 
+#include 
 
 #endif // BOOST_MATH_DISTRIBUTIONS_HPP
 
diff --git a/include/boost/math/distributions/chi_squared.hpp b/include/boost/math/distributions/chi_squared.hpp
index cbed73d24..0b7d2ef40 100644
--- a/include/boost/math/distributions/chi_squared.hpp
+++ b/include/boost/math/distributions/chi_squared.hpp
@@ -1,5 +1,5 @@
 // Copyright John Maddock 2006, 2007.
-// Copyright Paul A. Bristow 2007.
+// Copyright Paul A. Bristow 2008.
 
 // Use, modification and distribution are subject to the
 // Boost Software License, Version 1.0.
@@ -202,10 +202,22 @@ inline RealType mode(const chi_squared_distribution& dist)
 {
    RealType df = dist.degrees_of_freedom();
    static const char* function = "boost::math::mode(const chi_squared_distribution<%1%>&)";
-   if(df <= 2)
+   // Most sources only define mode for df >= 2,
+   // but for 0 <= df <= 2, the pdf maximum actually occurs at random variate = 0;
+   // So one could extend the definition of mode thus:
+   //if(df < 0)
+   //{
+   //   return policies::raise_domain_error(
+   //      function,
+   //      "Chi-Squared distribution only has a mode for degrees of freedom >= 0, but got degrees of freedom = %1%.",
+   //      df, Policy());
+   //}
+   //return (df <= 2) ? 0 : df - 2;
+
+   if(df < 2)
       return policies::raise_domain_error(
          function,
-         "The Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
+         "Chi-Squared distribution only has a mode for degrees of freedom >= 2, but got degrees of freedom = %1%.",
          df, Policy());
    return df - 2;
 }
@@ -306,7 +318,7 @@ RealType chi_squared_distribution::find_degrees_of_freedom(
    boost::uintmax_t max_iter = policies::get_max_root_iterations();
    std::pair r = tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy());
    RealType result = r.first + (r.second - r.first) / 2;
-   if(max_iter == policies::get_max_root_iterations())
+   if(max_iter >= policies::get_max_root_iterations())
    {
       policies::raise_evaluation_error(function, "Unable to locate solution in a reasonable time:"
          " either there is no answer to how many degrees of freedom are required"
diff --git a/include/boost/math/distributions/detail/common_error_handling.hpp b/include/boost/math/distributions/detail/common_error_handling.hpp
index d13776c6d..dad572a93 100644
--- a/include/boost/math/distributions/detail/common_error_handling.hpp
+++ b/include/boost/math/distributions/detail/common_error_handling.hpp
@@ -96,6 +96,60 @@ inline bool check_x(
    // leaving this test to catch any NaNs.  see Normal and cauchy for example.
 }
 
+template 
+inline bool check_positive_x(
+      const char* function,
+      RealType x,
+      RealType* result,
+      const Policy& pol)
+{
+   if(!(boost::math::isfinite)(x) || (x < 0))
+   {
+      *result = policies::raise_domain_error(
+         function,
+         "Random variate x is %1%, but must be finite and >= 0!", x, pol);
+      return false;
+   }
+   return true;
+   // Note that this test catches both infinity and NaN.
+   // Some special cases permit x to be infinite, so these must be tested 1st,
+   // leaving this test to catch any NaNs.  see Normal and cauchy for example.
+}
+
+template 
+inline bool check_non_centrality(
+      const char* function,
+      RealType ncp,
+      RealType* result,
+      const Policy& pol)
+{
+   if((ncp < 0) || !(boost::math::isfinite)(ncp))
+   { // Assume scale == 0 is NOT valid for any distribution.
+      *result = policies::raise_domain_error(
+         function,
+         "Non centrality parameter is %1%, but must be > 0 !", ncp, pol);
+      return false;
+   }
+   return true;
+}
+
+template 
+inline bool check_finite(
+      const char* function,
+      RealType x,
+      RealType* result,
+      const Policy& pol)
+{
+   if(!(boost::math::isfinite)(x))
+   { // Assume scale == 0 is NOT valid for any distribution.
+      *result = policies::raise_domain_error(
+         function,
+         "Parameter is %1%, but must be finite !", x, pol);
+      return false;
+   }
+   return true;
+}
+
 } // namespace detail
 } // namespace math
 } // namespace boost
diff --git a/include/boost/math/distributions/detail/generic_mode.hpp b/include/boost/math/distributions/detail/generic_mode.hpp
new file mode 100644
index 000000000..085dc691c
--- /dev/null
+++ b/include/boost/math/distributions/detail/generic_mode.hpp
@@ -0,0 +1,149 @@
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_DISTRIBUTIONS_DETAIL_MODE_HPP
+#define BOOST_MATH_DISTRIBUTIONS_DETAIL_MODE_HPP
+
+#include  // function minimization for mode
+#include 
+#include 
+
+namespace boost{ namespace math{ namespace detail{
+
+template 
+struct pdf_minimizer
+{
+   pdf_minimizer(const Dist& d)
+      : dist(d) {}
+
+   typename Dist::value_type operator()(const typename Dist::value_type& x)
+   {
+      return -pdf(dist, x);
+   }
+private:
+   Dist dist;
+};
+
+template 
+typename Dist::value_type generic_find_mode(const Dist& dist, typename Dist::value_type guess, const char* function, typename Dist::value_type step = 0)
+{
+   BOOST_MATH_STD_USING
+   typedef typename Dist::value_type value_type;
+   typedef typename Dist::policy_type policy_type;
+   //
+   // Need to begin by bracketing the maxima of the PDF:
+   //
+   value_type maxval;
+   value_type upper_bound = guess;
+   value_type lower_bound;
+   value_type v = pdf(dist, guess);
+   if(v == 0)
+   {
+      //
+      // Oops we don't know how to handle this, or even in which
+      // direction we should move in, treat as an evaluation error:
+      //
+      policies::raise_evaluation_error(
+         function, 
+         "Could not locate a starting location for the search for the mode, original guess was %1%", guess, policy_type());
+   }
+   do
+   {
+      maxval = v;
+      if(step != 0)
+         upper_bound += step;
+      else
+         upper_bound *= 2;
+      v = pdf(dist, upper_bound);
+   }while(maxval < v);
+
+   lower_bound = upper_bound;
+   do
+   {
+      maxval = v;
+      if(step != 0)
+         lower_bound -= step;
+      else
+         lower_bound /= 2;
+      v = pdf(dist, lower_bound);
+   }while(maxval < v);
+
+   boost::uintmax_t max_iter = policies::get_max_root_iterations();
+
+   value_type result = tools::brent_find_minima(
+      pdf_minimizer(dist), 
+      lower_bound, 
+      upper_bound, 
+      policies::digits(), 
+      max_iter).first;
+   if(max_iter >= policies::get_max_root_iterations())
+   {
+      return policies::raise_evaluation_error(
+         function, 
+         "Unable to locate solution in a reasonable time:"
+         " either there is no answer to the mode of the distribution"
+         " or the answer is infinite.  Current best guess is %1%", result, policy_type());
+   }
+   return result;
+}
+//
+// As above,but confined to the interval [0,1]:
+//
+template 
+typename Dist::value_type generic_find_mode_01(const Dist& dist, typename Dist::value_type guess, const char* function)
+{
+   BOOST_MATH_STD_USING
+   typedef typename Dist::value_type value_type;
+   typedef typename Dist::policy_type policy_type;
+   //
+   // Need to begin by bracketing the maxima of the PDF:
+   //
+   value_type maxval;
+   value_type upper_bound = guess;
+   value_type lower_bound;
+   value_type v = pdf(dist, guess);
+   do
+   {
+      maxval = v;
+      upper_bound = 1 - (1 - upper_bound) / 2;
+      if(upper_bound == 1)
+         return 1;
+      v = pdf(dist, upper_bound);
+   }while(maxval < v);
+
+   lower_bound = upper_bound;
+   do
+   {
+      maxval = v;
+      lower_bound /= 2;
+      if(lower_bound < tools::min_value())
+         return 0;
+      v = pdf(dist, lower_bound);
+   }while(maxval < v);
+
+   boost::uintmax_t max_iter = policies::get_max_root_iterations();
+
+   value_type result = tools::brent_find_minima(
+      pdf_minimizer(dist), 
+      lower_bound, 
+      upper_bound, 
+      policies::digits(), 
+      max_iter).first;
+   if(max_iter >= policies::get_max_root_iterations())
+   {
+      return policies::raise_evaluation_error(
+         function, 
+         "Unable to locate solution in a reasonable time:"
+         " either there is no answer to the mode of the distribution"
+         " or the answer is infinite.  Current best guess is %1%", result, policy_type());
+   }
+   return result;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_DISTRIBUTIONS_DETAIL_MODE_HPP
diff --git a/include/boost/math/distributions/detail/generic_quantile.hpp b/include/boost/math/distributions/detail/generic_quantile.hpp
new file mode 100644
index 000000000..acf8b48da
--- /dev/null
+++ b/include/boost/math/distributions/detail/generic_quantile.hpp
@@ -0,0 +1,87 @@
+
+#ifndef BOOST_MATH_DISTIBUTIONS_DETAIL_GENERIC_QUANTILE_HPP
+#define BOOST_MATH_DISTIBUTIONS_DETAIL_GENERIC_QUANTILE_HPP
+
+namespace boost{ namespace math{ namespace detail{
+
+template 
+struct generic_quantile_finder
+{
+   typedef typename Dist::value_type value_type;
+   typedef typename Dist::policy_type policy_type;
+
+   generic_quantile_finder(const Dist& d, value_type t, bool c)
+      : dist(d), target(t), comp(c) {}
+
+   value_type operator()(const value_type& x)
+   {
+      return comp ?
+         target - cdf(complement(dist, x))
+         : cdf(dist, x) - target;
+   }
+
+private:
+   Dist dist;
+   value_type target;
+   bool comp;
+};
+
+template 
+inline T check_range_result(const T& x, const Policy& pol, const char* function)
+{
+   if((x >= 0) && (x < tools::min_value()))
+      return policies::raise_underflow_error(function, 0, pol);
+   if(x <= -tools::max_value())
+      return -policies::raise_overflow_error(function, 0, pol);
+   if(x >= tools::max_value())
+      return policies::raise_overflow_error(function, 0, pol);
+   return x;
+}
+
+template 
+typename Dist::value_type generic_quantile(const Dist& dist, const typename Dist::value_type& p, const typename Dist::value_type& guess, bool comp, const char* function)
+{
+   typedef typename Dist::value_type value_type;
+   typedef typename Dist::policy_type policy_type;
+   typedef typename policies::normalise<
+      policy_type, 
+      policies::promote_float, 
+      policies::promote_double, 
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+
+   //
+   // Special cases first:
+   //
+   if(p == 0)
+   {
+      return comp
+      ? check_range_result(range(dist).second, forwarding_policy(), function)
+      : check_range_result(range(dist).first, forwarding_policy(), function);
+   }
+   if(p == 1)
+   {
+      return !comp
+      ? check_range_result(range(dist).second, forwarding_policy(), function)
+      : check_range_result(range(dist).first, forwarding_policy(), function);
+   }
+
+   generic_quantile_finder f(dist, p, comp);
+   tools::eps_tolerance tol(policies::digits() - 3);
+   boost::uintmax_t max_iter = policies::get_max_root_iterations();
+   std::pair ir = tools::bracket_and_solve_root(
+      f, guess, value_type(2), true, tol, max_iter, forwarding_policy());
+   value_type result = ir.first + (ir.second - ir.first) / 2;
+   if(max_iter >= policies::get_max_root_iterations())
+   {
+      policies::raise_evaluation_error(function, "Unable to locate solution in a reasonable time:"
+         " either there is no answer to quantile"
+         " or the answer is infinite.  Current best guess is %1%", result, forwarding_policy());
+   }
+   return result;
+}
+
+}}} // namespaces
+
+#endif // BOOST_MATH_DISTIBUTIONS_DETAIL_GENERIC_QUANTILE_HPP
+
diff --git a/include/boost/math/distributions/exponential.hpp b/include/boost/math/distributions/exponential.hpp
index 669636c37..e3316e97b 100644
--- a/include/boost/math/distributions/exponential.hpp
+++ b/include/boost/math/distributions/exponential.hpp
@@ -89,7 +89,9 @@ inline const std::pair support(const exponential_distributio
 { // Range of supported values for random variable x.
    // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
    using boost::math::tools::max_value;
-   return std::pair(0,  max_value());
+   using boost::math::tools::min_value;
+   return std::pair(min_value(),  max_value());
+   // min_value() to avoid a discontinuity at x = 0.
 }
 
 template 
diff --git a/include/boost/math/distributions/fwd.hpp b/include/boost/math/distributions/fwd.hpp
index 20a18d844..d99d381ed 100644
--- a/include/boost/math/distributions/fwd.hpp
+++ b/include/boost/math/distributions/fwd.hpp
@@ -90,5 +90,9 @@ class weibull_distribution;
    typedef boost::math::triangular_distribution triangular;\
    typedef boost::math::uniform_distribution uniform;\
    typedef boost::math::weibull_distribution weibull;\
+   typedef boost::math::non_central_chi_squared_distribution non_central_chi_squared;\
+   typedef boost::math::non_central_beta_distribution non_central_beta;\
+   typedef boost::math::non_central_f_distribution non_central_f;\
+   typedef boost::math::non_central_t_distribution non_central_t;\
 
 #endif // BOOST_MATH_DISTRIBUTIONS_FWD_HPP
diff --git a/include/boost/math/distributions/gamma.hpp b/include/boost/math/distributions/gamma.hpp
index 5ac4bb370..27d27dc00 100644
--- a/include/boost/math/distributions/gamma.hpp
+++ b/include/boost/math/distributions/gamma.hpp
@@ -111,7 +111,8 @@ inline const std::pair support(const gamma_distribution(0,  max_value());
+   using boost::math::tools::min_value;
+   return std::pair(min_value(),  max_value());
 }
 
 template 
diff --git a/include/boost/math/distributions/non_central_beta.hpp b/include/boost/math/distributions/non_central_beta.hpp
new file mode 100644
index 000000000..5e9eef2fe
--- /dev/null
+++ b/include/boost/math/distributions/non_central_beta.hpp
@@ -0,0 +1,845 @@
+// boost\math\distributions\non_central_beta.hpp
+
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP
+#define BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP
+
+#include 
+#include  // for incomplete gamma. gamma_q
+#include  // complements
+#include  // central distribution
+#include 
+#include  // error checks
+#include  // isnan.
+#include  // for root finding.
+
+namespace boost
+{
+   namespace math
+   {
+
+      template 
+      class non_central_beta_distribution;
+
+      namespace detail{
+
+         template 
+         T non_central_beta_p(T a, T b, T lam, T x, T y, const Policy& pol, T init_val = 0)
+         {
+            BOOST_MATH_STD_USING
+               using namespace boost::math;
+            //
+            // Variables come first:
+            //
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0f, -boost::math::policies::digits());
+            T l2 = lam / 2;
+            //
+            // k is the starting point for iteration, and is the
+            // maximum of the poisson weighting term:
+            //
+            int k = itrunc(l2);
+            if(k == 0)
+               k = 1;
+            // Starting Poisson weight:
+            T pois = gamma_p_derivative(T(k+1), l2, pol);
+            if(pois == 0)
+               return init_val;
+            // Starting beta term:
+            T beta = x < y 
+               ? ibeta(a + k, b, x, pol)
+               : ibetac(b, a + k, y, pol);
+            // recurance term:
+            T xterm = x < y
+               ? ibeta_derivative(a + k, b, x, pol)
+               : ibeta_derivative(b, a + k, y, pol);
+            xterm *= y / (a + b + k - 1);
+            T poisf(pois), betaf(beta), xtermf(xterm);
+            T sum = init_val;
+
+            if((beta == 0) && (xterm == 0))
+               return init_val;
+
+            //
+            // Backwards recursion first, this is the stable
+            // direction for recursion:
+            //
+            T last_term = 0;
+            boost::uintmax_t count = k;
+            for(int i = k; i >= 0; --i)
+            {
+               T term = beta * pois;
+               sum += term;
+               if(((fabs(term/sum) < errtol) && (last_term >= term)) || (term == 0))
+               {
+                  count = k - i;
+                  break;
+               }
+               pois *= i / l2;
+               beta += xterm;
+               xterm *= (a + i - 1) / (x * (a + b + i - 2));
+               last_term = term;
+            }
+            for(int i = k + 1; ; ++i)
+            {
+               poisf *= l2 / i;
+               xtermf *= (x * (a + b + i - 2)) / (a + i - 1);
+               betaf -= xtermf;
+
+               T term = poisf * betaf;
+               sum += term;
+               if((fabs(term/sum) < errtol) || (term == 0))
+               {
+                  break;
+               }
+               if(static_cast(count + i - k) > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "cdf(non_central_beta_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+            }
+            return sum;
+         }
+
+         template 
+         T non_central_beta_q(T a, T b, T lam, T x, T y, const Policy& pol, T init_val = 0)
+         {
+            BOOST_MATH_STD_USING
+               using namespace boost::math;
+            //
+            // Variables come first:
+            //
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0f, -boost::math::policies::digits());
+            T l2 = lam / 2;
+            //
+            // k is the starting point for iteration, and is the
+            // maximum of the poisson weighting term:
+            //
+            int k = itrunc(l2);
+            if(k == 0)
+               k = 1;
+            // Starting Poisson weight:
+            T pois = gamma_p_derivative(T(k+1), l2, pol);
+            if(pois == 0)
+               return init_val;
+            // Starting beta term:
+            T beta = x < y
+               ? ibetac(a + k, b, x, pol)
+               : ibeta(b, a + k, y, pol);
+            // recurance term:
+            T xterm = x < y 
+               ? ibeta_derivative(a + k, b, x, pol)
+               : ibeta_derivative(b, a + k, y, pol);
+            xterm *= y / (a + b + k - 1);
+            T poisf(pois), betaf(beta), xtermf(xterm);
+            T sum = init_val;
+            if((beta == 0) && (xterm == 0))
+               return init_val;
+            //
+            // Forwards recursion first, this is the stable
+            // direction for recursion, and the location
+            // of the bulk of the sum:
+            //
+            T last_term = 0;
+            boost::uintmax_t count = 0;
+            for(int i = k + 1; ; ++i)
+            {
+               poisf *= l2 / i;
+               xtermf *= (x * (a + b + i - 2)) / (a + i - 1);
+               betaf += xtermf;
+
+               T term = poisf * betaf;
+               sum += term;
+               if((fabs(term/sum) < errtol) && (last_term >= term))
+               {
+                  count = i - k;
+                  break;
+               }
+               if(static_cast(i - k) > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "cdf(non_central_beta_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+               last_term = term;
+            }
+            for(int i = k; i >= 0; --i)
+            {
+               T term = beta * pois;
+               sum += term;
+               if(fabs(term/sum) < errtol)
+               {
+                  break;
+               }
+               if(static_cast(count + k - i) > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "cdf(non_central_beta_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+               pois *= i / l2;
+               beta -= xterm;
+               xterm *= (a + i - 1) / (x * (a + b + i - 2));
+            }
+            return sum;
+         }
+
+         template 
+         inline RealType non_central_beta_cdf(RealType x, RealType y, RealType a, RealType b, RealType l, bool invert, const Policy&)
+         {
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            BOOST_MATH_STD_USING
+
+            if(x == 0)
+               return invert ? 1.0f : 0.0f;
+            if(y == 0)
+               return invert ? 0.0f : 1.0f;
+            value_type result;
+            value_type c = a + b + l / 2;
+            value_type cross = 1 - (b / c) * (1 + l / (2 * c * c));
+            if(l == 0)
+               result = cdf(boost::math::beta_distribution(a, b), x);
+            else if(x > cross)
+            {
+               // Complement is the smaller of the two:
+               result = detail::non_central_beta_q(
+                  static_cast(a), 
+                  static_cast(b), 
+                  static_cast(l), 
+                  static_cast(x), 
+                  static_cast(y), 
+                  forwarding_policy(), 
+                  static_cast(invert ? 0 : -1));
+               invert = !invert;
+            }
+            else
+            {
+               result = detail::non_central_beta_p(
+                  static_cast(a), 
+                  static_cast(b), 
+                  static_cast(l), 
+                  static_cast(x), 
+                  static_cast(y), 
+                  forwarding_policy(),
+                  static_cast(invert ? -1 : 0));
+            }
+            if(invert)
+               result = -result;
+            return policies::checked_narrowing_cast(
+               result, 
+               "boost::math::non_central_beta_cdf<%1%>(%1%, %1%, %1%)");
+         }
+
+         template 
+         struct nc_beta_quantile_functor
+         {
+            nc_beta_quantile_functor(const non_central_beta_distribution& d, T t, bool c)
+               : dist(d), target(t), comp(c) {}
+
+            T operator()(const T& x)
+            {
+               return comp ?
+                  target - cdf(complement(dist, x))
+                  : cdf(dist, x) - target;
+            }
+
+         private:
+            non_central_beta_distribution dist;
+            T target;
+            bool comp;
+         };
+
+         //
+         // This is more or less a copy of bracket_and_solve_root, but
+         // modified to search only the interval [0,1] using similar
+         // heuristics.
+         //
+         template 
+         std::pair bracket_and_solve_root_01(F f, const T& guess, T factor, bool rising, Tol tol, boost::uintmax_t& max_iter, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+               static const char* function = "boost::math::tools::bracket_and_solve_root_01<%1%>";
+            //
+            // Set up inital brackets:
+            //
+            T a = guess;
+            T b = a;
+            T fa = f(a);
+            T fb = fa;
+            //
+            // Set up invocation count:
+            //
+            boost::uintmax_t count = max_iter - 1;
+
+            if((fa < 0) == (guess < 0 ? !rising : rising))
+            {
+               //
+               // Zero is to the right of b, so walk upwards
+               // until we find it:
+               //
+               while((boost::math::sign)(fb) == (boost::math::sign)(fa))
+               {
+                  if(count == 0)
+                  {
+                     b = policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", b, pol);
+                     return std::make_pair(a, b);
+                  }
+                  //
+                  // Heuristic: every 20 iterations we double the growth factor in case the
+                  // initial guess was *really* bad !
+                  //
+                  if((max_iter - count) % 20 == 0)
+                     factor *= 2;
+                  //
+                  // Now go ahead and move are guess by "factor",
+                  // we do this by reducing 1-guess by factor:
+                  //
+                  a = b;
+                  fa = fb;
+                  b = 1 - ((1 - b) / factor);
+                  fb = f(b);
+                  --count;
+                  BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count);
+               }
+            }
+            else
+            {
+               //
+               // Zero is to the left of a, so walk downwards
+               // until we find it:
+               //
+               while((boost::math::sign)(fb) == (boost::math::sign)(fa))
+               {
+                  if(fabs(a) < tools::min_value())
+                  {
+                     // Escape route just in case the answer is zero!
+                     max_iter -= count;
+                     max_iter += 1;
+                     return a > 0 ? std::make_pair(T(0), T(a)) : std::make_pair(T(a), T(0)); 
+                  }
+                  if(count == 0)
+                  {
+                     a = policies::raise_evaluation_error(function, "Unable to bracket root, last nearest value was %1%", a, pol);
+                     return std::make_pair(a, b);
+                  }
+                  //
+                  // Heuristic: every 20 iterations we double the growth factor in case the
+                  // initial guess was *really* bad !
+                  //
+                  if((max_iter - count) % 20 == 0)
+                     factor *= 2;
+                  //
+                  // Now go ahead and move are guess by "factor":
+                  //
+                  b = a;
+                  fb = fa;
+                  a /= factor;
+                  fa = f(a);
+                  --count;
+                  BOOST_MATH_INSTRUMENT_CODE("a = " << a << " b = " << b << " fa = " << fa << " fb = " << fb << " count = " << count);
+               }
+            }
+            max_iter -= count;
+            max_iter += 1;
+            std::pair r = toms748_solve(
+               f, 
+               (a < 0 ? b : a), 
+               (a < 0 ? a : b), 
+               (a < 0 ? fb : fa), 
+               (a < 0 ? fa : fb), 
+               tol, 
+               count, 
+               pol);
+            max_iter += count;
+            BOOST_MATH_INSTRUMENT_CODE("max_iter = " << max_iter << " count = " << count);
+            return r;
+         }
+
+         template 
+         RealType nc_beta_quantile(const non_central_beta_distribution& dist, const RealType& p, bool comp)
+         {
+            static const char* function = "quantile(non_central_beta_distribution<%1%>, %1%)";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            value_type a = dist.alpha();
+            value_type b = dist.beta();
+            value_type l = dist.non_centrality();
+            value_type r;
+            if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               b, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !detail::check_probability(
+               function,
+               static_cast(p),
+               &r,
+               Policy()))
+                  return (RealType)r;
+            //
+            // Special cases first:
+            //
+            if(p == 0)
+               return comp
+               ? 1.0f
+               : 0.0f;
+            if(p == 1)
+               return !comp
+               ? 1.0f
+               : 0.0f;
+
+            value_type c = a + b + l / 2;
+            value_type mean = 1 - (b / c) * (1 + l / (2 * c * c));
+            /*
+            //
+            // Calculate a normal approximation to the quantile, 
+            // uses mean and variance approximations from:
+            // Algorithm AS 310: 
+            // Computing the Non-Central Beta Distribution Function
+            // R. Chattamvelli; R. Shanmugam
+            // Applied Statistics, Vol. 46, No. 1. (1997), pp. 146-156.
+            //
+            // Unfortunately, when this is wrong it tends to be *very*
+            // wrong, so it's disabled for now, even though it often
+            // gets the initial guess quite close.  Probably we could
+            // do much better by factoring in the skewness if only
+            // we could calculate it....
+            //
+            value_type delta = l / 2;
+            value_type delta2 = delta * delta;
+            value_type delta3 = delta * delta2;
+            value_type delta4 = delta2 * delta2;
+            value_type G = c * (c + 1) + delta;
+            value_type alpha = a + b;
+            value_type alpha2 = alpha * alpha;
+            value_type eta = (2 * alpha + 1) * (2 * alpha + 1) + 1;
+            value_type H = 3 * alpha2 + 5 * alpha + 2;
+            value_type F = alpha2 * (alpha + 1) + H * delta 
+               + (2 * alpha + 4) * delta2 + delta3;
+            value_type P = (3 * alpha + 1) * (9 * alpha + 17)
+               + 2 * alpha * (3 * alpha + 2) * (3 * alpha + 4) + 15;
+            value_type Q = 54 * alpha2 + 162 * alpha + 130;
+            value_type R = 6 * (6 * alpha + 11);
+            value_type D = delta 
+               * (H * H + 2 * P * delta + Q * delta2 + R * delta3 + 9 * delta4);
+            value_type variance = (b / G)
+               * (1 + delta * (l * l + 3 * l + eta) / (G * G))
+               - (b * b / F) * (1 + D / (F * F));
+            value_type sd = sqrt(variance);
+
+            value_type guess = comp 
+               ? quantile(complement(normal_distribution(static_cast(mean), static_cast(sd)), p))
+               : quantile(normal_distribution(static_cast(mean), static_cast(sd)), p);
+
+            if(guess >= 1)
+               guess = mean;
+            if(guess <= tools::min_value())
+               guess = mean;
+            */
+            value_type guess = mean;
+            detail::nc_beta_quantile_functor
+               f(non_central_beta_distribution(a, b, l), p, comp);
+            tools::eps_tolerance tol(policies::digits());
+            boost::uintmax_t max_iter = policies::get_max_root_iterations();
+
+            std::pair ir 
+               = bracket_and_solve_root_01(
+                  f, guess, value_type(2.5), true, tol, 
+                  max_iter, Policy());
+            value_type result = ir.first + (ir.second - ir.first) / 2;
+
+            if(max_iter >= policies::get_max_root_iterations())
+            {
+               return policies::raise_evaluation_error(function, "Unable to locate solution in a reasonable time:"
+                  " either there is no answer to quantile of the non central beta distribution"
+                  " or the answer is infinite.  Current best guess is %1%", 
+                  policies::checked_narrowing_cast(
+                     result, 
+                     function), Policy());
+            }
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+
+         template 
+         T non_central_beta_pdf(T a, T b, T lam, T x, T y, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+               using namespace boost::math;
+            //
+            // Variables come first:
+            //
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0f, -boost::math::policies::digits());
+            T l2 = lam / 2;
+            //
+            // k is the starting point for iteration, and is the
+            // maximum of the poisson weighting term:
+            //
+            int k = itrunc(l2);
+            // Starting Poisson weight:
+            T pois = gamma_p_derivative(T(k+1), l2, pol);
+            // Starting beta term:
+            T beta = x < y ? 
+               ibeta_derivative(a + k, b, x, pol)
+               : ibeta_derivative(b, a + k, y, pol);
+            T sum = 0;
+            T poisf(pois);
+            T betaf(beta);
+
+            //
+            // Stable backwards recursion first:
+            //
+            boost::uintmax_t count = k;
+            for(int i = k; i >= 0; --i)
+            {
+               T term = beta * pois;
+               sum += term;
+               if((fabs(term/sum) < errtol) || (term == 0))
+               {
+                  count = k - i;
+                  break;
+               }
+               pois *= i / l2;
+               beta *= (a + i - 1) / (x * (a + i + b - 1));
+            }
+            for(int i = k + 1; ; ++i)
+            {
+               poisf *= l2 / i;
+               betaf *= x * (a + b + i - 1) / (a + i - 1);
+
+               T term = poisf * betaf;
+               sum += term;
+               if((fabs(term/sum) < errtol) || (term == 0))
+               {
+                  break;
+               }
+               if(static_cast(count + i - k) > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "pdf(non_central_beta_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+            }
+            return sum;
+         }
+
+         template 
+         RealType nc_beta_pdf(const non_central_beta_distribution& dist, const RealType& x)
+         {
+            BOOST_MATH_STD_USING
+            static const char* function = "pdf(non_central_beta_distribution<%1%>, %1%)";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            value_type a = dist.alpha();
+            value_type b = dist.beta();
+            value_type l = dist.non_centrality();
+            value_type r;
+            if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               b, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !beta_detail::check_x(
+               function,
+               static_cast(x),
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+            BOOST_MATH_STD_USING
+            if(l == 0)
+               return pdf(boost::math::beta_distribution(dist.alpha(), dist.beta()), x);
+            return policies::checked_narrowing_cast(
+               non_central_beta_pdf(a, b, l, static_cast(x), 1 - static_cast(x), forwarding_policy()),
+               "function");
+         }
+
+      } // namespace detail
+
+      template  >
+      class non_central_beta_distribution
+      {
+      public:
+         typedef RealType value_type;
+         typedef Policy policy_type;
+
+         non_central_beta_distribution(RealType a_, RealType b_, RealType lambda) : a(a_), b(b_), ncp(lambda)
+         { 
+            const char* function = "boost::math::non_central_beta_distribution<%1%>::non_central_beta_distribution(%1%,%1%)";
+            RealType r;
+            beta_detail::check_alpha(
+               function,
+               a, &r, Policy());
+            beta_detail::check_beta(
+               function,
+               b, &r, Policy());
+            detail::check_non_centrality(
+               function,
+               lambda,
+               &r,
+               Policy());
+         } // non_central_beta_distribution constructor.
+
+         RealType alpha() const
+         { // Private data getter function.
+            return a;
+         }
+         RealType beta() const
+         { // Private data getter function.
+            return b;
+         }
+         RealType non_centrality() const
+         { // Private data getter function.
+            return ncp;
+         }
+      private:
+         // Data member, initialized by constructor.
+         RealType a;   // alpha.
+         RealType b;   // beta.
+         RealType ncp; // non-centrality parameter
+      }; // template  class non_central_beta_distribution
+
+      typedef non_central_beta_distribution non_central_beta; // Reserved name of type double.
+
+      // Non-member functions to give properties of the distribution.
+
+      template 
+      inline const std::pair range(const non_central_beta_distribution& /* dist */)
+      { // Range of permissible values for random variable k.
+         using boost::math::tools::max_value;
+         return std::pair(0, 1);
+      }
+
+      template 
+      inline const std::pair support(const non_central_beta_distribution& /* dist */)
+      { // Range of supported values for random variable k.
+         // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
+         using boost::math::tools::max_value;
+         return std::pair(0, 1);
+      }
+
+      template 
+      inline RealType mode(const non_central_beta_distribution& dist)
+      { // mode.
+         static const char* function = "mode(non_central_beta_distribution<%1%> const&)";
+
+         RealType a = dist.alpha();
+         RealType b = dist.beta();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               b, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+                  return (RealType)r;
+         RealType c = a + b + l / 2;
+         RealType mean = 1 - (b / c) * (1 + l / (2 * c * c));
+         return detail::generic_find_mode_01(
+            dist, 
+            mean, 
+            function);
+      }
+
+#if 0
+      //
+      // We don't have the necessary information to implement
+      // these at present.  These are just disabled for now,
+      // prototypes retained so we can fill in the blanks
+      // later:
+      //
+      template 
+      inline RealType mean(const non_central_beta_distribution& dist)
+      { 
+         // TODO
+         return 0;
+      } // mean
+
+      template 
+      inline RealType variance(const non_central_beta_distribution& dist)
+      { // variance.
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::variance()";
+         // TODO
+         return 0;
+      }
+
+      // RealType standard_deviation(const non_central_beta_distribution& dist)
+      // standard_deviation provided by derived accessors.
+
+      template 
+      inline RealType skewness(const non_central_beta_distribution& dist)
+      { // skewness = sqrt(l).
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::skewness()";
+         // TODO
+         return 0;
+      }
+
+      template 
+      inline RealType kurtosis_excess(const non_central_beta_distribution& dist)
+      { 
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::kurtosis_excess()";
+         // TODO
+         return 0;
+      } // kurtosis_excess
+
+      template 
+      inline RealType kurtosis(const non_central_beta_distribution& dist)
+      {
+         return kurtosis_excess(dist) + 3;
+      }
+#endif
+      template 
+      inline RealType pdf(const non_central_beta_distribution& dist, const RealType& x)
+      { // Probability Density/Mass Function.
+         return detail::nc_beta_pdf(dist, x);
+      } // pdf
+
+      template 
+      RealType cdf(const non_central_beta_distribution& dist, const RealType& x)
+      { 
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)";
+            RealType a = dist.alpha();
+            RealType b = dist.beta();
+            RealType l = dist.non_centrality();
+            RealType r;
+            if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               b, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !beta_detail::check_x(
+               function,
+               x,
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+         if(l == 0)
+            return cdf(beta_distribution(a, b), x);
+
+         return detail::non_central_beta_cdf(x, 1 - x, a, b, l, false, Policy());
+      } // cdf
+
+      template 
+      RealType cdf(const complemented2_type, RealType>& c)
+      { // Complemented Cumulative Distribution Function
+         const char* function = "boost::math::non_central_beta_distribution<%1%>::cdf(%1%)";
+         non_central_beta_distribution const& dist = c.dist;
+            RealType a = dist.alpha();
+            RealType b = dist.beta();
+            RealType l = dist.non_centrality();
+            RealType x = c.param;
+            RealType r;
+            if(!beta_detail::check_alpha(
+               function,
+               a, &r, Policy())
+               ||
+            !beta_detail::check_beta(
+               function,
+               b, &r, Policy())
+               ||            
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !beta_detail::check_x(
+               function,
+               x,
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+         if(l == 0)
+            return cdf(complement(beta_distribution(a, b), x));
+
+         return detail::non_central_beta_cdf(x, 1 - x, a, b, l, true, Policy());
+      } // ccdf
+
+      template 
+      inline RealType quantile(const non_central_beta_distribution& dist, const RealType& p)
+      { // Quantile (or Percent Point) function.
+         return detail::nc_beta_quantile(dist, p, false);
+      } // quantile
+
+      template 
+      inline RealType quantile(const complemented2_type, RealType>& c)
+      { // Quantile (or Percent Point) function.
+         return detail::nc_beta_quantile(c.dist, c.param, true);
+      } // quantile complement.
+
+   } // namespace math
+} // namespace boost
+
+// This include must be at the end, *after* the accessors
+// for this distribution have been defined, in order to
+// keep compilers that support two-phase lookup happy.
+#include 
+
+#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_BETA_HPP
+
diff --git a/include/boost/math/distributions/non_central_chi_squared.hpp b/include/boost/math/distributions/non_central_chi_squared.hpp
new file mode 100644
index 000000000..4bea2de3f
--- /dev/null
+++ b/include/boost/math/distributions/non_central_chi_squared.hpp
@@ -0,0 +1,964 @@
+// boost\math\distributions\non_central_chi_squared.hpp
+
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_SPECIAL_NON_CENTRAL_CHI_SQUARE_HPP
+#define BOOST_MATH_SPECIAL_NON_CENTRAL_CHI_SQUARE_HPP
+
+#include 
+#include  // for incomplete gamma. gamma_q
+#include  // for cyl_bessel_i
+#include  // for iround
+#include  // complements
+#include  // central distribution
+#include  // error checks
+#include  // isnan.
+#include  // for root finding.
+#include 
+#include 
+
+namespace boost
+{
+   namespace math
+   {
+
+      template 
+      class non_central_chi_squared_distribution;
+
+      namespace detail{
+
+         template 
+         T non_central_chi_square_q(T x, T f, T theta, const Policy& pol, T init_sum = 0)
+         {
+            //
+            // Computes the complement of the Non-Central Chi-Square
+            // Distribution CDF by summing a weighted sum of complements
+            // of the central-distributions.  The weighting factor is
+            // a Poisson Distribution.
+            //
+            // This is an application of the technique described in:
+            //
+            // Computing discrete mixtures of continuous
+            // distributions: noncentral chisquare, noncentral t
+            // and the distribution of the square of the sample
+            // multiple correlation coeficient.
+            // D. Benton, K. Krishnamoorthy.
+            // Computational Statistics & Data Analysis 43 (2003) 249 – 267
+            //
+            BOOST_MATH_STD_USING
+
+            // Special case:
+            if(x == 0)
+               return 1;
+
+            //
+            // Initialize the variables we'll be using:
+            //
+            T lambda = theta / 2;
+            T del = f / 2;
+            T y = x / 2;
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0, -boost::math::policies::digits());
+            T sum = init_sum;
+            //
+            // k is the starting location for iteration, we'll
+            // move both forwards and backwards from this point.
+            // k is chosen as the peek of the Poisson weights, which
+            // will occur *before* the largest term.
+            //
+            int k = iround(lambda, pol);
+            // Forwards and backwards Poisson weights:
+            T poisf = boost::math::gamma_p_derivative(1 + k, lambda, pol);
+            T poisb = poisf * k / lambda;
+            // Initial forwards central chi squared term:
+            T gamf = boost::math::gamma_q(del + k, y, pol);
+            // Forwards and backwards recursion terms on the central chi squared:
+            T xtermf = boost::math::gamma_p_derivative(del + 1 + k, y, pol);
+            T xtermb = xtermf * (del + k) / y;
+            // Initial backwards central chi squared term:
+            T gamb = gamf - xtermb;
+
+            //
+            // Forwards iteration first, this is the
+            // stable direction for the gamma function
+            // recurrences:
+            //
+            int i;
+            for(i = k; static_cast(i-k) < max_iter; ++i)
+            {
+               T term = poisf * gamf;
+               sum += term;
+               poisf *= lambda / (i + 1);
+               gamf += xtermf;
+               xtermf *= y / (del + i + 1);
+               if(((sum == 0) || (fabs(term / sum) < errtol)) && (term >= poisf * gamf))
+                  break;
+            }
+            //Error check:
+            if(static_cast(i-k) >= max_iter)
+               policies::raise_evaluation_error(
+                  "cdf(non_central_chi_squared_distribution<%1%>, %1%)", 
+                  "Series did not converge, closest value was %1%", sum, pol);
+            //
+            // Now backwards iteration: the gamma
+            // function recurrences are unstable in this
+            // direction, we rely on the terms deminishing in size
+            // faster than we introduce cancellation errors.  
+            // For this reason it's very important that we start
+            // *before* the largest term so that backwards iteration
+            // is strictly converging.
+            //
+            for(int i = k - 1; i >= 0; --i)
+            {
+               T term = poisb * gamb;
+               sum += term;
+               poisb *= i / lambda;
+               xtermb *= (del + i) / y;
+               gamb -= xtermb;
+               if((sum == 0) || (fabs(term / sum) < errtol))
+                  break;
+            }
+
+            return sum;
+         }
+
+         template 
+         T non_central_chi_square_p_ding(T x, T f, T theta, const Policy& pol, T init_sum = 0)
+         {
+            //
+            // This is an implementation of:
+            //
+            // Algorithm AS 275: 
+            // Computing the Non-Central #2 Distribution Function
+            // Cherng G. Ding
+            // Applied Statistics, Vol. 41, No. 2. (1992), pp. 478-482.
+            //
+            // This uses a stable forward iteration to sum the
+            // CDF, unfortunately this can not be used for large
+            // values of the non-centrality parameter because:
+            // * The first term may underfow to zero.
+            // * We may need an extra-ordinary number of terms
+            //   before we reach the first *significant* term.
+            //
+            BOOST_MATH_STD_USING
+            // Special case:
+            if(x == 0)
+               return 0;
+            T tk = boost::math::gamma_p_derivative(f/2 + 1, x/2, pol);
+            T lambda = theta / 2;
+            T vk = exp(-lambda);
+            T uk = vk;
+            T sum = init_sum + tk * vk;
+            if(sum == 0)
+               return sum;
+
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0, -boost::math::policies::digits());
+
+            int i;
+            T lterm(0), term(0);
+            for(i = 1; static_cast(i) < max_iter; ++i)
+            {
+               tk = tk * x / (f + 2 * i);
+               uk = uk * lambda / i;
+               vk = vk + uk;
+               lterm = term;
+               term = vk * tk;
+               sum += term;
+               if((fabs(term / sum) < errtol) && (term <= lterm))
+                  break;
+            }
+            //Error check:
+            if(static_cast(i) >= max_iter)
+               policies::raise_evaluation_error(
+                  "cdf(non_central_chi_squared_distribution<%1%>, %1%)", 
+                  "Series did not converge, closest value was %1%", sum, pol);
+            return sum;
+         }
+
+
+         template 
+         T non_central_chi_square_p(T y, T n, T lambda, const Policy& pol, T init_sum)
+         {
+            //
+            // This is taken more or less directly from:
+            //
+            // Computing discrete mixtures of continuous
+            // distributions: noncentral chisquare, noncentral t
+            // and the distribution of the square of the sample
+            // multiple correlation coeficient.
+            // D. Benton, K. Krishnamoorthy.
+            // Computational Statistics & Data Analysis 43 (2003) 249 – 267
+            //
+            // We're summing a Poisson weighting term multiplied by
+            // a central chi squared distribution.
+            //
+            BOOST_MATH_STD_USING
+            // Special case:
+            if(y == 0)
+               return 0;
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0, -boost::math::policies::digits());
+            T errorf(0), errorb(0);
+
+            T x = y / 2;
+            T del = lambda / 2;
+            //
+            // Starting location for the iteration, we'll iterate
+            // both forwards and backwards from this point.  The
+            // location chosen is the maximum of the Poisson weight
+            // function, which ocurrs *after* the largest term in the
+            // sum.
+            //
+            int k = iround(del, pol);
+            T a = n / 2 + k;
+            // Central chi squared term for forward iteration:
+            T gamkf = boost::math::gamma_p(a, x, pol);
+
+            if(lambda == 0)
+               return gamkf;
+            // Central chi squared term for backward iteration:
+            T gamkb = gamkf;
+            // Forwards Poisson weight:
+            T poiskf = gamma_p_derivative(k+1, del, pol);
+            // Backwards Poisson weight:
+            T poiskb = poiskf;
+            // Forwards gamma function recursion term:
+            T xtermf = boost::math::gamma_p_derivative(a, x, pol);
+            // Backwards gamma function recursion term:
+            T xtermb = xtermf * x / a;
+            T sum = init_sum + poiskf * gamkf;
+            if(sum == 0)
+               return sum;
+            int i = 1;
+            //
+            // Backwards recursion first, this is the stable
+            // direction for gamma function recurrences:
+            //
+            while(i <= k) 
+            {
+               xtermb *= (a - i + 1) / x;
+               gamkb += xtermb;
+               poiskb = poiskb * (k - i + 1) / del;
+               errorf = errorb;
+               errorb = gamkb * poiskb;
+               sum += errorb;
+               if((fabs(errorb / sum) < errtol) && (errorb <= errorf))
+                  break;
+               ++i;
+            }
+            i = 1;
+            //
+            // Now forwards recursion, the gamma function
+            // recurrence relation is unstable in this direction,
+            // so we rely on the magnitude of successive terms
+            // decreasing faster than we introduce cancellation error.
+            // For this reason it's vital that k is chosen to be *after*
+            // the largest term, so that successive forward iterations
+            // are strictly (and rapidly) converging.
+            //
+            do
+            {
+               xtermf = xtermf * x / (a + i - 1);
+               gamkf = gamkf - xtermf;
+               poiskf = poiskf * del / (k + i);
+               errorf = poiskf * gamkf;
+               sum += errorf;
+               ++i;
+            }while((fabs(errorf / sum) > errtol) && (static_cast(i) < max_iter));
+
+            //Error check:
+            if(static_cast(i) >= max_iter)
+               policies::raise_evaluation_error(
+                  "cdf(non_central_chi_squared_distribution<%1%>, %1%)", 
+                  "Series did not converge, closest value was %1%", sum, pol);
+
+            return sum;
+         }
+
+         template 
+         T non_central_chi_square_pdf(T x, T n, T lambda, const Policy& pol)
+         {
+            //
+            // As above but for the PDF:
+            //
+            BOOST_MATH_STD_USING
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0, -boost::math::policies::digits());
+            T x2 = x / 2;
+            T n2 = n / 2;
+            T l2 = lambda / 2;
+            T sum = 0;
+            int k = itrunc(l2);
+            T pois = gamma_p_derivative(k + 1, l2, pol) * gamma_p_derivative(n2 + k, x2);
+            if(pois == 0)
+               return 0;
+            T poisb = pois;
+            for(int i = k; ; ++i)
+            {
+               sum += pois;
+               if(pois / sum < errtol)
+                  break;
+               if(static_cast(i - k) >= max_iter)
+                  return policies::raise_evaluation_error(
+                     "pdf(non_central_chi_squared_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               pois *= l2 * x2 / ((i + 1) * (n2 + i));
+            }
+            for(int i = k - 1; i >= 0; --i)
+            {
+               poisb *= (i + 1) * (n2 + i) / (l2 * x2);
+               sum += poisb;
+               if(poisb / sum < errtol)
+                  break;
+            }
+            return sum / 2;
+         }
+
+         template 
+         inline RealType non_central_chi_squared_cdf(RealType x, RealType k, RealType l, bool invert, const Policy&)
+         {
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            BOOST_MATH_STD_USING
+            value_type result;
+            if(l == 0)
+               result = cdf(boost::math::chi_squared_distribution(k), x);
+            else if(x > k + l)
+            {
+               // Complement is the smaller of the two:
+               result = detail::non_central_chi_square_q(
+                  static_cast(x), 
+                  static_cast(k), 
+                  static_cast(l), 
+                  forwarding_policy(), 
+                  static_cast(invert ? 0 : -1));
+               invert = !invert;
+            }
+            else if(l < 200)
+            {
+               // For small values of the non-centrality parameter
+               // we can use Ding's method:
+               result = detail::non_central_chi_square_p_ding(
+                  static_cast(x), 
+                  static_cast(k), 
+                  static_cast(l), 
+                  forwarding_policy(),
+                  static_cast(invert ? -1 : 0));
+            }
+            else
+            {
+               // For largers values of the non-centrality
+               // parameter Ding's method will consume an
+               // extra-ordinary number of terms, and worse
+               // may return zero when the result is in fact
+               // finite, use Krishnamoorthy's method instead:
+               result = detail::non_central_chi_square_p(
+                  static_cast(x), 
+                  static_cast(k), 
+                  static_cast(l), 
+                  forwarding_policy(),
+                  static_cast(invert ? -1 : 0));
+            }
+            if(invert)
+               result = -result;
+            return policies::checked_narrowing_cast(
+               result, 
+               "boost::math::non_central_chi_squared_cdf<%1%>(%1%, %1%, %1%)");
+         }
+
+         template 
+         struct nccs_quantile_functor
+         {
+            nccs_quantile_functor(const non_central_chi_squared_distribution& d, T t, bool c)
+               : dist(d), target(t), comp(c) {}
+
+            T operator()(const T& x)
+            {
+               return comp ?
+                  target - cdf(complement(dist, x))
+                  : cdf(dist, x) - target;
+            }
+
+         private:
+            non_central_chi_squared_distribution dist;
+            T target;
+            bool comp;
+         };
+
+         template 
+         RealType nccs_quantile(const non_central_chi_squared_distribution& dist, const RealType& p, bool comp)
+         {
+            static const char* function = "quantile(non_central_chi_squared_distribution<%1%>, %1%)";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            value_type k = dist.degrees_of_freedom();
+            value_type l = dist.non_centrality();
+            value_type r;
+            if(!detail::check_df(
+               function,
+               k, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !detail::check_probability(
+               function,
+               static_cast(p),
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+            value_type b = (l * l) / (k + 3 * l);
+            value_type c = (k + 3 * l) / (k + 2 * l);
+            value_type ff = (k + 2 * l) / (c * c);
+            value_type guess;
+            if(comp)
+               guess = b + c * quantile(complement(chi_squared_distribution(ff), p));
+            else
+               guess = b + c * quantile(chi_squared_distribution(ff), p);
+
+            if(guess < 0)
+               guess = tools::min_value();
+
+            value_type result = detail::generic_quantile(
+               non_central_chi_squared_distribution(k, l), 
+               p, 
+               guess, 
+               comp, 
+               function);
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+
+         template 
+         RealType nccs_pdf(const non_central_chi_squared_distribution& dist, const RealType& x)
+         {
+            BOOST_MATH_STD_USING
+            static const char* function = "pdf(non_central_chi_squared_distribution<%1%>, %1%)";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+            value_type k = dist.degrees_of_freedom();
+            value_type l = dist.non_centrality();
+            value_type r;
+            if(!detail::check_df(
+               function,
+               k, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy())
+               ||
+            !detail::check_positive_x(
+               function,
+               (value_type)x,
+               &r,
+               Policy()))
+                  return (RealType)r;
+
+         BOOST_MATH_STD_USING
+         if(l == 0)
+            return pdf(boost::math::chi_squared_distribution(dist.degrees_of_freedom()), x);
+
+         // Special case:
+         if(x == 0)
+            return 0;
+         if(l > 50)
+         {
+            r = non_central_chi_square_pdf(static_cast(x), k, l, forwarding_policy());
+         }
+         else
+         {
+            r = log(x / l) * (k / 4 - 0.5f) - (x + l) / 2;
+            if(fabs(r) >= tools::log_max_value() / 4)
+            {
+               r = non_central_chi_square_pdf(static_cast(x), k, l, forwarding_policy());
+            }
+            else
+            {
+               r = exp(r);
+               r = 0.5f * r
+                  * boost::math::cyl_bessel_i(k/2 - 1, sqrt(l * x), forwarding_policy());
+            }
+         }
+         return policies::checked_narrowing_cast(
+               r, 
+               function);
+         }
+
+         template 
+         struct degrees_of_freedom_finder
+         {
+            degrees_of_freedom_finder(
+               RealType lam_, RealType x_, RealType p_, bool c)
+               : lam(lam_), x(x_), p(p_), comp(c) {}
+
+            RealType operator()(const RealType& v)
+            {
+               non_central_chi_squared_distribution d(v, lam);
+               return comp ?
+                  p - cdf(complement(d, x))
+                  : cdf(d, x) - p;
+            }
+         private:
+            RealType lam;
+            RealType x;
+            RealType p;
+            bool comp;
+         };
+
+         template 
+         inline RealType find_degrees_of_freedom(
+            RealType lam, RealType x, RealType p, RealType q, const Policy& pol)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom";
+            if((p == 0) || (q == 0))
+            {
+               //
+               // Can't a thing if one of p and q is zero:
+               //
+               return policies::raise_evaluation_error(function, 
+                  "Can't find degrees of freedom when the probability is 0 or 1, only possible answer is %1%", 
+                  RealType(std::numeric_limits::quiet_NaN()), Policy());
+            }
+            degrees_of_freedom_finder f(lam, x, p < q ? p : q, p < q ? false : true);
+            tools::eps_tolerance tol(policies::digits());
+            boost::uintmax_t max_iter = policies::get_max_root_iterations();
+            //
+            // Pick an initial guess that we know will give us a probability
+            // right around 0.5.
+            //
+            RealType guess = x - lam;
+            if(guess < 1)
+               guess = 1;
+            std::pair ir = tools::bracket_and_solve_root(
+               f, guess, RealType(2), false, tol, max_iter, pol);
+            RealType result = ir.first + (ir.second - ir.first) / 2;
+            if(max_iter >= policies::get_max_root_iterations())
+            {
+               policies::raise_evaluation_error(function, "Unable to locate solution in a reasonable time:"
+                  " or there is no answer to problem.  Current best guess is %1%", result, Policy());
+            }
+            return result;
+         }
+
+         template 
+         struct non_centrality_finder
+         {
+            non_centrality_finder(
+               RealType v_, RealType x_, RealType p_, bool c)
+               : v(v_), x(x_), p(p_), comp(c) {}
+
+            RealType operator()(const RealType& lam)
+            {
+               non_central_chi_squared_distribution d(v, lam);
+               return comp ?
+                  p - cdf(complement(d, x))
+                  : cdf(d, x) - p;
+            }
+         private:
+            RealType v;
+            RealType x;
+            RealType p;
+            bool comp;
+         };
+
+         template 
+         inline RealType find_non_centrality(
+            RealType v, RealType x, RealType p, RealType q, const Policy& pol)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_non_centrality";
+            if((p == 0) || (q == 0))
+            {
+               //
+               // Can't do a thing if one of p and q is zero:
+               //
+               return policies::raise_evaluation_error(function, 
+                  "Can't find non centrality parameter when the probability is 0 or 1, only possible answer is %1%", 
+                  RealType(std::numeric_limits::quiet_NaN()), Policy());
+            }
+            non_centrality_finder f(v, x, p < q ? p : q, p < q ? false : true);
+            tools::eps_tolerance tol(policies::digits());
+            boost::uintmax_t max_iter = policies::get_max_root_iterations();
+            //
+            // Pick an initial guess that we know will give us a probability
+            // right around 0.5.
+            //
+            RealType guess = x - v;
+            if(guess < 1)
+               guess = 1;
+            std::pair ir = tools::bracket_and_solve_root(
+               f, guess, RealType(2), false, tol, max_iter, pol);
+            RealType result = ir.first + (ir.second - ir.first) / 2;
+            if(max_iter >= policies::get_max_root_iterations())
+            {
+               policies::raise_evaluation_error(function, "Unable to locate solution in a reasonable time:"
+                  " or there is no answer to problem.  Current best guess is %1%", result, Policy());
+            }
+            return result;
+         }
+
+      }
+
+      template  >
+      class non_central_chi_squared_distribution
+      {
+      public:
+         typedef RealType value_type;
+         typedef Policy policy_type;
+
+         non_central_chi_squared_distribution(RealType df_, RealType lambda) : df(df_), ncp(lambda)
+         { 
+            const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::non_central_chi_squared_distribution(%1%,%1%)";
+            RealType r;
+            detail::check_df(
+               function,
+               df, &r, Policy());
+            detail::check_non_centrality(
+               function,
+               ncp,
+               &r,
+               Policy());
+         } // non_central_chi_squared_distribution constructor.
+
+         RealType degrees_of_freedom() const
+         { // Private data getter function.
+            return df;
+         }
+         RealType non_centrality() const
+         { // Private data getter function.
+            return ncp;
+         }
+         static RealType find_degrees_of_freedom(RealType lam, RealType x, RealType p)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+            value_type result = detail::find_degrees_of_freedom(
+               static_cast(lam), 
+               static_cast(x), 
+               static_cast(p), 
+               static_cast(1-p), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+         template 
+         static RealType find_degrees_of_freedom(const complemented3_type& c)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_degrees_of_freedom";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+            value_type result = detail::find_degrees_of_freedom(
+               static_cast(c.dist), 
+               static_cast(c.param1), 
+               static_cast(1-c.param2), 
+               static_cast(c.param2), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+         static RealType find_non_centrality(RealType v, RealType x, RealType p)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_non_centrality";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+            value_type result = detail::find_non_centrality(
+               static_cast(v), 
+               static_cast(x), 
+               static_cast(p), 
+               static_cast(1-p), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+         template 
+         static RealType find_non_centrality(const complemented3_type& c)
+         {
+            const char* function = "non_central_chi_squared<%1%>::find_non_centrality";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+            value_type result = detail::find_non_centrality(
+               static_cast(c.dist), 
+               static_cast(c.param1), 
+               static_cast(1-c.param2), 
+               static_cast(c.param2), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+      private:
+         // Data member, initialized by constructor.
+         RealType df; // degrees of freedom.
+         RealType ncp; // non-centrality parameter
+      }; // template  class non_central_chi_squared_distribution
+
+      typedef non_central_chi_squared_distribution non_central_chi_squared; // Reserved name of type double.
+
+      // Non-member functions to give properties of the distribution.
+
+      template 
+      inline const std::pair range(const non_central_chi_squared_distribution& /* dist */)
+      { // Range of permissible values for random variable k.
+         using boost::math::tools::max_value;
+         return std::pair(0, max_value()); // Max integer?
+      }
+
+      template 
+      inline const std::pair support(const non_central_chi_squared_distribution& /* dist */)
+      { // Range of supported values for random variable k.
+         // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
+         using boost::math::tools::max_value;
+         return std::pair(0,  max_value());
+      }
+
+      template 
+      inline RealType mean(const non_central_chi_squared_distribution& dist)
+      { // Mean of poisson distribution = lambda.
+         const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::mean()";
+         RealType k = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            k, &r, Policy())
+            ||
+         !detail::check_non_centrality(
+            function,
+            l,
+            &r,
+            Policy()))
+               return r;
+         return k + l;
+      } // mean
+
+      template 
+      inline RealType mode(const non_central_chi_squared_distribution& dist)
+      { // mode.
+         static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)";
+
+         RealType k = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            k, &r, Policy())
+            ||
+         !detail::check_non_centrality(
+            function,
+            l,
+            &r,
+            Policy()))
+               return (RealType)r;
+         return detail::generic_find_mode(dist, 1 + k, function);
+      }
+
+      template 
+      inline RealType variance(const non_central_chi_squared_distribution& dist)
+      { // variance.
+         const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::variance()";
+         RealType k = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            k, &r, Policy())
+            ||
+         !detail::check_non_centrality(
+            function,
+            l,
+            &r,
+            Policy()))
+               return r;
+         return 2 * (2 * l + k);
+      }
+
+      // RealType standard_deviation(const non_central_chi_squared_distribution& dist)
+      // standard_deviation provided by derived accessors.
+
+      template 
+      inline RealType skewness(const non_central_chi_squared_distribution& dist)
+      { // skewness = sqrt(l).
+         const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::skewness()";
+         RealType k = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            k, &r, Policy())
+            ||
+         !detail::check_non_centrality(
+            function,
+            l,
+            &r,
+            Policy()))
+               return r;
+         BOOST_MATH_STD_USING
+            return pow(2 / (k + 2 * l), RealType(3)/2) * (k + 3 * l);
+      }
+
+      template 
+      inline RealType kurtosis_excess(const non_central_chi_squared_distribution& dist)
+      { 
+         const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::kurtosis_excess()";
+         RealType k = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            k, &r, Policy())
+            ||
+         !detail::check_non_centrality(
+            function,
+            l,
+            &r,
+            Policy()))
+               return r;
+         return 12 * (k + 4 * l) / ((k + 2 * l) * (k + 2 * l));
+      } // kurtosis_excess
+
+      template 
+      inline RealType kurtosis(const non_central_chi_squared_distribution& dist)
+      {
+         return kurtosis_excess(dist) + 3;
+      }
+
+      template 
+      inline RealType pdf(const non_central_chi_squared_distribution& dist, const RealType& x)
+      { // Probability Density/Mass Function.
+         return detail::nccs_pdf(dist, x);
+      } // pdf
+
+      template 
+      RealType cdf(const non_central_chi_squared_distribution& dist, const RealType& x)
+      { 
+         const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::cdf(%1%)";
+         RealType k = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            k, &r, Policy())
+            ||
+         !detail::check_non_centrality(
+            function,
+            l,
+            &r,
+            Policy())
+            ||
+         !detail::check_positive_x(
+            function,
+            x,
+            &r,
+            Policy()))
+               return r;
+
+         return detail::non_central_chi_squared_cdf(x, k, l, false, Policy());
+      } // cdf
+
+      template 
+      RealType cdf(const complemented2_type, RealType>& c)
+      { // Complemented Cumulative Distribution Function
+         const char* function = "boost::math::non_central_chi_squared_distribution<%1%>::cdf(%1%)";
+         non_central_chi_squared_distribution const& dist = c.dist;
+         RealType x = c.param;
+         RealType k = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            k, &r, Policy())
+            ||
+         !detail::check_non_centrality(
+            function,
+            l,
+            &r,
+            Policy())
+            ||
+         !detail::check_positive_x(
+            function,
+            x,
+            &r,
+            Policy()))
+               return r;
+
+         return detail::non_central_chi_squared_cdf(x, k, l, true, Policy());
+      } // ccdf
+
+      template 
+      inline RealType quantile(const non_central_chi_squared_distribution& dist, const RealType& p)
+      { // Quantile (or Percent Point) function.
+         return detail::nccs_quantile(dist, p, false);
+      } // quantile
+
+      template 
+      inline RealType quantile(const complemented2_type, RealType>& c)
+      { // Quantile (or Percent Point) function.
+         return detail::nccs_quantile(c.dist, c.param, true);
+      } // quantile complement.
+
+   } // namespace math
+} // namespace boost
+
+// This include must be at the end, *after* the accessors
+// for this distribution have been defined, in order to
+// keep compilers that support two-phase lookup happy.
+#include 
+
+#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_CHI_SQUARE_HPP
+
+
+
diff --git a/include/boost/math/distributions/non_central_f.hpp b/include/boost/math/distributions/non_central_f.hpp
new file mode 100644
index 000000000..19dbde761
--- /dev/null
+++ b/include/boost/math/distributions/non_central_f.hpp
@@ -0,0 +1,408 @@
+// boost\math\distributions\non_central_f.hpp
+
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP
+#define BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP
+
+#include 
+#include 
+
+namespace boost
+{
+   namespace math
+   {
+      template  >
+      class non_central_f_distribution
+      {
+      public:
+         typedef RealType value_type;
+         typedef Policy policy_type;
+
+         non_central_f_distribution(RealType v1_, RealType v2_, RealType lambda) : v1(v1_), v2(v2_), ncp(lambda)
+         { 
+            const char* function = "boost::math::non_central_f_distribution<%1%>::non_central_f_distribution(%1%,%1%)";
+            RealType r;
+            detail::check_df(
+               function,
+               v1, &r, Policy());
+            detail::check_df(
+               function,
+               v2, &r, Policy());
+            detail::check_non_centrality(
+               function,
+               lambda,
+               &r,
+               Policy());
+         } // non_central_f_distribution constructor.
+
+         RealType degrees_of_freedom1()const
+         {
+            return v1;
+         }
+         RealType degrees_of_freedom2()const
+         {
+            return v2;
+         }
+         RealType non_centrality() const
+         { // Private data getter function.
+            return ncp;
+         }
+      private:
+         // Data member, initialized by constructor.
+         RealType v1;   // alpha.
+         RealType v2;   // beta.
+         RealType ncp; // non-centrality parameter
+      }; // template  class non_central_f_distribution
+
+      typedef non_central_f_distribution non_central_f; // Reserved name of type double.
+
+      // Non-member functions to give properties of the distribution.
+
+      template 
+      inline const std::pair range(const non_central_f_distribution& /* dist */)
+      { // Range of permissible values for random variable k.
+         using boost::math::tools::max_value;
+         return std::pair(0, max_value());
+      }
+
+      template 
+      inline const std::pair support(const non_central_f_distribution& /* dist */)
+      { // Range of supported values for random variable k.
+         // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
+         using boost::math::tools::max_value;
+         return std::pair(0, max_value());
+      }
+
+      template 
+      inline RealType mean(const non_central_f_distribution& dist)
+      { 
+         const char* function = "mean(non_central_f_distribution<%1%> const&)";
+         RealType v1 = dist.degrees_of_freedom1();
+         RealType v2 = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v1, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               v2, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         if(v2 <= 2)
+            return policies::raise_domain_error(
+               function, 
+               "Second degrees of freedom parameter was %1%, but must be > 2 !", 
+               v2, Policy());
+         return v2 * (v1 + l) / (v1 * (v2 - 2));
+      } // mean
+
+      template 
+      inline RealType mode(const non_central_f_distribution& dist)
+      { // mode.
+         static const char* function = "mode(non_central_chi_squared_distribution<%1%> const&)";
+
+         RealType n = dist.degrees_of_freedom1();
+         RealType m = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            n, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               m, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         return detail::generic_find_mode(
+            dist, 
+            m * (n + l) / (n * (m - 2)), 
+            function);
+      }
+
+      template 
+      inline RealType variance(const non_central_f_distribution& dist)
+      { // variance.
+         const char* function = "variance(non_central_f_distribution<%1%> const&)";
+         RealType n = dist.degrees_of_freedom1();
+         RealType m = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            n, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               m, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         if(m <= 4)
+            return policies::raise_domain_error(
+               function, 
+               "Second degrees of freedom parameter was %1%, but must be > 4 !", 
+               m, Policy());
+         RealType result = 2 * m * m * ((n + l) * (n + l)
+            + (m - 2) * (n + 2 * l));
+         result /= (m - 4) * (m - 2) * (m - 2) * n * n;
+         return result;
+      }
+
+      // RealType standard_deviation(const non_central_f_distribution& dist)
+      // standard_deviation provided by derived accessors.
+
+      template 
+      inline RealType skewness(const non_central_f_distribution& dist)
+      { // skewness = sqrt(l).
+         const char* function = "skewness(non_central_f_distribution<%1%> const&)";
+         BOOST_MATH_STD_USING
+         RealType n = dist.degrees_of_freedom1();
+         RealType m = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            n, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               m, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         if(m <= 6)
+            return policies::raise_domain_error(
+               function, 
+               "Second degrees of freedom parameter was %1%, but must be > 6 !", 
+               m, Policy());
+         RealType result = 2 * constants::root_two();
+         result *= sqrt(m - 4);
+         result *= (n * (m + n - 2) *(m + 2 * n - 2)
+            + 3 * (m + n - 2) * (m + 2 * n - 2) * l
+            + 6 * (m + n - 2) * l * l + 2 * l * l * l);
+         result /= (m - 6) * pow(n * (m + n - 2) + 2 * (m + n - 2) * l + l * l, RealType(1.5f));
+         return result;
+      }
+
+      template 
+      inline RealType kurtosis_excess(const non_central_f_distribution& dist)
+      { 
+         const char* function = "kurtosis_excess(non_central_f_distribution<%1%> const&)";
+         BOOST_MATH_STD_USING
+         RealType n = dist.degrees_of_freedom1();
+         RealType m = dist.degrees_of_freedom2();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            n, &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               m, &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               l,
+               &r,
+               Policy()))
+               return r;
+         if(m <= 8)
+            return policies::raise_domain_error(
+               function, 
+               "Second degrees of freedom parameter was %1%, but must be > 8 !", 
+               m, Policy());
+         RealType l2 = l * l;
+         RealType l3 = l2 * l;
+         RealType l4 = l2 * l2;
+         RealType result = (3 * (m - 4) * (n * (m + n - 2)
+            * (4 * (m - 2) * (m - 2) 
+            + (m - 2) * (m + 10) * n
+            + (10 + m) * n * n)
+            + 4 * (m + n - 2) * (4 * (m - 2) * (m - 2)
+            + (m - 2) * (10 + m) * n 
+            + (10 + m) * n * n) * l + 2 * (10 + m)
+            * (m + n - 2) * (2 * m + 3 * n - 4) * l2
+            + 4 * (10 + m) * (-2 + m + n) * l3
+            + (10 + m) * l4))
+            /
+            ((-8 + m) * (-6 + m) * pow(n * (-2 + m + n)
+            + 2 * (-2 + m + n) * l + l2, 2));
+            return result;
+      } // kurtosis_excess
+
+      template 
+      inline RealType kurtosis(const non_central_f_distribution& dist)
+      {
+         return kurtosis_excess(dist) + 3;
+      }
+
+      template 
+      inline RealType pdf(const non_central_f_distribution& dist, const RealType& x)
+      { // Probability Density/Mass Function.
+         typedef typename policies::evaluation::type value_type;
+         typedef typename policies::normalise<
+            Policy, 
+            policies::promote_float, 
+            policies::promote_double, 
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+
+         value_type alpha = dist.degrees_of_freedom1() / 2;
+         value_type beta = dist.degrees_of_freedom2() / 2;
+         value_type y = x * alpha / beta;
+         value_type r = pdf(boost::math::non_central_beta_distribution(alpha, beta, dist.non_centrality()), y / (1 + y));
+         return policies::checked_narrowing_cast(
+            r * (dist.degrees_of_freedom1() / dist.degrees_of_freedom2()) / ((1 + y) * (1 + y)),
+            "pdf(non_central_f_distribution<%1%>, %1%)");
+      } // pdf
+
+      template 
+      RealType cdf(const non_central_f_distribution& dist, const RealType& x)
+      { 
+         const char* function = "cdf(const non_central_f_distribution<%1%>&, %1%)";
+         RealType r;
+         if(!detail::check_df(
+            function,
+            dist.degrees_of_freedom1(), &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               dist.degrees_of_freedom2(), &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               dist.non_centrality(),
+               &r,
+               Policy()))
+               return r;
+         
+         if((x < 0) || !(boost::math::isfinite)(x))
+         {
+            return policies::raise_domain_error(
+               function, "Random Variable parameter was %1%, but must be > 0 !", x, Policy());
+         }
+
+         RealType alpha = dist.degrees_of_freedom1() / 2;
+         RealType beta = dist.degrees_of_freedom2() / 2;
+         RealType y = x * alpha / beta;
+         RealType c = y / (1 + y);
+         RealType cp = 1 / (1 + y);
+         //
+         // To ensure accuracy, we pass both x and 1-x to the
+         // non-central beta cdf routine, this ensures accuracy
+         // even when we compute x to be ~ 1:
+         //
+         r = detail::non_central_beta_cdf(c, cp, alpha, beta, 
+            dist.non_centrality(), false, Policy());
+         return r;
+      } // cdf
+
+      template 
+      RealType cdf(const complemented2_type, RealType>& c)
+      { // Complemented Cumulative Distribution Function
+         const char* function = "cdf(complement(const non_central_f_distribution<%1%>&, %1%))";
+         RealType r;
+         if(!detail::check_df(
+            function,
+            c.dist.degrees_of_freedom1(), &r, Policy())
+               ||
+            !detail::check_df(
+               function,
+               c.dist.degrees_of_freedom2(), &r, Policy())
+               ||
+            !detail::check_non_centrality(
+               function,
+               c.dist.non_centrality(),
+               &r,
+               Policy()))
+               return r;
+         
+         if((c.param < 0) || !(boost::math::isfinite)(c.param))
+         {
+            return policies::raise_domain_error(
+               function, "Random Variable parameter was %1%, but must be > 0 !", c.param, Policy());
+         }
+
+         RealType alpha = c.dist.degrees_of_freedom1() / 2;
+         RealType beta = c.dist.degrees_of_freedom2() / 2;
+         RealType y = c.param * alpha / beta;
+         RealType x = y / (1 + y);
+         RealType cx = 1 / (1 + y);
+         //
+         // To ensure accuracy, we pass both x and 1-x to the
+         // non-central beta cdf routine, this ensures accuracy
+         // even when we compute x to be ~ 1:
+         //
+         r = detail::non_central_beta_cdf(x, cx, alpha, beta, 
+            c.dist.non_centrality(), true, Policy());
+         return r;
+      } // ccdf
+
+      template 
+      inline RealType quantile(const non_central_f_distribution& dist, const RealType& p)
+      { // Quantile (or Percent Point) function.
+         RealType alpha = dist.degrees_of_freedom1() / 2;
+         RealType beta = dist.degrees_of_freedom2() / 2;
+         RealType x = quantile(boost::math::non_central_beta_distribution(alpha, beta, dist.non_centrality()), p);
+         if(x == 1)
+            return policies::raise_overflow_error(
+               "quantile(const non_central_f_distribution<%1%>&, %1%)", 
+               "Result of non central F quantile is too large to represent.", 
+               Policy());
+         return (x / (1 - x)) * (dist.degrees_of_freedom2() / dist.degrees_of_freedom1());
+      } // quantile
+
+      template 
+      inline RealType quantile(const complemented2_type, RealType>& c)
+      { // Quantile (or Percent Point) function.
+         RealType alpha = c.dist.degrees_of_freedom1() / 2;
+         RealType beta = c.dist.degrees_of_freedom2() / 2;
+         RealType x = quantile(complement(boost::math::non_central_beta_distribution(alpha, beta, c.dist.non_centrality()), c.param));
+         if(x == 1)
+            return policies::raise_overflow_error(
+               "quantile(complement(const non_central_f_distribution<%1%>&, %1%))", 
+               "Result of non central F quantile is too large to represent.", 
+               Policy());
+         return (x / (1 - x)) * (c.dist.degrees_of_freedom2() / c.dist.degrees_of_freedom1());
+      } // quantile complement.
+
+   } // namespace math
+} // namespace boost
+
+// This include must be at the end, *after* the accessors
+// for this distribution have been defined, in order to
+// keep compilers that support two-phase lookup happy.
+#include 
+
+#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_F_HPP
+
+
+
diff --git a/include/boost/math/distributions/non_central_t.hpp b/include/boost/math/distributions/non_central_t.hpp
new file mode 100644
index 000000000..f68efe6ce
--- /dev/null
+++ b/include/boost/math/distributions/non_central_t.hpp
@@ -0,0 +1,1067 @@
+// boost\math\distributions\non_central_t.hpp
+
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_SPECIAL_NON_CENTRAL_T_HPP
+#define BOOST_MATH_SPECIAL_NON_CENTRAL_T_HPP
+
+#include 
+#include  // for nc beta
+#include  // for normal CDF and quantile
+#include 
+#include  // quantile
+
+namespace boost
+{
+   namespace math
+   {
+
+      template 
+      class non_central_t_distribution;
+
+      namespace detail{
+
+         template 
+         T non_central_t2_p(T n, T delta, T x, T y, const Policy& pol, T init_val)
+         {
+            BOOST_MATH_STD_USING
+            //
+            // Variables come first:
+            //
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0f, -boost::math::policies::digits());
+            T d2 = delta * delta / 2;
+            //
+            // k is the starting point for iteration, and is the
+            // maximum of the poisson weighting term:
+            //
+            int k = boost::math::itrunc(d2);
+            // Starting Poisson weight:
+            T pois = gamma_p_derivative(T(k+1), d2, pol) 
+               * tgamma_delta_ratio(T(k + 1), T(0.5f))
+               * delta / constants::root_two();
+            if(pois == 0)
+               return init_val;
+            // Starting beta term:
+            T beta = x < y
+               ? ibeta(T(k + 1), n / 2, x, pol)
+               : ibetac(n / 2, T(k + 1), y, pol);
+            // Recurance term:
+            T xterm = x < y
+               ? ibeta_derivative(T(k + 1), n / 2, x, pol)
+               : ibeta_derivative(n / 2, T(k + 1), y, pol);
+            xterm *= y / (n / 2 + k);
+            T poisf(pois), betaf(beta), xtermf(xterm);
+            T sum = init_val;
+            if((xterm == 0) && (beta == 0))
+               return init_val;
+
+            //
+            // Backwards recursion first, this is the stable
+            // direction for recursion:
+            //
+            boost::uintmax_t count = 0;
+            for(int i = k; i >= 0; --i)
+            {
+               T term = beta * pois;
+               sum += term;
+               if(fabs(term/sum) < errtol)
+                  break;
+               pois *= (i + 0.5f) / d2;
+               beta += xterm;
+               xterm *= (i) / (x * (n / 2 + i - 1));
+               ++count;
+            }
+            for(int i = k + 1; ; ++i)
+            {
+               poisf *= d2 / (i + 0.5f);
+               xtermf *= (x * (n / 2 + i - 1)) / (i);
+               betaf -= xtermf;
+               T term = poisf * betaf;
+               sum += term;
+               if(fabs(term/sum) < errtol)
+                  break;
+               ++count;
+               if(count > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "cdf(non_central_t_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+            }
+            return sum;
+         }
+
+         template 
+         T non_central_t2_q(T n, T delta, T x, T y, const Policy& pol, T init_val)
+         {
+            BOOST_MATH_STD_USING
+            //
+            // Variables come first:
+            //
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0f, -boost::math::policies::digits());
+            T d2 = delta * delta / 2;
+            //
+            // k is the starting point for iteration, and is the
+            // maximum of the poisson weighting term:
+            //
+            int k = boost::math::itrunc(d2);
+            // Starting Poisson weight:
+            T pois = gamma_p_derivative(T(k+1), d2, pol) 
+               * tgamma_delta_ratio(T(k + 1), T(0.5f))
+               * delta / constants::root_two();
+            if(pois == 0)
+               return init_val;
+            // Starting beta term:
+            T beta = x < y 
+               ? ibetac(T(k + 1), n / 2, x, pol)
+               : ibeta(n / 2, T(k + 1), y, pol);
+            // Recurance term:
+            T xterm = x < y
+               ? ibeta_derivative(T(k + 1), n / 2, x, pol)
+               : ibeta_derivative(n / 2, T(k + 1), y, pol);
+            xterm *= y / (n / 2 + k);
+            T poisf(pois), betaf(beta), xtermf(xterm);
+            T sum = init_val;
+            if((xterm == 0) && (beta == 0))
+               return init_val;
+
+            //
+            // Forward recursion first, this is the stable direction:
+            //
+            boost::uintmax_t count = 0;
+            for(int i = k + 1; ; ++i)
+            {
+               poisf *= d2 / (i + 0.5f);
+               xtermf *= (x * (n / 2 + i - 1)) / (i);
+               betaf += xtermf;
+
+               T term = poisf * betaf;
+               sum += term;
+               if(fabs(term/sum) < errtol)
+                  break;
+               if(count > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "cdf(non_central_t_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+               ++count;
+            }
+            //
+            // Backwards recursion:
+            //
+            for(int i = k; i >= 0; --i)
+            {
+               T term = beta * pois;
+               sum += term;
+               if(fabs(term/sum) < errtol)
+                  break;
+               pois *= (i + 0.5f) / d2;
+               beta -= xterm;
+               xterm *= (i) / (x * (n / 2 + i - 1));
+               ++count;
+               if(count > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "cdf(non_central_t_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+            }
+            return sum;
+         }
+
+         template 
+         T non_central_t_cdf(T n, T delta, T t, bool invert, const Policy& pol)
+         {
+            //
+            // For t < 0 we have to use reflect:
+            //
+            if(t < 0)
+            {
+               t = -t;
+               delta = -delta;
+               invert = !invert;
+            }
+            //
+            // x and y are the corresponding random
+            // variables for the noncentral beta distribution,
+            // with y = 1 - x:
+            //
+            T x = t * t / (n + t * t);
+            T y = n / (n + t * t);
+            T d2 = delta * delta;
+            T a = 0.5f;
+            T b = n / 2;
+            T c = a + b + d2 / 2;
+            //
+            // Crossover point for calculating p or q is the same
+            // as for the noncentral beta:
+            //
+            T cross = 1 - (b / c) * (1 + d2 / (2 * c * c));
+            T result;
+            if(x < cross)
+            {
+               //
+               // Calculate p:
+               //
+               if(x != 0)
+               {
+                  result = non_central_beta_p(a, b, d2, x, y, pol);
+                  result = non_central_t2_p(n, delta, x, y, pol, result);
+                  result /= 2;
+               }
+               else
+                  result = 0;
+               result += cdf(boost::math::normal_distribution(), -delta);
+            }
+            else
+            {
+               //
+               // Calculate q:
+               //
+               invert = !invert;
+               if(x != 0)
+               {
+                  result = non_central_beta_q(a, b, d2, x, y, pol);
+                  result = non_central_t2_q(n, delta, x, y, pol, result);
+                  result /= 2;
+               }
+               else
+                  result = cdf(complement(boost::math::normal_distribution(), -delta));
+            }
+            if(invert)
+               result = 1 - result;
+            return result;
+         }
+
+         template 
+         T non_central_t_quantile(T v, T delta, T p, T q, const Policy&)
+         {
+            BOOST_MATH_STD_USING
+            static const char* function = "quantile(non_central_t_distribution<%1%>, %1%)";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+
+               T r;
+               if(!detail::check_df(
+                  function,
+                  v, &r, Policy())
+                  ||
+               !detail::check_finite(
+                  function,
+                  delta,
+                  &r,
+                  Policy())
+                  ||
+               !detail::check_probability(
+                  function,
+                  p,
+                  &r,
+                  Policy()))
+                     return r;
+
+            value_type guess = 0;
+            if(v > 3)
+            {
+               value_type mean = delta * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, T(0.5f));
+               value_type var = ((delta * delta + 1) * v) / (v - 2) - mean * mean;
+               if(p < q)
+                  guess = quantile(normal_distribution(mean, var), p);
+               else
+                  guess = quantile(complement(normal_distribution(mean, var), q));
+            }
+            //
+            // We *must* get the sign of the initial guess correct, 
+            // or our root-finder will fail, so double check it now:
+            //
+            value_type pzero = non_central_t_cdf(
+               static_cast(v), 
+               static_cast(delta), 
+               static_cast(0), 
+               !(p < q), 
+               forwarding_policy());
+            int s;
+            if(p < q)
+               s = boost::math::sign(p - pzero);
+            else
+               s = boost::math::sign(pzero - q);
+            if(s != boost::math::sign(guess))
+            {
+               guess = s;
+            }
+
+            value_type result = detail::generic_quantile(
+               non_central_t_distribution(v, delta), 
+               (p < q ? p : q), 
+               guess, 
+               (p >= q), 
+               function);
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+
+         template 
+         T non_central_t2_pdf(T n, T delta, T x, T y, const Policy& pol, T init_val)
+         {
+            BOOST_MATH_STD_USING
+            //
+            // Variables come first:
+            //
+            boost::uintmax_t max_iter = policies::get_max_series_iterations();
+            T errtol = ldexp(1.0f, -boost::math::policies::digits());
+            T d2 = delta * delta / 2;
+            //
+            // k is the starting point for iteration, and is the
+            // maximum of the poisson weighting term:
+            //
+            int k = boost::math::itrunc(d2);
+            // Starting Poisson weight:
+            T pois = gamma_p_derivative(T(k+1), d2, pol) 
+               * tgamma_delta_ratio(T(k + 1), T(0.5f))
+               * delta / constants::root_two();
+            // Starting beta term:
+            T xterm = x < y
+               ? ibeta_derivative(T(k + 1), n / 2, x, pol)
+               : ibeta_derivative(n / 2, T(k + 1), y, pol);
+            T poisf(pois), xtermf(xterm);
+            T sum = init_val;
+            if((pois == 0) || (xterm == 0))
+               return init_val;
+
+            //
+            // Backwards recursion first, this is the stable
+            // direction for recursion:
+            //
+            boost::uintmax_t count = 0;
+            for(int i = k; i >= 0; --i)
+            {
+               T term = xterm * pois;
+               sum += term;
+               if((fabs(term/sum) < errtol) || (term == 0))
+                  break;
+               pois *= (i + 0.5f) / d2;
+               xterm *= (i) / (x * (n / 2 + i));
+               ++count;
+               if(count > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "pdf(non_central_t_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+            }
+            for(int i = k + 1; ; ++i)
+            {
+               poisf *= d2 / (i + 0.5f);
+               xtermf *= (x * (n / 2 + i)) / (i);
+               T term = poisf * xtermf;
+               sum += term;
+               if((fabs(term/sum) < errtol) || (term == 0))
+                  break;
+               ++count;
+               if(count > max_iter)
+               {
+                  return policies::raise_evaluation_error(
+                     "pdf(non_central_t_distribution<%1%>, %1%)", 
+                     "Series did not converge, closest value was %1%", sum, pol);
+               }
+            }
+            return sum;
+         }
+
+         template 
+         T non_central_t_pdf(T n, T delta, T t, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+            //
+            // For t < 0 we have to use the reflection formula:
+            //
+            if(t < 0)
+            {
+               t = -t;
+               delta = -delta;
+            }
+            if(t == 0)
+            {
+               //
+               // Handle this as a special case, using the formula
+               // from Weisstein, Eric W. 
+               // "Noncentral Student's t-Distribution." 
+               // From MathWorld--A Wolfram Web Resource. 
+               // http://mathworld.wolfram.com/NoncentralStudentst-Distribution.html 
+               // 
+               // The formula is simplified thanks to the relation
+               // 1F1(a,b,0) = 1.
+               //
+               return tgamma_delta_ratio(n / 2 + 0.5f, T(0.5f))
+                  * sqrt(n / constants::pi()) 
+                  * exp(-delta * delta / 2) / 2;
+            }
+            //
+            // x and y are the corresponding random
+            // variables for the noncentral beta distribution,
+            // with y = 1 - x:
+            //
+            T x = t * t / (n + t * t);
+            T y = n / (n + t * t);
+            T a = 0.5f;
+            T b = n / 2;
+            T d2 = delta * delta;
+            //
+            // Calculate pdf:
+            //
+            T dt = n * t / (n * n + 2 * n * t * t + t * t * t * t);
+            T result = non_central_beta_pdf(a, b, d2, x, y, pol);
+            T tol = tools::epsilon() * result * 500;
+            result = non_central_t2_pdf(n, delta, x, y, pol, result);
+            if(result <= tol)
+               result = 0;
+            result *= dt;
+            return result;
+         }
+
+         template 
+         T mean(T v, T delta, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+            return delta * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, T(0.5f), pol);
+         }
+
+         template 
+         T variance(T v, T delta, const Policy& pol)
+         {
+            T result = ((delta * delta + 1) * v) / (v - 2);
+            T m = mean(v, delta, pol);
+            result -= m * m;
+            return result;
+         }
+
+         template 
+         T skewness(T v, T delta, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+            T mean = boost::math::detail::mean(v, delta, pol);
+            T l2 = delta * delta;
+            T var = ((l2 + 1) * v) / (v - 2) - mean * mean;
+            T result = -2 * var;
+            result += v * (l2 + 2 * v - 3) / ((v - 3) * (v - 2));
+            result *= mean;
+            result /= pow(var, T(1.5f));
+            return result;
+         }
+
+         template 
+         T kurtosis_excess(T v, T delta, const Policy& pol)
+         {
+            BOOST_MATH_STD_USING
+            T mean = boost::math::detail::mean(v, delta, pol);
+            T l2 = delta * delta;
+            T var = ((l2 + 1) * v) / (v - 2) - mean * mean;
+            T result = -3 * var;
+            result += v * (l2 * (v + 1) + 3 * (3 * v - 5)) / ((v - 3) * (v - 2));
+            result *= -mean * mean;
+            result += v * v * (l2 * l2 + 6 * l2 + 3) / ((v - 4) * (v - 2));
+            result /= var * var;
+            return result;
+         }
+
+#if 0
+         // 
+         // This code is disabled, since there can be multiple answers to the
+         // question, and it's not clear how to find the "right" one.
+         //
+         template 
+         struct t_degrees_of_freedom_finder
+         {
+            t_degrees_of_freedom_finder(
+               RealType delta_, RealType x_, RealType p_, bool c)
+               : delta(delta_), x(x_), p(p_), comp(c) {}
+
+            RealType operator()(const RealType& v)
+            {
+               non_central_t_distribution d(v, delta);
+               return comp ?
+                  p - cdf(complement(d, x))
+                  : cdf(d, x) - p;
+            }
+         private:
+            RealType delta;
+            RealType x;
+            RealType p;
+            bool comp;
+         };
+
+         template 
+         inline RealType find_t_degrees_of_freedom(
+            RealType delta, RealType x, RealType p, RealType q, const Policy& pol)
+         {
+            const char* function = "non_central_t<%1%>::find_degrees_of_freedom";
+            if((p == 0) || (q == 0))
+            {
+               //
+               // Can't a thing if one of p and q is zero:
+               //
+               return policies::raise_evaluation_error(function, 
+                  "Can't find degrees of freedom when the probability is 0 or 1, only possible answer is %1%", 
+                  RealType(std::numeric_limits::quiet_NaN()), Policy());
+            }
+            t_degrees_of_freedom_finder f(delta, x, p < q ? p : q, p < q ? false : true);
+            tools::eps_tolerance tol(policies::digits());
+            boost::uintmax_t max_iter = policies::get_max_root_iterations();
+            //
+            // Pick an initial guess:
+            //
+            RealType guess = 200;
+            std::pair ir = tools::bracket_and_solve_root(
+               f, guess, RealType(2), false, tol, max_iter, pol);
+            RealType result = ir.first + (ir.second - ir.first) / 2;
+            if(max_iter >= policies::get_max_root_iterations())
+            {
+               policies::raise_evaluation_error(function, "Unable to locate solution in a reasonable time:"
+                  " or there is no answer to problem.  Current best guess is %1%", result, Policy());
+            }
+            return result;
+         }
+
+         template 
+         struct t_non_centrality_finder
+         {
+            t_non_centrality_finder(
+               RealType v_, RealType x_, RealType p_, bool c)
+               : v(v_), x(x_), p(p_), comp(c) {}
+
+            RealType operator()(const RealType& delta)
+            {
+               non_central_t_distribution d(v, delta);
+               return comp ?
+                  p - cdf(complement(d, x))
+                  : cdf(d, x) - p;
+            }
+         private:
+            RealType v;
+            RealType x;
+            RealType p;
+            bool comp;
+         };
+
+         template 
+         inline RealType find_t_non_centrality(
+            RealType v, RealType x, RealType p, RealType q, const Policy& pol)
+         {
+            const char* function = "non_central_t<%1%>::find_t_non_centrality";
+            if((p == 0) || (q == 0))
+            {
+               //
+               // Can't do a thing if one of p and q is zero:
+               //
+               return policies::raise_evaluation_error(function, 
+                  "Can't find non centrality parameter when the probability is 0 or 1, only possible answer is %1%", 
+                  RealType(std::numeric_limits::quiet_NaN()), Policy());
+            }
+            t_non_centrality_finder f(v, x, p < q ? p : q, p < q ? false : true);
+            tools::eps_tolerance tol(policies::digits());
+            boost::uintmax_t max_iter = policies::get_max_root_iterations();
+            //
+            // Pick an initial guess that we know is the right side of
+            // zero:
+            //
+            RealType guess;
+            if(f(0) < 0)
+               guess = 1;
+            else
+               guess = -1;
+            std::pair ir = tools::bracket_and_solve_root(
+               f, guess, RealType(2), false, tol, max_iter, pol);
+            RealType result = ir.first + (ir.second - ir.first) / 2;
+            if(max_iter >= policies::get_max_root_iterations())
+            {
+               policies::raise_evaluation_error(function, "Unable to locate solution in a reasonable time:"
+                  " or there is no answer to problem.  Current best guess is %1%", result, Policy());
+            }
+            return result;
+         }
+#endif
+      } // namespace detail
+
+      template  >
+      class non_central_t_distribution
+      {
+      public:
+         typedef RealType value_type;
+         typedef Policy policy_type;
+
+         non_central_t_distribution(RealType v_, RealType lambda) : v(v_), ncp(lambda)
+         { 
+            const char* function = "boost::math::non_central_t_distribution<%1%>::non_central_t_distribution(%1%,%1%)";
+            RealType r;
+            detail::check_df(
+               function,
+               v, &r, Policy());
+            detail::check_finite(
+               function,
+               lambda,
+               &r,
+               Policy());
+         } // non_central_t_distribution constructor.
+
+         RealType degrees_of_freedom() const
+         { // Private data getter function.
+            return v;
+         }
+         RealType non_centrality() const
+         { // Private data getter function.
+            return ncp;
+         }
+#if 0
+         // 
+         // This code is disabled, since there can be multiple answers to the
+         // question, and it's not clear how to find the "right" one.
+         //
+         static RealType find_degrees_of_freedom(RealType delta, RealType x, RealType p)
+         {
+            const char* function = "non_central_t<%1%>::find_degrees_of_freedom";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+            value_type result = detail::find_t_degrees_of_freedom(
+               static_cast(delta), 
+               static_cast(x), 
+               static_cast(p), 
+               static_cast(1-p), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+         template 
+         static RealType find_degrees_of_freedom(const complemented3_type& c)
+         {
+            const char* function = "non_central_t<%1%>::find_degrees_of_freedom";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+            value_type result = detail::find_t_degrees_of_freedom(
+               static_cast(c.dist), 
+               static_cast(c.param1), 
+               static_cast(1-c.param2), 
+               static_cast(c.param2), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+         static RealType find_non_centrality(RealType v, RealType x, RealType p)
+         {
+            const char* function = "non_central_t<%1%>::find_t_non_centrality";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+            value_type result = detail::find_t_non_centrality(
+               static_cast(v), 
+               static_cast(x), 
+               static_cast(p), 
+               static_cast(1-p), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+         template 
+         static RealType find_non_centrality(const complemented3_type& c)
+         {
+            const char* function = "non_central_t<%1%>::find_t_non_centrality";
+            typedef typename policies::evaluation::type value_type;
+            typedef typename policies::normalise<
+               Policy, 
+               policies::promote_float, 
+               policies::promote_double, 
+               policies::discrete_quantile<>,
+               policies::assert_undefined<> >::type forwarding_policy;
+            value_type result = detail::find_t_non_centrality(
+               static_cast(c.dist), 
+               static_cast(c.param1), 
+               static_cast(1-c.param2), 
+               static_cast(c.param2), 
+               forwarding_policy());
+            return policies::checked_narrowing_cast(
+               result, 
+               function);
+         }
+#endif
+      private:
+         // Data member, initialized by constructor.
+         RealType v;   // degrees of freedom
+         RealType ncp; // non-centrality parameter
+      }; // template  class non_central_t_distribution
+
+      typedef non_central_t_distribution non_central_t; // Reserved name of type double.
+
+      // Non-member functions to give properties of the distribution.
+
+      template 
+      inline const std::pair range(const non_central_t_distribution& /* dist */)
+      { // Range of permissible values for random variable k.
+         using boost::math::tools::max_value;
+         return std::pair(-max_value(), max_value());
+      }
+
+      template 
+      inline const std::pair support(const non_central_t_distribution& /* dist */)
+      { // Range of supported values for random variable k.
+         // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.
+         using boost::math::tools::max_value;
+         return std::pair(-max_value(), max_value());
+      }
+
+      template 
+      inline RealType mode(const non_central_t_distribution& dist)
+      { // mode.
+         static const char* function = "mode(non_central_t_distribution<%1%> const&)";
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v, &r, Policy())
+            ||
+         !detail::check_finite(
+            function,
+            l,
+            &r,
+            Policy()))
+               return (RealType)r;
+
+         BOOST_MATH_STD_USING
+
+         RealType m = v < 3 ? 0 : detail::mean(v, l, Policy());
+         RealType var = v < 4 ? 1 : detail::variance(v, l, Policy());
+
+         return detail::generic_find_mode(
+            dist, 
+            m,
+            function,
+            sqrt(var));
+      }
+
+      template 
+      inline RealType mean(const non_central_t_distribution& dist)
+      { 
+         BOOST_MATH_STD_USING
+         const char* function = "mean(const non_central_t_distribution<%1%>&)";
+         typedef typename policies::evaluation::type value_type;
+         typedef typename policies::normalise<
+            Policy, 
+            policies::promote_float, 
+            policies::promote_double, 
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v, &r, Policy())
+            ||
+         !detail::check_finite(
+            function,
+            l,
+            &r,
+            Policy()))
+               return (RealType)r;
+         if(v <= 1)
+            return policies::raise_domain_error(
+               function, 
+               "The non central t distribution has no defined mean for degrees of freedom <= 1: got v=%1%.", v, Policy());
+         // return l * sqrt(v / 2) * tgamma_delta_ratio((v - 1) * 0.5f, RealType(0.5f));
+         return policies::checked_narrowing_cast(
+            detail::mean(static_cast(v), static_cast(l), forwarding_policy()), function);
+
+      } // mean
+
+      template 
+      inline RealType variance(const non_central_t_distribution& dist)
+      { // variance.
+         const char* function = "variance(const non_central_t_distribution<%1%>&)";
+         typedef typename policies::evaluation::type value_type;
+         typedef typename policies::normalise<
+            Policy, 
+            policies::promote_float, 
+            policies::promote_double, 
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+         BOOST_MATH_STD_USING
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v, &r, Policy())
+            ||
+         !detail::check_finite(
+            function,
+            l,
+            &r,
+            Policy()))
+               return (RealType)r;
+         if(v <= 2)
+            return policies::raise_domain_error(
+               function, 
+               "The non central t distribution has no defined variance for degrees of freedom <= 2: got v=%1%.", v, Policy());
+         return policies::checked_narrowing_cast(
+            detail::variance(static_cast(v), static_cast(l), forwarding_policy()), function);
+      }
+
+      // RealType standard_deviation(const non_central_t_distribution& dist)
+      // standard_deviation provided by derived accessors.
+
+      template 
+      inline RealType skewness(const non_central_t_distribution& dist)
+      { // skewness = sqrt(l).
+         const char* function = "skewness(const non_central_t_distribution<%1%>&)";
+         typedef typename policies::evaluation::type value_type;
+         typedef typename policies::normalise<
+            Policy, 
+            policies::promote_float, 
+            policies::promote_double, 
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v, &r, Policy())
+            ||
+         !detail::check_finite(
+            function,
+            l,
+            &r,
+            Policy()))
+               return (RealType)r;
+         if(v <= 3)
+            return policies::raise_domain_error(
+               function, 
+               "The non central t distribution has no defined skewness for degrees of freedom <= 3: got v=%1%.", v, Policy());;
+         return policies::checked_narrowing_cast(
+            detail::skewness(static_cast(v), static_cast(l), forwarding_policy()), function);
+      }
+
+      template 
+      inline RealType kurtosis_excess(const non_central_t_distribution& dist)
+      { 
+         const char* function = "kurtosis_excess(const non_central_t_distribution<%1%>&)";
+         typedef typename policies::evaluation::type value_type;
+         typedef typename policies::normalise<
+            Policy, 
+            policies::promote_float, 
+            policies::promote_double, 
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v, &r, Policy())
+            ||
+         !detail::check_finite(
+            function,
+            l,
+            &r,
+            Policy()))
+               return (RealType)r;
+         if(v <= 4)
+            return policies::raise_domain_error(
+               function, 
+               "The non central t distribution has no defined kurtosis for degrees of freedom <= 4: got v=%1%.", v, Policy());;
+         return policies::checked_narrowing_cast(
+            detail::kurtosis_excess(static_cast(v), static_cast(l), forwarding_policy()), function);
+      } // kurtosis_excess
+
+      template 
+      inline RealType kurtosis(const non_central_t_distribution& dist)
+      {
+         return kurtosis_excess(dist) + 3;
+      }
+
+      template 
+      inline RealType pdf(const non_central_t_distribution& dist, const RealType& t)
+      { // Probability Density/Mass Function.
+         const char* function = "cdf(non_central_t_distribution<%1%>, %1%)";
+         typedef typename policies::evaluation::type value_type;
+         typedef typename policies::normalise<
+            Policy, 
+            policies::promote_float, 
+            policies::promote_double, 
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v, &r, Policy())
+            ||
+         !detail::check_finite(
+            function,
+            l,
+            &r,
+            Policy())
+            ||
+         !detail::check_x(
+            function,
+            t,
+            &r,
+            Policy()))
+               return (RealType)r;
+         return policies::checked_narrowing_cast(
+            detail::non_central_t_pdf(static_cast(v), 
+               static_cast(l), 
+               static_cast(t), 
+               Policy()),
+            function);
+      } // pdf
+
+      template 
+      RealType cdf(const non_central_t_distribution& dist, const RealType& x)
+      { 
+         const char* function = "boost::math::non_central_t_distribution<%1%>::cdf(%1%)";
+         typedef typename policies::evaluation::type value_type;
+         typedef typename policies::normalise<
+            Policy, 
+            policies::promote_float, 
+            policies::promote_double, 
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v, &r, Policy())
+            ||
+         !detail::check_finite(
+            function,
+            l,
+            &r,
+            Policy())
+            ||
+         !detail::check_x(
+            function,
+            x,
+            &r,
+            Policy()))
+               return (RealType)r;
+
+         if(l == 0)
+            return cdf(students_t_distribution(v), x);
+
+         return policies::checked_narrowing_cast(
+            detail::non_central_t_cdf(
+               static_cast(v), 
+               static_cast(l), 
+               static_cast(x), 
+               false, Policy()),
+            function);
+      } // cdf
+
+      template 
+      RealType cdf(const complemented2_type, RealType>& c)
+      { // Complemented Cumulative Distribution Function
+         const char* function = "boost::math::non_central_t_distribution<%1%>::cdf(%1%)";
+         typedef typename policies::evaluation::type value_type;
+         typedef typename policies::normalise<
+            Policy, 
+            policies::promote_float, 
+            policies::promote_double, 
+            policies::discrete_quantile<>,
+            policies::assert_undefined<> >::type forwarding_policy;
+
+         non_central_t_distribution const& dist = c.dist;
+         RealType x = c.param;
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         RealType r;
+         if(!detail::check_df(
+            function,
+            v, &r, Policy())
+            ||
+         !detail::check_finite(
+            function,
+            l,
+            &r,
+            Policy())
+            ||
+         !detail::check_x(
+            function,
+            x,
+            &r,
+            Policy()))
+               return (RealType)r;
+
+         if(l == 0)
+            return cdf(complement(students_t_distribution(v), x));
+
+         return policies::checked_narrowing_cast(
+            detail::non_central_t_cdf(
+               static_cast(v), 
+               static_cast(l), 
+               static_cast(x), 
+               true, Policy()),
+            function);
+      } // ccdf
+
+      template 
+      inline RealType quantile(const non_central_t_distribution& dist, const RealType& p)
+      { // Quantile (or Percent Point) function.
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         return detail::non_central_t_quantile(v, l, p, 1-p, Policy());
+      } // quantile
+
+      template 
+      inline RealType quantile(const complemented2_type, RealType>& c)
+      { // Quantile (or Percent Point) function.
+         non_central_t_distribution const& dist = c.dist;
+         RealType q = c.param;
+         RealType v = dist.degrees_of_freedom();
+         RealType l = dist.non_centrality();
+         return detail::non_central_t_quantile(v, l, 1-q, q, Policy());
+      } // quantile complement.
+
+   } // namespace math
+} // namespace boost
+
+// This include must be at the end, *after* the accessors
+// for this distribution have been defined, in order to
+// keep compilers that support two-phase lookup happy.
+#include 
+
+#endif // BOOST_MATH_SPECIAL_NON_CENTRAL_T_HPP
+
diff --git a/include/boost/math/distributions/normal.hpp b/include/boost/math/distributions/normal.hpp
index f3776bc5f..69da2dc38 100644
--- a/include/boost/math/distributions/normal.hpp
+++ b/include/boost/math/distributions/normal.hpp
@@ -100,7 +100,7 @@ inline RealType pdf(const normal_distribution& dist, const Rea
    {
      return 0; // pdf + and - infinity is zero.
    }
-   // Theis produces MSVC 4127 warnings, so the above used instead.
+   // Below produces MSVC 4127 warnings, so the above used instead.
    //if(std::numeric_limits::has_infinity && abs(x) == std::numeric_limits::infinity())
    //{ // pdf + and - infinity is zero.
    //  return 0;
diff --git a/include/boost/math/distributions/poisson.hpp b/include/boost/math/distributions/poisson.hpp
index c88a655ef..bd4fd5f3d 100644
--- a/include/boost/math/distributions/poisson.hpp
+++ b/include/boost/math/distributions/poisson.hpp
@@ -38,6 +38,7 @@
 
 #include 
 #include  // for incomplete gamma. gamma_q
+#include  // for incomplete gamma. gamma_q
 #include  // complements
 #include  // error checks
 #include  // isnan.
diff --git a/include/boost/math/distributions/students_t.hpp b/include/boost/math/distributions/students_t.hpp
index 14bdf9cfe..38df1b628 100644
--- a/include/boost/math/distributions/students_t.hpp
+++ b/include/boost/math/distributions/students_t.hpp
@@ -277,7 +277,7 @@ RealType students_t_distribution::find_degrees_of_freedom(
    boost::uintmax_t max_iter = policies::get_max_root_iterations();
    std::pair r = tools::bracket_and_solve_root(f, hint, RealType(2), false, tol, max_iter, Policy());
    RealType result = r.first + (r.second - r.first) / 2;
-   if(max_iter == policies::get_max_root_iterations())
+   if(max_iter >= policies::get_max_root_iterations())
    {
       policies::raise_evaluation_error(function, "Unable to locate solution in a reasonable time:"
          " either there is no answer to how many degrees of freedom are required"
diff --git a/include/boost/math/distributions/triangular.hpp b/include/boost/math/distributions/triangular.hpp
index a23853ea1..520a350a9 100644
--- a/include/boost/math/distributions/triangular.hpp
+++ b/include/boost/math/distributions/triangular.hpp
@@ -106,12 +106,21 @@ namespace boost{ namespace math
       RealType upper,
       RealType* result, const Policy& pol)
     {
-      if(check_triangular_lower(function, lower, result, pol)
-        && check_triangular_mode(function, mode, result, pol)
-        && check_triangular_upper(function, upper, result, pol)
-        && (lower < upper) // lower == upper NOT useful.
-        )
-      {
+      if ((check_triangular_lower(function, lower, result, pol) == false)
+        || (check_triangular_mode(function, mode, result, pol) == false)
+        || (check_triangular_upper(function, upper, result, pol) == false))
+      { // Some parameter not finite.
+        return false;
+      }
+      else if (lower >= upper) // lower == upper NOT useful.
+      { // lower >= upper.
+        *result = policies::raise_domain_error(
+          function,
+          "lower parameter is %1%, but must be less than upper!", lower, pol);
+        return false;
+      }
+      else
+      { // Check lower <= mode <= upper.
         if (mode < lower)
         {
           *result = policies::raise_domain_error(
@@ -119,21 +128,14 @@ namespace boost{ namespace math
             "mode parameter is %1%, but must be >= than lower!", lower, pol);
           return false;
         }
-        if (mode > upper )
+        if (mode > upper)
         {
           *result = policies::raise_domain_error(
             function,
             "mode parameter is %1%, but must be <= than upper!", upper, pol);
           return false;
         }
-        return true;
-      }
-      else
-      { // upper and lower have each been checked before, so must be lower >= upper.
-        *result = policies::raise_domain_error(
-          function,
-          "lower parameter is %1%, but must be less than upper!", lower, pol);
-        return false;
+        return true; // All OK.
       }
     } // bool check_triangular
   } // namespace detail
diff --git a/include/boost/math/distributions/uniform.hpp b/include/boost/math/distributions/uniform.hpp
index 5efb5dd0e..2e17e18e7 100644
--- a/include/boost/math/distributions/uniform.hpp
+++ b/include/boost/math/distributions/uniform.hpp
@@ -89,19 +89,22 @@ namespace boost{ namespace math
       RealType upper,
       RealType* result, const Policy& pol)
     {
-      if(check_uniform_lower(function, lower, result, pol)
-        && check_uniform_upper(function, upper, result, pol)
-        && (lower < upper)) // If lower == upper then 1 / (upper-lower) = 1/0 = +infinity!
+      if((check_uniform_lower(function, lower, result, pol) == false)
+        || (check_uniform_upper(function, upper, result, pol) == false))
       {
-        return true;
+        return false;
       }
-      else
+      else if (lower >= upper) // If lower == upper then 1 / (upper-lower) = 1/0 = +infinity!
       { // upper and lower have been checked before, so must be lower >= upper.
         *result = policies::raise_domain_error(
           function,
           "lower parameter is %1%, but must be less than upper!", lower, pol);
         return false;
       }
+      else
+      { // All OK,
+        return true;
+      }
     } // bool check_uniform(
 
   } // namespace detail
@@ -141,7 +144,8 @@ namespace boost{ namespace math
   inline const std::pair range(const uniform_distribution& /* dist */)
   { // Range of permissible values for random variable x.
      using boost::math::tools::max_value;
-     return std::pair(-max_value(), max_value()); // - to + infinity
+     return std::pair(-max_value(), max_value()); // - to + 'infinity'.
+     // Note RealType infinity is NOT permitted, only max_value.
   }
 
   template 
diff --git a/include/boost/math/distributions/weibull.hpp b/include/boost/math/distributions/weibull.hpp
index c41704ba9..5368b830e 100644
--- a/include/boost/math/distributions/weibull.hpp
+++ b/include/boost/math/distributions/weibull.hpp
@@ -111,7 +111,9 @@ inline const std::pair support(const weibull_distribution(0,  max_value());
+   using boost::math::tools::min_value;
+   return std::pair(min_value(),  max_value());
+   // A discontinuity at x == 0, so only support down to min_value.
 }
 
 template 
@@ -131,8 +133,9 @@ inline RealType pdf(const weibull_distribution& dist, const Re
       return result;
 
    if(x == 0)
+   { // Special case, but x == min, pdf = 1 for shape = 1, 
       return 0;
-
+   }
    result = exp(-pow(x / scale, shape));
    result *= pow(x / scale, shape) * shape / x;
 
@@ -283,6 +286,8 @@ inline RealType mode(const weibull_distribution& dist)
    {
       return result;
    }
+   if(shape <= 1)
+      return 0;
    result = scale * pow((shape - 1) / shape, 1 / shape);
    return result;
 }
diff --git a/include/boost/math/policies/error_handling.hpp b/include/boost/math/policies/error_handling.hpp
index 353bec8f8..b0e562d6a 100644
--- a/include/boost/math/policies/error_handling.hpp
+++ b/include/boost/math/policies/error_handling.hpp
@@ -37,6 +37,12 @@ public:
    evaluation_error(const std::string& s) : std::runtime_error(s){}
 };
 
+class rounding_error : public std::runtime_error
+{
+public:
+   rounding_error(const std::string& s) : std::runtime_error(s){}
+};
+
 namespace policies{
 //
 // Forward declarations of user error handlers, 
@@ -54,6 +60,8 @@ template 
 T user_denorm_error(const char* function, const char* message, const T& val);
 template 
 T user_evaluation_error(const char* function, const char* message, const T& val);
+template 
+T user_rounding_error(const char* function, const char* message, const T& val);
 
 namespace detail
 {
@@ -371,6 +379,53 @@ inline T raise_evaluation_error(
    return user_evaluation_error(function, message, val);
 }
 
+template 
+inline T raise_rounding_error(
+           const char* function, 
+           const char* message, 
+           const T& val, 
+           const  ::boost::math::policies::rounding_error< ::boost::math::policies::throw_on_error>&)
+{
+   raise_error(function, message, val);
+   // we never get here:
+   return T(0);
+}
+
+template 
+inline T raise_rounding_error(
+           const char* , 
+           const char* , 
+           const T& val, 
+           const  ::boost::math::policies::rounding_error< ::boost::math::policies::ignore_error>&)
+{
+   // This may or may not do the right thing, but the user asked for the error
+   // to be ignored so here we go anyway:
+   return val;
+}
+
+template 
+inline T raise_rounding_error(
+           const char* , 
+           const char* , 
+           const T& val, 
+           const  ::boost::math::policies::rounding_error< ::boost::math::policies::errno_on_error>&)
+{
+   errno = ERANGE;
+   // This may or may not do the right thing, but the user asked for the error
+   // to be silent so here we go anyway:
+   return val;
+}
+
+template 
+inline T raise_rounding_error(
+           const char* function, 
+           const char* message, 
+           const T& val, 
+           const  ::boost::math::policies::rounding_error< ::boost::math::policies::user_error>&)
+{
+   return user_rounding_error(function, message, val);
+}
+
 }  // namespace detail
 
 template 
@@ -428,6 +483,15 @@ inline T raise_evaluation_error(const char* function, const char* message, const
       val, policy_type());
 }
 
+template 
+inline T raise_rounding_error(const char* function, const char* message, const T& val, const Policy&)
+{
+   typedef typename Policy::rounding_error_type policy_type;
+   return detail::raise_rounding_error(
+      function, message ? message : "Value %1% can not be represented in the target integer type.", 
+      val, policy_type());
+}
+
 //
 // checked_narrowing_cast:
 //
diff --git a/include/boost/math/policies/policy.hpp b/include/boost/math/policies/policy.hpp
index 2558c99b6..662b3850d 100644
--- a/include/boost/math/policies/policy.hpp
+++ b/include/boost/math/policies/policy.hpp
@@ -54,6 +54,9 @@ namespace policies{
 #ifndef BOOST_MATH_EVALUATION_ERROR_POLICY
 #define BOOST_MATH_EVALUATION_ERROR_POLICY throw_on_error
 #endif
+#ifndef BOOST_MATH_ROUNDING_ERROR_POLICY
+#define BOOST_MATH_ROUNDING_ERROR_POLICY throw_on_error
+#endif
 #ifndef BOOST_MATH_UNDERFLOW_ERROR_POLICY
 #define BOOST_MATH_UNDERFLOW_ERROR_POLICY ignore_error
 #endif
@@ -178,6 +181,7 @@ BOOST_MATH_META_INT(error_policy_type, overflow_error, BOOST_MATH_OVERFLOW_ERROR
 BOOST_MATH_META_INT(error_policy_type, underflow_error, BOOST_MATH_UNDERFLOW_ERROR_POLICY)
 BOOST_MATH_META_INT(error_policy_type, denorm_error, BOOST_MATH_DENORM_ERROR_POLICY)
 BOOST_MATH_META_INT(error_policy_type, evaluation_error, BOOST_MATH_EVALUATION_ERROR_POLICY)
+BOOST_MATH_META_INT(error_policy_type, rounding_error, BOOST_MATH_ROUNDING_ERROR_POLICY)
 
 //
 // Policy types for internal promotion:
@@ -398,6 +402,7 @@ public:
    typedef typename detail::find_arg, underflow_error<> >::type underflow_error_type;
    typedef typename detail::find_arg, denorm_error<> >::type denorm_error_type;
    typedef typename detail::find_arg, evaluation_error<> >::type evaluation_error_type;
+   typedef typename detail::find_arg, rounding_error<> >::type rounding_error_type;
 private:
    //
    // Now work out the precision:
@@ -440,6 +445,7 @@ public:
    typedef underflow_error<> underflow_error_type;
    typedef denorm_error<> denorm_error_type;
    typedef evaluation_error<> evaluation_error_type;
+   typedef rounding_error<> rounding_error_type;
 #if BOOST_MATH_DIGITS10_POLICY == 0
    typedef digits2<> precision_type;
 #else
@@ -463,6 +469,7 @@ public:
    typedef underflow_error<> underflow_error_type;
    typedef denorm_error<> denorm_error_type;
    typedef evaluation_error<> evaluation_error_type;
+   typedef rounding_error<> rounding_error_type;
 #if BOOST_MATH_DIGITS10_POLICY == 0
    typedef digits2<> precision_type;
 #else
@@ -500,6 +507,7 @@ private:
    typedef typename detail::find_arg, typename Policy::underflow_error_type >::type underflow_error_type;
    typedef typename detail::find_arg, typename Policy::denorm_error_type >::type denorm_error_type;
    typedef typename detail::find_arg, typename Policy::evaluation_error_type >::type evaluation_error_type;
+   typedef typename detail::find_arg, typename Policy::rounding_error_type >::type rounding_error_type;
    //
    // Now work out the precision:
    //
@@ -534,6 +542,7 @@ private:
       underflow_error_type,
       denorm_error_type,
       evaluation_error_type,
+      rounding_error_type,
       precision_type,
       promote_float_type,
       promote_double_type,
@@ -841,3 +850,4 @@ struct is_policy : public mpl::bool_< ::boost::math::policies::detail::is_policy
 #endif // BOOST_MATH_POLICY_HPP
 
 
+
diff --git a/include/boost/math/special_functions.hpp b/include/boost/math/special_functions.hpp
index 0575b7560..44ea43b8c 100644
--- a/include/boost/math/special_functions.hpp
+++ b/include/boost/math/special_functions.hpp
@@ -29,6 +29,7 @@
 #include 
 #include 
 #include 
+#include 
 #include 
 #include 
 #include 
@@ -47,5 +48,10 @@
 #include 
 #include 
 #include 
+#include 
+#include 
+#include 
+#include 
+#include 
 
 #endif // BOOST_MATH_SPECIAL_FUNCTIONS_HPP
diff --git a/include/boost/math/special_functions/acosh.hpp b/include/boost/math/special_functions/acosh.hpp
index 5fa16a807..48cce3545 100644
--- a/include/boost/math/special_functions/acosh.hpp
+++ b/include/boost/math/special_functions/acosh.hpp
@@ -10,6 +10,9 @@
 #ifndef BOOST_ACOSH_HPP
 #define BOOST_ACOSH_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
 
 #include 
 #include 
@@ -110,3 +113,4 @@ namespace boost
 
 
 
+
diff --git a/include/boost/math/special_functions/asinh.hpp b/include/boost/math/special_functions/asinh.hpp
index 502e514b0..6caa4bbc7 100644
--- a/include/boost/math/special_functions/asinh.hpp
+++ b/include/boost/math/special_functions/asinh.hpp
@@ -10,6 +10,10 @@
 #ifndef BOOST_ASINH_HPP
 #define BOOST_ASINH_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 
 #include 
 #include 
@@ -110,3 +114,4 @@ namespace boost
 }
 
 #endif /* BOOST_ASINH_HPP */
+
diff --git a/include/boost/math/special_functions/atanh.hpp b/include/boost/math/special_functions/atanh.hpp
index 35325a3d7..b67297ec3 100644
--- a/include/boost/math/special_functions/atanh.hpp
+++ b/include/boost/math/special_functions/atanh.hpp
@@ -10,6 +10,10 @@
 #ifndef BOOST_ATANH_HPP
 #define BOOST_ATANH_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 
 #include 
 #include 
@@ -120,3 +124,4 @@ namespace boost
 #endif /* BOOST_ATANH_HPP */
 
 
+
diff --git a/include/boost/math/special_functions/bessel.hpp b/include/boost/math/special_functions/bessel.hpp
index 98b32b33c..043b7a38a 100644
--- a/include/boost/math/special_functions/bessel.hpp
+++ b/include/boost/math/special_functions/bessel.hpp
@@ -10,6 +10,10 @@
 #ifndef BOOST_MATH_BESSEL_HPP
 #define BOOST_MATH_BESSEL_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -20,6 +24,8 @@
 #include 
 #include 
 #include 
+#include 
+#include 
 #include 
 #include 
 
@@ -123,7 +129,7 @@ T cyl_bessel_j_imp(T v, T x, const bessel_no_int_tag& t, const Policy& pol)
       if(floor(v) == v)
       {
          T r = cyl_bessel_j_imp(v, -x, t, pol);
-         if(tools::real_cast(v) & 1)
+         if(iround(v, pol) & 1)
             r = -r;
          return r;
       }
@@ -159,7 +165,7 @@ inline T cyl_bessel_j_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& p
       if(fabs(x) > asymptotic_bessel_j_limit(v, tag_type()))
          return asymptotic_bessel_j_large_x_2(v, x);
       else
-         return bessel_jn(tools::real_cast(v), x, pol);
+         return bessel_jn(iround(v, pol), x, pol);
    }
    return cyl_bessel_j_imp(v, x, bessel_no_int_tag(), pol);
 }
@@ -222,7 +228,7 @@ T cyl_bessel_i_imp(T v, T x, const Policy& pol)
       if(floor(v) == v)
       {
          T r = cyl_bessel_i_imp(v, -x, pol);
-         if(tools::real_cast(v) & 1)
+         if(iround(v, pol) & 1)
             r = -r;
          return r;
       }
@@ -286,7 +292,7 @@ inline T cyl_bessel_k_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& p
    BOOST_MATH_STD_USING
    if((floor(v) == v))
    {
-      return bessel_kn(tools::real_cast(v), x, pol);
+      return bessel_kn(itrunc(v), x, pol);
    }
    return cyl_bessel_k_imp(v, x, bessel_no_int_tag(), pol);
 }
@@ -331,12 +337,12 @@ inline T cyl_neumann_imp(T v, T x, const bessel_maybe_int_tag&, const Policy& po
       if((fabs(x) > asymptotic_bessel_y_limit(tag_type())) && (fabs(x) > 5 * abs(v)))
       {
          T r = asymptotic_bessel_y_large_x_2(static_cast(abs(v)), x);
-         if((v < 0) && (tools::real_cast(v) & 1))
+         if((v < 0) && (itrunc(v, pol) & 1))
             r = -r;
          return r;
       }
       else
-         return bessel_yn(tools::real_cast(v), x, pol);
+         return bessel_yn(itrunc(v, pol), x, pol);
    }
    return cyl_neumann_imp(v, x, bessel_no_int_tag(), pol);
 }
@@ -354,7 +360,7 @@ inline T cyl_neumann_imp(int v, T x, const bessel_int_tag&, const Policy& pol)
       return r;
    }
    else
-      return bessel_yn(tools::real_cast(v), x, pol);
+      return bessel_yn(v, x, pol);
 }
 
 template 
@@ -482,3 +488,4 @@ inline typename detail::bessel_traits >::result_type sp
 } // namespace boost
 
 #endif // BOOST_MATH_BESSEL_HPP
+
diff --git a/include/boost/math/special_functions/beta.hpp b/include/boost/math/special_functions/beta.hpp
index 5add7d874..917984621 100644
--- a/include/boost/math/special_functions/beta.hpp
+++ b/include/boost/math/special_functions/beta.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SPECIAL_BETA_HPP
 #define BOOST_MATH_SPECIAL_BETA_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -13,6 +17,7 @@
 #include 
 #include 
 #include 
+#include 
 #include 
 #include 
 #include 
@@ -817,7 +822,7 @@ inline T binomial_ccdf(T n, T k, T x, T y)
    BOOST_MATH_STD_USING // ADL of std names
    T result = pow(x, n);
    T term = result;
-   for(unsigned i = tools::real_cast(n - 1); i > k; --i)
+   for(unsigned i = itrunc(n - 1); i > k; --i)
    {
       term *= ((i + 1) * y) / ((n - i) * x) ;
       result += term;
@@ -1055,7 +1060,7 @@ T ibeta_imp(T a, T b, T x, const Policy& pol, bool inv, bool normalised, T* p_de
          else if(a > 15)
          {
             // sidestep so we can use the series representation:
-            int n = static_cast(boost::math::tools::real_cast(floor(b)));
+            int n = itrunc(floor(b), pol);
             if(n == b)
                --n;
             T bbar = b - n;
@@ -1077,7 +1082,7 @@ T ibeta_imp(T a, T b, T x, const Policy& pol, bool inv, bool normalised, T* p_de
             // the formula here for the non-normalised case is tricky to figure
             // out (for me!!), and requires two pochhammer calculations rather
             // than one, so leave it for now....
-            int n = static_cast(boost::math::tools::real_cast(floor(b)));
+            int n = itrunc(floor(b), pol);
             T bbar = b - n;
             if(bbar <= 0)
             {
@@ -1348,3 +1353,4 @@ inline typename tools::promote_args::type
 
 
 
+
diff --git a/include/boost/math/special_functions/binomial.hpp b/include/boost/math/special_functions/binomial.hpp
index 74f8da018..d394b0488 100644
--- a/include/boost/math/special_functions/binomial.hpp
+++ b/include/boost/math/special_functions/binomial.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SF_BINOMIAL_HPP
 #define BOOST_MATH_SF_BINOMIAL_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -73,3 +77,4 @@ inline T binomial_coefficient(unsigned n, unsigned k)
 #endif // BOOST_MATH_SF_BINOMIAL_HPP
 
 
+
diff --git a/include/boost/math/special_functions/cbrt.hpp b/include/boost/math/special_functions/cbrt.hpp
index d8c9ad4e6..c43f9b625 100644
--- a/include/boost/math/special_functions/cbrt.hpp
+++ b/include/boost/math/special_functions/cbrt.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SF_CBRT_HPP
 #define BOOST_MATH_SF_CBRT_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 
@@ -70,3 +74,4 @@ inline typename tools::promote_args::type cbrt(T z)
 
 
 
+
diff --git a/include/boost/math/special_functions/cos_pi.hpp b/include/boost/math/special_functions/cos_pi.hpp
index ad877a7af..4a2eb2393 100644
--- a/include/boost/math/special_functions/cos_pi.hpp
+++ b/include/boost/math/special_functions/cos_pi.hpp
@@ -6,16 +6,20 @@
 #ifndef BOOST_MATH_COS_PI_HPP
 #define BOOST_MATH_COS_PI_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
-#include 
+#include 
 #include 
 #include 
 
 namespace boost{ namespace math{ namespace detail{
 
-template 
-T cos_pi_imp(T x)
+template 
+T cos_pi_imp(T x, const Policy& pol)
 {
    BOOST_MATH_STD_USING // ADL of std names
    // cos of pi*x:
@@ -28,7 +32,7 @@ T cos_pi_imp(T x)
    }
 
    T rem = floor(x);
-   if(tools::real_cast(rem) & 1)
+   if(itrunc(rem, pol) & 1)
       invert = !invert;
    rem = x - rem;
    if(rem > 0.5f)
@@ -43,22 +47,22 @@ T cos_pi_imp(T x)
    return invert ? -rem : rem;
 }
 
-}
+} // namespace detail
 
 template 
-inline typename tools::promote_args::type cos_pi(T x, const Policy&)
+inline typename tools::promote_args::type cos_pi(T x, const Policy& pol)
 {
    typedef typename tools::promote_args::type result_type;
-   return boost::math::detail::cos_pi_imp(x);
+   return boost::math::detail::cos_pi_imp(x, pol);
 }
 
 template 
 inline typename tools::promote_args::type cos_pi(T x)
 {
-   typedef typename tools::promote_args::type result_type;
-   return boost::math::detail::cos_pi_imp(x);
+   return boost::math::cos_pi(x, policies::policy<>());
 }
 
 } // namespace math
 } // namespace boost
 #endif
+
diff --git a/include/boost/math/special_functions/detail/bessel_i0.hpp b/include/boost/math/special_functions/detail/bessel_i0.hpp
index dde226e0f..c8325f093 100644
--- a/include/boost/math/special_functions/detail/bessel_i0.hpp
+++ b/include/boost/math/special_functions/detail/bessel_i0.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_I0_HPP
 #define BOOST_MATH_BESSEL_I0_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 
@@ -94,3 +98,4 @@ T bessel_i0(T x)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_I0_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_i1.hpp b/include/boost/math/special_functions/detail/bessel_i1.hpp
index 928b47510..9df0e69c4 100644
--- a/include/boost/math/special_functions/detail/bessel_i1.hpp
+++ b/include/boost/math/special_functions/detail/bessel_i1.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_I1_HPP
 #define BOOST_MATH_BESSEL_I1_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 
@@ -97,3 +101,4 @@ T bessel_i1(T x)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_I1_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_ik.hpp b/include/boost/math/special_functions/detail/bessel_ik.hpp
index c20a6641f..fdc9273f7 100644
--- a/include/boost/math/special_functions/detail/bessel_ik.hpp
+++ b/include/boost/math/special_functions/detail/bessel_ik.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_IK_HPP
 #define BOOST_MATH_BESSEL_IK_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -230,7 +234,7 @@ int bessel_ik(T v, T x, T* I, T* K, int kind, const Policy& pol)
         v = -v;                             // v is non-negative from here
         kind |= need_k;
     }
-    n = tools::real_cast(v + 0.5f);
+    n = iround(v, pol);
     u = v - n;                              // -1/2 <= u < 1/2
     BOOST_MATH_INSTRUMENT_VARIABLE(n);
     BOOST_MATH_INSTRUMENT_VARIABLE(u);
@@ -329,3 +333,4 @@ int bessel_ik(T v, T x, T* I, T* K, int kind, const Policy& pol)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_IK_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_j0.hpp b/include/boost/math/special_functions/detail/bessel_j0.hpp
index 9191dccb5..59783f620 100644
--- a/include/boost/math/special_functions/detail/bessel_j0.hpp
+++ b/include/boost/math/special_functions/detail/bessel_j0.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_J0_HPP
 #define BOOST_MATH_BESSEL_J0_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -145,3 +149,4 @@ T bessel_j0(T x)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_J0_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_j1.hpp b/include/boost/math/special_functions/detail/bessel_j1.hpp
index 906f2a8a4..ea98bc227 100644
--- a/include/boost/math/special_functions/detail/bessel_j1.hpp
+++ b/include/boost/math/special_functions/detail/bessel_j1.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_J1_HPP
 #define BOOST_MATH_BESSEL_J1_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -150,3 +154,4 @@ T bessel_j1(T x)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_J1_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_jn.hpp b/include/boost/math/special_functions/detail/bessel_jn.hpp
index cf89d28ce..b1f1a0246 100644
--- a/include/boost/math/special_functions/detail/bessel_jn.hpp
+++ b/include/boost/math/special_functions/detail/bessel_jn.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_JN_HPP
 #define BOOST_MATH_BESSEL_JN_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -84,3 +88,4 @@ T bessel_jn(int n, T x, const Policy& pol)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_JN_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_jy.hpp b/include/boost/math/special_functions/detail/bessel_jy.hpp
index 9ef303ec6..4ef0deeea 100644
--- a/include/boost/math/special_functions/detail/bessel_jy.hpp
+++ b/include/boost/math/special_functions/detail/bessel_jy.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_JY_HPP
 #define BOOST_MATH_BESSEL_JY_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -221,7 +225,7 @@ int bessel_jy(T v, T x, T* J, T* Y, int kind, const Policy& pol)
         v = -v;                             // v is non-negative from here
         kind = need_j|need_y;               // need both for reflection formula
     }
-    n = real_cast(v + 0.5L);
+    n = iround(v, pol);
     u = v - n;                              // -1/2 <= u < 1/2
 
     if (x == 0)
@@ -359,3 +363,4 @@ int bessel_jy(T v, T x, T* J, T* Y, int kind, const Policy& pol)
 }} // namespaces
 
 #endif // BOOST_MATH_BESSEL_JY_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_jy_asym.hpp b/include/boost/math/special_functions/detail/bessel_jy_asym.hpp
index 478c84306..098cb8b14 100644
--- a/include/boost/math/special_functions/detail/bessel_jy_asym.hpp
+++ b/include/boost/math/special_functions/detail/bessel_jy_asym.hpp
@@ -12,6 +12,10 @@
 #ifndef BOOST_MATH_SF_DETAIL_BESSEL_JY_ASYM_HPP
 #define BOOST_MATH_SF_DETAIL_BESSEL_JY_ASYM_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 
 namespace boost{ namespace math{ namespace detail{
@@ -295,3 +299,4 @@ T asymptotic_bessel_i_large_x(T v, T x, const Policy& pol)
 }}} // namespaces
 
 #endif
+
diff --git a/include/boost/math/special_functions/detail/bessel_k0.hpp b/include/boost/math/special_functions/detail/bessel_k0.hpp
index a86a055dc..fae03e485 100644
--- a/include/boost/math/special_functions/detail/bessel_k0.hpp
+++ b/include/boost/math/special_functions/detail/bessel_k0.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_K0_HPP
 #define BOOST_MATH_BESSEL_K0_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -114,3 +118,4 @@ T bessel_k0(T x, const Policy& pol)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_K0_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_k1.hpp b/include/boost/math/special_functions/detail/bessel_k1.hpp
index 198c3eb57..5830a7f8f 100644
--- a/include/boost/math/special_functions/detail/bessel_k1.hpp
+++ b/include/boost/math/special_functions/detail/bessel_k1.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_K1_HPP
 #define BOOST_MATH_BESSEL_K1_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -110,3 +114,4 @@ T bessel_k1(T x, const Policy& pol)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_K1_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_kn.hpp b/include/boost/math/special_functions/detail/bessel_kn.hpp
index 8d30462e8..fdee7d44f 100644
--- a/include/boost/math/special_functions/detail/bessel_kn.hpp
+++ b/include/boost/math/special_functions/detail/bessel_kn.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_KN_HPP
 #define BOOST_MATH_BESSEL_KN_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -67,3 +71,4 @@ T bessel_kn(int n, T x, const Policy& pol)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_KN_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_y0.hpp b/include/boost/math/special_functions/detail/bessel_y0.hpp
index 4e6db50dc..d2b65b854 100644
--- a/include/boost/math/special_functions/detail/bessel_y0.hpp
+++ b/include/boost/math/special_functions/detail/bessel_y0.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_Y0_HPP
 #define BOOST_MATH_BESSEL_Y0_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -175,3 +179,4 @@ T bessel_y0(T x, const Policy& pol)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_Y0_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_y1.hpp b/include/boost/math/special_functions/detail/bessel_y1.hpp
index de0bef519..e8372eee4 100644
--- a/include/boost/math/special_functions/detail/bessel_y1.hpp
+++ b/include/boost/math/special_functions/detail/bessel_y1.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_Y1_HPP
 #define BOOST_MATH_BESSEL_Y1_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -148,3 +152,4 @@ T bessel_y1(T x, const Policy& pol)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_Y1_HPP
+
diff --git a/include/boost/math/special_functions/detail/bessel_yn.hpp b/include/boost/math/special_functions/detail/bessel_yn.hpp
index 3ae9d12c5..e0788f844 100644
--- a/include/boost/math/special_functions/detail/bessel_yn.hpp
+++ b/include/boost/math/special_functions/detail/bessel_yn.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_BESSEL_YN_HPP
 #define BOOST_MATH_BESSEL_YN_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -77,3 +81,4 @@ T bessel_yn(int n, T x, const Policy& pol)
 }}} // namespaces
 
 #endif // BOOST_MATH_BESSEL_YN_HPP
+
diff --git a/include/boost/math/special_functions/detail/erf_inv.hpp b/include/boost/math/special_functions/detail/erf_inv.hpp
index 5d3afe5d8..3b0a175aa 100644
--- a/include/boost/math/special_functions/detail/erf_inv.hpp
+++ b/include/boost/math/special_functions/detail/erf_inv.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SF_ERF_INV_HPP
 #define BOOST_MATH_SF_ERF_INV_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 namespace boost{ namespace math{ 
 
 namespace detail{
@@ -462,3 +466,4 @@ inline typename tools::promote_args::type erf_inv(T z)
 } // namespace boost
 
 #endif // BOOST_MATH_SF_ERF_INV_HPP
+
diff --git a/include/boost/math/special_functions/detail/gamma_inva.hpp b/include/boost/math/special_functions/detail/gamma_inva.hpp
index 8e6f90ff5..62adac86e 100644
--- a/include/boost/math/special_functions/detail/gamma_inva.hpp
+++ b/include/boost/math/special_functions/detail/gamma_inva.hpp
@@ -13,6 +13,10 @@
 #ifndef BOOST_MATH_SP_DETAIL_GAMMA_INVA
 #define BOOST_MATH_SP_DETAIL_GAMMA_INVA
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 
@@ -226,3 +230,4 @@ inline typename tools::promote_args::type
 #endif // BOOST_MATH_SP_DETAIL_GAMMA_INVA
 
 
+
diff --git a/include/boost/math/special_functions/detail/ibeta_inv_ab.hpp b/include/boost/math/special_functions/detail/ibeta_inv_ab.hpp
index ff9b1b122..55e2c65b6 100644
--- a/include/boost/math/special_functions/detail/ibeta_inv_ab.hpp
+++ b/include/boost/math/special_functions/detail/ibeta_inv_ab.hpp
@@ -13,6 +13,10 @@
 #ifndef BOOST_MATH_SP_DETAIL_BETA_INV_AB
 #define BOOST_MATH_SP_DETAIL_BETA_INV_AB
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 
@@ -317,3 +321,4 @@ inline typename tools::promote_args::type
 #endif // BOOST_MATH_SP_DETAIL_BETA_INV_AB
 
 
+
diff --git a/include/boost/math/special_functions/detail/ibeta_inverse.hpp b/include/boost/math/special_functions/detail/ibeta_inverse.hpp
index bf1fe189f..04898db87 100644
--- a/include/boost/math/special_functions/detail/ibeta_inverse.hpp
+++ b/include/boost/math/special_functions/detail/ibeta_inverse.hpp
@@ -7,6 +7,10 @@
 #ifndef BOOST_MATH_SPECIAL_FUNCTIONS_IBETA_INVERSE_HPP
 #define BOOST_MATH_SPECIAL_FUNCTIONS_IBETA_INVERSE_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -932,3 +936,4 @@ inline typename tools::promote_args::type
 
 
 
+
diff --git a/include/boost/math/special_functions/detail/igamma_inverse.hpp b/include/boost/math/special_functions/detail/igamma_inverse.hpp
index 8fd564faa..ff182bb2d 100644
--- a/include/boost/math/special_functions/detail/igamma_inverse.hpp
+++ b/include/boost/math/special_functions/detail/igamma_inverse.hpp
@@ -6,11 +6,15 @@
 #ifndef BOOST_MATH_SPECIAL_FUNCTIONS_IGAMMA_INVERSE_HPP
 #define BOOST_MATH_SPECIAL_FUNCTIONS_IGAMMA_INVERSE_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include 
 #include 
 #include 
 #include 
 #include 
-#include 
 
 namespace boost{ namespace math{
 
@@ -464,3 +468,4 @@ inline typename tools::promote_args::type
 #endif // BOOST_MATH_SPECIAL_FUNCTIONS_IGAMMA_INVERSE_HPP
 
 
+
diff --git a/include/boost/math/special_functions/detail/igamma_large.hpp b/include/boost/math/special_functions/detail/igamma_large.hpp
index 539489a57..f3de0df03 100644
--- a/include/boost/math/special_functions/detail/igamma_large.hpp
+++ b/include/boost/math/special_functions/detail/igamma_large.hpp
@@ -45,6 +45,10 @@
 #ifndef BOOST_MATH_DETAIL_IGAMMA_LARGE
 #define BOOST_MATH_DETAIL_IGAMMA_LARGE
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 namespace boost{ namespace math{ namespace detail{
 
 // This version will never be called (at runtime), it's a stub used
@@ -762,3 +766,4 @@ T igamma_temme_large(T a, T x, const Policy& pol, mpl::int_<113> const *)
 
 
 #endif // BOOST_MATH_DETAIL_IGAMMA_LARGE
+
diff --git a/include/boost/math/special_functions/detail/lgamma_small.hpp b/include/boost/math/special_functions/detail/lgamma_small.hpp
index c112c2784..161bf9fb6 100644
--- a/include/boost/math/special_functions/detail/lgamma_small.hpp
+++ b/include/boost/math/special_functions/detail/lgamma_small.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SPECIAL_FUNCTIONS_DETAIL_LGAMMA_SMALL
 #define BOOST_MATH_SPECIAL_FUNCTIONS_DETAIL_LGAMMA_SMALL
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 namespace boost{ namespace math{ namespace detail{
 
 //
@@ -505,3 +509,4 @@ T lgamma_small_imp(T z, T zm1, T zm2, const mpl::int_<0>&, const Policy& pol, co
 }}} // namespaces
 
 #endif // BOOST_MATH_SPECIAL_FUNCTIONS_DETAIL_LGAMMA_SMALL
+
diff --git a/include/boost/math/special_functions/detail/simple_complex.hpp b/include/boost/math/special_functions/detail/simple_complex.hpp
index e01cf5efb..5a1568e43 100644
--- a/include/boost/math/special_functions/detail/simple_complex.hpp
+++ b/include/boost/math/special_functions/detail/simple_complex.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SF_DETAIL_SIMPLE_COMPLEX_HPP
 #define BOOST_MATH_SF_DETAIL_SIMPLE_COMPLEX_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 namespace boost{ namespace math{ namespace detail{ namespace sc{
 
 template 
@@ -165,3 +169,4 @@ inline T abs(const simple_complex& c)
 
 #endif
 
+
diff --git a/include/boost/math/special_functions/detail/t_distribution_inv.hpp b/include/boost/math/special_functions/detail/t_distribution_inv.hpp
index 2af3cb957..5b965add6 100644
--- a/include/boost/math/special_functions/detail/t_distribution_inv.hpp
+++ b/include/boost/math/special_functions/detail/t_distribution_inv.hpp
@@ -7,7 +7,12 @@
 #ifndef BOOST_MATH_SF_DETAIL_INV_T_HPP
 #define BOOST_MATH_SF_DETAIL_INV_T_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
+#include 
 
 namespace boost{ namespace math{ namespace detail{
 
@@ -200,7 +205,7 @@ T inverse_students_t(T df, T u, T v, const Policy& pol, bool* pexact = 0)
       //
       T tolerance = ldexp(1.0f, (2 * policies::digits()) / 3);
 
-      switch(boost::math::tools::real_cast(df))
+      switch(itrunc(df, Policy()))
       {
       case 1:
          {
@@ -364,7 +369,7 @@ calculate_real:
          // where we use Shaw's tail series.
          // The crossover point is roughly exponential in -df:
          //
-         T crossover = ldexp(1.0f, tools::real_cast(df / -0.654f));
+         T crossover = ldexp(1.0f, iround(df / -0.654f, pol));
          if(u > crossover)
          {
             result = boost::math::detail::inverse_students_t_hill(df, u, pol);
@@ -507,3 +512,4 @@ inline T fast_students_t_quantile(T df, T p, const Policy& pol)
 #endif // BOOST_MATH_SF_DETAIL_INV_T_HPP
 
 
+
diff --git a/include/boost/math/special_functions/detail/unchecked_factorial.hpp b/include/boost/math/special_functions/detail/unchecked_factorial.hpp
index f58b54ed5..1189933ad 100644
--- a/include/boost/math/special_functions/detail/unchecked_factorial.hpp
+++ b/include/boost/math/special_functions/detail/unchecked_factorial.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SP_UC_FACTORIALS_HPP
 #define BOOST_MATH_SP_UC_FACTORIALS_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #ifdef BOOST_MSVC
 #pragma warning(push) // Temporary until lexical cast fixed.
@@ -395,3 +399,4 @@ struct max_factorial
 } // namespace boost
 
 #endif // BOOST_MATH_SP_UC_FACTORIALS_HPP
+
diff --git a/include/boost/math/special_functions/digamma.hpp b/include/boost/math/special_functions/digamma.hpp
index 12946cec7..a1008d2bb 100644
--- a/include/boost/math/special_functions/digamma.hpp
+++ b/include/boost/math/special_functions/digamma.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SF_DIGAMMA_HPP
 #define BOOST_MATH_SF_DIGAMMA_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -443,3 +447,4 @@ inline typename tools::promote_args::type
 } // namespace math
 } // namespace boost
 #endif
+
diff --git a/include/boost/math/special_functions/ellint_1.hpp b/include/boost/math/special_functions/ellint_1.hpp
index 8b10cf044..9de2f66f6 100644
--- a/include/boost/math/special_functions/ellint_1.hpp
+++ b/include/boost/math/special_functions/ellint_1.hpp
@@ -14,6 +14,10 @@
 #ifndef BOOST_MATH_ELLINT_1_HPP
 #define BOOST_MATH_ELLINT_1_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -180,3 +184,4 @@ inline typename tools::promote_args::type ellint_1(T1 k, T2 phi)
 }} // namespaces
 
 #endif // BOOST_MATH_ELLINT_1_HPP
+
diff --git a/include/boost/math/special_functions/ellint_2.hpp b/include/boost/math/special_functions/ellint_2.hpp
index 341fd8be3..182157833 100644
--- a/include/boost/math/special_functions/ellint_2.hpp
+++ b/include/boost/math/special_functions/ellint_2.hpp
@@ -14,6 +14,10 @@
 #ifndef BOOST_MATH_ELLINT_2_HPP
 #define BOOST_MATH_ELLINT_2_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -161,3 +165,4 @@ inline typename tools::promote_args::type ellint_2(T1 k, T2 phi, const P
 }} // namespaces
 
 #endif // BOOST_MATH_ELLINT_2_HPP
+
diff --git a/include/boost/math/special_functions/ellint_3.hpp b/include/boost/math/special_functions/ellint_3.hpp
index ee5aa8359..d60fa822d 100644
--- a/include/boost/math/special_functions/ellint_3.hpp
+++ b/include/boost/math/special_functions/ellint_3.hpp
@@ -14,6 +14,10 @@
 #ifndef BOOST_MATH_ELLINT_3_HPP
 #define BOOST_MATH_ELLINT_3_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -325,3 +329,4 @@ inline typename tools::promote_args::type ellint_3(T1 k, T2 v)
 }} // namespaces
 
 #endif // BOOST_MATH_ELLINT_3_HPP
+
diff --git a/include/boost/math/special_functions/ellint_rc.hpp b/include/boost/math/special_functions/ellint_rc.hpp
index ace2851b3..c78d4d450 100644
--- a/include/boost/math/special_functions/ellint_rc.hpp
+++ b/include/boost/math/special_functions/ellint_rc.hpp
@@ -13,6 +13,10 @@
 #ifndef BOOST_MATH_ELLINT_RC_HPP
 #define BOOST_MATH_ELLINT_RC_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -108,3 +112,4 @@ inline typename tools::promote_args::type
 }} // namespaces
 
 #endif // BOOST_MATH_ELLINT_RC_HPP
+
diff --git a/include/boost/math/special_functions/ellint_rd.hpp b/include/boost/math/special_functions/ellint_rd.hpp
index 0a8f946c1..639a05ab8 100644
--- a/include/boost/math/special_functions/ellint_rd.hpp
+++ b/include/boost/math/special_functions/ellint_rd.hpp
@@ -11,6 +11,10 @@
 #ifndef BOOST_MATH_ELLINT_RD_HPP
 #define BOOST_MATH_ELLINT_RD_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -123,3 +127,4 @@ inline typename tools::promote_args::type
 }} // namespaces
 
 #endif // BOOST_MATH_ELLINT_RD_HPP
+
diff --git a/include/boost/math/special_functions/ellint_rf.hpp b/include/boost/math/special_functions/ellint_rf.hpp
index f573b21c7..6be76d876 100644
--- a/include/boost/math/special_functions/ellint_rf.hpp
+++ b/include/boost/math/special_functions/ellint_rf.hpp
@@ -12,6 +12,10 @@
 #ifndef BOOST_MATH_ELLINT_RF_HPP
 #define BOOST_MATH_ELLINT_RF_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 
@@ -125,3 +129,4 @@ inline typename tools::promote_args::type
 }} // namespaces
 
 #endif // BOOST_MATH_ELLINT_RF_HPP
+
diff --git a/include/boost/math/special_functions/ellint_rj.hpp b/include/boost/math/special_functions/ellint_rj.hpp
index 7adc67671..48a0fc61a 100644
--- a/include/boost/math/special_functions/ellint_rj.hpp
+++ b/include/boost/math/special_functions/ellint_rj.hpp
@@ -13,6 +13,10 @@
 #ifndef BOOST_MATH_ELLINT_RJ_HPP
 #define BOOST_MATH_ELLINT_RJ_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -172,3 +176,4 @@ inline typename tools::promote_args::type
 }} // namespaces
 
 #endif // BOOST_MATH_ELLINT_RJ_HPP
+
diff --git a/include/boost/math/special_functions/erf.hpp b/include/boost/math/special_functions/erf.hpp
index 3e1894dec..2f3455b1c 100644
--- a/include/boost/math/special_functions/erf.hpp
+++ b/include/boost/math/special_functions/erf.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SPECIAL_ERF_HPP
 #define BOOST_MATH_SPECIAL_ERF_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -203,9 +207,27 @@ T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<53>& t)
       }
       else
       {
-         static const T n[7] = { 0.00337916709551257778174L, -0.000147024115786688745475L, -0.37463022236812520164L, 0.0163061594494816999803L, -0.0534354147807331748737L, 0.00161898096813581982844L, -0.0059528010489182840404L };
-         static const T d[7] = { 1, -0.0435089806536379531594L, 0.442761965043509204727L, -0.017375974533016704678L, 0.0772756490303260060769L, -0.00210552465858669941879L, 0.00544772980263244037286L };
-         result = static_cast(z * 1.125f + z * tools::evaluate_polynomial(n, z) / tools::evaluate_polynomial(d, z));
+         // Maximum Deviation Found:                     1.561e-17
+         // Expected Error Term:                         1.561e-17
+         // Maximum Relative Change in Control Points:   1.155e-04
+         // Max Error found at double precision =        2.961182e-17
+
+         static const T Y = 1.044948577880859375f;
+         static const T P[] = {    
+            0.0834305892146531832907L,
+            -0.338165134459360935041L,
+            -0.0509990735146777432841L,
+            -0.00772758345802133288487L,
+            -0.000322780120964605683831L,
+         };
+         static const T Q[] = {    
+            1L,
+            0.455004033050794024546L,
+            0.0875222600142252549554L,
+            0.00858571925074406212772L,
+            0.000370900071787748000569L,
+         };
+         result = z * (Y + tools::evaluate_polynomial(P, z * z) / tools::evaluate_polynomial(Q, z * z));
       }
    }
    else if((z < 14) || ((z < 28) && invert))
@@ -214,90 +236,113 @@ T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<53>& t)
       // We'll be calculating erfc:
       //
       invert = !invert;
-      T r, b;
-      if(z < 0.75)
+      if(z < 1.5f)
       {
-         // Worst case absolute error found: 8.554649561e-018
-         static const T n[5] = { -0.0361790390718262468222L, 0.301888464724047222196L, 0.201731143672633894981L, 0.0659353268087389983319L, 0.00721876720062364930761L };
-         static const T d[6] = { 1, 1.58814245739127341535L, 0.99354580430196422336L, 0.291753007176902027213L, 0.033994791234913855515L, -0.000104234653166533504303L };
-         static const float f0 =  0.3440242112F;
-         r = tools::evaluate_polynomial(n, z - 0.5) / tools::evaluate_polynomial(d, z - 0.5);
-         b = f0;
+         // Maximum Deviation Found:                     3.702e-17
+         // Expected Error Term:                         3.702e-17
+         // Maximum Relative Change in Control Points:   2.845e-04
+         // Max Error found at double precision =        4.841816e-17
+         static const T Y = 0.405935764312744140625f;
+         static const T P[] = {    
+            -0.098090592216281240205L,
+            0.178114665841120341155L,
+            0.191003695796775433986L,
+            0.0888900368967884466578L,
+            0.0195049001251218801359L,
+            0.00180424538297014223957L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.84759070983002217845L,
+            1.42628004845511324508L,
+            0.578052804889902404909L,
+            0.12385097467900864233L,
+            0.0113385233577001411017L,
+            0.337511472483094676155e-5L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 0.5) / tools::evaluate_polynomial(Q, z - 0.5);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 1.25)
+      else if(z < 2.5f)
       {
-         // Worst case absolute error found: 6.50251514e-018
-         static const T n[6] = { -0.039787689261113685983L, 0.160309168830518003303L, 0.163049978514596540313L, 0.0710685660158400750009L, 0.01497188097404877543L, 0.00130080628375002584279L };
-         static const T d[6] = { 1, 1.77564880074171280407L, 1.31438791181040008779L, 0.509359151038517059748L, 0.103958527905812829559L, 0.00901292460643094469406L };
-         static const float f0 =  0.419990927F;
-         r = tools::evaluate_polynomial(n, z - 0.75) / tools::evaluate_polynomial(d, z - 0.75);
-         b = f0;
+         // Max Error found at double precision =        6.599585e-18
+         // Maximum Deviation Found:                     3.909e-18
+         // Expected Error Term:                         3.909e-18
+         // Maximum Relative Change in Control Points:   9.886e-05
+         static const T Y = 0.50672817230224609375f;
+         static const T P[] = {    
+            -0.0243500476207698441272L,
+            0.0386540375035707201728L,
+            0.04394818964209516296L,
+            0.0175679436311802092299L,
+            0.00323962406290842133584L,
+            0.000235839115596880717416L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.53991494948552447182L,
+            0.982403709157920235114L,
+            0.325732924782444448493L,
+            0.0563921837420478160373L,
+            0.00410369723978904575884L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 1.5) / tools::evaluate_polynomial(Q, z - 1.5);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 2.25)
+      else if(z < 4.5f)
       {
-         // Worst case absolute error found: 1.132743504e-017
-         static const T n[6] = { -0.0300838560557949724172L, 0.0592886319615167248092L, 0.0622294724048409148736L, 0.0248575228109427909578L, 0.00463781847004901844581L, 0.000347305179334822548368L };
-         static const T d[7] = { 1, 1.57915060645728571344L, 1.03342495188878679417L, 0.35158678814344218974L, 0.062469256580984456783L, 0.00466640448020624599948L, 0.290106403940303572448e-6L };
-         static const float f0 = 0.4898625016F;
-         r = tools::evaluate_polynomial(n, z - 1.25) / tools::evaluate_polynomial(d, z - 1.25);
-         b = f0;
-      }
-      else if(z < 3.5)
-      {
-         // Worst case absolute error found: 3.446364609e-018
-         static const T n[6] = { -0.0117907570137227857015L, 0.0162667227692515660221L, 0.0175329212378413544794L, 0.00620897681269247137578L, 0.000986614895094589251706L, 0.601354618401624353425e-4L };
-         static const T d[6] = { 1, 1.33374851361555383557L, 0.73227756904205983415L, 0.207410266363727673685L, 0.0304034048466731110163L, 0.00185296959991832048613L };
-         static const float f0 = 0.5317370892F;
-         r = tools::evaluate_polynomial(n, z - 2.25) / tools::evaluate_polynomial(d, z - 2.25);
-         b = f0;
-      }
-      else if(z < 5.5)
-      {
-         // Worst case absolute error found: 1.579588208e-018
-         static const T n[6] = { -0.00588219091116732271979L, 0.00434428684527812140098L, 0.00466899990542371512895L, 0.00139937567253199794533L, 0.000179205902444982389766L, 0.845033527560949509345e-5L };
-         static const T d[6] = { 1, 1.07389345953392962127L, 0.470965611895885060643L, 0.105594730223366124873L, 0.0121252833787344059719L, 0.000571755036133730341579L };
-         static const float f0 = 0.5494099855F;
-         r = tools::evaluate_polynomial(n, z - 3.5) / tools::evaluate_polynomial(d, z - 3.5);
-         b = f0;
-      }
-      else if(z < 9)
-      {
-         // Worst case absolute error found: 1.410768708e-017
-         static const T n[5] = { -0.00273864253749621265032L, 0.0013089921066773026803L, 0.000775841526778089659703L, 0.000110909476102006410909L, 0.472577590124068298534e-5L };
-         static const T d[6] = { 1, 0.650694792327863647878L, 0.161126734432670927888L, 0.0180081468446110640846L, 0.000767341359508884026192L, -0.287636719206664167616e-9L };
-         static const float f0 = 0.5580308437F;
-         r = tools::evaluate_polynomial(n, z - 5.5) / tools::evaluate_polynomial(d, z - 5.5);
-         b = f0;
-      }
-      else if(z < 14)
-      {
-         // Worst case absolute error found: 1.458310511e-018
-         static const T n[5] = { -0.000995856413171151859346L, 0.000320252910249376187643L, 0.000129085624923151780987L, 0.121577881306587454509e-4L, 0.33293110334156470348e-6L };
-         static const T d[5] = { 1, 0.428034987547594828954L, 0.0692297359775940896439L, 0.00501515176145997560701L, 0.00013733589151338416322L };
-         static const float f0 = 0.5617653728F;
-         r = tools::evaluate_polynomial(n, z - 9) / tools::evaluate_polynomial(d, z - 9);
-         b = f0;
-      }
-      else if(z < 21)
-      {
-         // Worst case absolute error found: 1.08182873e-019
-         static const T n[5] = { -0.000395463268432048215535L, 0.91155953112698182321e-4L, 0.237451641259281193813e-4L, 0.145759953022524466816e-5L, 0.259395907606548998142e-7L };
-         static const T d[5] = { 1, 0.281604524251560309285L, 0.0298468482900092392397L, 0.00141114575715338885136L, 0.251128951158576064819e-4L };
-         static const float f0 = 0.5631566644F;
-         r = tools::evaluate_polynomial(n, z - 14) / tools::evaluate_polynomial(d, z - 14);
-         b = f0;
+         // Maximum Deviation Found:                     1.512e-17
+         // Expected Error Term:                         1.512e-17
+         // Maximum Relative Change in Control Points:   2.222e-04
+         // Max Error found at double precision =        2.062515e-17
+         static const T Y = 0.5405750274658203125f;
+         static const T P[] = {    
+            0.00295276716530971662634L,
+            0.0137384425896355332126L,
+            0.00840807615555585383007L,
+            0.00212825620914618649141L,
+            0.000250269961544794627958L,
+            0.113212406648847561139e-4L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.04217814166938418171L,
+            0.442597659481563127003L,
+            0.0958492726301061423444L,
+            0.0105982906484876531489L,
+            0.000479411269521714493907L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 3.5) / tools::evaluate_polynomial(Q, z - 3.5);
+         result *= exp(-z * z) / z;
       }
       else
       {
-         // Worst case absolute error found: 7.010370259e-018
-         static const T n[4] = { -0.000139182098873874523526L, 0.395254617101737287826e-4L, 0.376801239136290345387e-5L, 0.629017242098850415839e-7L };
-         static const T d[4] = { 1, 0.15077096006891495258L, 0.00756136203065884121997L, 0.000126226197336507576933L };
-         static const float f0 = 0.5636912584F;
-         r = tools::evaluate_polynomial(n, z - 21) / tools::evaluate_polynomial(d, z - 21);
-         b = f0;
+         // Max Error found at double precision =        2.997958e-17
+         // Maximum Deviation Found:                     2.860e-17
+         // Expected Error Term:                         2.859e-17
+         // Maximum Relative Change in Control Points:   1.357e-05
+         static const T Y = 0.5579090118408203125f;
+         static const T P[] = {    
+            0.00628057170626964891937L,
+            0.0175389834052493308818L,
+            -0.212652252872804219852L,
+            -0.687717681153649930619L,
+            -2.5518551727311523996L,
+            -3.22729451764143718517L,
+            -2.8175401114513378771L,
+         };
+         static const T Q[] = {    
+            1L,
+            2.79257750980575282228L,
+            11.0567237927800161565L,
+            15.930646027911794143L,
+            22.9367376522880577224L,
+            13.5064170191802889145L,
+            5.48409182238641741584L,
+         };
+         result = Y + tools::evaluate_polynomial(P, 1 / z) / tools::evaluate_polynomial(Q, 1 / z);
+         result *= exp(-z * z) / z;
       }
-      T g = exp(-z * z) / z;
-      result = g * b + g * r;
    }
    else
    {
@@ -356,10 +401,28 @@ T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<64>& t)
       }
       else
       {
-         // Worst case absolute error found: 6.688618532e-21
-         static const T n[8] = { 0.00337916709551257388990745L, -0.00073695653048167948530905L, -0.374732337392919607868241L, 0.0817442448733587196071743L, -0.0421089319936548595203468L, 0.0070165709512095756344528L, -0.00495091255982435110337458L, 0.000871646599037922480317225L };
-         static const T d[8] = { 1L, -0.218088218087924645390535L, 0.412542972725442099083918L, -0.0841891147873106755410271L, 0.0655338856400241519690695L, -0.0120019604454941768171266L, 0.00408165558926174048329689L, -0.000615900721557769691924509L };
-         result = z * 1.125 + z * tools::evaluate_polynomial(n, z) / tools::evaluate_polynomial(d, z);
+         // Max Error found at long double precision =   1.623299e-20
+         // Maximum Deviation Found:                     4.326e-22
+         // Expected Error Term:                         -4.326e-22
+         // Maximum Relative Change in Control Points:   1.474e-04
+         static const T Y = 1.044948577880859375f;
+         static const T P[] = {    
+            0.0834305892146531988966L,
+            -0.338097283075565413695L,
+            -0.0509602734406067204596L,
+            -0.00904906346158537794396L,
+            -0.000489468651464798669181L,
+            -0.200305626366151877759e-4L,
+         };
+         static const T Q[] = {    
+            1L,
+            0.455817300515875172439L,
+            0.0916537354356241792007L,
+            0.0102722652675910031202L,
+            0.000650511752687851548735L,
+            0.189532519105655496778e-4L,
+         };
+         result = z * (Y + tools::evaluate_polynomial(P, z * z) / tools::evaluate_polynomial(Q, z * z));
       }
    }
    else if((z < 110) || ((z < 110) && invert))  // TODO FIXME!!!
@@ -368,134 +431,128 @@ T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<64>& t)
       // We'll be calculating erfc:
       //
       invert = !invert;
-      T r, b;
-      if(z < 0.75)
+      if(z < 1.5)
       {
-         // Worst case absolute error found: 5.582813374e-21
-         static const T n[6] = { -0.0361790390718262471360258L, 0.292251883444882683221149L, 0.281447041797604512774415L, 0.125610208862766947294894L, 0.0274135028268930549240776L, 0.00250839672168065762786937L };
-         static const T d[6] = { 1L, 1.8545005897903486499845L, 1.43575803037831418074962L, 0.582827658753036572454135L, 0.124810476932949746447682L, 0.0113724176546353285778481L };
-         static const float f0 =  0.3440242112F;
-         r = tools::evaluate_polynomial(n, z - 0.5) / tools::evaluate_polynomial(d, z - 0.5);
-         b = f0;
+         // Max Error found at long double precision =   3.239590e-20
+         // Maximum Deviation Found:                     2.241e-20
+         // Expected Error Term:                         -2.241e-20
+         // Maximum Relative Change in Control Points:   5.110e-03
+         static const T Y = 0.405935764312744140625f;
+         static const T P[] = {    
+            -0.0980905922162812031672L,
+            0.159989089922969141329L,
+            0.222359821619935712378L,
+            0.127303921703577362312L,
+            0.0384057530342762400273L,
+            0.00628431160851156719325L,
+            0.000441266654514391746428L,
+            0.266689068336295642561e-7L,
+         };
+         static const T Q[] = {    
+            1L,
+            2.03237474985469469291L,
+            1.78355454954969405222L,
+            0.867940326293760578231L,
+            0.248025606990021698392L,
+            0.0396649631833002269861L,
+            0.00279220237309449026796L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 0.5f) / tools::evaluate_polynomial(Q, z - 0.5f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 1.25)
+      else if(z < 2.5)
       {
-         // Worst case absolute error found: 4.01854729e-21
-         static const T n[7] = { -0.0397876892611136856954425L, 0.153165212467878293257683L, 0.191260295600936245503129L, 0.10276327061989304213645L, 0.029637090615738836726027L, 0.0046093486780275489468812L, 0.000307607820348680180548455L };
-         static const T d[7] = { 1L, 1.95520072987627704987886L, 1.64762317199384860109595L, 0.768238607022126250082483L, 0.209793185936509782784315L, 0.0319569316899913392596356L, 0.00213363160895785378615014L };
-         static const float f0 =  0.419990927F;
-         r = tools::evaluate_polynomial(n, z - 0.75) / tools::evaluate_polynomial(d, z - 0.75);
-         b = f0;
+         // Max Error found at long double precision =   3.686211e-21
+         // Maximum Deviation Found:                     1.495e-21
+         // Expected Error Term:                         -1.494e-21
+         // Maximum Relative Change in Control Points:   1.793e-04
+         static const T Y = 0.50672817230224609375f;
+         static const T P[] = {    
+            -0.024350047620769840217L,
+            0.0343522687935671451309L,
+            0.0505420824305544949541L,
+            0.0257479325917757388209L,
+            0.00669349844190354356118L,
+            0.00090807914416099524444L,
+            0.515917266698050027934e-4L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.71657861671930336344L,
+            1.26409634824280366218L,
+            0.512371437838969015941L,
+            0.120902623051120950935L,
+            0.0158027197831887485261L,
+            0.000897871370778031611439L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 1.5f) / tools::evaluate_polynomial(Q, z - 1.5f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 2.25)
+      else if(z < 4.5)
       {
-         // Worst case absolute error found: 2.866005373e-21
-         static const T n[7] = { -0.0300838560557949717328341L, 0.0538578829844454508530552L, 0.0726211541651914182692959L, 0.0367628469888049348429018L, 0.00964629015572527529605267L, 0.00133453480075291076745275L, 0.778087599782504251917881e-4L };
-         static const T d[8] = { 1L, 1.75967098147167528287343L, 1.32883571437961120556307L, 0.552528596508757581287907L, 0.133793056941332861912279L, 0.0179509645176280768640766L, 0.00104712440019937356634038L, -0.106640381820357337177643e-7L };
-         static const float f0 = 0.4898625016F;
-         r = tools::evaluate_polynomial(n, z - 1.25) / tools::evaluate_polynomial(d, z - 1.25);
-         b = f0;
-      }
-      else if(z < 3.5)
-      {
-         // Worst case absolute error found: 1.045355789e-21
-         static const T n[7] = { -0.0117907570137227847827732L, 0.014262132090538809896674L, 0.0202234435902960820020765L, 0.00930668299990432009042239L, 0.00213357802422065994322516L, 0.00025022987386460102395382L, 0.120534912219588189822126e-4L };
-         static const T d[7] = { 1L, 1.50376225203620482047419L, 0.965397786204462896346934L, 0.339265230476796681555511L, 0.0689740649541569716897427L, 0.00771060262491768307365526L, 0.000371421101531069302990367L };
-         static const float f0 = 0.5317370892F;
-         r = tools::evaluate_polynomial(n, z - 2.25) / tools::evaluate_polynomial(d, z - 2.25);
-         b = f0;
-      }
-      else if(z < 5.25)
-      {
-         // Worst case absolute error found: 8.300028706e-22
-         static const T n[7] = { -0.00546954795538729307482955L, 0.00404190278731707110245394L, 0.0054963369553161170521356L, 0.00212616472603945399437862L, 0.000394984014495083900689956L, 0.365565477064442377259271e-4L, 0.135485897109932323253786e-5L };
-         static const T d[8] = { 1L, 1.21019697773630784832251L, 0.620914668221143886601045L, 0.173038430661142762569515L, 0.0276550813773432047594539L, 0.00240625974424309709745382L, 0.891811817251336577241006e-4L, -0.465528836283382684461025e-11L };
-         static const float f0 = 0.5489973426F;
-         r = tools::evaluate_polynomial(n, z - 3.5) / tools::evaluate_polynomial(d, z - 3.5);
-         b = f0;
-      }
-      else if(z < 8)
-      {
-         // Worst case absolute error found: 1.700157534e-21
-         static const T n[6] = { -0.00270722535905778347999196L, 0.0013187563425029400461378L, 0.00119925933261002333923989L, 0.00027849619811344664248235L, 0.267822988218331849989363e-4L, 0.923043672315028197865066e-6L };
-         static const T d[7] = { 1L, 0.814632808543141591118279L, 0.268901665856299542168425L, 0.0449877216103041118694989L, 0.00381759663320248459168994L, 0.000131571897888596914350697L, 0.404815359675764138445257e-11L };
-         static const float f0 = 0.5571740866F;
-         r = tools::evaluate_polynomial(n, z - 5.25) / tools::evaluate_polynomial(d, z - 5.25);
-         b = f0;
-      }
-      else if(z < 11.5)
-      {
-         //Worst case absolute error found: 3.002278011e-22
-         static const T n[6] = { -0.00109946720691742196814323L, 0.000406425442750422675169153L, 0.000274499489416900707787024L, 0.465293770646659383436343e-4L, 0.320955425395767463401993e-5L, 0.778286018145020892261936e-7L };
-         static const T d[6] = { 1L, 0.588173710611846046373373L, 0.139363331289409746077541L, 0.0166329340417083678763028L, 0.00100023921310234908642639L, 0.24254837521587225125068e-4L };
-         static const float f0 = 0.5609807968F;
-         r = tools::evaluate_polynomial(n, z - 8) / tools::evaluate_polynomial(d, z - 8);
-         b = f0;
-      }
-      else if(z < 17)
-      {
-         //Worst case absolute error found: 6.741114695e-21
-         static const T n[5] = { -0.00056907993601094962855594L, 0.000169498540373762264416984L, 0.518472354581100890120501e-4L, 0.382819312231928859704678e-5L, 0.824989931281894431781794e-7L };
-         static const T d[6] = { 1L, 0.339637250051139347430323L, 0.043472647870310663055044L, 0.00248549335224637114641629L, 0.535633305337152900549536e-4L, -0.117490944405459578783846e-12L };
-         static const float f0 = 0.5626493692F;
-         r = tools::evaluate_polynomial(n, z - 11.5) / tools::evaluate_polynomial(d, z - 11.5);
-         b = f0;
-      }
-      else if(z < 24)
-      {
-         // Worst case absolute error found: 7.802346984e-22
-         static const T n[5] = { -0.000241313599483991337479091L, 0.574224975202501512365975e-4L, 0.115998962927383778460557e-4L, 0.581762134402593739370875e-6L, 0.853971555085673614607418e-8L };
-         static const T d[5] = { 1L, 0.233044138299687841018015L, 0.0204186940546440312625597L, 0.000797185647564398289151125L, 0.117019281670172327758019e-4L };
-         static const float f0 = 0.5634598136F;
-         r = tools::evaluate_polynomial(n, z - 17) / tools::evaluate_polynomial(d, z - 17);
-         b = f0;
-      }
-      else if(z < 38)
-      {
-         // Worst case absolute error found: 2.414228989e-22
-         static const T n[5] = { -0.000146674699277760365803642L, 0.162666552112280519955647e-4L, 0.269116248509165239294897e-5L, 0.979584479468091935086972e-7L, 0.101994647625723465722285e-8L };
-         static const T d[5] = { 1L, 0.165907812944847226546036L, 0.0103361716191505884359634L, 0.000286593026373868366935721L, 0.298401570840900340874568e-5L };
-         static const float f0 = 0.5638477802F;
-         r = tools::evaluate_polynomial(n, z - 24) / tools::evaluate_polynomial(d, z - 24);
-         b = f0;
-      }
-      else if(z < 60)
-      {
-         // Worst case absolute error found: 5.896543869e-24
-         static const T n[5] = { -0.583905797629771786720406e-4L, 0.412510325105496173512992e-5L, 0.431790922420250949096906e-6L, 0.993365155590013193345569e-8L, 0.653480510020104699270084e-10L };
-         static const T d[5] = { 1L, 0.105077086072039915406159L, 0.00414278428675475620830226L, 0.726338754644523769144108e-4L, 0.477818471047398785369849e-6L };
-         static const float f0 = 0.5640528202F;
-         r = tools::evaluate_polynomial(n, z - 38) / tools::evaluate_polynomial(d, z - 38);
-         b = f0;
-      }
-      else if(z < 85)
-      {
-         // Worst case absolute error found: 3.080612264e-21
-         static const T n[4] = { -0.196457797609229579459841e-4L, 0.157243887666800692441195e-5L, 0.543902511192700878690335e-7L, 0.317472492369117710852685e-9L };
-         static const T d[5] = { 1L, 0.052803989240957632204885L, 0.000926876069151753290378112L, 0.541011723226630257077328e-5L, 0.535093845803642394908747e-15L };
-         static const float f0 = 0.5641309023F;
-         r = tools::evaluate_polynomial(n, z - 60) / tools::evaluate_polynomial(d, z - 60);
-         b = f0;
+         // Maximum Deviation Found:                     1.107e-20
+         // Expected Error Term:                         -1.106e-20
+         // Maximum Relative Change in Control Points:   1.709e-04
+         // Max Error found at long double precision =   1.446908e-20
+         static const T Y  = 0.5405750274658203125f;
+         static const T P[] = {    
+            0.0029527671653097284033L,
+            0.0141853245895495604051L,
+            0.0104959584626432293901L,
+            0.00343963795976100077626L,
+            0.00059065441194877637899L,
+            0.523435380636174008685e-4L,
+            0.189896043050331257262e-5L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.19352160185285642574L,
+            0.603256964363454392857L,
+            0.165411142458540585835L,
+            0.0259729870946203166468L,
+            0.00221657568292893699158L,
+            0.804149464190309799804e-4L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 3.5f) / tools::evaluate_polynomial(Q, z - 3.5f);
+         result *= exp(-z * z) / z;
       }
       else
       {
-         // Worst case absolute error found: 8.094633491e-22
-         static const T n[4] = { -0.789224703978722689089794e-5L, 0.622088451660986955124162e-6L, 0.145728445676882396797184e-7L, 0.603715505542715364529243e-10L };
-         static const T d[4] = { 1L, 0.0375328846356293715248719L, 0.000467919535974625308126054L, 0.193847039275845656900547e-5L };
-         static const float f0 = 0.5641584396F;
-         r = tools::evaluate_polynomial(n, z - 85) / tools::evaluate_polynomial(d, z - 85);
-         b = f0;
+         // Max Error found at long double precision =   7.961166e-21
+         // Maximum Deviation Found:                     6.677e-21
+         // Expected Error Term:                         6.676e-21
+         // Maximum Relative Change in Control Points:   2.319e-05
+         static const T Y = 0.55825519561767578125f;
+         static const T P[] = {    
+            0.00593438793008050214106L,
+            0.0280666231009089713937L,
+            -0.141597835204583050043L,
+            -0.978088201154300548842L,
+            -5.47351527796012049443L,
+            -13.8677304660245326627L,
+            -27.1274948720539821722L,
+            -29.2545152747009461519L,
+            -16.8865774499799676937L,
+         };
+         static const T Q[] = {    
+            1L,
+            4.72948911186645394541L,
+            23.6750543147695749212L,
+            60.0021517335693186785L,
+            131.766251645149522868L,
+            178.167924971283482513L,
+            182.499390505915222699L,
+            104.365251479578577989L,
+            30.8365511891224291717L,
+         };
+         result = Y + tools::evaluate_polynomial(P, 1 / z) / tools::evaluate_polynomial(Q, 1 / z);
+         result *= exp(-z * z) / z;
       }
-      T g = exp(-z * z) / z;
-      result = g * b + g * r;
-      BOOST_MATH_INSTRUMENT_CODE("r = " << r);
-      BOOST_MATH_INSTRUMENT_CODE("b = " << b);
-      BOOST_MATH_INSTRUMENT_CODE("g = " << g);
    }
    else
    {
       //
-      // Any value of z larger than 28 will underflow to zero:
+      // Any value of z larger than 110 will underflow to zero:
       //
       result = 0;
       invert = !invert;
@@ -549,184 +606,352 @@ T erf_imp(T z, bool invert, const Policy& pol, const mpl::int_<113>& t)
       }
       else
       {
-         // Worst case absolute error found: 1.928180863e-35
-         static const T n[13] = { 0.0033791670955125738961589031215451706772L, -0.000356604747854533671135323429762519216044L, -0.374476838669183581687167228866769133591L, 0.0395338132469809122364498388174446488042L, -0.070405473508786506375820161461872523315L, 0.00575264725772369303419496752516485264994L, -0.0122324470706306942925087773122510971344L, 0.000982833333252586078523570049842642796291L, -0.000937806155615159592441487275938040285833L, 0.485407838108763091860415874932955355755e-4L, -0.50171236926234625577876479444632561922e-4L, 0.19406068817888598455243350289053451571e-5L, -0.119351103792049576459000102632508734863e-5L };
-         static const T d[13] = { 1L, -0.105530368216503232473476334993759958083L, 0.488152943026846232046726653294817930988L, -0.0470361716364117780901924633553851211874L, 0.107663671943702835026199580597519084906L, -0.00919493879447389180633447493128337242362L, 0.0138231121717229362691899919242806829805L, -0.000994048559663865788847688218108232247441L, 0.00109769834527023265969224251892094019735L, -0.600458401801636062015615549258555311545e-4L, 0.51530723974502946291624848874654212384e-4L, -0.164121264470361558910636548509486296153e-5L, 0.112643498977070218963888579607359294396e-5L };
-
-         result = z * 1.125 + z * tools::evaluate_rational(n, d, z);
+         // Max Error found at long double precision =   2.342380e-35
+         // Maximum Deviation Found:                     6.124e-36
+         // Expected Error Term:                         -6.124e-36
+         // Maximum Relative Change in Control Points:   3.492e-10
+         static const T Y = 1.0841522216796875f;
+         static const T P[] = {    
+            0.0442269454158250738961589031215451778L,
+            -0.35549265736002144875335323556961233L,
+            -0.0582179564566667896225454670863270393L,
+            -0.0112694696904802304229950538453123925L,
+            -0.000805730648981801146251825329609079099L,
+            -0.566304966591936566229702842075966273e-4L,
+            -0.169655010425186987820201021510002265e-5L,
+            -0.344448249920445916714548295433198544e-7L,
+         };
+         static const T Q[] = {    
+            1L,
+            0.466542092785657604666906909196052522L,
+            0.100005087012526447295176964142107611L,
+            0.0128341535890117646540050072234142603L,
+            0.00107150448466867929159660677016658186L,
+            0.586168368028999183607733369248338474e-4L,
+            0.196230608502104324965623171516808796e-5L,
+            0.313388521582925207734229967907890146e-7L,
+         };
+         result = z * (Y + tools::evaluate_polynomial(P, z * z) / tools::evaluate_polynomial(Q, z * z));
       }
    }
-   else if((z < 9) || ((z < 110) && invert)) // TODO FIXME!!
+   else if((z < 9) || ((z < 110) && invert))
    {
       //
       // We'll be calculating erfc:
       //
       invert = !invert;
-      T r, b;
-      if(z < 0.75)
+      if(z < 1)
       {
-         // Worst case absolute error found: 9.46579566e-36
-         static const T n[10] = { -0.0361790390718262471349157886581290316118L, 0.268773785250238404882137450640472787307L, 0.46350995084084251624649426251701042395L, 0.368375435727102373204587584306335625665L, 0.177618123820303858190236222513516291818L, 0.0566304173556669007529719743050764079095L, 0.0121631149481817424284077180037019529004L, 0.00171397353209314111395429418066990259845L, 0.000144662387395699594624184141956722488753L, 0.559870522050008635715382724858714587198e-5L };
-         static const T d[10] = { 1L, 2.50344259590701770420935329380375393716L, 2.84905597172139276093882199286535521011L, 1.93691730181297099541395314232750876411L, 0.868059574796050528229446630538462280596L, 0.266360035323208212078527036132085926692L, 0.0560555526482963925944703505114360693216L, 0.0078174400311465420803366235814673576269L, 0.000657067309046405057499687417839930873806L, 0.254293850077789079098316521097979388983e-4L };
-         static const float f0 =  0.3440242112F;
-         r = tools::evaluate_rational(n, d, z - 0.5);
-         b = f0;
+         // Max Error found at long double precision =   3.246278e-35
+         // Maximum Deviation Found:                     1.388e-35
+         // Expected Error Term:                         1.387e-35
+         // Maximum Relative Change in Control Points:   6.127e-05
+         static const T Y = 0.371877193450927734375f;
+         static const T P[] = {    
+            -0.0640320213544647969396032886581290455L,
+            0.200769874440155895637857443946706731L,
+            0.378447199873537170666487408805779826L,
+            0.30521399466465939450398642044975127L,
+            0.146890026406815277906781824723458196L,
+            0.0464837937749539978247589252732769567L,
+            0.00987895759019540115099100165904822903L,
+            0.00137507575429025512038051025154301132L,
+            0.0001144764551085935580772512359680516L,
+            0.436544865032836914773944382339900079e-5L,
+         };
+         static const T Q[] = {    
+            1L,
+            2.47651182872457465043733800302427977L,
+            2.78706486002517996428836400245547955L,
+            1.87295924621659627926365005293130693L,
+            0.829375825174365625428280908787261065L,
+            0.251334771307848291593780143950311514L,
+            0.0522110268876176186719436765734722473L,
+            0.00718332151250963182233267040106902368L,
+            0.000595279058621482041084986219276392459L,
+            0.226988669466501655990637599399326874e-4L,
+            0.270666232259029102353426738909226413e-10L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 0.5f) / tools::evaluate_polynomial(Q, z - 0.5f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 1.25)
+      else if(z < 1.5)
       {
-         // Worst case absolute error found: 1.222145602e-35
-         static const T n[10] = { -0.03978768926111368569548863384587917014L, 0.136218360681765349252731304877153919181L, 0.252782160406474440925641829129129001834L, 0.198264231106182362320012632943145619752L, 0.0923045825293507328801206570363391760624L, 0.0281157216148097885766639832985410722743L, 0.00573041663561645197870019701493117161792L, 0.000762341440133027349203518836487137709687L, 0.60471020134417423449877859375492618899e-4L, 0.219005333943510376644902615714724932217e-5L };
-         static const T d[11] = { 1L, 2.38113277319993574121349184069891082204L, 2.57380422881476860215664207822277590181L, 1.65937045609044738941173490190122101824L, 0.704055811320312044285417250966993014161L, 0.20414913933328592198279939394283925451L, 0.0405162285360227740710964820549709038107L, 0.00531638867177288975915820230980317499728L, 0.000419364368135139398723983192742319455284L, 0.151874665979234971229096136924566078234e-4L, 0.807869459506748684117962248796937508011e-11L };
-         static const float f0 =  0.419990927F;
-         r = tools::evaluate_polynomial(n, z - 0.75) / tools::evaluate_polynomial(d, z - 0.75);
-         b = f0;
+         // Max Error found at long double precision =   2.215785e-35
+         // Maximum Deviation Found:                     1.539e-35
+         // Expected Error Term:                         1.538e-35
+         // Maximum Relative Change in Control Points:   6.104e-05
+         static const T Y = 0.45658016204833984375f;
+         static const T P[] = {    
+            -0.0289965858925328393392496555094848345L,
+            0.0868181194868601184627743162571779226L,
+            0.169373435121178901746317404936356745L,
+            0.13350446515949251201104889028133486L,
+            0.0617447837290183627136837688446313313L,
+            0.0185618495228251406703152962489700468L,
+            0.00371949406491883508764162050169531013L,
+            0.000485121708792921297742105775823900772L,
+            0.376494706741453489892108068231400061e-4L,
+            0.133166058052466262415271732172490045e-5L,
+         };
+         static const T Q[] = {    
+            1L,
+            2.32970330146503867261275580968135126L,
+            2.46325715420422771961250513514928746L,
+            1.55307882560757679068505047390857842L,
+            0.644274289865972449441174485441409076L,
+            0.182609091063258208068606847453955649L,
+            0.0354171651271241474946129665801606795L,
+            0.00454060370165285246451879969534083997L,
+            0.000349871943711566546821198612518656486L,
+            0.123749319840299552925421880481085392e-4L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 1.0f) / tools::evaluate_polynomial(Q, z - 1.0f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 2)
+      else if(z < 2.25)
       {
-         // Worst case absolute error found: 5.893842955e-36
-         static const T n[11] = { -0.0255063683486569102096736247449691465143L, 0.045782379672906795594927072060091308408L, 0.113248439610400562258072020811195716817L, 0.0996016254422112410086711272219455446695L, 0.0508749250027894453228337309651895478017L, 0.0171081937013828309576540212196644542209L, 0.00395354196550210630440706013523069756354L, 0.000629022203390154585475081628606234279007L, 0.664903286194855400689101617763591823345e-4L, 0.423935693893425355108071655059640137208e-5L, 0.124304036910852727351487636048151737214e-6L };
-         static const T d[11] = { 1L, 2.39207679390801118396945702674440915308L, 2.62237869972649377524874287442154430843L, 1.73645189911172997548091140085423843725L, 0.769812706091926741262865732006953282036L, 0.238986814887891859065369830215615790694L, 0.0526759147274379214313767032352419949829L, 0.00814993801398361741777997755108018659382L, 0.00084829993036396244429607826663252633817L, 0.537276435448416921594616417908288527881e-4L, 0.157537193656690184073389824392669625417e-5L };
-         static const float f0 = 0.4852850139F;
-         r = tools::evaluate_rational(n, d, z - 1.25);
-         b = f0;
+         // Maximum Deviation Found:                     1.418e-35
+         // Expected Error Term:                         1.418e-35
+         // Maximum Relative Change in Control Points:   1.316e-04
+         // Max Error found at long double precision =   1.998462e-35
+         static const T Y = 0.50250148773193359375f;
+         static const T P[] = {    
+            -0.0201233630504573402185161184151016606L,
+            0.0331864357574860196516686996302305002L,
+            0.0716562720864787193337475444413405461L,
+            0.0545835322082103985114927569724880658L,
+            0.0236692635189696678976549720784989593L,
+            0.00656970902163248872837262539337601845L,
+            0.00120282643299089441390490459256235021L,
+            0.000142123229065182650020762792081622986L,
+            0.991531438367015135346716277792989347e-5L,
+            0.312857043762117596999398067153076051e-6L,
+         };
+         static const T Q[] = {    
+            1L,
+            2.13506082409097783827103424943508554L,
+            2.06399257267556230937723190496806215L,
+            1.18678481279932541314830499880691109L,
+            0.447733186643051752513538142316799562L,
+            0.11505680005657879437196953047542148L,
+            0.020163993632192726170219663831914034L,
+            0.00232708971840141388847728782209730585L,
+            0.000160733201627963528519726484608224112L,
+            0.507158721790721802724402992033269266e-5L,
+            0.18647774409821470950544212696270639e-12L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 1.5f) / tools::evaluate_polynomial(Q, z - 1.5f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 2.75)
+      else if (z < 3)
       {
-         // Worst case absolute error found: 4.024770853e-36
-         static const T n[10] = { -0.0108897177067473013323228381829144739013L, 0.0202210475357865979950082670101965963435L, 0.0403242149078991892599316678797913295452L, 0.0288492313188655084113941326565482276741L, 0.0116982647742533555237861890442866083526L, 0.00301908913020213436098518520436147263177L, 0.000511140165864993121203730804407968689429L, 0.555507897975436549741754647662158917103e-4L, 0.354571088276496768574495922471690102061e-5L, 0.101789333060641482357520298518780163915e-6L };
-         static const T d[11] = { 1L, 1.98184247277299581801610266575921553552L, 1.77518826058984218945272444617044495028L, 0.943934346956188464279312722940302202684L, 0.328630002685235061519039528479761588138L, 0.0777535542351039388345270792222146705189L, 0.0125143974181120800829065248546370953609L, 0.00132270605931460450441108147393979771563L, 0.834118048375722123506409257130329786209e-4L, 0.239456257167492104073765911366304033453e-5L, 0.197067742893785800814802969598122120027e-13L };
-         static const float f0 = 0.5216810703F;
-         r = tools::evaluate_polynomial(n, z - 2) / tools::evaluate_polynomial(d, z - 2);
-         b = f0;
+         // Maximum Deviation Found:                     3.575e-36
+         // Expected Error Term:                         3.575e-36
+         // Maximum Relative Change in Control Points:   7.103e-05
+         // Max Error found at long double precision =   5.794737e-36
+         static const T Y = 0.52896785736083984375f;
+         static const T P[] = {    
+            -0.00902152521745813634562524098263360074L,
+            0.0145207142776691539346923710537580927L,
+            0.0301681239582193983824211995978678571L,
+            0.0215548540823305814379020678660434461L,
+            0.00864683476267958365678294164340749949L,
+            0.00219693096885585491739823283511049902L,
+            0.000364961639163319762492184502159894371L,
+            0.388174251026723752769264051548703059e-4L,
+            0.241918026931789436000532513553594321e-5L,
+            0.676586625472423508158937481943649258e-7L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.93669171363907292305550231764920001L,
+            1.69468476144051356810672506101377494L,
+            0.880023580986436640372794392579985511L,
+            0.299099106711315090710836273697708402L,
+            0.0690593962363545715997445583603382337L,
+            0.0108427016361318921960863149875360222L,
+            0.00111747247208044534520499324234317695L,
+            0.686843205749767250666787987163701209e-4L,
+            0.192093541425429248675532015101904262e-5L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 2.25f) / tools::evaluate_polynomial(Q, z - 2.25f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 3.75)
+      else if(z < 3.5)
       {
-         // Worst case absolute error found: 2.119317982e-36
-         static const T n[10] = { -0.00669534469911386821762042893742722704704L, 0.00779239067529714323524154862288379264056L, 0.0167670669587476509267036865033136655094L, 0.0113887916348251443051357686146040093464L, 0.00426976750247047946700539147728477144579L, 0.00100469100574064832665606356894416652764L, 0.000153533145320881108157829902752192859922L, 0.149337551064665413462766906201269176262e-4L, 0.846377837919513024118176704010972579138e-6L, 0.214045773545256889299689737489755489478e-7L };
-         static const T d[11] = { 1L, 1.78724215851193637544287795626580411105L, 1.44052576962222794702178612920219772782L, 0.687639905608366315245841860669607532265L, 0.214374367225822611754443822822738563207L, 0.0452948320968245754796139856381504201504L, 0.00649108394178118005887118777181540680812L, 0.000608904720665003139414993591868256489088L, 0.33959064390570911588709483563995284603e-4L, 0.858811916085393051026834431509997486704e-6L, 0.618878592093890510233502654703683447468e-15L };
-         static const float f0 = 0.5392661095F;
-         r = tools::evaluate_polynomial(n, z - 2.75) / tools::evaluate_polynomial(d, z - 2.75);
-         b = f0;
+         // Maximum Deviation Found:                     8.126e-37
+         // Expected Error Term:                         -8.126e-37
+         // Maximum Relative Change in Control Points:   1.363e-04
+         // Max Error found at long double precision =   1.747062e-36
+         static const T Y = 0.54037380218505859375f;
+         static const T P[] = {    
+            -0.0033703486408887424921155540591370375L,
+            0.0104948043110005245215286678898115811L,
+            0.0148530118504000311502310457390417795L,
+            0.00816693029245443090102738825536188916L,
+            0.00249716579989140882491939681805594585L,
+            0.0004655591010047353023978045800916647L,
+            0.531129557920045295895085236636025323e-4L,
+            0.343526765122727069515775194111741049e-5L,
+            0.971120407556888763695313774578711839e-7L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.59911256167540354915906501335919317L,
+            1.136006830764025173864831382946934L,
+            0.468565867990030871678574840738423023L,
+            0.122821824954470343413956476900662236L,
+            0.0209670914950115943338996513330141633L,
+            0.00227845718243186165620199012883547257L,
+            0.000144243326443913171313947613547085553L,
+            0.407763415954267700941230249989140046e-5L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 3.0f) / tools::evaluate_polynomial(Q, z - 3.0f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 5)
+      else if(z < 5.5)
       {
-         // Worst case absolute error found: 3.131502824e-36
-         static const T n[10] = { -0.00378088626017041998499190989910098718437L, 0.0029008905292996011997575492874095588328L, 0.00662431938391549599757244232386689480515L, 0.00417809740399798845564363621020984935218L, 0.00142019749135652688012034919213168974543L, 0.000299107980170253223293530710056814995102L, 0.405161538841561396150507786831930770839e-4L, 0.346344371670880861875666253626975779945e-5L, 0.171091054330494778613793054233437928605e-6L, 0.373924433717749484258186454458704819755e-8L };
-         static const T d[10] = { 1L, 1.5810750672399887547849540367499389454L, 1.12479852885403050655678225945856872694L, 0.47277272679268851560291322980574597267L, 0.129444913616967588584693095240544707208L, 0.0239544490709674941887988416318107990646L, 0.00299775294496053944060700963645084591246L, 0.00024478412843088575835960648397300177201L, 0.118424712755145205302405346348931402917e-4L, 0.2588206250858483868392167535345681119e-6L };
-         static const float f0 = 0.549742341F;
-         r = tools::evaluate_rational(n, d, z - 3.75);
-         b = f0;
+         // Maximum Deviation Found:                     5.804e-36
+         // Expected Error Term:                         -5.803e-36
+         // Maximum Relative Change in Control Points:   2.475e-05
+         // Max Error found at long double precision =   1.349545e-35
+         static const T Y = 0.55000019073486328125f;
+         static const T P[] = {    
+            0.00118142849742309772151454518093813615L,
+            0.0072201822885703318172366893469382745L,
+            0.0078782276276860110721875733778481505L,
+            0.00418229166204362376187593976656261146L,
+            0.00134198400587769200074194304298642705L,
+            0.000283210387078004063264777611497435572L,
+            0.405687064094911866569295610914844928e-4L,
+            0.39348283801568113807887364414008292e-5L,
+            0.248798540917787001526976889284624449e-6L,
+            0.929502490223452372919607105387474751e-8L,
+            0.156161469668275442569286723236274457e-9L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.52955245103668419479878456656709381L,
+            1.06263944820093830054635017117417064L,
+            0.441684612681607364321013134378316463L,
+            0.121665258426166960049773715928906382L,
+            0.0232134512374747691424978642874321434L,
+            0.00310778180686296328582860464875562636L,
+            0.000288361770756174705123674838640161693L,
+            0.177529187194133944622193191942300132e-4L,
+            0.655068544833064069223029299070876623e-6L,
+            0.11005507545746069573608988651927452e-7L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 4.5f) / tools::evaluate_polynomial(Q, z - 4.5f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 6.5)
+      else if(z < 7.5)
       {
-         // Worst case absolute error found: 3.352877573e-35
-         static const T n[9] = { -0.00210683958249012010206456754123471415706L, 0.00146329021314062287670019911742786780092L, 0.00242029064025351202243048169807220157512L, 0.0011321990764681390160708960047630195582L, 0.000277123780759366982673218537550876769487L, 0.401236501288775561636453586216146028714e-4L, 0.347799938323835778216424009916867086167e-5L, 0.167678812729975154456097184107934455429e-6L, 0.346722083660429051057284107535869165775e-8L };
-         static const T d[10] = { 1L, 1.22334833521124956366395053444841951468L, 0.661433457507589455018784737495591428263L, 0.206503622658778732280997770028712044451L, 0.0407323027711252752353388616742333806362L, 0.00519969889874877079704615143005539754407L, 0.000419679230772141031030427156828631265963L, 0.195896640254171597965013007459411704085e-4L, 0.405070207572551760879797790899826058473e-6L, -0.949400883467250846930389103621356900319e-17L };
-         static const float f0 = 0.5556300282F;
-         r = tools::evaluate_polynomial(n, z - 5) / tools::evaluate_polynomial(d, z - 5);
-         b = f0;
+         // Maximum Deviation Found:                     1.007e-36
+         // Expected Error Term:                         1.007e-36
+         // Maximum Relative Change in Control Points:   1.027e-03
+         // Max Error found at long double precision =   2.646420e-36
+         static const T Y = 0.5574436187744140625f;
+         static const T P[] = {    
+            0.000293236907400849056269309713064107674L,
+            0.00225110719535060642692275221961480162L,
+            0.00190984458121502831421717207849429799L,
+            0.000747757733460111743833929141001680706L,
+            0.000170663175280949889583158597373928096L,
+            0.246441188958013822253071608197514058e-4L,
+            0.229818000860544644974205957895688106e-5L,
+            0.134886977703388748488480980637704864e-6L,
+            0.454764611880548962757125070106650958e-8L,
+            0.673002744115866600294723141176820155e-10L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.12843690320861239631195353379313367L,
+            0.569900657061622955362493442186537259L,
+            0.169094404206844928112348730277514273L,
+            0.0324887449084220415058158657252147063L,
+            0.00419252877436825753042680842608219552L,
+            0.00036344133176118603523976748563178578L,
+            0.204123895931375107397698245752850347e-4L,
+            0.674128352521481412232785122943508729e-6L,
+            0.997637501418963696542159244436245077e-8L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z - 6.5f) / tools::evaluate_polynomial(Q, z - 6.5f);
+         result *= exp(-z * z) / z;
       }
-      else if(z < 8)
+      else if(z < 11.5)
       {
-         // Worst case absolute error found: 2.10254551e-36
-         static const T n[9] = { -0.00107224589975857477185569028693588970638L, 0.00081159959093417892787006088639848404179L, 0.00105587689576932891666032146026668833287L, 0.000416243954540394829165805666548948771809L, 0.861189599093384016322579078144012057531e-4L, 0.105064862265647286966467927732505059558e-4L, 0.763674245263385902692134637353517251296e-6L, 0.306964079269190247526141442183490066292e-7L, 0.525762928524110511201313708396204710874e-9L };
-         static const T d[9] = { 1L, 1.03391233015873996503551085347368889767L, 0.471295765635712684194436077437130977978L, 0.123736066749315618886080242926593910851L, 0.0204690897886919138685460664198600282119L, 0.00218521816743913946855947853274936296576L, 0.000147057386621380823003258590658747813774L, 0.570514093706434168568509838021466564264e-5L, 0.977166974697066620826028345712327325748e-7L };
-         static const float f0 = 0.5588091016F;
-         r = tools::evaluate_rational(n, d, z - 6.5);
-         b = f0;
-      }
-      else if(z < 10)
-      {
-         // Worst case absolute error found: 8.006848023e-37
-         static const T n[9] = { -0.000764310289345400483607004463638641680792L, 0.000375959928342415987920641866513058424701L, 0.000477297615927227258961911005347799033473L, 0.000165573027183931250708334564452626717999L, 0.296617493157889183515359094859055088531e-4L, 0.310848843632513098624143817615592253324e-5L, 0.192932185180269434271810693046412848027e-6L, 0.658630702075882625552897504189436319318e-8L, 0.952880249971934343233104137698620618851e-10L };
-         static const T d[9] = { 1L, 0.885953297549629585611202995885653291163L, 0.345435500008639080844920938390800739845L, 0.0774289910213823638414558561872084410517L, 0.0109142290775434200609901181618181718948L, 0.000990815749814504617347317658063197107511L, 0.565801964505889288566864514277149126893e-4L, 0.185846832474795168475989869562411740416e-5L, 0.268875677412705938842038805073576012915e-7L };
-         static const float f0 = 0.5606456399F;
-         r = tools::evaluate_rational(n, d, z - 8);
-         b = f0;
-      }
-      else if(z < 12.5)
-      {
-         // Worst case absolute error found: 1.920487881e-37
-         static const T n[9] = { -0.00049563543942917072170112779531688430711L, 0.000181627479476470045833245371263435213396L, 0.000205326116055098869964168775605689851547L, 0.602131211119027087508128340443602490578e-4L, 0.904046610725767796892834734953040318357e-5L, 0.790026495730279360618915285828083295597e-6L, 0.407154634490633661408148126521656550974e-7L, 0.114947371191075676274146563385045083492e-8L, 0.136959786076422777905476122283384578138e-10L };
-         static const T d[9] = { 1L, 0.738936412939629363226408445024616124644L, 0.239911614287295587917806937612822134282L, 0.0447038494121568822243673246874110377585L, 0.00522920850086320874490830611785659031521L, 0.000393238307986133717620560371515858231357L, 0.18566831172454022627187937328433090172e-4L, 0.503267648562793696253090536560738864711e-6L, 0.599643373938283798258195761814169705225e-8L };
-         static const float f0 = 0.5619055629F;
-         r = tools::evaluate_rational(n, d, z - 10);
-         b = f0;
-      }
-      else if(z < 15.5)
-      {
-         // Worst case absolute error found: 1.257535398e-36
-         static const T n[8] = { -0.000310716603972278501158850534578560332617L, 0.00011678083970731888844953949114132723885L, 0.800190190430061077253903477346761222901e-4L, 0.156297703728913451581100601056534652076e-4L, 0.151432948873760306237990776980248434808e-5L, 0.798843820137664551611401320879346402013e-7L, 0.219398460602279142004550137383605410162e-8L, 0.244774638611231694720102050826438123042e-10L };
-         static const T d[9] = { 1L, 0.536396467095662522242258924420035847546L, 0.12368534422025248132153213926057643819L, 0.0158935327926481775020421628983323726346L, 0.00122923842249710594941031294559763761829L, 0.572250268558063378795115723535491980973e-4L, 0.148480028895780193980507551658637328542e-5L, 0.165653602646537759781637790321962585489e-7L, 0.159564067829807076335030582566349996674e-21L };
-         static const float f0 = 0.5627119541F;
-         r = tools::evaluate_polynomial(n, z - 12.5) / tools::evaluate_polynomial(d, z - 12.5);
-         b = f0;
-      }
-      else if(z < 20)
-      {
-         // Worst case absolute error found: 8.757869781e-37
-         static const T n[8] = { -0.000232165799411403604511899928682939571679L, 0.473280617901953093430938763139716601257e-4L, 0.322197983787538821545512424866901113822e-4L, 0.53341606003892328294004958671866936958e-5L, 0.429392533762301420884052643595872389588e-6L, 0.186707830002841677949013638707964861935e-7L, 0.420531779988891521855765212230340499168e-9L, 0.38311153882270641561622347190918577449e-11L };
-         static const T d[9] = { 1L, 0.440698415779467873589164469370853517393L, 0.0834079018864546179293964148377602724235L, 0.00878845776227345123101968908701592510214L, 0.000556792236817609981676018545344816931862L, 0.212109697877283363015270621439889468055e-4L, 0.449886743173619367191275104721917344569e-6L, 0.409854405005280582884236774230760402868e-8L, 0.185071069100878210011727114952196630136e-23L };
-         static const float f0 = 0.5632548332F;
-         r = tools::evaluate_polynomial(n, z - 15.5) / tools::evaluate_polynomial(d, z - 15.5);
-         b = f0;
-      }
-      else if(z < 26)
-      {
-         // Worst case absolute error found: 6.571456853e-37
-         static const T n[8] = { -0.000143129243915019877016909310584833592972L, 0.203555078616578752774553439209122798188e-4L, 0.116664173863253360297276766667046754002e-4L, 0.153607643549360281089355497044679566329e-5L, 0.976486412462035616905934994399021437658e-7L, 0.33416295362298759817564985788402188186e-8L, 0.590812660432887787644458409396105030781e-10L, 0.421471133628743008309458424282421874073e-12L };
-         static const T d[8] = { 1L, 0.346848503043261151874606241871432055165L, 0.0516236057301875770334953837585483539519L, 0.0042740199483843978391191804633398315544L, 0.000212586135154357046245694533825075007902L, 0.635258188334431428038271842518161892901e-5L, 0.105600415847309067601860633252823051505e-6L, 0.753327238218310630683194279382721367469e-9L };
-         static const float f0 = 0.5636301041F;
-         r = tools::evaluate_polynomial(n, z - 20) / tools::evaluate_polynomial(d, z - 20);
-         b = f0;
-      }
-      else if(z < 34)
-      {
-         // Worst case absolute error found: 2.529847851e-38
-         static const T n[8] = { -0.863162280463127451272161303767299107489e-4L, 0.876391266908317792353253474461536821127e-5L, 0.407624004719762912183133597708988715137e-5L, 0.418371930808379615690956857824418800194e-6L, 0.206376792034344913360458422974245946873e-7L, 0.546878311460852031076829190722479684e-9L, 0.74760305098509923829341087347518769626e-11L, 0.411832046806658129073165530819472782663e-13L };
-         static const T d[9] = { 1L, 0.268714425336129161136892060316889824437L, 0.0309686025544536788982104017649851516554L, 0.00198426609900573235086828549632290797514L, 0.763402107420631006526499294753645914808e-4L, 0.176354119917411263184292422389304506735e-5L, 0.226504369338582253171306523992412653547e-7L, 0.124774448034213281307712525982862926228e-9L, 0.541581693417048102342931921476367282462e-28L };
-         static const float f0 = 0.5638595223F;
-         r = tools::evaluate_polynomial(n, z - 26) / tools::evaluate_polynomial(d, z - 26);
-         b = f0;
-      }
-      else if(z < 46)
-      {
-         // Worst case absolute error found: 4.880939969e-36
-         static const T n[7] = { -0.552701065525823960321509114250962372959e-4L, 0.459798238451342341380837226471283129117e-5L, 0.117462487430397988459985818542278619172e-5L, 0.704965053290383355071079647747711714696e-7L, 0.191250482739845326510859812663255140286e-8L, 0.245913419605775857221974833985059356312e-10L, 0.120466123381598216554945834019040289508e-12L };
-         static const T d[8] = { 1L, 0.175852634004021068883919193145643406305L, 0.0128923775281953424344037205817061020944L, 0.000504385604406829419856756492198778141939L, 0.111061123996047697713589874603922096536e-4L, 0.130499191758882778721577274330215931713e-6L, 0.639279131688964342759306361922751772829e-9L, -0.10503012469906917938721140272475203112e-26L };
-         static const float f0 = 0.564001143F;
-         r = tools::evaluate_polynomial(n, z - 34) / tools::evaluate_polynomial(d, z - 34);
-         b = f0;
-      }
-      else if(z < 62)
-      {
-         // Worst case absolute error found: 8.634961697e-37
-         static const T n[7] = { -0.299551937061912926289705712581858190494e-4L, 0.188783643501597286680709990049243153264e-5L, 0.353403900815908094401075506391935032602e-6L, 0.156779149815977342177830075875441013335e-7L, 0.31456307256618424444443489905810774564e-9L, 0.29912544832845265905351204765862702307e-11L, 0.108360038290329929702659864116372774364e-13L };
-         static const T d[7] = { 1L, 0.13020345740128026085404079010013007005L, 0.00706598549835633149505923515407700416484L, 0.000204578844720147762058725212299415091588L, 0.333280847765611305843836201217690887394e-5L, 0.289666303356425428524772241712503072453e-7L, 0.104933404691983708511908027657434756019e-9L };
-         static const float f0 = 0.564086318F;
-         r = tools::evaluate_polynomial(n, z - 46) / tools::evaluate_polynomial(d, z - 46);
-         b = f0;
-      }
-      else if(z < 80)
-      {
-         // Worst case absolute error found: 6.10700166e-39
-         static const T n[7] = { -0.146162619512779884168960178459825270831e-4L, 0.952303834226435420147786300516273108344e-6L, 0.114559890033396819882468040960469980168e-6L, 0.368994353517438072494331750992706039868e-8L, 0.545158660461829568567388818070830588533e-10L, 0.383569328729331398089160922704933035281e-12L, 0.103104113324271568678309317039606225294e-14L };
-         static const T d[7] = { 1L, 0.0966822058944670599111360985490948186413L, 0.00389546596914826027568119425228340291579L, 0.837237328321088890541798035513749762375e-4L, 0.101236677684940943809478588316884539423e-5L, 0.652985528810044575089151077574382356898e-8L, 0.175523663960756825512727785416137345625e-10L };
-         static const float f0 = 0.5641308427F;
-         r = tools::evaluate_polynomial(n, z - 62) / tools::evaluate_polynomial(d, z - 62);
-         b = f0;
+         // Maximum Deviation Found:                     8.380e-36
+         // Expected Error Term:                         8.380e-36
+         // Maximum Relative Change in Control Points:   2.632e-06
+         // Max Error found at long double precision =   9.849522e-36
+         static const T Y = 0.56083202362060546875f;
+         static const T P[] = {    
+            0.000282420728751494363613829834891390121L,
+            0.00175387065018002823433704079355125161L,
+            0.0021344978564889819420775336322920375L,
+            0.00124151356560137532655039683963075661L,
+            0.000423600733566948018555157026862139644L,
+            0.914030340865175237133613697319509698e-4L,
+            0.126999927156823363353809747017945494e-4L,
+            0.110610959842869849776179749369376402e-5L,
+            0.55075079477173482096725348704634529e-7L,
+            0.119735694018906705225870691331543806e-8L,
+         };
+         static const T Q[] = {    
+            1L,
+            1.69889613396167354566098060039549882L,
+            1.28824647372749624464956031163282674L,
+            0.572297795434934493541628008224078717L,
+            0.164157697425571712377043857240773164L,
+            0.0315311145224594430281219516531649562L,
+            0.00405588922155632380812945849777127458L,
+            0.000336929033691445666232029762868642417L,
+            0.164033049810404773469413526427932109e-4L,
+            0.356615210500531410114914617294694857e-6L,
+         };
+         result = Y + tools::evaluate_polynomial(P, z / 2 - 4.75f) / tools::evaluate_polynomial(Q, z / 2 - 4.75f);
+         result *= exp(-z * z) / z;
       }
       else
       {
-         // Worst case absolute error found: 3.409761622e-39
-         static const T n[7] = { -0.103600733768855845278685109220598569282e-4L, 0.324846376725138276091774803419773168357e-6L, 0.376580042454826796817160322889753111347e-7L, 0.971125540805193703472871419997820785081e-9L, 0.112499588573918670534994853431614458564e-10L, 0.6161310085325929027114924903443564594e-13L, 0.128358125353302055468778305481781957985e-15L };
-         static const T d[7] = { 1L, 0.0749579802028981336679035635535776767532L, 0.00234137768051079846068630120744888560113L, 0.390095348825177571970348898222511084593e-4L, 0.365628111271063883320224395719085602867e-6L, 0.182790705425846241876560215158605843026e-8L, 0.380806548535012144489621218246876843627e-11L };
-         static const float f0 = 0.5641558766F;
-         r = tools::evaluate_polynomial(n, z - 80) / tools::evaluate_polynomial(d, z - 80);
-         b = f0;
+         // Maximum Deviation Found:                     1.132e-35
+         // Expected Error Term:                         -1.132e-35
+         // Maximum Relative Change in Control Points:   4.674e-04
+         // Max Error found at long double precision =   1.162590e-35
+         static const T Y = 0.5632686614990234375f;
+         static const T P[] = {    
+            0.000920922048732849448079451574171836943L,
+            0.00321439044532288750501700028748922439L,
+            -0.250455263029390118657884864261823431L,
+            -0.906807635364090342031792404764598142L,
+            -8.92233572835991735876688745989985565L,
+            -21.7797433494422564811782116907878495L,
+            -91.1451915251976354349734589601171659L,
+            -144.1279109655993927069052125017673L,
+            -313.845076581796338665519022313775589L,
+            -273.11378811923343424081101235736475L,
+            -271.651566205951067025696102600443452L,
+            -60.0530577077238079968843307523245547L,
+         };
+         static const T Q[] = {    
+            1L,
+            3.49040448075464744191022350947892036L,
+            34.3563592467165971295915749548313227L,
+            84.4993232033879023178285731843850461L,
+            376.005865281206894120659401340373818L,
+            629.95369438888946233003926191755125L,
+            1568.35771983533158591604513304269098L,
+            1646.02452040831961063640827116581021L,
+            2299.96860633240298708910425594484895L,
+            1222.73204392037452750381340219906374L,
+            799.359797306084372350264298361110448L,
+            72.7415265778588087243442792401576737L,
+         };
+         result = Y + tools::evaluate_polynomial(P, 1 / z) / tools::evaluate_polynomial(Q, 1 / z);
+         result *= exp(-z * z) / z;
       }
-      T g = exp(-z * z) / z;
-      result = g * b + g * r;
    }
    else
    {
@@ -856,3 +1081,4 @@ inline typename tools::promote_args::type erfc(T z)
 
 
 
+
diff --git a/include/boost/math/special_functions/expint.hpp b/include/boost/math/special_functions/expint.hpp
new file mode 100644
index 000000000..71b851185
--- /dev/null
+++ b/include/boost/math/special_functions/expint.hpp
@@ -0,0 +1,1513 @@
+//  Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_EXPINT_HPP
+#define BOOST_MATH_EXPINT_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+namespace boost{ namespace math{
+
+template 
+inline typename tools::promote_args::type
+   expint(unsigned n, T z, const Policy& /*pol*/);
+   
+namespace detail{
+
+template 
+inline T expint_1_rational(const T& z, const mpl::int_<0>&)
+{
+   // this function is never actually called
+   BOOST_ASSERT(0);
+   return z;
+}
+
+template 
+T expint_1_rational(const T& z, const mpl::int_<53>&)
+{
+   BOOST_MATH_STD_USING
+   T result;
+   if(z <= 1)
+   {
+      // Maximum Deviation Found:                     2.006e-18
+      // Expected Error Term:                         2.006e-18
+      // Max error found at double precision:         2.760e-17
+      static const T Y = 0.66373538970947265625F;
+      static const T P[6] = {    
+         0.0865197248079397976498L,
+         0.0320913665303559189999L,
+         -0.245088216639761496153L,
+         -0.0368031736257943745142L,
+         -0.00399167106081113256961L,
+         -0.000111507792921197858394L
+      };
+      static const T Q[6] = {    
+         1L,
+         0.37091387659397013215L,
+         0.056770677104207528384L,
+         0.00427347600017103698101L,
+         0.000131049900798434683324L,
+         -0.528611029520217142048e-6L
+      };
+      result = tools::evaluate_polynomial(P, z) 
+         / tools::evaluate_polynomial(Q, z);
+      result += z - log(z) - Y;
+   }
+   else if(z < -boost::math::tools::log_min_value())
+   {
+      // Maximum Deviation Found (interpolated):      1.444e-17
+      // Max error found at double precision:         3.119e-17
+      static const T P[11] = {    
+         -0.121013190657725568138e-18L,
+         -0.999999999999998811143L,
+         -43.3058660811817946037L,
+         -724.581482791462469795L,
+         -6046.8250112711035463L,
+         -27182.6254466733970467L,
+         -66598.2652345418633509L,
+         -86273.1567711649528784L,
+         -54844.4587226402067411L,
+         -14751.4895786128450662L,
+         -1185.45720315201027667L
+      };
+      static const T Q[12] = {    
+         1L,
+         45.3058660811801465927L,
+         809.193214954550328455L,
+         7417.37624454689546708L,
+         38129.5594484818471461L,
+         113057.05869159631492L,
+         192104.047790227984431L,
+         180329.498380501819718L,
+         86722.3403467334749201L,
+         18455.4124737722049515L,
+         1229.20784182403048905L,
+         -0.776491285282330997549L
+      };
+      T recip = 1 / z;
+      result = 1 + tools::evaluate_polynomial(P, recip)
+         / tools::evaluate_polynomial(Q, recip);
+      result *= exp(-z) * recip;
+   }
+   else
+   {
+      result = 0;
+   }
+   return result;
+}
+
+template 
+T expint_1_rational(const T& z, const mpl::int_<64>&)
+{
+   BOOST_MATH_STD_USING
+   T result;
+   if(z <= 1)
+   {
+      // Maximum Deviation Found:                     3.807e-20
+      // Expected Error Term:                         3.807e-20
+      // Max error found at long double precision:    6.249e-20
+
+      static const T Y = 0.66373538970947265625F;
+      static const T P[6] = {    
+         0.0865197248079397956816L,
+         0.0275114007037026844633L,
+         -0.246594388074877139824L,
+         -0.0237624819878732642231L,
+         -0.00259113319641673986276L,
+         0.30853660894346057053e-4L
+      };
+      static const T Q[7] = {    
+         1L,
+         0.317978365797784100273L,
+         0.0393622602554758722511L,
+         0.00204062029115966323229L,
+         0.732512107100088047854e-5L,
+         -0.202872781770207871975e-5L,
+         0.52779248094603709945e-7L
+      };
+      result = tools::evaluate_polynomial(P, z) 
+         / tools::evaluate_polynomial(Q, z);
+      result += z - log(z) - Y;
+   }
+   else if(z < -boost::math::tools::log_min_value())
+   {
+      // Maximum Deviation Found (interpolated):     2.220e-20
+      // Max error found at long double precision:   1.346e-19
+      static const T P[14] = {    
+         -0.534401189080684443046e-23L,
+         -0.999999999999999999905L,
+         -62.1517806091379402505L,
+         -1568.45688271895145277L,
+         -21015.3431990874009619L,
+         -164333.011755931661949L,
+         -777917.270775426696103L,
+         -2244188.56195255112937L,
+         -3888702.98145335643429L,
+         -3909822.65621952648353L,
+         -2149033.9538897398457L,
+         -584705.537139793925189L,
+         -65815.2605361889477244L,
+         -2038.82870680427258038L
+      };
+      static const T Q[14] = {    
+         1L,
+         64.1517806091379399478L,
+         1690.76044393722763785L,
+         24035.9534033068949426L,
+         203679.998633572361706L,
+         1074661.58459976978285L,
+         3586552.65020899358773L,
+         7552186.84989547621411L,
+         9853333.79353054111434L,
+         7689642.74550683631258L,
+         3385553.35146759180739L,
+         763218.072732396428725L,
+         73930.2995984054930821L,
+         2063.86994219629165937L
+      };
+      T recip = 1 / z;
+      result = 1 + tools::evaluate_polynomial(P, recip)
+         / tools::evaluate_polynomial(Q, recip);
+      result *= exp(-z) * recip;
+   }
+   else
+   {
+      result = 0;
+   }
+   return result;
+}
+
+template 
+T expint_1_rational(const T& z, const mpl::int_<113>&)
+{
+   BOOST_MATH_STD_USING
+   T result;
+   if(z <= 1)
+   {
+      // Maximum Deviation Found:                     2.477e-35
+      // Expected Error Term:                         2.477e-35
+      // Max error found at long double precision:    6.810e-35
+
+      static const T Y = 0.66373538970947265625F;
+      static const T P[10] = {    
+         0.0865197248079397956434879099175975937L,
+         0.0369066175910795772830865304506087759L,
+         -0.24272036838415474665971599314725545L,
+         -0.0502166331248948515282379137550178307L,
+         -0.00768384138547489410285101483730424919L,
+         -0.000612574337702109683505224915484717162L,
+         -0.380207107950635046971492617061708534e-4L,
+         -0.136528159460768830763009294683628406e-5L,
+         -0.346839106212658259681029388908658618e-7L,
+         -0.340500302777838063940402160594523429e-9L
+      };
+      static const T Q[10] = {    
+         1L,
+         0.426568827778942588160423015589537302L,
+         0.0841384046470893490592450881447510148L,
+         0.0100557215850668029618957359471132995L,
+         0.000799334870474627021737357294799839363L,
+         0.434452090903862735242423068552687688e-4L,
+         0.15829674748799079874182885081231252e-5L,
+         0.354406206738023762100882270033082198e-7L,
+         0.369373328141051577845488477377890236e-9L,
+         -0.274149801370933606409282434677600112e-12L
+      };
+      result = tools::evaluate_polynomial(P, z) 
+         / tools::evaluate_polynomial(Q, z);
+      result += z - log(z) - Y;
+   }
+   else if(z <= 4)
+   {
+      // Max error in interpolated form:             5.614e-35
+      // Max error found at long double precision:   7.979e-35
+
+      static const T Y = 0.70190334320068359375F;
+
+      static const T P[17] = {    
+         0.298096656795020369955077350585959794L,
+         12.9314045995266142913135497455971247L,
+         226.144334921582637462526628217345501L,
+         2070.83670924261732722117682067381405L,
+         10715.1115684330959908244769731347186L,
+         30728.7876355542048019664777316053311L,
+         38520.6078609349855436936232610875297L,
+         -27606.0780981527583168728339620565165L,
+         -169026.485055785605958655247592604835L,
+         -254361.919204983608659069868035092282L,
+         -195765.706874132267953259272028679935L,
+         -83352.6826013533205474990119962408675L,
+         -19251.6828496869586415162597993050194L,
+         -2226.64251774578542836725386936102339L,
+         -109.009437301400845902228611986479816L,
+         -1.51492042209561411434644938098833499L
+      };
+      static const T Q[16] = {    
+         1L,
+         46.734521442032505570517810766704587L,
+         908.694714348462269000247450058595655L,
+         9701.76053033673927362784882748513195L,
+         63254.2815292641314236625196594947774L,
+         265115.641285880437335106541757711092L,
+         732707.841188071900498536533086567735L,
+         1348514.02492635723327306628712057794L,
+         1649986.81455283047769673308781585991L,
+         1326000.828522976970116271208812099L,
+         683643.09490612171772350481773951341L,
+         217640.505137263607952365685653352229L,
+         40288.3467237411710881822569476155485L,
+         3932.89353979531632559232883283175754L,
+         169.845369689596739824177412096477219L,
+         2.17607292280092201170768401876895354L
+      };
+      T recip = 1 / z;
+      result = Y + tools::evaluate_polynomial(P, recip)
+         / tools::evaluate_polynomial(Q, recip);
+      result *= exp(-z) * recip;
+   }
+   else if(z < -boost::math::tools::log_min_value())
+   {
+      // Max error in interpolated form:             4.413e-35
+      // Max error found at long double precision:   8.928e-35
+
+      static const T P[19] = {    
+         -0.559148411832951463689610809550083986e-40L,
+         -0.999999999999999999999999999999999997L,
+         -166.542326331163836642960118190147367L,
+         -12204.639128796330005065904675153652L,
+         -520807.069767086071806275022036146855L,
+         -14435981.5242137970691490903863125326L,
+         -274574945.737064301247496460758654196L,
+         -3691611582.99810039356254671781473079L,
+         -35622515944.8255047299363690814678763L,
+         -248040014774.502043161750715548451142L,
+         -1243190389769.53458416330946622607913L,
+         -4441730126135.54739052731990368425339L,
+         -11117043181899.7388524310281751971366L,
+         -18976497615396.9717776601813519498961L,
+         -21237496819711.1011661104761906067131L,
+         -14695899122092.5161620333466757812848L,
+         -5737221535080.30569711574295785864903L,
+         -1077042281708.42654526404581272546244L,
+         -68028222642.1941480871395695677675137L
+      };
+      static const T Q[20] = {    
+         1L,
+         168.542326331163836642960118190147311L,
+         12535.7237814586576783518249115343619L,
+         544891.263372016404143120911148640627L,
+         15454474.7241010258634446523045237762L,
+         302495899.896629522673410325891717381L,
+         4215565948.38886507646911672693270307L,
+         42552409471.7951815668506556705733344L,
+         313592377066.753173979584098301610186L,
+         1688763640223.4541980740597514904542L,
+         6610992294901.59589748057620192145704L,
+         18601637235659.6059890851321772682606L,
+         36944278231087.2571020964163402941583L,
+         50425858518481.7497071917028793820058L,
+         45508060902865.0899967797848815980644L,
+         25649955002765.3817331501988304758142L,
+         8259575619094.6518520988612711292331L,
+         1299981487496.12607474362723586264515L,
+         70242279152.8241187845178443118302693L,
+         -37633302.9409263839042721539363416685L
+      };
+      T recip = 1 / z;
+      result = 1 + tools::evaluate_polynomial(P, recip)
+         / tools::evaluate_polynomial(Q, recip);
+      result *= exp(-z) * recip;
+   }
+   else
+   {
+      result = 0;
+   }
+   return result;
+}
+
+template 
+struct expint_fraction
+{
+   typedef std::pair result_type;
+   expint_fraction(unsigned n_, T z_) : b(n_ + z_), i(-1), n(n_){}
+   std::pair operator()()
+   {
+      std::pair result = std::make_pair(-static_cast((i+1) * (n+i)), b);
+      b += 2;
+      ++i;
+      return result;
+   }
+private:
+   T b;
+   int i;
+   unsigned n;
+};
+
+template 
+inline T expint_as_fraction(unsigned n, T z, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   BOOST_MATH_INSTRUMENT_VARIABLE(z)
+   boost::uintmax_t max_iter = policies::get_max_series_iterations();
+   expint_fraction f(n, z);
+   T result = tools::continued_fraction_b(
+      f, 
+      tools::digits(),
+      max_iter);
+   policies::check_series_iterations("boost::math::expint_continued_fraction<%1%>(unsigned,%1%)", max_iter, pol);
+   BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   BOOST_MATH_INSTRUMENT_VARIABLE(max_iter)
+   result = exp(-z) / result;
+   BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   return result;
+}
+
+template 
+struct expint_series
+{
+   typedef T result_type;
+   expint_series(unsigned k_, T z_, T x_k_, T denom_, T fact_) 
+      : k(k_), z(z_), x_k(x_k_), denom(denom_), fact(fact_){}
+   T operator()()
+   {
+      x_k *= -z;
+      denom += 1;
+      fact *= ++k;
+      return x_k / (denom * fact);
+   }
+private:
+   unsigned k;
+   T z;
+   T x_k;
+   T denom;
+   T fact;
+};
+
+template 
+inline T expint_as_series(unsigned n, T z, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   boost::uintmax_t max_iter = policies::get_max_series_iterations();
+
+   BOOST_MATH_INSTRUMENT_VARIABLE(z)
+
+   T result = 0;
+   T x_k = -1;
+   T denom = T(1) - n;
+   T fact = 1;
+   unsigned k = 0;
+   for(; k < n - 1;)
+   {
+      result += x_k / (denom * fact);
+      denom += 1;
+      x_k *= -z;
+      fact *= ++k;
+   }
+   BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   result += pow(-z, (int)n - 1) 
+      * (boost::math::digamma(static_cast(n)) - log(z)) / fact;
+   BOOST_MATH_INSTRUMENT_VARIABLE(result)
+
+   expint_series s(k, z, x_k, denom, fact);
+   result = tools::sum_series(s, policies::digits(), max_iter, result);
+   policies::check_series_iterations("boost::math::expint_series<%1%>(unsigned,%1%)", max_iter, pol);
+   BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   BOOST_MATH_INSTRUMENT_VARIABLE(max_iter)
+   return result;
+}
+
+template 
+T expint_imp(unsigned n, T z, const Policy& pol, const Tag& tag)
+{
+   BOOST_MATH_STD_USING
+   static const char* function = "boost::math::expint<%1%>(unsigned, %1%)";
+   if(z < 0)
+      return policies::raise_domain_error(function, "Function requires z >= 0 but got %1%.", z, pol);
+   if(z == 0)
+      return n == 1 ? policies::raise_overflow_error(function, 0, pol) : 1 / (static_cast(n - 1));
+
+   T result;
+
+   bool f;
+   if(n < 3)
+   {
+      f = z < 0.5;
+   }
+   else
+   {
+      f = z < (static_cast(n - 2) / static_cast(n - 1));
+   }
+#ifdef BOOST_MSVC
+#  pragma warning(push)
+#  pragma warning(disable:4127) // conditional expression is constant
+#endif
+   if(n == 0)
+      result = exp(-z) / z;
+   else if((n == 1) && (Tag::value))
+   {
+      result = expint_1_rational(z, tag);
+   }
+   else if(f)
+      result = expint_as_series(n, z, pol);
+   else
+      result = expint_as_fraction(n, z, pol);
+#ifdef BOOST_MSVC
+#  pragma warning(pop)
+#endif
+
+   return result;
+}
+
+template 
+struct expint_i_series
+{
+   typedef T result_type;
+   expint_i_series(T z_) : k(0), z_k(1), z(z_){}
+   T operator()()
+   {
+      z_k *= z / ++k;
+      return z_k / k;
+   }
+private:
+   unsigned k;
+   T z_k;
+   T z;
+};
+
+template 
+T expint_i_as_series(T z, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   T result = log(z); // (log(z) - log(1 / z)) / 2;
+   result += constants::euler();
+   expint_i_series s(z);
+   boost::uintmax_t max_iter = policies::get_max_series_iterations();
+   result = tools::sum_series(s, policies::digits(), max_iter, result);
+   policies::check_series_iterations("boost::math::expint_i_series<%1%>(%1%)", max_iter, pol);
+   return result;
+}
+
+template 
+T expint_i_imp(T z, const Policy& pol, const Tag& tag)
+{
+   static const char* function = "boost::math::expint<%1%>(%1%)";
+   if(z < 0)
+      return -expint_imp(1, -z, pol, tag);
+   if(z == 0)
+      return -policies::raise_overflow_error(function, 0, pol);
+   return expint_i_as_series(z, pol);
+}
+
+template 
+T expint_i_imp(T z, const Policy& pol, const mpl::int_<53>& tag)
+{
+   BOOST_MATH_STD_USING
+   static const char* function = "boost::math::expint<%1%>(%1%)";
+   if(z < 0)
+      return -expint_imp(1, -z, pol, tag);
+   if(z == 0)
+      return -policies::raise_overflow_error(function, 0, pol);
+
+   T result;
+
+   if(z <= 6)
+   {
+      // Maximum Deviation Found:                     2.852e-18
+      // Expected Error Term:                         2.852e-18
+      // Max Error found at double precision =        Poly: 2.636335e-16   Cheb: 4.187027e-16
+      static const T P[10] = {    
+         2.98677224343598593013L,
+         0.356343618769377415068L,
+         0.780836076283730801839L,
+         0.114670926327032002811L,
+         0.0499434773576515260534L,
+         0.00726224593341228159561L,
+         0.00115478237227804306827L,
+         0.000116419523609765200999L,
+         0.798296365679269702435e-5L,
+         0.2777056254402008721e-6L
+      };
+      static const T Q[8] = {    
+         1L,
+         -1.17090412365413911947L,
+         0.62215109846016746276L,
+         -0.195114782069495403315L,
+         0.0391523431392967238166L,
+         -0.00504800158663705747345L,
+         0.000389034007436065401822L,
+         -0.138972589601781706598e-4L
+      };
+
+      static const T r1 = static_cast(1677624236387711.0L) / 4503599627370496uLL;
+      static const T r2 = 0.131401834143860282009280387409357165515556574352422001206362e-16L;
+      static const T r = static_cast(0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392L);
+      T t = (z / 3) - 1;
+      result = tools::evaluate_polynomial(P, t) 
+         / tools::evaluate_polynomial(Q, t);
+      t = (z - r1) - r2;
+      result *= t;
+      if(fabs(t) < 0.1)
+      {
+         result += boost::math::log1p(t / r);
+      }
+      else
+      {
+         result += log(z / r);
+      }
+   }
+   else if (z <= 10)
+   {
+      // Maximum Deviation Found:                     6.546e-17
+      // Expected Error Term:                         6.546e-17
+      // Max Error found at double precision =        Poly: 6.890169e-17   Cheb: 6.772128e-17
+      static const T Y = 1.158985137939453125F;
+      static const T P[8] = {    
+         0.00139324086199402804173L,
+         -0.0349921221823888744966L,
+         -0.0264095520754134848538L,
+         -0.00761224003005476438412L,
+         -0.00247496209592143627977L,
+         -0.000374885917942100256775L,
+         -0.554086272024881826253e-4L,
+         -0.396487648924804510056e-5L
+      };
+      static const T Q[8] = {    
+         1L,
+         0.744625566823272107711L,
+         0.329061095011767059236L,
+         0.100128624977313872323L,
+         0.0223851099128506347278L,
+         0.00365334190742316650106L,
+         0.000402453408512476836472L,
+         0.263649630720255691787e-4L
+      };
+      T t = z / 2 - 4;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      result *= exp(z) / z;
+      result += z;
+   }
+   else if(z <= 20)
+   {
+      // Maximum Deviation Found:                     1.843e-17
+      // Expected Error Term:                         -1.842e-17
+      // Max Error found at double precision =        Poly: 4.375868e-17   Cheb: 5.860967e-17
+
+      static const T Y = 1.0869731903076171875F;
+      static const T P[9] = {    
+         -0.00893891094356945667451L,
+         -0.0484607730127134045806L,
+         -0.0652810444222236895772L,
+         -0.0478447572647309671455L,
+         -0.0226059218923777094596L,
+         -0.00720603636917482065907L,
+         -0.00155941947035972031334L,
+         -0.000209750022660200888349L,
+         -0.138652200349182596186e-4L
+      };
+      static const T Q[9] = {    
+         1L,
+         1.97017214039061194971L,
+         1.86232465043073157508L,
+         1.09601437090337519977L,
+         0.438873285773088870812L,
+         0.122537731979686102756L,
+         0.0233458478275769288159L,
+         0.00278170769163303669021L,
+         0.000159150281166108755531L
+      };
+      T t = z / 5 - 3;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      result *= exp(z) / z;
+      result += z;
+   }
+   else if(z <= 40)
+   {
+      // Maximum Deviation Found:                     5.102e-18
+      // Expected Error Term:                         5.101e-18
+      // Max Error found at double precision =        Poly: 1.441088e-16   Cheb: 1.864792e-16
+
+
+      static const T Y = 1.03937530517578125F;
+      static const T P[9] = {    
+         -0.00356165148914447597995L,
+         -0.0229930320357982333406L,
+         -0.0449814350482277917716L,
+         -0.0453759383048193402336L,
+         -0.0272050837209380717069L,
+         -0.00994403059883350813295L,
+         -0.00207592267812291726961L,
+         -0.000192178045857733706044L,
+         -0.113161784705911400295e-9L
+      };
+      static const T Q[9] = {    
+         1L,
+         2.84354408840148561131L,
+         3.6599610090072393012L,
+         2.75088464344293083595L,
+         1.2985244073998398643L,
+         0.383213198510794507409L,
+         0.0651165455496281337831L,
+         0.00488071077519227853585L
+      };
+      T t = z / 10 - 3;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      result *= exp(z) / z;
+      result += z;
+   }
+   else
+   {
+      // Max Error found at double precision =        3.381886e-17
+      static const T exp40 = static_cast(2.35385266837019985407899910749034804508871617254555467236651e17L);
+      static const T Y= 1.013065338134765625F;
+      static const T P[6] = {    
+         -0.0130653381347656243849L,
+         0.19029710559486576682L,
+         94.7365094537197236011L,
+         -2516.35323679844256203L,
+         18932.0850014925993025L,
+         -38703.1431362056714134L
+      };
+      static const T Q[7] = {    
+         1L,
+         61.9733592849439884145L,
+         -2354.56211323420194283L,
+         22329.1459489893079041L,
+         -70126.245140396567133L,
+         54738.2833147775537106L,
+         8297.16296356518409347L
+      };
+      T t = 1 / z;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      if(z < 41)
+         result *= exp(z) / z;
+      else
+      {
+         // Avoid premature overflow if we can:
+         t = z - 40;
+         if(t > tools::log_max_value())
+         {
+            result = policies::raise_overflow_error(function, 0, pol);
+         }
+         else
+         {
+            result *= exp(z - 40) / z;
+            if(result > tools::max_value() / exp40)
+            {
+               result = policies::raise_overflow_error(function, 0, pol);
+            }
+            else
+            {
+               result *= exp40;
+            }
+         }
+      }
+      result += z;
+   }
+   return result;
+}
+
+template 
+T expint_i_imp(T z, const Policy& pol, const mpl::int_<64>& tag)
+{
+   BOOST_MATH_STD_USING
+   static const char* function = "boost::math::expint<%1%>(%1%)";
+   if(z < 0)
+      return -expint_imp(1, -z, pol, tag);
+   if(z == 0)
+      return -policies::raise_overflow_error(function, 0, pol);
+
+   T result;
+
+   if(z <= 6)
+   {
+      // Maximum Deviation Found:                     3.883e-21
+      // Expected Error Term:                         3.883e-21
+      // Max Error found at long double precision =   Poly: 3.344801e-19   Cheb: 4.989937e-19
+
+      static const T P[11] = {    
+         2.98677224343598593764L,
+         0.25891613550886736592L,
+         0.789323584998672832285L,
+         0.092432587824602399339L,
+         0.0514236978728625906656L,
+         0.00658477469745132977921L,
+         0.00124914538197086254233L,
+         0.000131429679565472408551L,
+         0.11293331317982763165e-4L,
+         0.629499283139417444244e-6L,
+         0.177833045143692498221e-7L
+      };
+      static const T Q[9] = {    
+         1L,
+         -1.20352377969742325748L,
+         0.66707904942606479811L,
+         -0.223014531629140771914L,
+         0.0493340022262908008636L,
+         -0.00741934273050807310677L,
+         0.00074353567782087939294L,
+         -0.455861727069603367656e-4L,
+         0.131515429329812837701e-5L
+      };
+
+      static const T r1 = static_cast(1677624236387711.0L) / 4503599627370496uLL;
+      static const T r2 = 0.131401834143860282009280387409357165515556574352422001206362e-16L;
+      static const T r = static_cast(0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392L);
+      T t = (z / 3) - 1;
+      result = tools::evaluate_polynomial(P, t) 
+         / tools::evaluate_polynomial(Q, t);
+      t = (z - r1) - r2;
+      result *= t;
+      if(fabs(t) < 0.1)
+      {
+         result += boost::math::log1p(t / r);
+      }
+      else
+      {
+         result += log(z / r);
+      }
+   }
+   else if (z <= 10)
+   {
+      // Maximum Deviation Found:                     2.622e-21
+      // Expected Error Term:                         -2.622e-21
+      // Max Error found at long double precision =   Poly: 1.208328e-20   Cheb: 1.073723e-20
+
+      static const T Y = 1.158985137939453125F;
+      static const T P[9] = {    
+         0.00139324086199409049399L,
+         -0.0345238388952337563247L,
+         -0.0382065278072592940767L,
+         -0.0156117003070560727392L,
+         -0.00383276012430495387102L,
+         -0.000697070540945496497992L,
+         -0.877310384591205930343e-4L,
+         -0.623067256376494930067e-5L,
+         -0.377246883283337141444e-6L
+      };
+      static const T Q[10] = {    
+         1L,
+         1.08073635708902053767L,
+         0.553681133533942532909L,
+         0.176763647137553797451L,
+         0.0387891748253869928121L,
+         0.0060603004848394727017L,
+         0.000670519492939992806051L,
+         0.4947357050100855646e-4L,
+         0.204339282037446434827e-5L,
+         0.146951181174930425744e-7L
+      };
+      T t = z / 2 - 4;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      result *= exp(z) / z;
+      result += z;
+   }
+   else if(z <= 20)
+   {
+      // Maximum Deviation Found:                     3.220e-20
+      // Expected Error Term:                         3.220e-20
+      // Max Error found at long double precision =   Poly: 7.696841e-20   Cheb: 6.205163e-20
+
+
+      static const T Y = 1.0869731903076171875F;
+      static const T P[10] = {    
+         -0.00893891094356946995368L,
+         -0.0487562980088748775943L,
+         -0.0670568657950041926085L,
+         -0.0509577352851442932713L,
+         -0.02551800927409034206L,
+         -0.00892913759760086687083L,
+         -0.00224469630207344379888L,
+         -0.000392477245911296982776L,
+         -0.44424044184395578775e-4L,
+         -0.252788029251437017959e-5L
+      };
+      static const T Q[10] = {    
+         1L,
+         2.00323265503572414261L,
+         1.94688958187256383178L,
+         1.19733638134417472296L,
+         0.513137726038353385661L,
+         0.159135395578007264547L,
+         0.0358233587351620919881L,
+         0.0056716655597009417875L,
+         0.000577048986213535829925L,
+         0.290976943033493216793e-4L
+      };
+      T t = z / 5 - 3;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      result *= exp(z) / z;
+      result += z;
+   }
+   else if(z <= 40)
+   {
+      // Maximum Deviation Found:                     2.940e-21
+      // Expected Error Term:                         -2.938e-21
+      // Max Error found at long double precision =   Poly: 3.419893e-19   Cheb: 3.359874e-19
+
+      static const T Y = 1.03937530517578125F;
+      static const T P[12] = {    
+         -0.00356165148914447278177L,
+         -0.0240235006148610849678L,
+         -0.0516699967278057976119L,
+         -0.0586603078706856245674L,
+         -0.0409960120868776180825L,
+         -0.0185485073689590665153L,
+         -0.00537842101034123222417L,
+         -0.000920988084778273760609L,
+         -0.716742618812210980263e-4L,
+         -0.504623302166487346677e-9L,
+         0.712662196671896837736e-10L,
+         -0.533769629702262072175e-11L
+      };
+      static const T Q[9] = {    
+         1L,
+         3.13286733695729715455L,
+         4.49281223045653491929L,
+         3.84900294427622911374L,
+         2.15205199043580378211L,
+         0.802912186540269232424L,
+         0.194793170017818925388L,
+         0.0280128013584653182994L,
+         0.00182034930799902922549L
+      };
+      T t = z / 10 - 3;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result *= exp(z) / z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result += z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   }
+   else
+   {
+      // Maximum Deviation Found:                     3.536e-20
+      // Max Error found at long double precision =   Poly: 1.310671e-19   Cheb: 8.630943e-11
+
+      static const T exp40 = static_cast(2.35385266837019985407899910749034804508871617254555467236651e17L);
+      static const T Y= 1.013065338134765625F;
+      static const T P[9] = {    
+         -0.0130653381347656250004L,
+         0.644487780349757303739L,
+         143.995670348227433964L,
+         -13918.9322758014173709L,
+         476260.975133624194484L,
+         -7437102.15135982802122L,
+         53732298.8764767916542L,
+         -160695051.957997452509L,
+         137839271.592778020028L
+      };
+      static const T Q[9] = {    
+         1L,
+         27.2103343964943718802L,
+         -8785.48528692879413676L,
+         397530.290000322626766L,
+         -7356441.34957799368252L,
+         63050914.5343400957524L,
+         -246143779.638307701369L,
+         384647824.678554961174L,
+         -166288297.874583961493L
+      };
+      T t = 1 / z;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      if(z < 41)
+         result *= exp(z) / z;
+      else
+      {
+         // Avoid premature overflow if we can:
+         t = z - 40;
+         if(t > tools::log_max_value())
+         {
+            result = policies::raise_overflow_error(function, 0, pol);
+         }
+         else
+         {
+            result *= exp(z - 40) / z;
+            if(result > tools::max_value() / exp40)
+            {
+               result = policies::raise_overflow_error(function, 0, pol);
+            }
+            else
+            {
+               result *= exp40;
+            }
+         }
+      }
+      result += z;
+   }
+   return result;
+}
+
+template 
+T expint_i_imp(T z, const Policy& pol, const mpl::int_<113>& tag)
+{
+   BOOST_MATH_STD_USING
+   static const char* function = "boost::math::expint<%1%>(%1%)";
+   if(z < 0)
+      return -expint_imp(1, -z, pol, tag);
+   if(z == 0)
+      return -policies::raise_overflow_error(function, 0, pol);
+
+   T result;
+
+   if(z <= 6)
+   {
+      // Maximum Deviation Found:                     1.230e-36
+      // Expected Error Term:                         -1.230e-36
+      // Max Error found at long double precision =   Poly: 4.355299e-34   Cheb: 7.512581e-34
+
+
+      static const T P[15] = {    
+         2.98677224343598593765287235997328555L,
+         -0.333256034674702967028780537349334037L,
+         0.851831522798101228384971644036708463L,
+         -0.0657854833494646206186773614110374948L,
+         0.0630065662557284456000060708977935073L,
+         -0.00311759191425309373327784154659649232L,
+         0.00176213568201493949664478471656026771L,
+         -0.491548660404172089488535218163952295e-4L,
+         0.207764227621061706075562107748176592e-4L,
+         -0.225445398156913584846374273379402765e-6L,
+         0.996939977231410319761273881672601592e-7L,
+         0.212546902052178643330520878928100847e-9L,
+         0.154646053060262871360159325115980023e-9L,
+         0.143971277122049197323415503594302307e-11L,
+         0.306243138978114692252817805327426657e-13L
+      };
+      static const T Q[15] = {    
+         1L,
+         -1.40178870313943798705491944989231793L,
+         0.943810968269701047641218856758605284L,
+         -0.405026631534345064600850391026113165L,
+         0.123924153524614086482627660399122762L,
+         -0.0286364505373369439591132549624317707L,
+         0.00516148845910606985396596845494015963L,
+         -0.000738330799456364820380739850924783649L,
+         0.843737760991856114061953265870882637e-4L,
+         -0.767957673431982543213661388914587589e-5L,
+         0.549136847313854595809952100614840031e-6L,
+         -0.299801381513743676764008325949325404e-7L,
+         0.118419479055346106118129130945423483e-8L,
+         -0.30372295663095470359211949045344607e-10L,
+         0.382742953753485333207877784720070523e-12L
+      };
+
+      static const T r1 = static_cast(1677624236387711.0L) / 4503599627370496uLL;
+      static const T r2 = (static_cast(266514582277687.0L) / 4503599627370496uLL) / 4503599627370496uLL;
+      static const T r3 = static_cast(0.283806480836357377069325311780969887585024578164571984232357e-31L);
+      static const T r = static_cast(0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392L);
+      T t = (z / 3) - 1;
+      result = tools::evaluate_polynomial(P, t) 
+         / tools::evaluate_polynomial(Q, t);
+      t = ((z - r1) - r2) - r3;
+      result *= t;
+      if(fabs(t) < 0.1)
+      {
+         result += boost::math::log1p(t / r);
+      }
+      else
+      {
+         result += log(z / r);
+      }
+   }
+   else if (z <= 10)
+   {
+      // Maximum Deviation Found:                     7.779e-36
+      // Expected Error Term:                         -7.779e-36
+      // Max Error found at long double precision =   Poly: 2.576723e-35   Cheb: 1.236001e-34
+
+      static const T Y = 1.158985137939453125F;
+      static const T P[15] = {    
+         0.00139324086199409049282472239613554817L,
+         -0.0338173111691991289178779840307998955L,
+         -0.0555972290794371306259684845277620556L,
+         -0.0378677976003456171563136909186202177L,
+         -0.0152221583517528358782902783914356667L,
+         -0.00428283334203873035104248217403126905L,
+         -0.000922782631491644846511553601323435286L,
+         -0.000155513428088853161562660696055496696L,
+         -0.205756580255359882813545261519317096e-4L,
+         -0.220327406578552089820753181821115181e-5L,
+         -0.189483157545587592043421445645377439e-6L,
+         -0.122426571518570587750898968123803867e-7L,
+         -0.635187358949437991465353268374523944e-9L,
+         -0.203015132965870311935118337194860863e-10L,
+         -0.384276705503357655108096065452950822e-12L
+      };
+      static const T Q[15] = {    
+         1L,
+         1.58784732785354597996617046880946257L,
+         1.18550755302279446339364262338114098L,
+         0.55598993549661368604527040349702836L,
+         0.184290888380564236919107835030984453L,
+         0.0459658051803613282360464632326866113L,
+         0.0089505064268613225167835599456014705L,
+         0.00139042673882987693424772855926289077L,
+         0.000174210708041584097450805790176479012L,
+         0.176324034009707558089086875136647376e-4L,
+         0.142935845999505649273084545313710581e-5L,
+         0.907502324487057260675816233312747784e-7L,
+         0.431044337808893270797934621235918418e-8L,
+         0.139007266881450521776529705677086902e-9L,
+         0.234715286125516430792452741830364672e-11L
+      };
+      T t = z / 2 - 4;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      result *= exp(z) / z;
+      result += z;
+   }
+   else if(z <= 18)
+   {
+      // Maximum Deviation Found:                     1.082e-34
+      // Expected Error Term:                         1.080e-34
+      // Max Error found at long double precision =   Poly: 1.958294e-34   Cheb: 2.472261e-34
+
+
+      static const T Y = 1.091579437255859375F;
+      static const T P[17] = {    
+         -0.00685089599550151282724924894258520532L,
+         -0.0443313550253580053324487059748497467L,
+         -0.071538561252424027443296958795814874L,
+         -0.0622923153354102682285444067843300583L,
+         -0.0361631270264607478205393775461208794L,
+         -0.0153192826839624850298106509601033261L,
+         -0.00496967904961260031539602977748408242L,
+         -0.00126989079663425780800919171538920589L,
+         -0.000258933143097125199914724875206326698L,
+         -0.422110326689204794443002330541441956e-4L,
+         -0.546004547590412661451073996127115221e-5L,
+         -0.546775260262202177131068692199272241e-6L,
+         -0.404157632825805803833379568956559215e-7L,
+         -0.200612596196561323832327013027419284e-8L,
+         -0.502538501472133913417609379765434153e-10L,
+         -0.326283053716799774936661568391296584e-13L,
+         0.869226483473172853557775877908693647e-15L
+      };
+      static const T Q[15] = {    
+         1L,
+         2.23227220874479061894038229141871087L,
+         2.40221000361027971895657505660959863L,
+         1.65476320985936174728238416007084214L,
+         0.816828602963895720369875535001248227L,
+         0.306337922909446903672123418670921066L,
+         0.0902400121654409267774593230720600752L,
+         0.0212708882169429206498765100993228086L,
+         0.00404442626252467471957713495828165491L,
+         0.0006195601618842253612635241404054589L,
+         0.755930932686543009521454653994321843e-4L,
+         0.716004532773778954193609582677482803e-5L,
+         0.500881663076471627699290821742924233e-6L,
+         0.233593219218823384508105943657387644e-7L,
+         0.554900353169148897444104962034267682e-9L
+      };
+      T t = z / 4 - 3.5;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      result *= exp(z) / z;
+      result += z;
+   }
+   else if(z <= 26)
+   {
+      // Maximum Deviation Found:                     3.163e-35
+      // Expected Error Term:                         3.163e-35
+      // Max Error found at long double precision =   Poly: 4.158110e-35   Cheb: 5.385532e-35
+
+      static const T Y = 1.051731109619140625F;
+      static const T P[14] = {    
+         -0.00144552494420652573815404828020593565L,
+         -0.0126747451594545338365684731262912741L,
+         -0.01757394877502366717526779263438073L,
+         -0.0126838952395506921945756139424722588L,
+         -0.0060045057928894974954756789352443522L,
+         -0.00205349237147226126653803455793107903L,
+         -0.000532606040579654887676082220195624207L,
+         -0.000107344687098019891474772069139014662L,
+         -0.169536802705805811859089949943435152e-4L,
+         -0.20863311729206543881826553010120078e-5L,
+         -0.195670358542116256713560296776654385e-6L,
+         -0.133291168587253145439184028259772437e-7L,
+         -0.595500337089495614285777067722823397e-9L,
+         -0.133141358866324100955927979606981328e-10L
+      };
+      static const T Q[14] = {    
+         1L,
+         1.72490783907582654629537013560044682L,
+         1.44524329516800613088375685659759765L,
+         0.778241785539308257585068744978050181L,
+         0.300520486589206605184097270225725584L,
+         0.0879346899691339661394537806057953957L,
+         0.0200802415843802892793583043470125006L,
+         0.00362842049172586254520256100538273214L,
+         0.000519731362862955132062751246769469957L,
+         0.584092147914050999895178697392282665e-4L,
+         0.501851497707855358002773398333542337e-5L,
+         0.313085677467921096644895738538865537e-6L,
+         0.127552010539733113371132321521204458e-7L,
+         0.25737310826983451144405899970774587e-9L
+      };
+      T t = z / 4 - 5.5;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result *= exp(z) / z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result += z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   }
+   else if(z <= 42)
+   {
+      // Maximum Deviation Found:                     7.972e-36
+      // Expected Error Term:                         7.962e-36
+      // Max Error found at long double precision =   Poly: 1.711721e-34   Cheb: 3.100018e-34
+
+      static const T Y = 1.032726287841796875F;
+      static const T P[15] = {    
+         -0.00141056919297307534690895009969373233L,
+         -0.0123384175302540291339020257071411437L,
+         -0.0298127270706864057791526083667396115L,
+         -0.0390686759471630584626293670260768098L,
+         -0.0338226792912607409822059922949035589L,
+         -0.0211659736179834946452561197559654582L,
+         -0.0100428887460879377373158821400070313L,
+         -0.00370717396015165148484022792801682932L,
+         -0.0010768667551001624764329000496561659L,
+         -0.000246127328761027039347584096573123531L,
+         -0.437318110527818613580613051861991198e-4L,
+         -0.587532682329299591501065482317771497e-5L,
+         -0.565697065670893984610852937110819467e-6L,
+         -0.350233957364028523971768887437839573e-7L,
+         -0.105428907085424234504608142258423505e-8L
+      };
+      static const T Q[16] = {    
+         1L,
+         3.17261315255467581204685605414005525L,
+         4.85267952971640525245338392887217426L,
+         4.74341914912439861451492872946725151L,
+         3.31108463283559911602405970817931801L,
+         1.74657006336994649386607925179848899L,
+         0.718255607416072737965933040353653244L,
+         0.234037553177354542791975767960643864L,
+         0.0607470145906491602476833515412605389L,
+         0.0125048143774226921434854172947548724L,
+         0.00201034366420433762935768458656609163L,
+         0.000244823338417452367656368849303165721L,
+         0.213511655166983177960471085462540807e-4L,
+         0.119323998465870686327170541547982932e-5L,
+         0.322153582559488797803027773591727565e-7L,
+         -0.161635525318683508633792845159942312e-16L
+      };
+      T t = z / 8 - 4.25;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result *= exp(z) / z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result += z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   }
+   else if(z <= 56)
+   {
+      // Maximum Deviation Found:                     4.469e-36
+      // Expected Error Term:                         4.468e-36
+      // Max Error found at long double precision =   Poly: 1.288958e-35   Cheb: 2.304586e-35
+
+      static const T Y = 1.0216197967529296875F;
+      static const T P[12] = {    
+         -0.000322999116096627043476023926572650045L,
+         -0.00385606067447365187909164609294113346L,
+         -0.00686514524727568176735949971985244415L,
+         -0.00606260649593050194602676772589601799L,
+         -0.00334382362017147544335054575436194357L,
+         -0.00126108534260253075708625583630318043L,
+         -0.000337881489347846058951220431209276776L,
+         -0.648480902304640018785370650254018022e-4L,
+         -0.87652644082970492211455290209092766e-5L,
+         -0.794712243338068631557849449519994144e-6L,
+         -0.434084023639508143975983454830954835e-7L,
+         -0.107839681938752337160494412638656696e-8L
+      };
+      static const T Q[12] = {    
+         1L,
+         2.09913805456661084097134805151524958L,
+         2.07041755535439919593503171320431849L,
+         1.26406517226052371320416108604874734L,
+         0.529689923703770353961553223973435569L,
+         0.159578150879536711042269658656115746L,
+         0.0351720877642000691155202082629857131L,
+         0.00565313621289648752407123620997063122L,
+         0.000646920278540515480093843570291218295L,
+         0.499904084850091676776993523323213591e-4L,
+         0.233740058688179614344680531486267142e-5L,
+         0.498800627828842754845418576305379469e-7L
+      };
+      T t = z / 7 - 7;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result *= exp(z) / z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result += z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   }
+   else if(z <= 84)
+   {
+      // Maximum Deviation Found:                     5.588e-35
+      // Expected Error Term:                         -5.566e-35
+      // Max Error found at long double precision =   Poly: 9.976345e-35   Cheb: 8.358865e-35
+
+      static const T Y = 1.015148162841796875F;
+      static const T P[11] = {    
+         -0.000435714784725086961464589957142615216L,
+         -0.00432114324353830636009453048419094314L,
+         -0.0100740363285526177522819204820582424L,
+         -0.0116744115827059174392383504427640362L,
+         -0.00816145387784261141360062395898644652L,
+         -0.00371380272673500791322744465394211508L,
+         -0.00112958263488611536502153195005736563L,
+         -0.000228316462389404645183269923754256664L,
+         -0.29462181955852860250359064291292577e-4L,
+         -0.21972450610957417963227028788460299e-5L,
+         -0.720558173805289167524715527536874694e-7L
+      };
+      static const T Q[11] = {    
+         1L,
+         2.95918362458402597039366979529287095L,
+         3.96472247520659077944638411856748924L,
+         3.15563251550528513747923714884142131L,
+         1.64674612007093983894215359287448334L,
+         0.58695020129846594405856226787156424L,
+         0.144358385319329396231755457772362793L,
+         0.024146911506411684815134916238348063L,
+         0.0026257132337460784266874572001650153L,
+         0.000167479843750859222348869769094711093L,
+         0.475673638665358075556452220192497036e-5L
+      };
+      T t = z / 14 - 5;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result *= exp(z) / z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+      result += z;
+      BOOST_MATH_INSTRUMENT_VARIABLE(result)
+   }
+   else if(z <= 210)
+   {
+      // Maximum Deviation Found:                     4.448e-36
+      // Expected Error Term:                         4.445e-36
+      // Max Error found at long double precision =   Poly: 2.058532e-35   Cheb: 2.165465e-27
+
+      static const T Y= 1.00849151611328125F;
+      static const T P[9] = {    
+         -0.0084915161132812500000001440233607358L,
+         1.84479378737716028341394223076147872L,
+         -130.431146923726715674081563022115568L,
+         4336.26945491571504885214176203512015L,
+         -76279.0031974974730095170437591004177L,
+         729577.956271997673695191455111727774L,
+         -3661928.69330208734947103004900349266L,
+         8570600.041606912735872059184527855L,
+         -6758379.93672362080947905580906028645L
+      };
+      static const T Q[10] = {    
+         1L,
+         -99.4868026047611434569541483506091713L,
+         3879.67753690517114249705089803055473L,
+         -76495.82413252517165830203774900806L,
+         820773.726408311894342553758526282667L,
+         -4803087.64956923577571031564909646579L,
+         14521246.227703545012713173740895477L,
+         -19762752.0196769712258527849159393044L,
+         8354144.67882768405803322344185185517L,
+         355076.853106511136734454134915432571L
+      };
+      T t = 1 / z;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      result *= exp(z) / z;
+      result += z;
+   }
+   else // z > 210
+   {
+      // Maximum Deviation Found:                     3.963e-37
+      // Expected Error Term:                         3.963e-37
+      // Max Error found at long double precision =   Poly: 1.248049e-36   Cheb: 2.843486e-29
+
+      static const T exp40 = static_cast(2.35385266837019985407899910749034804508871617254555467236651e17L);
+      static const T Y= 1.00252532958984375F;
+      static const T P[8] = {    
+         -0.00252532958984375000000000000000000085L,
+         1.16591386866059087390621952073890359L,
+         -67.8483431314018462417456828499277579L,
+         1567.68688154683822956359536287575892L,
+         -17335.4683325819116482498725687644986L,
+         93632.6567462673524739954389166550069L,
+         -225025.189335919133214440347510936787L,
+         175864.614717440010942804684741336853L
+      };
+      static const T Q[9] = {    
+         1L,
+         -65.6998869881600212224652719706425129L,
+         1642.73850032324014781607859416890077L,
+         -19937.2610222467322481947237312818575L,
+         124136.267326632742667972126625064538L,
+         -384614.251466704550678760562965502293L,
+         523355.035910385688578278384032026998L,
+         -217809.552260834025885677791936351294L,
+         -8555.81719551123640677261226549550872L
+      };
+      T t = 1 / z;
+      result = Y + tools::evaluate_polynomial(P, t)
+         / tools::evaluate_polynomial(Q, t);
+      if(z < 41)
+         result *= exp(z) / z;
+      else
+      {
+         // Avoid premature overflow if we can:
+         t = z - 40;
+         if(t > tools::log_max_value())
+         {
+            result = policies::raise_overflow_error(function, 0, pol);
+         }
+         else
+         {
+            result *= exp(z - 40) / z;
+            if(result > tools::max_value() / exp40)
+            {
+               result = policies::raise_overflow_error(function, 0, pol);
+            }
+            else
+            {
+               result *= exp40;
+            }
+         }
+      }
+      result += z;
+   }
+   return result;
+}
+
+template 
+inline typename tools::promote_args::type
+   expint_forwarder(T z, const Policy& /*pol*/, mpl::true_ const&)
+{
+   typedef typename tools::promote_args::type result_type;
+   typedef typename policies::evaluation::type value_type;
+   typedef typename policies::precision::type precision_type;
+   typedef typename policies::normalise<
+      Policy, 
+      policies::promote_float, 
+      policies::promote_double, 
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   typedef typename mpl::if_<
+      mpl::less_equal >,
+      mpl::int_<0>,
+      typename mpl::if_<
+         mpl::less_equal >,
+         mpl::int_<53>,  // double
+         typename mpl::if_<
+            mpl::less_equal >,
+            mpl::int_<64>, // 80-bit long double
+            typename mpl::if_<
+               mpl::less_equal >,
+               mpl::int_<113>, // 128-bit long double
+               mpl::int_<0> // too many bits, use generic version.
+            >::type
+         >::type
+      >::type
+   >::type tag_type;
+
+   return policies::checked_narrowing_cast(detail::expint_i_imp(
+      static_cast(z),
+      forwarding_policy(),
+      tag_type()), "boost::math::expint<%1%>(%1%)");
+}
+
+template 
+inline typename tools::promote_args::type
+expint_forwarder(unsigned n, T z, const mpl::false_&)
+{
+   return boost::math::expint(n, z, policies::policy<>());
+}
+
+} // namespace detail
+
+template 
+inline typename tools::promote_args::type
+   expint(unsigned n, T z, const Policy& /*pol*/)
+{
+   typedef typename tools::promote_args::type result_type;
+   typedef typename policies::evaluation::type value_type;
+   typedef typename policies::precision::type precision_type;
+   typedef typename policies::normalise<
+      Policy, 
+      policies::promote_float, 
+      policies::promote_double, 
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   typedef typename mpl::if_<
+      mpl::less_equal >,
+      mpl::int_<0>,
+      typename mpl::if_<
+         mpl::less_equal >,
+         mpl::int_<53>,  // double
+         typename mpl::if_<
+            mpl::less_equal >,
+            mpl::int_<64>, // 80-bit long double
+            typename mpl::if_<
+               mpl::less_equal >,
+               mpl::int_<113>, // 128-bit long double
+               mpl::int_<0> // too many bits, use generic version.
+            >::type
+         >::type
+      >::type
+   >::type tag_type;
+
+   return policies::checked_narrowing_cast(detail::expint_imp(
+      n,
+      static_cast(z),
+      forwarding_policy(),
+      tag_type()), "boost::math::expint<%1%>(unsigned, %1%)");
+}
+
+template 
+inline typename detail::expint_result::type
+   expint(T const z, U const u)
+{
+   typedef typename policies::is_policy::type tag_type;
+   return detail::expint_forwarder(z, u, tag_type());
+}
+
+template 
+inline typename tools::promote_args::type
+   expint(T z)
+{
+   return expint(z, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_EXPINT_HPP
+
+
diff --git a/include/boost/math/special_functions/expm1.hpp b/include/boost/math/special_functions/expm1.hpp
index cb88a18d1..7f83e559e 100644
--- a/include/boost/math/special_functions/expm1.hpp
+++ b/include/boost/math/special_functions/expm1.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_EXPM1_INCLUDED
 #define BOOST_MATH_EXPM1_INCLUDED
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include  // platform's ::expm1
 #include 
@@ -267,3 +271,4 @@ inline long double expm1(long double z)
 #endif // BOOST_MATH_HYPOT_INCLUDED
 
 
+
diff --git a/include/boost/math/special_functions/factorials.hpp b/include/boost/math/special_functions/factorials.hpp
index 8bb640d1d..a6ab66247 100644
--- a/include/boost/math/special_functions/factorials.hpp
+++ b/include/boost/math/special_functions/factorials.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SP_FACTORIALS_HPP
 #define BOOST_MATH_SP_FACTORIALS_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -159,7 +163,7 @@ inline T falling_factorial_imp(T x, unsigned n, const Policy& pol)
       // handle it, split the product up into three parts:
       //
       T xp1 = x + 1;
-      unsigned n2 = tools::real_cast(floor(xp1));
+      unsigned n2 = itrunc(floor(xp1), pol);
       if(n2 == xp1)
          return 0;
       T result = boost::math::tgamma_delta_ratio(xp1, -static_cast(n2), pol);
@@ -222,3 +226,4 @@ inline typename tools::promote_args::type
 } // namespace boost
 
 #endif // BOOST_MATH_SP_FACTORIALS_HPP
+
diff --git a/include/boost/math/special_functions/fpclassify.hpp b/include/boost/math/special_functions/fpclassify.hpp
index f777bdba5..51723787b 100644
--- a/include/boost/math/special_functions/fpclassify.hpp
+++ b/include/boost/math/special_functions/fpclassify.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_FPCLASSIFY_HPP
 #define BOOST_MATH_FPCLASSIFY_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -238,3 +242,4 @@ inline bool isnormal BOOST_NO_MACRO_EXPAND(T t)
 
 
 
+
diff --git a/include/boost/math/special_functions/gamma.hpp b/include/boost/math/special_functions/gamma.hpp
index 11706ad38..0a0ed8f2b 100644
--- a/include/boost/math/special_functions/gamma.hpp
+++ b/include/boost/math/special_functions/gamma.hpp
@@ -8,6 +8,10 @@
 #ifndef BOOST_MATH_SF_GAMMA_HPP
 #define BOOST_MATH_SF_GAMMA_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #ifdef BOOST_MSVC
 # pragma warning(push)
@@ -23,12 +27,12 @@
 #include 
 #include 
 #include 
-#include 
 #include 
 #include 
 #include 
 #include 
 #include 
+#include 
 #include 
 #include 
 #include 
@@ -161,7 +165,7 @@ T gamma_imp(T z, const Policy& pol, const L& l)
    }
    if((floor(z) == z) && (z < max_factorial::value))
    {
-      result *= unchecked_factorial(tools::real_cast(z) - 1);
+      result *= unchecked_factorial(itrunc(z, pol) - 1);
    }
    else
    {
@@ -366,7 +370,7 @@ T gamma_imp(T z, const Policy& pol, const lanczos::undefined_lanczos& l)
    BOOST_MATH_INSTRUMENT_CODE(prefix);
    if((floor(z) == z) && (z < max_factorial::value))
    {
-      prefix *= unchecked_factorial(tools::real_cast(z) - 1);
+      prefix *= unchecked_factorial(itrunc(z, pol) - 1);
    }
    else
    {
@@ -1091,7 +1095,7 @@ T tgamma_delta_ratio_imp(T z, T delta, const Policy& pol)
          //
          if((z <= max_factorial::value) && (z + delta <= max_factorial::value))
          {
-            return unchecked_factorial(tools::real_cast(z) - 1) / unchecked_factorial(tools::real_cast(z + delta) - 1);
+            return unchecked_factorial((unsigned)itrunc(z, pol) - 1) / unchecked_factorial((unsigned)itrunc(z + delta) - 1);
          }
       }
       if(fabs(delta) < 20)
@@ -1469,3 +1473,4 @@ inline typename tools::promote_args::type
 
 
 
+
diff --git a/include/boost/math/special_functions/hermite.hpp b/include/boost/math/special_functions/hermite.hpp
index 39c297a5b..1221f414d 100644
--- a/include/boost/math/special_functions/hermite.hpp
+++ b/include/boost/math/special_functions/hermite.hpp
@@ -7,6 +7,10 @@
 #ifndef BOOST_MATH_SPECIAL_HERMITE_HPP
 #define BOOST_MATH_SPECIAL_HERMITE_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -69,3 +73,4 @@ inline typename tools::promote_args::type
 #endif // BOOST_MATH_SPECIAL_HERMITE_HPP
 
 
+
diff --git a/include/boost/math/special_functions/hypot.hpp b/include/boost/math/special_functions/hypot.hpp
index ba97b9937..c182ada83 100644
--- a/include/boost/math/special_functions/hypot.hpp
+++ b/include/boost/math/special_functions/hypot.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_HYPOT_INCLUDED
 #define BOOST_MATH_HYPOT_INCLUDED
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -79,3 +83,4 @@ inline typename tools::promote_args::type
 #endif // BOOST_MATH_HYPOT_INCLUDED
 
 
+
diff --git a/include/boost/math/special_functions/laguerre.hpp b/include/boost/math/special_functions/laguerre.hpp
index d41eafaad..070927f26 100644
--- a/include/boost/math/special_functions/laguerre.hpp
+++ b/include/boost/math/special_functions/laguerre.hpp
@@ -7,6 +7,10 @@
 #ifndef BOOST_MATH_SPECIAL_LAGUERRE_HPP
 #define BOOST_MATH_SPECIAL_LAGUERRE_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -132,3 +136,4 @@ inline typename laguerre_result::type
 #endif // BOOST_MATH_SPECIAL_LAGUERRE_HPP
 
 
+
diff --git a/include/boost/math/special_functions/lanczos.hpp b/include/boost/math/special_functions/lanczos.hpp
index 2f984f615..730bb0bc0 100644
--- a/include/boost/math/special_functions/lanczos.hpp
+++ b/include/boost/math/special_functions/lanczos.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS
 #define BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -1229,3 +1233,4 @@ struct lanczos
 
 
 
+
diff --git a/include/boost/math/special_functions/legendre.hpp b/include/boost/math/special_functions/legendre.hpp
index 019df1ed1..074383ddb 100644
--- a/include/boost/math/special_functions/legendre.hpp
+++ b/include/boost/math/special_functions/legendre.hpp
@@ -7,6 +7,10 @@
 #ifndef BOOST_MATH_SPECIAL_LEGENDRE_HPP
 #define BOOST_MATH_SPECIAL_LEGENDRE_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -187,3 +191,4 @@ inline typename tools::promote_args::type
 #endif // BOOST_MATH_SPECIAL_LEGENDRE_HPP
 
 
+
diff --git a/include/boost/math/special_functions/log1p.hpp b/include/boost/math/special_functions/log1p.hpp
index d5d95eec6..0e093a618 100644
--- a/include/boost/math/special_functions/log1p.hpp
+++ b/include/boost/math/special_functions/log1p.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_LOG1P_INCLUDED
 #define BOOST_MATH_LOG1P_INCLUDED
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include  // platform's ::log1p
 #include 
@@ -275,3 +279,4 @@ inline T log1pmx(T x)
 #endif // BOOST_MATH_LOG1P_INCLUDED
 
 
+
diff --git a/include/boost/math/special_functions/math_fwd.hpp b/include/boost/math/special_functions/math_fwd.hpp
index 0414ec066..1c810b4c0 100644
--- a/include/boost/math/special_functions/math_fwd.hpp
+++ b/include/boost/math/special_functions/math_fwd.hpp
@@ -19,6 +19,10 @@
 #ifndef BOOST_MATH_SPECIAL_MATH_FWD_HPP
 #define BOOST_MATH_SPECIAL_MATH_FWD_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include  // for argument promotion.
 #include 
 #include 
@@ -621,10 +625,74 @@ namespace boost
    template 
    bool isnormal BOOST_NO_MACRO_EXPAND(T t);
 
+   // Exponential integrals:
+   namespace detail{
+
+   template 
+   struct expint_result
+   {
+      typedef typename mpl::if_<
+         policies::is_policy,
+         typename tools::promote_args::type,
+         typename tools::promote_args::type
+      >::type type;
+   };
+
+   } // namespace detail
+
+   template 
+   typename tools::promote_args::type expint(unsigned n, T z, const Policy&);
+
+   template 
+   typename detail::expint_result::type expint(T const z, U const u);
+
+   template 
+   typename tools::promote_args::type expint(T z);
+
+   // Zeta:
+   template 
+   typename tools::promote_args::type zeta(T s, const Policy&);
+
+   template 
+   typename tools::promote_args::type zeta(T s);
+
+   template 
+   T trunc(const T& v, const Policy& pol);
+   template 
+   T trunc(const T& v);
+   template 
+   int itrunc(const T& v, const Policy& pol);
+   template 
+   int itrunc(const T& v);
+   template 
+   long ltrunc(const T& v, const Policy& pol);
+   template 
+   long ltrunc(const T& v);
+
+
     } // namespace math
 } // namespace boost
 
+#ifdef BOOST_HAS_LONG_LONG
+#define BOOST_MATH_DETAIL_LL_FUNC(Policy)\
+   \
+   template \
+   inline T modf(const T& v, long long* ipart){ return boost::math::modf(v, ipart, Policy()); }\
+   \
+   template \
+   inline long long lltrunc(const T& v){ return boost::math::lltrunc(v, Policy()); }\
+   \
+   template \
+   inline long long llround(const T& v){ return boost::math::llround(v, Policy()); }\
+
+#else
+#define BOOST_MATH_DETAIL_LL_FUNC(Policy)
+#endif
+
 #define BOOST_MATH_DECLARE_SPECIAL_FUNCTIONS(Policy)\
+   \
+   BOOST_MATH_DETAIL_LL_FUNC(Policy)\
+   \
    template \
    inline typename boost::math::tools::promote_args::type \
    beta(RT1 a, RT2 b) { return ::boost::math::beta(a, b, Policy()); }\
@@ -907,6 +975,47 @@ namespace boost
    using boost::math::isfinite;\
    using boost::math::isinf;\
    using boost::math::isnan;\
-   using boost::math::isnormal;
+   using boost::math::isnormal;\
+   \
+   template \
+   inline typename boost::math::tools::promote_args::type expint(T const& z, U const& u)\
+   { return boost::math::expint(z, u, Policy()); }\
+   \
+   template \
+   inline typename boost::math::tools::promote_args::type expint(T z){ return boost::math::expint(z, Policy()); }\
+   \
+   template \
+   inline typename boost::math::tools::promote_args::type zeta(T s){ return boost::math::zeta(s, Policy()); }\
+   \
+   template \
+   inline T round(const T& v){ return boost::math::round(v, Policy()); }\
+   \
+   template \
+   inline int iround(const T& v){ return boost::math::iround(v, Policy()); }\
+   \
+   template \
+   inline long lround(const T& v){ return boost::math::lround(v, Policy()); }\
+   \
+   template \
+   inline T trunc(const T& v){ return boost::math::trunc(v, Policy()); }\
+   \
+   template \
+   inline int itrunc(const T& v){ return boost::math::itrunc(v, Policy()); }\
+   \
+   template \
+   inline long ltrunc(const T& v){ return boost::math::ltrunc(v, Policy()); }\
+   \
+   template \
+   inline T modf(const T& v, T* ipart){ return boost::math::modf(v, ipart, Policy()); }\
+   \
+   template \
+   inline T modf(const T& v, int* ipart){ return boost::math::modf(v, ipart, Policy()); }\
+   \
+   template \
+   inline T modf(const T& v, long* ipart){ return boost::math::modf(v, ipart, Policy()); }\
+   \
+   template \
+   inline typename boost::math::tools::promote_args::type pow(T v){ return boost::math::pow(v, Policy()); }\
 
 #endif // BOOST_MATH_SPECIAL_MATH_FWD_HPP
+
diff --git a/include/boost/math/special_functions/modf.hpp b/include/boost/math/special_functions/modf.hpp
new file mode 100644
index 000000000..a44b909d4
--- /dev/null
+++ b/include/boost/math/special_functions/modf.hpp
@@ -0,0 +1,70 @@
+//  Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_MODF_HPP
+#define BOOST_MATH_MODF_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include 
+#include 
+
+namespace boost{ namespace math{
+
+template 
+inline T modf(const T& v, T* ipart, const Policy& pol)
+{
+   *ipart = trunc(v, pol);
+   return v - *ipart;
+}
+template 
+inline T modf(const T& v, T* ipart)
+{
+   return modf(v, ipart, policies::policy<>());
+}
+
+template 
+inline T modf(const T& v, int* ipart, const Policy& pol)
+{
+   *ipart = itrunc(v, pol);
+   return v - *ipart;
+}
+template 
+inline T modf(const T& v, int* ipart)
+{
+   return modf(v, ipart, policies::policy<>());
+}
+
+template 
+inline T modf(const T& v, long* ipart, const Policy& pol)
+{
+   *ipart = ltrunc(v, pol);
+   return v - *ipart;
+}
+template 
+inline T modf(const T& v, long* ipart)
+{
+   return modf(v, ipart, policies::policy<>());
+}
+
+#ifdef BOOST_HAS_LONG_LONG
+template 
+inline T modf(const T& v, long long* ipart, const Policy& pol)
+{
+   *ipart = lltrunc(v, pol);
+   return v - *ipart;
+}
+template 
+inline T modf(const T& v, long long* ipart)
+{
+   return modf(v, ipart, policies::policy<>());
+}
+#endif
+
+}} // namespaces
+
+#endif // BOOST_MATH_MODF_HPP
diff --git a/include/boost/math/special_functions/pow.hpp b/include/boost/math/special_functions/pow.hpp
new file mode 100644
index 000000000..3dfc66c3c
--- /dev/null
+++ b/include/boost/math/special_functions/pow.hpp
@@ -0,0 +1,120 @@
+//   Boost pow.hpp header file
+//   Computes a power with exponent known at compile-time
+
+//  (C) Copyright Bruno Lalande 2008.
+//  Distributed under the Boost Software License, Version 1.0.
+//  (See accompanying file LICENSE_1_0.txt or copy at
+//  http://www.boost.org/LICENSE_1_0.txt)
+
+//  See http://www.boost.org for updates, documentation, and revision history.
+
+
+#ifndef BOOST_MATH_POW_HPP
+#define BOOST_MATH_POW_HPP
+
+
+#include 
+#include 
+#include 
+#include 
+
+
+namespace boost {
+namespace math {
+
+
+namespace detail {
+
+
+template 
+struct positive_power;
+
+template <>
+struct positive_power<0>
+{
+    template 
+    static typename tools::promote_args::type result(T)
+    { return 1; }
+};
+
+template <>
+struct positive_power<2>
+{
+    template 
+    static typename tools::promote_args::type result(T base)
+    { return base*base; }
+};
+
+template 
+struct positive_power
+{
+    template 
+    static typename tools::promote_args::type result(T base)
+    {
+        return (N%2) ? base*positive_power::result(base)
+                     : positive_power<2>::result(
+                           positive_power::result(base)
+                       );
+    }
+};
+
+
+template 
+struct power_if_positive
+{
+    template 
+    static typename tools::promote_args::type result(T base, const Policy&)
+    { return positive_power::result(base); }
+};
+
+template 
+struct power_if_positive
+{
+    template 
+    static typename tools::promote_args::type
+    result(T base, const Policy& policy)
+    {
+        if (base == 0)
+        {
+            return policies::raise_overflow_error(
+                       "boost::math::pow(%1%)",
+                       "Attempted to compute a negative power of 0",
+                       policy
+                   );
+        }
+
+        return T(1) / positive_power<-N>::result(base);
+    }
+};
+
+
+template 
+struct select_power_if_positive
+{
+    typedef typename mpl::greater_equal<
+                         mpl::int_,
+                         mpl::int_<0>
+                     >::type is_positive;
+
+    typedef power_if_positive type;
+};
+
+
+}  // namespace detail
+
+
+template 
+inline typename tools::promote_args::type pow(T base, const Policy& policy)
+{ return detail::select_power_if_positive::type::result(base, policy); }
+
+
+template 
+inline typename tools::promote_args::type pow(T base)
+{ return pow(base, policies::policy<>()); }
+
+
+}  // namespace math
+}  // namespace boost
+
+
+#endif
diff --git a/include/boost/math/special_functions/powm1.hpp b/include/boost/math/special_functions/powm1.hpp
index dd1467d42..cb33ae03d 100644
--- a/include/boost/math/special_functions/powm1.hpp
+++ b/include/boost/math/special_functions/powm1.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_POWM1
 #define BOOST_MATH_POWM1
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -54,3 +58,4 @@ inline typename tools::promote_args::type
 
 
 
+
diff --git a/include/boost/math/special_functions/round.hpp b/include/boost/math/special_functions/round.hpp
new file mode 100644
index 000000000..e436a639e
--- /dev/null
+++ b/include/boost/math/special_functions/round.hpp
@@ -0,0 +1,92 @@
+//  Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_ROUND_HPP
+#define BOOST_MATH_ROUND_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include 
+#include 
+#include 
+
+namespace boost{ namespace math{
+
+template 
+inline T round(const T& v, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   if(!(boost::math::isfinite)(v))
+      return policies::raise_rounding_error("boost::math::round<%1%>(%1%)", 0, v, pol);
+   return floor(v + 0.5f);
+}
+template 
+inline T round(const T& v)
+{
+   return round(v, policies::policy<>());
+}
+//
+// The following functions will not compile unless T has an
+// implicit convertion to the integer types.  For user-defined
+// number types this will likely not be the case.  In that case
+// these functions should either be specialized for the UDT in
+// question, or else overloads should be placed in the same 
+// namespace as the UDT: these will then be found via argument
+// dependent lookup.  See our concept archetypes for examples.
+//
+template 
+inline int iround(const T& v, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   T r = boost::math::round(v, pol);
+   if(fabs(r) > (std::numeric_limits::max)())
+      return static_cast(policies::raise_rounding_error("boost::math::iround<%1%>(%1%)", 0, v, pol));
+   return static_cast(r);
+}
+template 
+inline int iround(const T& v)
+{
+   return iround(v, policies::policy<>());
+}
+
+template 
+inline long lround(const T& v, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   T r = boost::math::round(v, pol);
+   if(fabs(r) > (std::numeric_limits::max)())
+      return static_cast(policies::raise_rounding_error("boost::math::lround<%1%>(%1%)", 0, v, pol));
+   return static_cast(r);
+}
+template 
+inline long lround(const T& v)
+{
+   return lround(v, policies::policy<>());
+}
+
+#ifdef BOOST_HAS_LONG_LONG
+
+template 
+inline long long llround(const T& v, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   T r = boost::math::round(v, pol);
+   if(fabs(r) > (std::numeric_limits::max)())
+      return static_cast(policies::raise_rounding_error("boost::math::llround<%1%>(%1%)", 0, v, pol));
+   return static_cast(r);
+}
+template 
+inline long long llround(const T& v)
+{
+   return llround(v, policies::policy<>());
+}
+
+#endif
+
+}} // namespaces
+
+#endif // BOOST_MATH_ROUND_HPP
diff --git a/include/boost/math/special_functions/sign.hpp b/include/boost/math/special_functions/sign.hpp
index dd4cb8618..7ff450422 100644
--- a/include/boost/math/special_functions/sign.hpp
+++ b/include/boost/math/special_functions/sign.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_SIGN_HPP
 #define BOOST_MATH_TOOLS_SIGN_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 
@@ -36,3 +40,4 @@ inline T copysign BOOST_NO_MACRO_EXPAND(const T& x, const T& y)
 
 #endif // BOOST_MATH_TOOLS_SIGN_HPP
 
+
diff --git a/include/boost/math/special_functions/sin_pi.hpp b/include/boost/math/special_functions/sin_pi.hpp
index c57177d8c..551492882 100644
--- a/include/boost/math/special_functions/sin_pi.hpp
+++ b/include/boost/math/special_functions/sin_pi.hpp
@@ -6,18 +6,24 @@
 #ifndef BOOST_MATH_SIN_PI_HPP
 #define BOOST_MATH_SIN_PI_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
-#include 
+#include 
 #include 
 #include 
 
 namespace boost{ namespace math{ namespace detail{
 
-template 
-T sin_pi_imp(T x)
+template 
+T sin_pi_imp(T x, const Policy& pol)
 {
    BOOST_MATH_STD_USING // ADL of std names
+   if(x < 0)
+      return -sin_pi(-x);
    // sin of pi*x:
    bool invert;
    if(x < 0.5)
@@ -31,7 +37,7 @@ T sin_pi_imp(T x)
       invert = false;
 
    T rem = floor(x);
-   if(tools::real_cast(rem) & 1)
+   if(itrunc(rem, pol) & 1)
       invert = !invert;
    rem = x - rem;
    if(rem > 0.5f)
@@ -43,22 +49,22 @@ T sin_pi_imp(T x)
    return invert ? -rem : rem;
 }
 
-}
+} // namespace detail
 
 template 
-inline typename tools::promote_args::type sin_pi(T x, const Policy&)
+inline typename tools::promote_args::type sin_pi(T x, const Policy& pol)
 {
    typedef typename tools::promote_args::type result_type;
-   return boost::math::detail::sin_pi_imp(x);
+   return boost::math::detail::sin_pi_imp(x, pol);
 }
 
 template 
 inline typename tools::promote_args::type sin_pi(T x)
 {
-   typedef typename tools::promote_args::type result_type;
-   return boost::math::detail::sin_pi_imp(x);
+   return boost::math::sin_pi(x, policies::policy<>());
 }
 
 } // namespace math
 } // namespace boost
 #endif
+
diff --git a/include/boost/math/special_functions/sinc.hpp b/include/boost/math/special_functions/sinc.hpp
index 50788edc8..62b2cad96 100644
--- a/include/boost/math/special_functions/sinc.hpp
+++ b/include/boost/math/special_functions/sinc.hpp
@@ -11,6 +11,10 @@
 #define BOOST_SINC_HPP
 
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -170,3 +174,4 @@ namespace boost
 }
 
 #endif /* BOOST_SINC_HPP */
+
diff --git a/include/boost/math/special_functions/sinhc.hpp b/include/boost/math/special_functions/sinhc.hpp
index f5bde4ce9..808b3fd41 100644
--- a/include/boost/math/special_functions/sinhc.hpp
+++ b/include/boost/math/special_functions/sinhc.hpp
@@ -11,6 +11,10 @@
 #define BOOST_SINHC_HPP
 
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -161,3 +165,4 @@ namespace boost
 }
 
 #endif /* BOOST_SINHC_HPP */
+
diff --git a/include/boost/math/special_functions/spherical_harmonic.hpp b/include/boost/math/special_functions/spherical_harmonic.hpp
index fae32ad97..bd0c7eef0 100644
--- a/include/boost/math/special_functions/spherical_harmonic.hpp
+++ b/include/boost/math/special_functions/spherical_harmonic.hpp
@@ -7,6 +7,10 @@
 #ifndef BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP
 #define BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -197,3 +201,4 @@ inline typename tools::promote_args::type
 #endif // BOOST_MATH_SPECIAL_SPHERICAL_HARMONIC_HPP
 
 
+
diff --git a/include/boost/math/special_functions/sqrt1pm1.hpp b/include/boost/math/special_functions/sqrt1pm1.hpp
index ea4929e1f..ad0203e72 100644
--- a/include/boost/math/special_functions/sqrt1pm1.hpp
+++ b/include/boost/math/special_functions/sqrt1pm1.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_SQRT1PM1
 #define BOOST_MATH_SQRT1PM1
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -41,3 +45,4 @@ inline typename tools::promote_args::type sqrt1pm1(const T& val)
 
 
 
+
diff --git a/include/boost/math/special_functions/trunc.hpp b/include/boost/math/special_functions/trunc.hpp
new file mode 100644
index 000000000..6a19e81d1
--- /dev/null
+++ b/include/boost/math/special_functions/trunc.hpp
@@ -0,0 +1,92 @@
+//  Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_TRUNC_HPP
+#define BOOST_MATH_TRUNC_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include 
+#include 
+#include 
+
+namespace boost{ namespace math{
+
+template 
+inline T trunc(const T& v, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   if(!(boost::math::isfinite)(v))
+      return policies::raise_rounding_error("boost::math::trunc<%1%>(%1%)", 0, v, pol);
+   return (v >= 0) ? floor(v) : ceil(v);
+}
+template 
+inline T trunc(const T& v)
+{
+   return trunc(v, policies::policy<>());
+}
+//
+// The following functions will not compile unless T has an
+// implicit convertion to the integer types.  For user-defined
+// number types this will likely not be the case.  In that case
+// these functions should either be specialized for the UDT in
+// question, or else overloads should be placed in the same 
+// namespace as the UDT: these will then be found via argument
+// dependent lookup.  See our concept archetypes for examples.
+//
+template 
+inline int itrunc(const T& v, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   T r = boost::math::trunc(v, pol);
+   if(fabs(r) > (std::numeric_limits::max)())
+      return static_cast(policies::raise_rounding_error("boost::math::itrunc<%1%>(%1%)", 0, v, pol));
+   return static_cast(r);
+}
+template 
+inline int itrunc(const T& v)
+{
+   return itrunc(v, policies::policy<>());
+}
+
+template 
+inline long ltrunc(const T& v, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   T r = boost::math::trunc(v, pol);
+   if(fabs(r) > (std::numeric_limits::max)())
+      return static_cast(policies::raise_rounding_error("boost::math::ltrunc<%1%>(%1%)", 0, v, pol));
+   return static_cast(r);
+}
+template 
+inline long ltrunc(const T& v)
+{
+   return ltrunc(v, policies::policy<>());
+}
+
+#ifdef BOOST_HAS_LONG_LONG
+
+template 
+inline long long lltrunc(const T& v, const Policy& pol)
+{
+   BOOST_MATH_STD_USING
+   T r = boost::math::trunc(v, pol);
+   if(fabs(r) > (std::numeric_limits::max)())
+      return static_cast(policies::raise_rounding_error("boost::math::lltrunc<%1%>(%1%)", 0, v, pol));
+   return static_cast(r);
+}
+template 
+inline long long lltrunc(const T& v)
+{
+   return lltrunc(v, policies::policy<>());
+}
+
+#endif
+
+}} // namespaces
+
+#endif // BOOST_MATH_TRUNC_HPP
diff --git a/include/boost/math/special_functions/zeta.hpp b/include/boost/math/special_functions/zeta.hpp
new file mode 100644
index 000000000..7e2ac109d
--- /dev/null
+++ b/include/boost/math/special_functions/zeta.hpp
@@ -0,0 +1,903 @@
+//  Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_ZETA_HPP
+#define BOOST_MATH_ZETA_HPP
+
+#ifdef _MSC_VER
+#pragma once
+#endif
+
+#include 
+#include 
+#include 
+#include 
+#include 
+
+namespace boost{ namespace math{ namespace detail{
+
+template 
+struct zeta_series_cache_size
+{
+   //
+   // Work how large to make our cache size when evaluating the series 
+   // evaluation:  normally this is just large enough for the series
+   // to have converged, but for arbitrary precision types we need a 
+   // really large cache to achieve reasonable precision in a reasonable 
+   // time.  This is important when constructing rational approximations
+   // to zeta for example.
+   //
+   typedef typename boost::math::policies::precision::type precision_type;
+   typedef typename mpl::if_<
+      mpl::less_equal >,
+      mpl::int_<5000>,
+      typename mpl::if_<
+         mpl::less_equal >,
+         mpl::int_<70>,
+         typename mpl::if_<
+            mpl::less_equal >,
+            mpl::int_<100>,
+            mpl::int_<5000>
+         >::type
+      >::type
+   >::type type;
+};
+
+template 
+T zeta_series_imp(T s, T sc, const Policy&)
+{
+   //
+   // Series evaluation from:
+   // Havil, J. Gamma: Exploring Euler's Constant. 
+   // Princeton, NJ: Princeton University Press, 2003.
+   //
+   // See also http://mathworld.wolfram.com/RiemannZetaFunction.html
+   //
+   BOOST_MATH_STD_USING
+   T sum = 0;
+   T mult = 0.5;
+   T change;
+   typedef typename zeta_series_cache_size::type cache_size;
+   T powers[cache_size::value] = { 0, };
+   unsigned n = 0;
+   do{
+      T binom = -static_cast(n);
+      T nested_sum = 1;
+      if(n < sizeof(powers) / sizeof(powers[0]))
+         powers[n] = pow(static_cast(n + 1), -s);
+      for(unsigned k = 1; k <= n; ++k)
+      {
+         T p;
+         if(k < sizeof(powers) / sizeof(powers[0]))
+         {
+            p = powers[k];
+            //p = pow(k + 1, -s);
+         }
+         else
+            p = pow(static_cast(k + 1), -s);
+         nested_sum += binom * p;
+        binom *= (k - static_cast(n)) / (k + 1);
+      }
+      change = mult * nested_sum;
+      sum += change;
+      mult /= 2;
+      ++n;
+   }while(fabs(change / sum) > tools::epsilon());
+
+   return sum * 1 / -boost::math::powm1(T(2), sc);
+}
+//
+// Classical p-series:
+//
+template 
+struct zeta_series2
+{
+   typedef T result_type;
+   zeta_series2(T _s) : s(-_s), k(1){}
+   T operator()()
+   {
+      BOOST_MATH_STD_USING
+      return pow(static_cast(k++), s);
+   }
+private:
+   T s;
+   unsigned k;
+};
+
+template 
+inline T zeta_series2_imp(T s, const Policy& pol)
+{
+   boost::uintmax_t max_iter = policies::get_max_series_iterations();;
+   zeta_series2 f(s);
+   T result = tools::sum_series(
+      f, 
+      tools::digits(),
+      max_iter);
+   policies::check_series_iterations("boost::math::zeta_series2<%1%>(%1%)", max_iter, pol);
+   return result;
+}
+
+template 
+T zeta_imp_prec(T s, T sc, const Policy& pol, const mpl::int_<0>&)
+{
+   BOOST_MATH_STD_USING
+   T result; 
+   //
+   // Only use power series if it will converge in 100 
+   // iterations or less: the more iterations it consumes
+   // the slower convergence becomes so we have to be very 
+   // careful in it's usage.
+   //
+   if (s > -log(tools::epsilon()) / 4.5)
+      result = detail::zeta_series2_imp(s, pol);
+   else
+      result = detail::zeta_series_imp(s, sc, pol);
+   return result;
+}
+
+template 
+inline T zeta_imp_prec(T s, T sc, const Policy&, const mpl::int_<53>&)
+{
+   BOOST_MATH_STD_USING
+   T result;
+   if(s < 1)
+   {
+      // Rational Approximation
+      // Maximum Deviation Found:                     2.020e-18
+      // Expected Error Term:                         -2.020e-18
+      // Max error found at double precision:         3.994987e-17
+      static const T P[6] = {    
+         0.24339294433593750202L,
+         -0.49092470516353571651L,
+         0.0557616214776046784287L,
+         -0.00320912498879085894856L,
+         0.000451534528645796438704L,
+         -0.933241270357061460782e-5L,
+        };
+      static const T Q[6] = {    
+         1L,
+         -0.279960334310344432495L,
+         0.0419676223309986037706L,
+         -0.00413421406552171059003L,
+         0.00024978985622317935355L,
+         -0.101855788418564031874e-4L,
+      };
+      result = tools::evaluate_polynomial(P, sc) / tools::evaluate_polynomial(Q, sc);
+      result -= 1.2433929443359375F;
+      result += (sc);
+      result /= (sc);
+   }
+   else if(s <= 2)
+   {
+      // Maximum Deviation Found:        9.007e-20
+      // Expected Error Term:            9.007e-20
+      static const T P[6] = {    
+         0.577215664901532860516,
+         0.243210646940107164097,
+         0.0417364673988216497593,
+         0.00390252087072843288378,
+         0.000249606367151877175456,
+         0.110108440976732897969e-4,
+      };
+      static const T Q[6] = {    
+         1,
+         0.295201277126631761737,
+         0.043460910607305495864,
+         0.00434930582085826330659,
+         0.000255784226140488490982,
+         0.10991819782396112081e-4,
+      };
+      result = tools::evaluate_polynomial(P, -sc) / tools::evaluate_polynomial(Q, -sc);
+      result += 1 / (-sc);
+   }
+   else if(s <= 4)
+   {
+      // Maximum Deviation Found:          5.946e-22
+      // Expected Error Term:              -5.946e-22
+      static const float Y = 0.6986598968505859375;
+      static const T P[6] = {    
+         -0.0537258300023595030676,
+         0.0445163473292365591906,
+         0.0128677673534519952905,
+         0.00097541770457391752726,
+         0.769875101573654070925e-4,
+         0.328032510000383084155e-5,
+      };
+      static const T Q[7] = {    
+         1,
+         0.33383194553034051422,
+         0.0487798431291407621462,
+         0.00479039708573558490716,
+         0.000270776703956336357707,
+         0.106951867532057341359e-4,
+         0.236276623974978646399e-7,
+      };
+      result = tools::evaluate_polynomial(P, s - 2) / tools::evaluate_polynomial(Q, s - 2);
+      result += Y + 1 / (-sc);
+   }
+   else if(s <= 7)
+   {
+      // Maximum Deviation Found:                     2.955e-17
+      // Expected Error Term:                         2.955e-17
+      // Max error found at double precision:         2.009135e-16
+
+      static const T P[6] = {    
+         -2.49710190602259410021,
+         -2.60013301809475665334,
+         -0.939260435377109939261,
+         -0.138448617995741530935,
+         -0.00701721240549802377623,
+         -0.229257310594893932383e-4,
+      };
+      static const T Q[9] = {    
+         1,
+         0.706039025937745133628,
+         0.15739599649558626358,
+         0.0106117950976845084417,
+         -0.36910273311764618902e-4,
+         0.493409563927590008943e-5,
+         -0.234055487025287216506e-6,
+         0.718833729365459760664e-8,
+         -0.1129200113474947419e-9,
+      };
+      result = tools::evaluate_polynomial(P, s - 4) / tools::evaluate_polynomial(Q, s - 4);
+      result = 1 + exp(result);
+   }
+   else if(s < 15)
+   {
+      // Maximum Deviation Found:                     7.117e-16
+      // Expected Error Term:                         7.117e-16
+      // Max error found at double precision:         9.387771e-16
+      static const T P[7] = {    
+         -4.78558028495135619286,
+         -1.89197364881972536382,
+         -0.211407134874412820099,
+         -0.000189204758260076688518,
+         0.00115140923889178742086,
+         0.639949204213164496988e-4,
+         0.139348932445324888343e-5,
+        };
+      static const T Q[9] = {    
+         1,
+         0.244345337378188557777,
+         0.00873370754492288653669,
+         -0.00117592765334434471562,
+         -0.743743682899933180415e-4,
+         -0.21750464515767984778e-5,
+         0.471001264003076486547e-8,
+         -0.833378440625385520576e-10,
+         0.699841545204845636531e-12,
+        };
+      result = tools::evaluate_polynomial(P, s - 7) / tools::evaluate_polynomial(Q, s - 7);
+      result = 1 + exp(result);
+   }
+   else if(s < 36)
+   {
+      // Max error in interpolated form:             1.668e-17
+      // Max error found at long double precision:   1.669714e-17
+      static const T P[8] = {    
+         -10.3948950573308896825,
+         -2.85827219671106697179,
+         -0.347728266539245787271,
+         -0.0251156064655346341766,
+         -0.00119459173416968685689,
+         -0.382529323507967522614e-4,
+         -0.785523633796723466968e-6,
+         -0.821465709095465524192e-8,
+      };
+      static const T Q[10] = {    
+         1,
+         0.208196333572671890965,
+         0.0195687657317205033485,
+         0.00111079638102485921877,
+         0.408507746266039256231e-4,
+         0.955561123065693483991e-6,
+         0.118507153474022900583e-7,
+         0.222609483627352615142e-14,
+      };
+      result = tools::evaluate_polynomial(P, s - 15) / tools::evaluate_polynomial(Q, s - 15);
+      result = 1 + exp(result);
+   }
+   else if(s < 56)
+   {
+      result = 1 + pow(T(2), -s);
+   }
+   else
+   {
+      result = 1;
+   }
+   return result;
+}
+
+template 
+T zeta_imp_prec(T s, T sc, const Policy&, const mpl::int_<64>&)
+{
+   BOOST_MATH_STD_USING
+   T result;
+   if(s < 1)
+   {
+      // Rational Approximation
+      // Maximum Deviation Found:                     3.099e-20
+      // Expected Error Term:                         3.099e-20
+      // Max error found at long double precision:    5.890498e-20
+      static const T P[6] = {    
+         0.243392944335937499969L,
+         -0.496837806864865688082L,
+         0.0680008039723709987107L,
+         -0.00511620413006619942112L,
+         0.000455369899250053003335L,
+         -0.279496685273033761927e-4L,
+        };
+      static const T Q[7] = {    
+         1L,
+         -0.30425480068225790522L,
+         0.050052748580371598736L,
+         -0.00519355671064700627862L,
+         0.000360623385771198350257L,
+         -0.159600883054550987633e-4L,
+         0.339770279812410586032e-6L,
+      };
+      result = tools::evaluate_polynomial(P, sc) / tools::evaluate_polynomial(Q, sc);
+      result -= 1.2433929443359375F;
+      result += (sc);
+      result /= (sc);
+   }
+   else if(s <= 2)
+   {
+      // Maximum Deviation Found:                     1.059e-21
+      // Expected Error Term:                         1.059e-21
+      // Max error found at long double precision:    1.626303e-19
+
+      static const T P[6] = {    
+         0.577215664901532860605L,
+         0.222537368917162139445L,
+         0.0356286324033215682729L,
+         0.00304465292366350081446L,
+         0.000178102511649069421904L,
+         0.700867470265983665042e-5L,
+      };
+      static const T Q[7] = {    
+         1L,
+         0.259385759149531030085L,
+         0.0373974962106091316854L,
+         0.00332735159183332820617L,
+         0.000188690420706998606469L,
+         0.635994377921861930071e-5L,
+         0.226583954978371199405e-7L,
+      };
+      result = tools::evaluate_polynomial(P, -sc) / tools::evaluate_polynomial(Q, -sc);
+      result += 1 / (-sc);
+   }
+   else if(s <= 4)
+   {
+      // Maximum Deviation Found:          5.946e-22
+      // Expected Error Term:              -5.946e-22
+      static const float Y = 0.6986598968505859375;
+      static const T P[7] = {    
+         -0.053725830002359501027L,
+         0.0470551187571475844778L,
+         0.0101339410415759517471L,
+         0.00100240326666092854528L,
+         0.685027119098122814867e-4L,
+         0.390972820219765942117e-5L,
+         0.540319769113543934483e-7L,
+      };
+      static const T Q[8] = {    
+         1,
+         0.286577739726542730421L,
+         0.0447355811517733225843L,
+         0.00430125107610252363302L,
+         0.000284956969089786662045L,
+         0.116188101609848411329e-4L,
+         0.278090318191657278204e-6L,
+         -0.19683620233222028478e-8L,
+      };
+      result = tools::evaluate_polynomial(P, s - 2) / tools::evaluate_polynomial(Q, s - 2);
+      result += Y + 1 / (-sc);
+   }
+   else if(s <= 7)
+   {
+      // Max error found at long double precision: 8.132216e-19
+      static const T P[8] = {    
+         -2.49710190602259407065L,
+         -3.36664913245960625334L,
+         -1.77180020623777595452L,
+         -0.464717885249654313933L,
+         -0.0643694921293579472583L,
+         -0.00464265386202805715487L,
+         -0.000165556579779704340166L,
+         -0.252884970740994069582e-5L,
+      };
+      static const T Q[9] = {    
+         1,
+         1.01300131390690459085L,
+         0.387898115758643503827L,
+         0.0695071490045701135188L,
+         0.00586908595251442839291L,
+         0.000217752974064612188616L,
+         0.397626583349419011731e-5L,
+         -0.927884739284359700764e-8L,
+         0.119810501805618894381e-9L,
+      };
+      result = tools::evaluate_polynomial(P, s - 4) / tools::evaluate_polynomial(Q, s - 4);
+      result = 1 + exp(result);
+   }
+   else if(s < 15)
+   {
+      // Max error in interpolated form:              1.133e-18
+      // Max error found at long double precision:    2.183198e-18
+      static const T P[9] = {    
+         -4.78558028495135548083L,
+         -3.23873322238609358947L,
+         -0.892338582881021799922L,
+         -0.131326296217965913809L,
+         -0.0115651591773783712996L,
+         -0.000657728968362695775205L,
+         -0.252051328129449973047e-4L,
+         -0.626503445372641798925e-6L,
+         -0.815696314790853893484e-8L,
+        };
+      static const T Q[9] = {    
+         1,
+         0.525765665400123515036L,
+         0.10852641753657122787L,
+         0.0115669945375362045249L,
+         0.000732896513858274091966L,
+         0.30683952282420248448e-4L,
+         0.819649214609633126119e-6L,
+         0.117957556472335968146e-7L,
+         -0.193432300973017671137e-12L,
+        };
+      result = tools::evaluate_polynomial(P, s - 7) / tools::evaluate_polynomial(Q, s - 7);
+      result = 1 + exp(result);
+   }
+   else if(s < 42)
+   {
+      // Max error in interpolated form:             1.668e-17
+      // Max error found at long double precision:   1.669714e-17
+      static const T P[9] = {    
+         -10.3948950573308861781L,
+         -2.82646012777913950108L,
+         -0.342144362739570333665L,
+         -0.0249285145498722647472L,
+         -0.00122493108848097114118L,
+         -0.423055371192592850196e-4L,
+         -0.1025215577185967488e-5L,
+         -0.165096762663509467061e-7L,
+         -0.145392555873022044329e-9L,
+      };
+      static const T Q[10] = {    
+         1,
+         0.205135978585281988052L,
+         0.0192359357875879453602L,
+         0.00111496452029715514119L,
+         0.434928449016693986857e-4L,
+         0.116911068726610725891e-5L,
+         0.206704342290235237475e-7L,
+         0.209772836100827647474e-9L,
+         -0.939798249922234703384e-16L,
+         0.264584017421245080294e-18L,
+      };
+      result = tools::evaluate_polynomial(P, s - 15) / tools::evaluate_polynomial(Q, s - 15);
+      result = 1 + exp(result);
+   }
+   else if(s < 63)
+   {
+      result = 1 + pow(T(2), -s);
+   }
+   else
+   {
+      result = 1;
+   }
+   return result;
+}
+
+template 
+T zeta_imp_prec(T s, T sc, const Policy& pol, const mpl::int_<113>&)
+{
+   BOOST_MATH_STD_USING
+   T result;
+   if(s < 1)
+   {
+      // Rational Approximation
+      // Maximum Deviation Found:                     9.493e-37
+      // Expected Error Term:                         9.492e-37
+      // Max error found at long double precision:    7.281332e-31
+
+      static const T P[10] = {    
+         -1L,
+         -0.0353008629988648122808504280990313668L,
+         0.0107795651204927743049369868548706909L,
+         0.000523961870530500751114866884685172975L,
+         -0.661805838304910731947595897966487515e-4L,
+         -0.658932670403818558510656304189164638e-5L,
+         -0.103437265642266106533814021041010453e-6L,
+         0.116818787212666457105375746642927737e-7L,
+         0.660690993901506912123512551294239036e-9L,
+         0.113103113698388531428914333768142527e-10L,
+        };
+      static const T Q[11] = {    
+         1L,
+         -0.387483472099602327112637481818565459L,
+         0.0802265315091063135271497708694776875L,
+         -0.0110727276164171919280036408995078164L,
+         0.00112552716946286252000434849173787243L,
+         -0.874554160748626916455655180296834352e-4L,
+         0.530097847491828379568636739662278322e-5L,
+         -0.248461553590496154705565904497247452e-6L,
+         0.881834921354014787309644951507523899e-8L,
+         -0.217062446168217797598596496310953025e-9L,
+         0.315823200002384492377987848307151168e-11L,
+      };
+      result = tools::evaluate_polynomial(P, sc) / tools::evaluate_polynomial(Q, sc);
+      result += (sc);
+      result /= (sc);
+   }
+   else if(s <= 2)
+   {
+      // Maximum Deviation Found:                     1.616e-37
+      // Expected Error Term:                         -1.615e-37
+
+      static const T P[10] = {    
+         0.577215664901532860606512090082402431L,
+         0.255597968739771510415479842335906308L,
+         0.0494056503552807274142218876983542205L,
+         0.00551372778611700965268920983472292325L,
+         0.00043667616723970574871427830895192731L,
+         0.268562259154821957743669387915239528e-4L,
+         0.109249633923016310141743084480436612e-5L,
+         0.273895554345300227466534378753023924e-7L,
+         0.583103205551702720149237384027795038e-9L,
+         -0.835774625259919268768735944711219256e-11L,
+      };
+      static const T Q[11] = {    
+         1L,
+         0.316661751179735502065583176348292881L,
+         0.0540401806533507064453851182728635272L,
+         0.00598621274107420237785899476374043797L,
+         0.000474907812321704156213038740142079615L,
+         0.272125421722314389581695715835862418e-4L,
+         0.112649552156479800925522445229212933e-5L,
+         0.301838975502992622733000078063330461e-7L,
+         0.422960728687211282539769943184270106e-9L,
+         -0.377105263588822468076813329270698909e-11L,
+         -0.581926559304525152432462127383600681e-13L,
+      };
+      result = tools::evaluate_polynomial(P, -sc) / tools::evaluate_polynomial(Q, -sc);
+      result += 1 / (-sc);
+   }
+   else if(s <= 4)
+   {
+      // Maximum Deviation Found:                     1.891e-36
+      // Expected Error Term:                         -1.891e-36
+      // Max error found: 2.171527e-35
+
+      static const float Y = 0.6986598968505859375;
+      static const T P[11] = {    
+         -0.0537258300023595010275848333539748089L,
+         0.0429086930802630159457448174466342553L,
+         0.0136148228754303412510213395034056857L,
+         0.00190231601036042925183751238033763915L,
+         0.000186880390916311438818302549192456581L,
+         0.145347370745893262394287982691323657e-4L,
+         0.805843276446813106414036600485884885e-6L,
+         0.340818159286739137503297172091882574e-7L,
+         0.115762357488748996526167305116837246e-8L,
+         0.231904754577648077579913403645767214e-10L,
+         0.340169592866058506675897646629036044e-12L,
+      };
+      static const T Q[12] = {    
+         1L,
+         0.363755247765087100018556983050520554L,
+         0.0696581979014242539385695131258321598L,
+         0.00882208914484611029571547753782014817L,
+         0.000815405623261946661762236085660996718L,
+         0.571366167062457197282642344940445452e-4L,
+         0.309278269271853502353954062051797838e-5L,
+         0.12822982083479010834070516053794262e-6L,
+         0.397876357325018976733953479182110033e-8L,
+         0.8484432107648683277598472295289279e-10L,
+         0.105677416606909614301995218444080615e-11L,
+         0.547223964564003701979951154093005354e-15L,
+      };
+      result = tools::evaluate_polynomial(P, s - 2) / tools::evaluate_polynomial(Q, s - 2);
+      result += Y + 1 / (-sc);
+   }
+   else if(s <= 6)
+   {
+      // Max error in interpolated form:             1.510e-37
+      // Max error found at long double precision:   2.769266e-34
+
+      static const T Y = 3.28348541259765625F;
+
+      static const T P[13] = {    
+         0.786383506575062179339611614117697622L,
+         0.495766593395271370974685959652073976L,
+         -0.409116737851754766422360889037532228L,
+         -0.57340744006238263817895456842655987L,
+         -0.280479899797421910694892949057963111L,
+         -0.0753148409447590257157585696212649869L,
+         -0.0122934003684672788499099362823748632L,
+         -0.00126148398446193639247961370266962927L,
+         -0.828465038179772939844657040917364896e-4L,
+         -0.361008916706050977143208468690645684e-5L,
+         -0.109879825497910544424797771195928112e-6L,
+         -0.214539416789686920918063075528797059e-8L,
+         -0.15090220092460596872172844424267351e-10L,
+      };
+      static const T Q[14] = {    
+         1L,
+         1.69490865837142338462982225731926485L,
+         1.22697696630994080733321401255942464L,
+         0.495409420862526540074366618006341533L,
+         0.122368084916843823462872905024259633L,
+         0.0191412993625268971656513890888208623L,
+         0.00191401538628980617753082598351559642L,
+         0.000123318142456272424148930280876444459L,
+         0.531945488232526067889835342277595709e-5L,
+         0.161843184071894368337068779669116236e-6L,
+         0.305796079600152506743828859577462778e-8L,
+         0.233582592298450202680170811044408894e-10L,
+         -0.275363878344548055574209713637734269e-13L,
+         0.221564186807357535475441900517843892e-15L,
+      };
+      result = tools::evaluate_polynomial(P, s - 4) / tools::evaluate_polynomial(Q, s - 4);
+      result -= Y;
+      result = 1 + exp(result);
+   }
+   else if(s < 10)
+   {
+      // Max error in interpolated form:             1.999e-34
+      // Max error found at long double precision:   2.156186e-33
+
+      static const T P[13] = {    
+         -4.0545627381873738086704293881227365L,
+         -4.70088348734699134347906176097717782L,
+         -2.36921550900925512951976617607678789L,
+         -0.684322583796369508367726293719322866L,
+         -0.126026534540165129870721937592996324L,
+         -0.015636903921778316147260572008619549L,
+         -0.00135442294754728549644376325814460807L,
+         -0.842793965853572134365031384646117061e-4L,
+         -0.385602133791111663372015460784978351e-5L,
+         -0.130458500394692067189883214401478539e-6L,
+         -0.315861074947230418778143153383660035e-8L,
+         -0.500334720512030826996373077844707164e-10L,
+         -0.420204769185233365849253969097184005e-12L,
+        };
+      static const T Q[14] = {    
+         1L,
+         0.97663511666410096104783358493318814L,
+         0.40878780231201806504987368939673249L,
+         0.0963890666609396058945084107597727252L,
+         0.0142207619090854604824116070866614505L,
+         0.00139010220902667918476773423995750877L,
+         0.940669540194694997889636696089994734e-4L,
+         0.458220848507517004399292480807026602e-5L,
+         0.16345521617741789012782420625435495e-6L,
+         0.414007452533083304371566316901024114e-8L,
+         0.68701473543366328016953742622661377e-10L,
+         0.603461891080716585087883971886075863e-12L,
+         0.294670713571839023181857795866134957e-16L,
+         -0.147003914536437243143096875069813451e-18L,
+        };
+      result = tools::evaluate_polynomial(P, s - 6) / tools::evaluate_polynomial(Q, s - 6);
+      result = 1 + exp(result);
+   }
+   else if(s < 17)
+   {
+      // Max error in interpolated form:             1.641e-32
+      // Max error found at long double precision:   1.696121e-32
+      static const T P[13] = {    
+         -6.91319491921722925920883787894829678L,
+         -3.65491257639481960248690596951049048L,
+         -0.813557553449954526442644544105257881L,
+         -0.0994317301685870959473658713841138083L,
+         -0.00726896610245676520248617014211734906L,
+         -0.000317253318715075854811266230916762929L,
+         -0.66851422826636750855184211580127133e-5L,
+         0.879464154730985406003332577806849971e-7L,
+         0.113838903158254250631678791998294628e-7L,
+         0.379184410304927316385211327537817583e-9L,
+         0.612992858643904887150527613446403867e-11L,
+         0.347873737198164757035457841688594788e-13L,
+         -0.289187187441625868404494665572279364e-15L,
+        };
+      static const T Q[14] = {    
+         1L,
+         0.427310044448071818775721584949868806L,
+         0.074602514873055756201435421385243062L,
+         0.00688651562174480772901425121653945942L,
+         0.000360174847635115036351323894321880445L,
+         0.973556847713307543918865405758248777e-5L,
+         -0.853455848314516117964634714780874197e-8L,
+         -0.118203513654855112421673192194622826e-7L,
+         -0.462521662511754117095006543363328159e-9L,
+         -0.834212591919475633107355719369463143e-11L,
+         -0.5354594751002702935740220218582929e-13L,
+         0.406451690742991192964889603000756203e-15L,
+         0.887948682401000153828241615760146728e-19L,
+         -0.34980761098820347103967203948619072e-21L,
+        };
+      result = tools::evaluate_polynomial(P, s - 10) / tools::evaluate_polynomial(Q, s - 10);
+      result = 1 + exp(result);
+   }
+   else if(s < 30)
+   {
+      // Max error in interpolated form:             1.563e-31
+      // Max error found at long double precision:   1.562725e-31
+
+      static const T P[13] = {    
+         -11.7824798233959252791987402769438322L,
+         -4.36131215284987731928174218354118102L,
+         -0.732260980060982349410898496846972204L,
+         -0.0744985185694913074484248803015717388L,
+         -0.00517228281320594683022294996292250527L,
+         -0.000260897206152101522569969046299309939L,
+         -0.989553462123121764865178453128769948e-5L,
+         -0.286916799741891410827712096608826167e-6L,
+         -0.637262477796046963617949532211619729e-8L,
+         -0.106796831465628373325491288787760494e-9L,
+         -0.129343095511091870860498356205376823e-11L,
+         -0.102397936697965977221267881716672084e-13L,
+         -0.402663128248642002351627980255756363e-16L,
+      };
+      static const T Q[14] = {    
+         1L,
+         0.311288325355705609096155335186466508L,
+         0.0438318468940415543546769437752132748L,
+         0.00374396349183199548610264222242269536L,
+         0.000218707451200585197339671707189281302L,
+         0.927578767487930747532953583797351219e-5L,
+         0.294145760625753561951137473484889639e-6L,
+         0.704618586690874460082739479535985395e-8L,
+         0.126333332872897336219649130062221257e-9L,
+         0.16317315713773503718315435769352765e-11L,
+         0.137846712823719515148344938160275695e-13L,
+         0.580975420554224366450994232723910583e-16L,
+         -0.291354445847552426900293580511392459e-22L,
+         0.73614324724785855925025452085443636e-25L,
+      };
+      result = tools::evaluate_polynomial(P, s - 17) / tools::evaluate_polynomial(Q, s - 17);
+      result = 1 + exp(result);
+   }
+   else if(s < 74)
+   {
+      // Max error in interpolated form:             2.311e-27
+      // Max error found at long double precision:   2.297544e-27
+      static const T P[14] = {    
+         -20.7944102007844314586649688802236072L,
+         -4.95759941987499442499908748130192187L,
+         -0.563290752832461751889194629200298688L,
+         -0.0406197001137935911912457120706122877L,
+         -0.0020846534789473022216888863613422293L,
+         -0.808095978462109173749395599401375667e-4L,
+         -0.244706022206249301640890603610060959e-5L,
+         -0.589477682919645930544382616501666572e-7L,
+         -0.113699573675553496343617442433027672e-8L,
+         -0.174767860183598149649901223128011828e-10L,
+         -0.210051620306761367764549971980026474e-12L,
+         -0.189187969537370950337212675466400599e-14L,
+         -0.116313253429564048145641663778121898e-16L,
+         -0.376708747782400769427057630528578187e-19L,
+      };
+      static const T Q[16] = {    
+         1L,
+         0.205076752981410805177554569784219717L,
+         0.0202526722696670378999575738524540269L,
+         0.001278305290005994980069466658219057L,
+         0.576404779858501791742255670403304787e-4L,
+         0.196477049872253010859712483984252067e-5L,
+         0.521863830500876189501054079974475762e-7L,
+         0.109524209196868135198775445228552059e-8L,
+         0.181698713448644481083966260949267825e-10L,
+         0.234793316975091282090312036524695562e-12L,
+         0.227490441461460571047545264251399048e-14L,
+         0.151500292036937400913870642638520668e-16L,
+         0.543475775154780935815530649335936121e-19L,
+         0.241647013434111434636554455083309352e-28L,
+         -0.557103423021951053707162364713587374e-31L,
+         0.618708773442584843384712258199645166e-34L,
+      };
+      result = tools::evaluate_polynomial(P, s - 30) / tools::evaluate_polynomial(Q, s - 30);
+      result = 1 + exp(result);
+   }
+   else if(s < 117)
+   {
+      result = 1 + pow(T(2), -s);
+   }
+   else
+   {
+      result = 1;
+   }
+   return result;
+}
+
+template 
+T zeta_imp(T s, T sc, const Policy& pol, const Tag& tag)
+{
+   BOOST_MATH_STD_USING
+   if(s == 1)
+      return policies::raise_pole_error(
+         "boost::math::zeta<%1%>", 
+         "Evaluation of zeta function at pole %1%", 
+         s, pol);
+   T result;
+   if(s == 0)
+   {
+      result = -0.5;
+   }
+   else if(s < 0)
+   {
+      std::swap(s, sc);
+      if(floor(sc/2) == sc/2)
+         result = 0;
+      else
+      {
+         result = boost::math::sin_pi(0.5f * sc, pol)
+            * 2 * pow(2 * constants::pi(), -s) 
+            * boost::math::tgamma(s, pol) 
+            * zeta_imp(s, sc, pol, tag);
+      }
+   }
+   else
+   {
+      result = zeta_imp_prec(s, sc, pol, tag);
+   }
+   return result;
+}
+
+} // detail
+
+template 
+inline typename tools::promote_args::type zeta(T s, const Policy&)
+{
+   typedef typename tools::promote_args::type result_type;
+   typedef typename policies::evaluation::type value_type;
+   typedef typename policies::precision::type precision_type;
+   typedef typename policies::normalise<
+      Policy, 
+      policies::promote_float, 
+      policies::promote_double, 
+      policies::discrete_quantile<>,
+      policies::assert_undefined<> >::type forwarding_policy;
+   typedef typename mpl::if_<
+      mpl::less_equal >,
+      mpl::int_<0>,
+      typename mpl::if_<
+         mpl::less_equal >,
+         mpl::int_<53>,  // double
+         typename mpl::if_<
+            mpl::less_equal >,
+            mpl::int_<64>, // 80-bit long double
+            typename mpl::if_<
+               mpl::less_equal >,
+               mpl::int_<113>, // 128-bit long double
+               mpl::int_<0> // too many bits, use generic version.
+            >::type
+         >::type
+      >::type
+   >::type tag_type;
+   //typedef mpl::int_<0> tag_type;
+
+   return policies::checked_narrowing_cast(detail::zeta_imp(
+      static_cast(s),
+      1 - static_cast(s),
+      forwarding_policy(),
+      tag_type()), "boost::math::zeta<%1%>(%1%)");
+}
+
+template 
+inline typename tools::promote_args::type zeta(T s)
+{
+   return zeta(s, policies::policy<>());
+}
+
+}} // namespaces
+
+#endif // BOOST_MATH_ZETA_HPP
+
+
+
diff --git a/include/boost/math/tools/config.hpp b/include/boost/math/tools/config.hpp
index aaab87aba..e58b995dd 100644
--- a/include/boost/math/tools/config.hpp
+++ b/include/boost/math/tools/config.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_CONFIG_HPP
 #define BOOST_MATH_TOOLS_CONFIG_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include  // for boost::uintmax_t
 #include 
 #include 
@@ -55,6 +59,11 @@
 #  define BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
 #endif
 
+#ifdef BOOST_MSVC
+   // Better safe than sorry, our tests don't support hardware exceptions:
+#  define BOOST_MATH_CONTROL_FP _control87(MCW_EM,MCW_EM)
+#endif
+
 #ifdef __IBMCPP__
 #  define BOOST_MATH_NO_DEDUCED_FUNCTION_POINTERS
 #endif
@@ -244,3 +253,5 @@ inline T max BOOST_PREVENT_MACRO_SUBSTITUTION(T a, T b, T c, T d)
 
 
 
+
+
diff --git a/include/boost/math/tools/fraction.hpp b/include/boost/math/tools/fraction.hpp
index f5b3df5a4..344012d3b 100644
--- a/include/boost/math/tools/fraction.hpp
+++ b/include/boost/math/tools/fraction.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_FRACTION_INCLUDED
 #define BOOST_MATH_TOOLS_FRACTION_INCLUDED
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -257,3 +261,4 @@ typename detail::fraction_traits::result_type continued_fraction_a(Gen& g,
 } // namespace boost
 
 #endif // BOOST_MATH_TOOLS_FRACTION_INCLUDED
+
diff --git a/include/boost/math/tools/minima.hpp b/include/boost/math/tools/minima.hpp
index 14ec95795..94c5de3c4 100644
--- a/include/boost/math/tools/minima.hpp
+++ b/include/boost/math/tools/minima.hpp
@@ -7,6 +7,10 @@
 #ifndef BOOST_MATH_TOOLS_MINIMA_HPP
 #define BOOST_MATH_TOOLS_MINIMA_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -145,3 +149,4 @@ inline std::pair brent_find_minima(F f, T min, T max, int digits)
 
 
 
+
diff --git a/include/boost/math/tools/polynomial.hpp b/include/boost/math/tools/polynomial.hpp
index c2d5a091c..7ad920f16 100644
--- a/include/boost/math/tools/polynomial.hpp
+++ b/include/boost/math/tools/polynomial.hpp
@@ -6,14 +6,96 @@
 #ifndef BOOST_MATH_TOOLS_POLYNOMIAL_HPP
 #define BOOST_MATH_TOOLS_POLYNOMIAL_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
+#include 
 
 #include 
 
 namespace boost{ namespace math{ namespace tools{
 
+template 
+T chebyshev_coefficient(unsigned n, unsigned m)
+{
+   BOOST_MATH_STD_USING
+   if(m > n)
+      return 0;
+   if((n & 1) != (m & 1))
+      return 0;
+   if(n == 0)
+      return 1;
+   T result = T(n) / 2;
+   unsigned r = n - m;
+   r /= 2;
+
+   BOOST_ASSERT(n - 2 * r == m);
+
+   if(r & 1)
+      result = -result;
+   result /= n - r;
+   result *= boost::math::binomial_coefficient(n - r, r);
+   result *= ldexp(1.0f, m);
+   return result;
+}
+
+template 
+Seq polynomial_to_chebyshev(const Seq& s)
+{
+   // Converts a Polynomial into Chebyshev form:
+   typedef typename Seq::value_type value_type;
+   typedef typename Seq::difference_type difference_type;
+   Seq result(s);
+   difference_type order = s.size() - 1;
+   difference_type even_order = order & 1 ? order - 1 : order;
+   difference_type odd_order = order & 1 ? order : order - 1;
+
+   for(difference_type i = even_order; i >= 0; i -= 2)
+   {
+      value_type val = s[i];
+      for(difference_type k = even_order; k > i; k -= 2)
+      {
+         val -= result[k] * chebyshev_coefficient(static_cast(k), static_cast(i));
+      }
+      val /= chebyshev_coefficient(static_cast(i), static_cast(i));
+      result[i] = val;
+   }
+   result[0] *= 2;
+
+   for(difference_type i = odd_order; i >= 0; i -= 2)
+   {
+      value_type val = s[i];
+      for(difference_type k = odd_order; k > i; k -= 2)
+      {
+         val -= result[k] * chebyshev_coefficient(static_cast(k), static_cast(i));
+      }
+      val /= chebyshev_coefficient(static_cast(i), static_cast(i));
+      result[i] = val;
+   }
+   return result;
+}
+
+template 
+T evaluate_chebyshev(const Seq& a, const T& x)
+{
+   // Clenshaw's formula:
+   typedef typename Seq::difference_type difference_type;
+   T yk2 = 0;
+   T yk1 = 0;
+   T yk = 0;
+   for(difference_type i = a.size() - 1; i >= 1; --i)
+   {
+      yk2 = yk1;
+      yk1 = yk;
+      yk = 2 * x * yk1 - yk2 + a[i];
+   }
+   return a[0] / 2 + yk * x - yk1;
+}
+
 template 
 class polynomial
 {
@@ -63,6 +145,10 @@ public:
    {
       return boost::math::tools::evaluate_polynomial(&m_data[0], z, m_data.size());;
    }
+   std::vector chebyshev()const
+   {
+      return polynomial_to_chebyshev(m_data);
+   }
 
    // operators:
    template 
@@ -232,3 +318,4 @@ inline std::basic_ostream& operator << (std::basic_ostream
 #include 
 #include 
@@ -233,3 +237,4 @@ inline T epsilon(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE(T))
 } // namespace boost
 
 #endif // BOOST_MATH_TOOLS_PRECISION_INCLUDED
+
diff --git a/include/boost/math/tools/promotion.hpp b/include/boost/math/tools/promotion.hpp
index 913574b31..e2e6fd1cc 100644
--- a/include/boost/math/tools/promotion.hpp
+++ b/include/boost/math/tools/promotion.hpp
@@ -18,6 +18,10 @@
 #ifndef BOOST_MATH_PROMOTION_HPP
 #define BOOST_MATH_PROMOTION_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 // Boost type traits:
 #include 
 #include  // for boost::is_floating_point;
@@ -118,3 +122,4 @@ namespace boost
 } // namespace boost
 
 #endif // BOOST_MATH_PROMOTION_HPP
+
diff --git a/include/boost/math/tools/rational.hpp b/include/boost/math/tools/rational.hpp
index 81c348af5..59cb5b7e0 100644
--- a/include/boost/math/tools/rational.hpp
+++ b/include/boost/math/tools/rational.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_RATIONAL_HPP
 #define BOOST_MATH_TOOLS_RATIONAL_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -204,3 +208,4 @@ inline V evaluate_rational(const boost::array& a, const boost::array&
 
 
 
+
diff --git a/include/boost/math/tools/real_cast.hpp b/include/boost/math/tools/real_cast.hpp
index 7334cd460..9b854e301 100644
--- a/include/boost/math/tools/real_cast.hpp
+++ b/include/boost/math/tools/real_cast.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_REAL_CAST_HPP
 #define BOOST_MATH_TOOLS_REAL_CAST_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 namespace boost{ namespace math
 {
   namespace tools
@@ -22,3 +26,4 @@ namespace boost{ namespace math
 #endif // BOOST_MATH_TOOLS_REAL_CAST_HPP
 
 
+
diff --git a/include/boost/math/tools/remez.hpp b/include/boost/math/tools/remez.hpp
index e02183332..afcbe25af 100644
--- a/include/boost/math/tools/remez.hpp
+++ b/include/boost/math/tools/remez.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_REMEZ_HPP
 #define BOOST_MATH_TOOLS_REMEZ_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -660,3 +664,4 @@ polynomial remez_minimax::denominator()const
 #endif // BOOST_MATH_TOOLS_REMEZ_HPP
 
 
+
diff --git a/include/boost/math/tools/roots.hpp b/include/boost/math/tools/roots.hpp
index 6412fe9f2..bbe722916 100644
--- a/include/boost/math/tools/roots.hpp
+++ b/include/boost/math/tools/roots.hpp
@@ -6,10 +6,15 @@
 #ifndef BOOST_MATH_TOOLS_NEWTON_SOLVER_HPP
 #define BOOST_MATH_TOOLS_NEWTON_SOLVER_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
 
+#include 
 #include 
 #include 
 #include 
@@ -520,3 +525,4 @@ inline T schroeder_iterate(F f, T guess, T min, T max, int digits)
 #endif // BOOST_MATH_TOOLS_NEWTON_SOLVER_HPP
 
 
+
diff --git a/include/boost/math/tools/series.hpp b/include/boost/math/tools/series.hpp
index 94f264de8..f5f659d24 100644
--- a/include/boost/math/tools/series.hpp
+++ b/include/boost/math/tools/series.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_SERIES_INCLUDED
 #define BOOST_MATH_TOOLS_SERIES_INCLUDED
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -169,3 +173,4 @@ typename Functor::result_type kahan_sum_series(Functor& func, int bits, boost::u
 } // namespace boost
 
 #endif // BOOST_MATH_TOOLS_SERIES_INCLUDED
+
diff --git a/include/boost/math/tools/solve.hpp b/include/boost/math/tools/solve.hpp
index 9683ad561..64b01e521 100644
--- a/include/boost/math/tools/solve.hpp
+++ b/include/boost/math/tools/solve.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_SOLVE_HPP
 #define BOOST_MATH_TOOLS_SOLVE_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 
@@ -72,3 +76,4 @@ boost::numeric::ublas::vector solve(
 
 #endif // BOOST_MATH_TOOLS_SOLVE_HPP
 
+
diff --git a/include/boost/math/tools/stats.hpp b/include/boost/math/tools/stats.hpp
index e9e55456f..bbc1c44eb 100644
--- a/include/boost/math/tools/stats.hpp
+++ b/include/boost/math/tools/stats.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_STATS_INCLUDED
 #define BOOST_MATH_TOOLS_STATS_INCLUDED
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -81,3 +85,4 @@ private:
 } // namespace boost
 
 #endif
+
diff --git a/include/boost/math/tools/test.hpp b/include/boost/math/tools/test.hpp
index 3000e0818..2dfd31425 100644
--- a/include/boost/math/tools/test.hpp
+++ b/include/boost/math/tools/test.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_TEST_HPP
 #define BOOST_MATH_TOOLS_TEST_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -240,3 +244,4 @@ test_result::value_type> test(const A& a, F1 t
 
 #endif
 
+
diff --git a/include/boost/math/tools/test_data.hpp b/include/boost/math/tools/test_data.hpp
index c9cab05dd..3cc09c093 100644
--- a/include/boost/math/tools/test_data.hpp
+++ b/include/boost/math/tools/test_data.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_TEST_DATA_HPP
 #define BOOST_MATH_TOOLS_TEST_DATA_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #ifdef BOOST_MSVC
@@ -754,3 +758,4 @@ std::ostream& write_code(std::ostream& os,
 
 #endif // BOOST_MATH_TOOLS_TEST_DATA_HPP
 
+
diff --git a/include/boost/math/tools/toms748_solve.hpp b/include/boost/math/tools/toms748_solve.hpp
index b52c4ba9f..1ab96d5f6 100644
--- a/include/boost/math/tools/toms748_solve.hpp
+++ b/include/boost/math/tools/toms748_solve.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_SOLVE_ROOT_HPP
 #define BOOST_MATH_TOOLS_SOLVE_ROOT_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 #include 
 #include 
@@ -92,11 +96,11 @@ void bracket(F f, T& a, T& b, T c, T& fa, T& fb, T& d, T& fd)
    }
    else if(c <= a + fabs(a) * tol)
    {
-      c = a * (1 + tol);
+      c = a + fabs(a) * tol;
    }
    else if(c >= b - fabs(b) * tol)
    {
-      c = b * (1 - tol);
+      c = b - fabs(a) * tol;
    }
    //
    // OK, lets invoke f(c):
@@ -505,7 +509,7 @@ std::pair bracket_and_solve_root(F f, const T& guess, T factor, bool risin
          if((max_iter - count) % 20 == 0)
             factor *= 2;
          //
-         // Now go ahead and move are guess by "factor":
+         // Now go ahead and move our guess by "factor":
          //
          a = b;
          fa = fb;
@@ -577,3 +581,4 @@ inline std::pair bracket_and_solve_root(F f, const T& guess, const T& fact
 
 
 #endif // BOOST_MATH_TOOLS_SOLVE_ROOT_HPP
+
diff --git a/include/boost/math/tools/traits.hpp b/include/boost/math/tools/traits.hpp
index 79c2e625c..c49bf19b8 100644
--- a/include/boost/math/tools/traits.hpp
+++ b/include/boost/math/tools/traits.hpp
@@ -21,6 +21,10 @@ as defined above, and has member functions "scale" and "location".
 #ifndef BOOST_STATS_IS_DISTRIBUTION_HPP
 #define BOOST_STATS_IS_DISTRIBUTION_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 // should be the last #include
 #include 
@@ -104,3 +108,4 @@ BOOST_TT_AUX_BOOL_TRAIT_DEF1(is_scaled_distribution,T,::boost::math::tools::deta
 
 #endif
 
+
diff --git a/include/boost/math/tools/user.hpp b/include/boost/math/tools/user.hpp
index bcf78b389..c1bdaf7d8 100644
--- a/include/boost/math/tools/user.hpp
+++ b/include/boost/math/tools/user.hpp
@@ -9,6 +9,10 @@
 #ifndef BOOST_MATH_TOOLS_USER_HPP
 #define BOOST_MATH_TOOLS_USER_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 // This file can be modified by the user to change the default policies.
 // See "Changing the Policy Defaults" in documentation.
 
@@ -90,3 +94,4 @@
 
 #endif // BOOST_MATH_TOOLS_USER_HPP
 
+
diff --git a/include/boost/math/tools/workaround.hpp b/include/boost/math/tools/workaround.hpp
index 4e0035f8e..20106814c 100644
--- a/include/boost/math/tools/workaround.hpp
+++ b/include/boost/math/tools/workaround.hpp
@@ -6,6 +6,10 @@
 #ifndef BOOST_MATH_TOOLS_WORHAROUND_HPP
 #define BOOST_MATH_TOOLS_WORHAROUND_HPP
 
+#ifdef _MSC_VER
+#pragma once
+#endif
+
 #include 
 
 namespace boost{ namespace math{ namespace tools{
@@ -31,3 +35,4 @@ inline long double fmod_workaround(long double a, long double b)
 }}} // namespaces
 
 #endif // BOOST_MATH_TOOLS_WORHAROUND_HPP
+
diff --git a/minimax/f.cpp b/minimax/f.cpp
index 86f55b87e..0508b2253 100644
--- a/minimax/f.cpp
+++ b/minimax/f.cpp
@@ -9,6 +9,8 @@
 #include 
 #include 
 #include 
+#include 
+#include 
 
 #include 
 
@@ -19,13 +21,18 @@ boost::math::ntl::RR f(const boost::math::ntl::RR& x, int variant)
    switch(variant)
    {
    case 0:
-      return boost::math::erfc(x) * x / exp(-x * x);
+      {
+      boost::math::ntl::RR x_ = sqrt(x == 0 ? 1e-80 : x);
+      return boost::math::erf(x_) / x_;
+      }
    case 1:
-      return boost::math::erf(x);
+      {
+      boost::math::ntl::RR x_ = 1 / x;
+      return boost::math::erfc(x_) * x_ / exp(-x_ * x_);
+      }
    case 2:
       {
-         boost::math::ntl::RR x_ = x == 0 ? 1e-80 : x;
-      return boost::math::erf(x_) / x_;
+      return boost::math::erfc(x) * x / exp(-x * x);
       }
    case 3:
       {
@@ -145,7 +152,8 @@ boost::math::ntl::RR f(const boost::math::ntl::RR& x, int variant)
          //
          static boost::math::tools::eps_tolerance tol(1000);
          static boost::uintmax_t max_iter = 1000;
-         static const boost::math::ntl::RR root = boost::math::tools::bracket_and_solve_root(&boost::math::digamma, boost::math::ntl::RR(1.4), boost::math::ntl::RR(1.5), true, tol, max_iter).first;
+         boost::math::ntl::RR (*pdg)(boost::math::ntl::RR) = &boost::math::digamma;
+         static const boost::math::ntl::RR root = boost::math::tools::bracket_and_solve_root(pdg, boost::math::ntl::RR(1.4), boost::math::ntl::RR(1.5), true, tol, max_iter).first;
 
          boost::math::ntl::RR x2 = x;
          double lim = 1e-65;
@@ -198,14 +206,29 @@ boost::math::ntl::RR f(const boost::math::ntl::RR& x, int variant)
    case 14:
       // K(k)
       {
+         static double P[] =
+         {
+            1.38629436111989062502E0,
+            9.65735902811690126535E-2,
+            3.08851465246711995998E-2,
+            1.49380448916805252718E-2,
+            8.79078273952743772254E-3,
+            6.18901033637687613229E-3,
+            6.87489687449949877925E-3,
+            9.85821379021226008714E-3,
+            7.97404013220415179367E-3,
+            2.28025724005875567385E-3,
+            1.37982864606273237150E-4
+         };
+
          // x = 1 - k^2
          boost::math::ntl::RR mp = x;
          if(mp < 1e-20)
             mp = 1e-20;
+         if(mp == 1)
+            mp -= 1e-20;
          boost::math::ntl::RR k = sqrt(1 - mp);
-         static const boost::math::ntl::RR l4 = log(boost::math::ntl::RR(4));
-         boost::math::ntl::RR p2 = boost::math::constants::pi() / 2;
-         return (boost::math::ellint_1(k) + 1) / (1 + l4 - log(mp));
+         return (boost::math::ellint_1(k) - mp/*boost::math::tools::evaluate_polynomial(P, mp)*/) / -log(mp);
       }
    case 15:
       // E(k)
@@ -225,6 +248,68 @@ boost::math::ntl::RR f(const boost::math::ntl::RR& x, int variant)
          boost::math::ntl::RR z = 1 / (boost::math::ntl::RR(1)/16 - x);
          return boost::math::cyl_bessel_i(0, z) * sqrt(z) / exp(z);
       }
+   case 18:
+      // Zeta over [0, 1]
+      {
+         return boost::math::zeta(1 - x) * x - x;
+      }
+   case 19:
+      // Zeta over [1, n]
+      {
+         return boost::math::zeta(x) - 1 / (x - 1);
+      }
+   case 20:
+      // Zeta over [a, b] : a >> 1
+      {
+         return log(boost::math::zeta(x) - 1);
+      }
+   case 21:
+      // expint[1] over [0,1]:
+      {
+         boost::math::ntl::RR tiny = boost::lexical_cast("1e-5000");
+         boost::math::ntl::RR z = (x <= tiny) ? tiny : x;
+         return boost::math::expint(1, z) - z + log(z);
+      }
+   case 22:
+      // expint[1] over [1,N],
+      // Note that x varies from [0,1]:
+      {
+         boost::math::ntl::RR z = 1 / x;
+         return boost::math::expint(1, z) * exp(z) * z;
+      }
+   case 23:
+      // expin Ei over [0,R]
+      {
+         static const boost::math::ntl::RR root = 
+            boost::lexical_cast("0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392");
+         boost::math::ntl::RR z = x < (std::numeric_limits::min)() ? (std::numeric_limits::min)() : x;
+         return (boost::math::expint(z) - log(z / root)) / (z - root);
+      }
+   case 24:
+      // Expint Ei for large x:
+      {
+         static const boost::math::ntl::RR root = 
+            boost::lexical_cast("0.372507410781366634461991866580119133535689497771654051555657435242200120636201854384926049951548942392");
+         boost::math::ntl::RR z = x < (std::numeric_limits::min)() ? (std::numeric_limits::max)() : 1 / x;
+         return (boost::math::expint(z) - z) * z * exp(-z);
+         //return (boost::math::expint(z) - log(z)) * z * exp(-z);
+      }
+   case 25:
+      // Expint Ei for large x:
+      {
+         return (boost::math::expint(x) - x) * x * exp(-x);
+      }
+   case 26:
+      {
+         //
+         // erf_inv in range [0, 0.5]
+         //
+         boost::math::ntl::RR y = x;
+         if(y == 0)
+            y = boost::math::tools::epsilon() / 64;
+         y = sqrt(y);
+         return boost::math::erf_inv(y) / (y);
+      }
    }
    return 0;
 }
diff --git a/minimax/main.cpp b/minimax/main.cpp
index 16551df86..99df43976 100644
--- a/minimax/main.cpp
+++ b/minimax/main.cpp
@@ -5,10 +5,15 @@
 
 #define BOOST_UBLAS_TYPE_CHECK_EPSILON (type_traits::type_sqrt (boost::math::tools::epsilon ()))
 #define BOOST_UBLAS_TYPE_CHECK_MIN (type_traits::type_sqrt ( boost::math::tools::min_value()))
+#define BOOST_UBLAS_NDEBUG
 
 #include 
+namespace std{
+using boost::math::ntl::pow;
+} // workaround for spirit parser.
 #include 
 #include 
+#include 
 #include 
 #include 
 #include 
@@ -32,20 +37,20 @@ bool rel_error(true);
 bool pin(false);
 int orderN(3);
 int orderD(1);
-int target_precision(53);
-int working_precision(250);
+int target_precision = boost::math::tools::digits();
+int working_precision = target_precision * 2;
 bool started(false);
 int variant(0);
 int skew(0);
 int brake(50);
-boost::math::ntl::RR x_offset(0), y_offset(0);
+boost::math::ntl::RR x_offset(0), y_offset(0), x_scale(1);
 bool auto_offset_y;
 
 boost::shared_ptr > p_remez;
 
 boost::math::ntl::RR the_function(const boost::math::ntl::RR& val)
 {
-   return f(val + x_offset, variant) + y_offset;
+   return f(x_scale * (val + x_offset), variant) + y_offset;
 }
 
 void step_some(unsigned count)
@@ -60,9 +65,9 @@ void step_some(unsigned count)
          if(auto_offset_y)
          {
             boost::math::ntl::RR fa, fb, fm;
-            fa = f(a + x_offset, variant);
-            fb = f(b + x_offset, variant);
-            fm = f((a+b)/2 + x_offset, variant);
+            fa = f(x_scale * (a + x_offset), variant);
+            fb = f(x_scale * (b + x_offset), variant);
+            fm = f(x_scale * ((a+b)/2 + x_offset), variant);
             y_offset = -(fa + fb + fm) / 3;
             NTL::RR::SetOutputPrecision(5);
             std::cout << "Setting auto-y-offset to " << y_offset << std::endl;
@@ -120,6 +125,8 @@ void show(const char*, const char*)
    {
       boost::math::tools::polynomial n = p_remez->numerator();
       boost::math::tools::polynomial d = p_remez->denominator();
+      std::vector cn = n.chebyshev();
+      std::vector cd = d.chebyshev();
       int prec = 2 + (target_precision * 3010LL)/10000;
       std::cout << std::scientific << std::setprecision(prec);
       NTL::RR::SetOutputPrecision(prec);
@@ -142,19 +149,34 @@ void show(const char*, const char*)
       std::cout << "  }\n";
 
       std::cout << "X offset: " << x_offset << std::endl;
+      std::cout << "X scale:  " << x_scale << std::endl;
       std::cout << "Y offset: " << y_offset << std::endl;
 
       std::cout << "P = {";
       for(i = 0; i < n.size(); ++i)
       {
-         std::cout << "    " << n[i] << std::endl;
+         std::cout << "    " << n[i] << "L," << std::endl;
       }
       std::cout << "  }\n";
 
       std::cout << "Q = {";
       for(i = 0; i < d.size(); ++i)
       {
-         std::cout << "    " << d[i] << std::endl;
+         std::cout << "    " << d[i] << "L," << std::endl;
+      }
+      std::cout << "  }\n";
+
+      std::cout << "CP = {";
+      for(i = 0; i < cn.size(); ++i)
+      {
+         std::cout << "    " << cn[i] << "L," << std::endl;
+      }
+      std::cout << "  }\n";
+
+      std::cout << "CQ = {";
+      for(i = 0; i < cd.size(); ++i)
+      {
+         std::cout << "    " << cd[i] << "L," << std::endl;
       }
       std::cout << "  }\n";
 
@@ -200,8 +222,24 @@ void do_test(T, const char* name)
       // polynomials:
       //
       boost::math::tools::polynomial n, d;
-      n = p_remez->numerator();
-      d = p_remez->denominator();
+      boost::math::tools::polynomial nr, dr;
+      nr = p_remez->numerator();
+      dr = p_remez->denominator();
+      n = nr;
+      d = dr;
+
+      std::vector cn1, cd1;
+      cn1 = nr.chebyshev();
+      cd1 = dr.chebyshev();
+      std::vector cn, cd;
+      for(unsigned i = 0; i < cn1.size(); ++i)
+      {
+         cn.push_back(boost::math::tools::real_cast(cn1[i]));
+      }
+      for(unsigned i = 0; i < cd1.size(); ++i)
+      {
+         cd.push_back(boost::math::tools::real_cast(cd1[i]));
+      }
       //
       // We'll test at the Chebeshev control points which is where
       // (in theory) the largest deviation should occur.  For good
@@ -211,56 +249,69 @@ void do_test(T, const char* name)
          zeros(p_remez->zero_points()),
          cheb(p_remez->chebyshev_points());
 
-      boost::math::ntl::RR max_error(0);
+      boost::math::ntl::RR max_error(0), cheb_max_error(0);
 
       //
       // Do the tests at the zeros:
       //
       std::cout << "Starting tests at " << name << " precision...\n";
-      std::cout << "Absissa        Error\n";
-      unsigned i;
-      for(i = 0; i < zeros.size(); ++i)
+      std::cout << "Absissa        Error (Poly)   Error (Cheb)\n";
+      for(unsigned i = 0; i < zeros.size(); ++i)
       {
          boost::math::ntl::RR true_result = the_function(zeros[i]);
          T absissa = boost::math::tools::real_cast(zeros[i]);
          boost::math::ntl::RR test_result = n.evaluate(absissa) / d.evaluate(absissa);
-         boost::math::ntl::RR err;
+         boost::math::ntl::RR cheb_result = boost::math::tools::evaluate_chebyshev(cn, absissa) / boost::math::tools::evaluate_chebyshev(cd, absissa);
+         boost::math::ntl::RR err, cheb_err;
          if(rel_error)
          {
             err = boost::math::tools::relative_error(test_result, true_result);
+            cheb_err = boost::math::tools::relative_error(cheb_result, true_result);
          }
          else
          {
             err = fabs(test_result - true_result);
+            cheb_err = fabs(cheb_result - true_result);
          }
          if(err > max_error)
             max_error = err;
+         if(cheb_err > cheb_max_error)
+            cheb_max_error = cheb_err;
          std::cout << std::setprecision(6) << std::setw(15) << std::left << absissa
-            << boost::math::tools::real_cast(err) << std::endl;
+            << std::setw(15) << std::left << boost::math::tools::real_cast(err) << boost::math::tools::real_cast(cheb_err) << std::endl;
       }
       //
       // Do the tests at the Chebeshev control points:
       //
-      for(i = 0; i < cheb.size(); ++i)
+      for(unsigned i = 0; i < cheb.size(); ++i)
       {
          boost::math::ntl::RR true_result = the_function(cheb[i]);
          T absissa = boost::math::tools::real_cast(cheb[i]);
          boost::math::ntl::RR test_result = n.evaluate(absissa) / d.evaluate(absissa);
-         boost::math::ntl::RR err;
+         boost::math::ntl::RR cheb_result = boost::math::tools::evaluate_chebyshev(cn, absissa) / boost::math::tools::evaluate_chebyshev(cd, absissa);
+         boost::math::ntl::RR err, cheb_err;
          if(rel_error)
          {
             err = boost::math::tools::relative_error(test_result, true_result);
+            cheb_err = boost::math::tools::relative_error(cheb_result, true_result);
          }
          else
          {
             err = fabs(test_result - true_result);
+            cheb_err = fabs(cheb_result - true_result);
          }
          if(err > max_error)
             max_error = err;
          std::cout << std::setprecision(6) << std::setw(15) << std::left << absissa
-            << boost::math::tools::real_cast(err) << std::endl;
+            << std::setw(15) << std::left << boost::math::tools::real_cast(err) << 
+            boost::math::tools::real_cast(cheb_err) << std::endl;
       }
-      std::cout << "Max error found: " << std::setprecision(6) << boost::math::tools::real_cast(max_error) << std::endl;
+      std::string msg = "Max Error found at ";
+      msg += name;
+      msg += " precision = ";
+      msg.append(62 - 17 - msg.size(), ' ');
+      std::cout << msg << std::setprecision(6) << "Poly: " << std::setw(20) << std::left
+         << boost::math::tools::real_cast(max_error) << "Cheb: " << boost::math::tools::real_cast(cheb_max_error) << std::endl;
    }
    else
    {
@@ -302,37 +353,67 @@ void do_test_n(T, const char* name, unsigned count)
       // polynomials:
       //
       boost::math::tools::polynomial n, d;
-      n = p_remez->numerator();
-      d = p_remez->denominator();
+      boost::math::tools::polynomial nr, dr;
+      nr = p_remez->numerator();
+      dr = p_remez->denominator();
+      n = nr;
+      d = dr;
 
-      boost::math::ntl::RR max_error(0);
+      std::vector cn1, cd1;
+      cn1 = nr.chebyshev();
+      cd1 = dr.chebyshev();
+      std::vector cn, cd;
+      for(unsigned i = 0; i < cn1.size(); ++i)
+      {
+         cn.push_back(boost::math::tools::real_cast(cn1[i]));
+      }
+      for(unsigned i = 0; i < cd1.size(); ++i)
+      {
+         cd.push_back(boost::math::tools::real_cast(cd1[i]));
+      }
+
+      boost::math::ntl::RR max_error(0), max_cheb_error(0);
       boost::math::ntl::RR step = (b - a) / count;
 
       //
       // Do the tests at the zeros:
       //
       std::cout << "Starting tests at " << name << " precision...\n";
-      std::cout << "Absissa        Error\n";
+      std::cout << "Absissa        Error (poly)   Error (Cheb)\n";
       for(boost::math::ntl::RR x = a; x <= b; x += step)
       {
          boost::math::ntl::RR true_result = the_function(x);
          T absissa = boost::math::tools::real_cast(x);
          boost::math::ntl::RR test_result = n.evaluate(absissa) / d.evaluate(absissa);
-         boost::math::ntl::RR err;
+         boost::math::ntl::RR cheb_result = boost::math::tools::evaluate_chebyshev(cn, absissa) / boost::math::tools::evaluate_chebyshev(cd, absissa);
+         boost::math::ntl::RR err, cheb_err;
          if(rel_error)
          {
             err = boost::math::tools::relative_error(test_result, true_result);
+            cheb_err = boost::math::tools::relative_error(cheb_result, true_result);
          }
          else
          {
             err = fabs(test_result - true_result);
+            cheb_err = fabs(cheb_result - true_result);
          }
          if(err > max_error)
             max_error = err;
+         if(cheb_err > max_cheb_error)
+            max_cheb_error = cheb_err;
          std::cout << std::setprecision(6) << std::setw(15) << std::left << boost::math::tools::real_cast(absissa)
-            << (test_result < true_result ? "-" : "") << boost::math::tools::real_cast(err) << std::endl;
+            << (test_result < true_result ? "-" : "") << std::setw(20) << std::left 
+            << boost::math::tools::real_cast(err) 
+            << boost::math::tools::real_cast(cheb_err) << std::endl;
       }
-      std::cout << "Max error found: " << std::setprecision(6) << boost::math::tools::real_cast(max_error) << std::endl;
+      std::string msg = "Max Error found at ";
+      msg += name;
+      msg += " precision = ";
+      msg.append(62 - 17 - msg.size(), ' ');
+      std::cout << msg << "Poly: " << std::setprecision(6) 
+         << std::setw(15) << std::left 
+         << boost::math::tools::real_cast(max_error) 
+         << "Cheb: " << boost::math::tools::real_cast(max_cheb_error) << std::endl;
    }
    else
    {
@@ -419,6 +500,7 @@ void graph_poly(const char*, const char*)
 int test_main(int, char* [])
 {
    std::string line;
+   real_parser const rr_p;
    while(std::getline(std::cin, line))
    {
       if(parse(line.c_str(), str_p("quit"), space_p).full)
@@ -469,6 +551,8 @@ int test_main(int, char* [])
             str_p("graph")[&graph]
       ||
             str_p("x-offset") && real_p[assign_a(x_offset)]
+      ||
+            str_p("x-scale") && real_p[assign_a(x_scale)]
       ||
             str_p("y-offset") && str_p("auto")[assign_a(auto_offset_y, true)]
       ||
@@ -500,20 +584,24 @@ int test_main(int, char* [])
       }
       else
       {
-         std::cout << "a                    = " << a << std::endl;
-         std::cout << "b                    = " << b << std::endl;
+         std::cout << "Variant              = " << variant << std::endl;
+         std::cout << "range                = [" << a << "," << b << "]" << std::endl;
          std::cout << "Relative Error       = " << rel_error << std::endl;
          std::cout << "Pin to Origin        = " << pin << std::endl;
-         std::cout << "Order (Numerator)    = " << orderN << std::endl;
-         std::cout << "Order (Denominator)  = " << orderD << std::endl;
+         std::cout << "Order (Num/Denom)    = " << orderN << "/" << orderD << std::endl;
          std::cout << "Target Precision     = " << target_precision << std::endl;
          std::cout << "Working Precision    = " << working_precision << std::endl;
-         std::cout << "Variant              = " << variant << std::endl;
          std::cout << "Skew                 = " << skew << std::endl;
          std::cout << "Brake                = " << brake << std::endl;
          std::cout << "X Offset             = " << x_offset << std::endl;
-         std::cout << "Y Offset             = " << y_offset << std::endl;
-         std::cout << "Automatic Y Offset   = " << auto_offset_y << std::endl;
+         std::cout << "X scale              = " << x_scale << std::endl;
+         std::cout << "Y Offset             = ";
+         if(auto_offset_y)
+            std::cout << "Auto (";
+         std::cout << y_offset;
+         if(auto_offset_y)
+            std::cout << ")";
+         std::cout << std::endl;
      }
    }
    return 0;
diff --git a/performance/distributions.cpp b/performance/distributions.cpp
index 1c483749f..810d24de7 100644
--- a/performance/distributions.cpp
+++ b/performance/distributions.cpp
@@ -7,19 +7,7 @@
 
 #include "performance_measure.hpp"
 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
-#include 
+#include 
 
 double probabilities[] = {
    1e-5,
@@ -57,6 +45,20 @@ int int_values[] = {
    100000
 };
 
+int small_int_values[] = {
+   1,
+   2,
+   3,
+   5,
+   10,
+   15,
+   20,
+   30,
+   50,
+   100,
+   150
+};
+
 double real_values[] = {
    1e-5,
    1e-4,
@@ -70,6 +72,83 @@ double real_values[] = {
    100000
 };
 
+#define BOOST_MATH_DISTRIBUTION3_TEST(name, param1_table, param2_table, param3_table, random_variable_table, probability_table) \
+   BOOST_MATH_PERFORMANCE_TEST(BOOST_JOIN(dist, name), "dist-" BOOST_STRINGIZE(name) "-cdf")\
+   {\
+   double result = 0;\
+   unsigned a_size = sizeof(param1_table)/sizeof(param1_table[0]);\
+   unsigned b_size = sizeof(param2_table)/sizeof(param2_table[0]);\
+   unsigned c_size = sizeof(param3_table)/sizeof(param3_table[0]);\
+   unsigned d_size = sizeof(random_variable_table)/sizeof(random_variable_table[0]);\
+   \
+   for(unsigned i = 0; i < a_size; ++i)\
+   {\
+      for(unsigned j = 0; j < b_size; ++j)\
+      {\
+         for(unsigned k = 0; k < c_size; ++k)\
+         {\
+            for(unsigned l = 0; l < d_size; ++l)\
+            {\
+               result += cdf(boost::math:: BOOST_JOIN(name, _distribution) <>(param1_table[i], param2_table[j], param3_table[k]), random_variable_table[l]);\
+            }\
+         }\
+      }\
+   }\
+   \
+   consume_result(result);\
+   set_call_count(a_size * b_size * c_size * d_size);\
+   }\
+   BOOST_MATH_PERFORMANCE_TEST(BOOST_JOIN(dist_pdf_, name), "dist-" BOOST_STRINGIZE(name) "-pdf")\
+   {\
+   double result = 0;\
+   unsigned a_size = sizeof(param1_table)/sizeof(param1_table[0]);\
+   unsigned b_size = sizeof(param2_table)/sizeof(param2_table[0]);\
+   unsigned c_size = sizeof(param3_table)/sizeof(param3_table[0]);\
+   unsigned d_size = sizeof(random_variable_table)/sizeof(random_variable_table[0]);\
+   \
+   for(unsigned i = 0; i < a_size; ++i)\
+   {\
+      for(unsigned j = 0; j < b_size; ++j)\
+      {\
+         for(unsigned k = 0; k < c_size; ++k)\
+         {\
+            for(unsigned l = 0; l < d_size; ++l)\
+            {\
+               result += pdf(boost::math:: BOOST_JOIN(name, _distribution) <>(param1_table[i], param2_table[j], param3_table[k]), random_variable_table[l]);\
+            }\
+         }\
+      }\
+   }\
+   \
+   consume_result(result);\
+   set_call_count(a_size * b_size * c_size * d_size);\
+   }\
+   BOOST_MATH_PERFORMANCE_TEST(BOOST_JOIN(dist_quant, name), "dist-" BOOST_STRINGIZE(name) "-quantile")\
+   {\
+      double result = 0;\
+      unsigned a_size = sizeof(param1_table)/sizeof(param1_table[0]);\
+      unsigned b_size = sizeof(param2_table)/sizeof(param2_table[0]);\
+      unsigned c_size = sizeof(param3_table)/sizeof(param3_table[0]);\
+      unsigned d_size = sizeof(probability_table)/sizeof(probability_table[0]);\
+      \
+      for(unsigned i = 0; i < a_size; ++i)\
+      {\
+         for(unsigned j = 0; j < b_size; ++j)\
+         {\
+            for(unsigned k = 0; k < c_size; ++k)\
+            {\
+               for(unsigned l = 0; l < d_size; ++l)\
+               {\
+                  result += quantile(boost::math:: BOOST_JOIN(name, _distribution) <>(param1_table[i], param2_table[j], param3_table[k]), probability_table[l]);\
+               }\
+            }\
+         }\
+      }\
+      \
+      consume_result(result);\
+      set_call_count(a_size * b_size * c_size * d_size);\
+   }
+
 #define BOOST_MATH_DISTRIBUTION2_TEST(name, param1_table, param2_table, random_variable_table, probability_table) \
    BOOST_MATH_PERFORMANCE_TEST(BOOST_JOIN(dist, name), "dist-" BOOST_STRINGIZE(name) "-cdf")\
    {\
@@ -201,6 +280,10 @@ BOOST_MATH_DISTRIBUTION2_TEST(normal, real_values, real_values, real_values, pro
 BOOST_MATH_DISTRIBUTION1_TEST(poisson, real_values, int_values, probabilities)
 BOOST_MATH_DISTRIBUTION1_TEST(students_t, int_values, real_values, probabilities)
 BOOST_MATH_DISTRIBUTION2_TEST(weibull, real_values, real_values, real_values, probabilities)
+BOOST_MATH_DISTRIBUTION2_TEST(non_central_chi_squared, int_values, int_values, real_values, probabilities)
+BOOST_MATH_DISTRIBUTION3_TEST(non_central_beta, int_values, int_values, real_values, real_values, probabilities)
+BOOST_MATH_DISTRIBUTION3_TEST(non_central_f, int_values, int_values, real_values, real_values, probabilities)
+BOOST_MATH_DISTRIBUTION2_TEST(non_central_t, int_values, small_int_values, real_values, probabilities)
 
 #ifdef TEST_R
 
@@ -208,7 +291,90 @@ BOOST_MATH_DISTRIBUTION2_TEST(weibull, real_values, real_values, real_values, pr
 
 extern "C" {
 #include "Rmath.h"
+/*
+double qnchisq(double, double, double, int, int)
+{
+   return 0;
 }
+*/
+}
+
+#define BOOST_MATH_R_DISTRIBUTION3_TEST(name, param1_table, param2_table, param3_table, random_variable_table, probability_table) \
+   BOOST_MATH_PERFORMANCE_TEST(BOOST_JOIN(dist, name), "dist-" #name "-R-cdf")\
+   {\
+   double result = 0;\
+   unsigned a_size = sizeof(param1_table)/sizeof(param1_table[0]);\
+   unsigned b_size = sizeof(param2_table)/sizeof(param2_table[0]);\
+   unsigned c_size = sizeof(param3_table)/sizeof(param3_table[0]);\
+   unsigned d_size = sizeof(random_variable_table)/sizeof(random_variable_table[0]);\
+   \
+   for(unsigned i = 0; i < a_size; ++i)\
+   {\
+      for(unsigned j = 0; j < b_size; ++j)\
+      {\
+         for(unsigned k = 0; k < c_size; ++k)\
+         {\
+            for(unsigned l = 0; l < d_size; ++l)\
+            {\
+               result += p##name (random_variable_table[l], param1_table[i], param2_table[j], param3_table[k], 1, 0);\
+            }\
+         }\
+      }\
+   }\
+   \
+   consume_result(result);\
+   set_call_count(a_size * b_size * c_size * d_size);\
+   }\
+   BOOST_MATH_PERFORMANCE_TEST(BOOST_JOIN(dist_pdf_, name), "dist-" #name "-R-pdf")\
+   {\
+   double result = 0;\
+   unsigned a_size = sizeof(param1_table)/sizeof(param1_table[0]);\
+   unsigned b_size = sizeof(param2_table)/sizeof(param2_table[0]);\
+   unsigned c_size = sizeof(param3_table)/sizeof(param3_table[0]);\
+   unsigned d_size = sizeof(random_variable_table)/sizeof(random_variable_table[0]);\
+   \
+   for(unsigned i = 0; i < a_size; ++i)\
+   {\
+      for(unsigned j = 0; j < b_size; ++j)\
+      {\
+         for(unsigned k = 0; k < c_size; ++k)\
+         {\
+            for(unsigned l = 0; l < d_size; ++l)\
+            {\
+               result += d##name (random_variable_table[l], param1_table[i], param2_table[j], param3_table[k], 0);\
+            }\
+         }\
+      }\
+   }\
+   \
+   consume_result(result);\
+   set_call_count(a_size * b_size * c_size * d_size);\
+   }\
+   BOOST_MATH_PERFORMANCE_TEST(BOOST_JOIN(dist_quant, name), "dist-" #name "-R-quantile")\
+   {\
+      double result = 0;\
+      unsigned a_size = sizeof(param1_table)/sizeof(param1_table[0]);\
+      unsigned b_size = sizeof(param2_table)/sizeof(param2_table[0]);\
+      unsigned c_size = sizeof(param3_table)/sizeof(param3_table[0]);\
+      unsigned d_size = sizeof(probability_table)/sizeof(probability_table[0]);\
+      \
+      for(unsigned i = 0; i < a_size; ++i)\
+      {\
+         for(unsigned j = 0; j < b_size; ++j)\
+         {\
+            for(unsigned k = 0; k < c_size; ++k)\
+            {\
+               for(unsigned l = 0; l < d_size; ++l)\
+               {\
+                  result += q##name (probability_table[l], param1_table[i], param2_table[j], param3_table[k], 1, 0);\
+               }\
+            }\
+         }\
+      }\
+      \
+      consume_result(result);\
+      set_call_count(a_size * b_size * c_size * d_size);\
+   }
 
 #define BOOST_MATH_R_DISTRIBUTION2_TEST(name, param1_table, param2_table, random_variable_table, probability_table) \
    BOOST_MATH_PERFORMANCE_TEST(BOOST_JOIN(dist, name), "dist-" #name "-R-cdf")\
@@ -341,6 +507,10 @@ BOOST_MATH_R_DISTRIBUTION2_TEST(norm, real_values, real_values, real_values, pro
 BOOST_MATH_R_DISTRIBUTION1_TEST(pois, real_values, int_values, probabilities)
 BOOST_MATH_R_DISTRIBUTION1_TEST(t, int_values, real_values, probabilities)
 BOOST_MATH_R_DISTRIBUTION2_TEST(weibull, real_values, real_values, real_values, probabilities)
+BOOST_MATH_R_DISTRIBUTION2_TEST(nchisq, int_values, int_values, real_values, probabilities)
+BOOST_MATH_R_DISTRIBUTION3_TEST(nf, int_values, int_values, real_values, real_values, probabilities)
+BOOST_MATH_R_DISTRIBUTION3_TEST(nbeta, int_values, int_values, real_values, real_values, probabilities)
+BOOST_MATH_R_DISTRIBUTION2_TEST(nt, int_values, small_int_values, real_values, probabilities)
 
 #endif
 
diff --git a/performance/main.cpp b/performance/main.cpp
index c70f1182a..6b78a05f5 100644
--- a/performance/main.cpp
+++ b/performance/main.cpp
@@ -12,6 +12,7 @@
 #include 
 #include 
 #include 
+#include 
 #include 
 #include "performance_measure.hpp"
 #include 
@@ -56,6 +57,8 @@ void show_help()
       ++i;
    }
    std::cout << "Or use --all to test everything." << std::endl;
+   std::cout << "You can also specify what to test as a regular expression,\n"
+      " for example --dist.* to test all the distributions." << std::endl;
 }
 
 void run_tests()
@@ -77,14 +80,14 @@ void run_tests()
 bool add_named_test(const char* name)
 {
    bool found = false;
+   boost::regex e(name);
    std::set::const_iterator a(all_tests().begin()), b(all_tests().end());
    while(a != b)
    {
-      if(std::strcmp(name, (*a).name) == 0)
+      if(regex_match((*a).name, e))
       {
          found = true;
          tests.insert(*a);
-         break;
       }
       ++a;
    }
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 9cfbf74f9..5a7e73249 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -39,11 +39,16 @@ project
     ;
 
 run hypot_test.cpp ;
+run pow_test.cpp ;
 run log1p_expm1_test.cpp ;
 run powm1_sqrtp1m1_test.cpp ;
 run special_functions_test.cpp ../../test/build//boost_unit_test_framework/static ;
 run test_bernoulli.cpp ;
 run test_constants.cpp ;
+run test_bessel_j.cpp ;
+run test_bessel_y.cpp ;
+run test_bessel_i.cpp ;
+run test_bessel_k.cpp ;
 run test_beta.cpp ;
 run test_beta_dist.cpp ;
 run test_binomial.cpp  
@@ -83,6 +88,7 @@ run test_ellint_2.cpp ;
 run test_ellint_3.cpp ;
 run test_erf.cpp ;
 run test_error_handling.cpp ;
+run test_expint.cpp ;
 run test_exponential_dist.cpp ;
 run test_extreme_value.cpp ;
 run test_factorials.cpp ;
@@ -242,6 +248,79 @@ run test_negative_binomial.cpp
         : # requirements
 	      TEST_REAL_CONCEPT
         : test_negative_binomial_real_concept ;
+run test_nc_chi_squared.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_FLOAT
+        : test_nc_chi_squared_float ;
+run test_nc_chi_squared.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_DOUBLE
+        : test_nc_chi_squared_double ;
+run test_nc_chi_squared.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_LDOUBLE
+        : test_nc_chi_squared_long_double ;
+run test_nc_chi_squared.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_REAL_CONCEPT
+        : test_nc_chi_squared_real_concept ;
+run test_nc_beta.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_FLOAT
+        : test_nc_beta_float ;
+run test_nc_beta.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_DOUBLE
+        : test_nc_beta_double ;
+run test_nc_beta.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_LDOUBLE
+        : test_nc_beta_long_double ;
+run test_nc_beta.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_REAL_CONCEPT
+        : test_nc_beta_real_concept ;
+run test_nc_f.cpp ;
+run test_nc_t.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_FLOAT
+        : test_nc_t_float ;
+run test_nc_t.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_DOUBLE
+        : test_nc_t_double ;
+run test_nc_t.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_LDOUBLE
+        : test_nc_t_long_double ;
+run test_nc_t.cpp  
+        : # command line
+        : # input files
+        : # requirements
+	      TEST_REAL_CONCEPT
+        : test_nc_t_real_concept ;
 run test_normal.cpp ;
 run test_pareto.cpp ;
 run test_poisson.cpp  
@@ -294,6 +373,7 @@ test_rational_instances/test_rational_real_concept5.cpp
 
 run test_remez.cpp ;
 run test_roots.cpp ;
+run test_round.cpp ;
 run test_spherical_harmonic.cpp ;
 run test_students_t.cpp ;
 run test_tgamma_ratio.cpp ;
@@ -301,15 +381,12 @@ run test_toms748_solve.cpp ;
 run test_triangular.cpp ;
 run test_uniform.cpp ;
 run test_weibull.cpp ;
+run test_zeta.cpp ;
+
 run test_policy.cpp ;
 run test_policy_2.cpp ;
 run test_policy_sf.cpp ;
 
-run test_bessel_j.cpp ;
-run test_bessel_y.cpp ;
-run test_bessel_i.cpp ;
-run test_bessel_k.cpp ;
-
 compile  compile_test/compl_abs_incl_test.cpp ;
 compile  compile_test/compl_acos_incl_test.cpp ;
 compile  compile_test/compl_acosh_incl_test.cpp ;
@@ -331,6 +408,10 @@ compile  compile_test/dist_fisher_f_incl_test.cpp ;
 compile  compile_test/dist_gamma_incl_test.cpp ;
 compile  compile_test/dist_lognormal_incl_test.cpp ;
 compile  compile_test/dist_neg_binom_incl_test.cpp ;
+compile  compile_test/dist_nc_chi_squ_incl_test.cpp ;
+compile  compile_test/dist_nc_beta_incl_test.cpp ;
+compile  compile_test/dist_nc_f_incl_test.cpp ;
+compile  compile_test/dist_nc_t_incl_test.cpp ;
 compile  compile_test/dist_normal_incl_test.cpp ;
 compile  compile_test/dist_poisson_incl_test.cpp ;
 compile  compile_test/dist_students_t_incl_test.cpp ;
@@ -352,6 +433,7 @@ compile  compile_test/sf_ellint_rd_incl_test.cpp ;
 compile  compile_test/sf_ellint_rf_incl_test.cpp ;
 compile  compile_test/sf_ellint_rj_incl_test.cpp ;
 compile  compile_test/sf_erf_incl_test.cpp ;
+compile  compile_test/sf_expint_incl_test.cpp ;
 compile  compile_test/sf_expm1_incl_test.cpp ;
 compile  compile_test/sf_factorials_incl_test.cpp ;
 compile  compile_test/sf_fpclassify_incl_test.cpp ;
@@ -363,13 +445,17 @@ compile  compile_test/sf_lanczos_incl_test.cpp ;
 compile  compile_test/sf_legendre_incl_test.cpp ;
 compile  compile_test/sf_log1p_incl_test.cpp ;
 compile  compile_test/sf_math_fwd_incl_test.cpp ;
+compile  compile_test/sf_modf_incl_test.cpp ;
 compile  compile_test/sf_powm1_incl_test.cpp ;
+compile  compile_test/sf_round_incl_test.cpp ;
 compile  compile_test/sf_sign_incl_test.cpp ;
 compile  compile_test/sf_sin_pi_incl_test.cpp ;
 compile  compile_test/sf_sinc_incl_test.cpp ;
 compile  compile_test/sf_sinhc_incl_test.cpp ;
 compile  compile_test/sf_sph_harm_incl_test.cpp ;
 compile  compile_test/sf_sqrt1pm1_incl_test.cpp ;
+compile  compile_test/sf_trunc_incl_test.cpp ;
+compile  compile_test/sf_zeta_incl_test.cpp ;
 compile  compile_test/std_real_concept_check.cpp ;
 compile  compile_test/test_traits.cpp ;
 compile  compile_test/tools_config_inc_test.cpp ;
@@ -405,9 +491,3 @@ run ../quaternion/quaternion_mult_incl_test.cpp
 run complex_test.cpp ;
 
 
-
-
-
-
-
-
diff --git a/test/compile_test/dist_nc_beta_incl_test.cpp b/test/compile_test/dist_nc_beta_incl_test.cpp
new file mode 100644
index 000000000..c6d2ac58d
--- /dev/null
+++ b/test/compile_test/dist_nc_beta_incl_test.cpp
@@ -0,0 +1,44 @@
+//  Copyright John Maddock 2008.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void check()
+{
+   TEST_DIST_FUNC(non_central_beta)
+}
+
+namespace boost{ namespace math{
+
+template 
+T mean(const non_central_beta_distribution&);
+
+template 
+T variance(const non_central_beta_distribution&);
+
+template 
+T skewness(const non_central_beta_distribution&);
+
+template 
+T kurtosis(const non_central_beta_distribution&);
+
+template 
+T kurtosis_excess(const non_central_beta_distribution&);
+
+}}
+
+template class boost::math::non_central_beta_distribution >;
+template class boost::math::non_central_beta_distribution >;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template class boost::math::non_central_beta_distribution >;
+#endif
diff --git a/test/compile_test/dist_nc_chi_squ_incl_test.cpp b/test/compile_test/dist_nc_chi_squ_incl_test.cpp
new file mode 100644
index 000000000..cd67ca522
--- /dev/null
+++ b/test/compile_test/dist_nc_chi_squ_incl_test.cpp
@@ -0,0 +1,25 @@
+//  Copyright John Maddock 2008.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void check()
+{
+   TEST_DIST_FUNC(non_central_chi_squared)
+}
+
+template class boost::math::non_central_chi_squared_distribution >;
+template class boost::math::non_central_chi_squared_distribution >;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template class boost::math::non_central_chi_squared_distribution >;
+#endif
diff --git a/test/compile_test/dist_nc_f_incl_test.cpp b/test/compile_test/dist_nc_f_incl_test.cpp
new file mode 100644
index 000000000..9cef3ad1e
--- /dev/null
+++ b/test/compile_test/dist_nc_f_incl_test.cpp
@@ -0,0 +1,25 @@
+//  Copyright John Maddock 2008.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void check()
+{
+   TEST_DIST_FUNC(non_central_f)
+}
+
+template class boost::math::non_central_f_distribution >;
+template class boost::math::non_central_f_distribution >;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template class boost::math::non_central_f_distribution >;
+#endif
diff --git a/test/compile_test/dist_nc_t_incl_test.cpp b/test/compile_test/dist_nc_t_incl_test.cpp
new file mode 100644
index 000000000..4370be4f7
--- /dev/null
+++ b/test/compile_test/dist_nc_t_incl_test.cpp
@@ -0,0 +1,25 @@
+//  Copyright John Maddock 2008.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void check()
+{
+   TEST_DIST_FUNC(non_central_t)
+}
+
+template class boost::math::non_central_t_distribution >;
+template class boost::math::non_central_t_distribution >;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+template class boost::math::non_central_t_distribution >;
+#endif
diff --git a/test/compile_test/distribution_concept_check.cpp b/test/compile_test/distribution_concept_check.cpp
index 66c5f476a..2e895f991 100644
--- a/test/compile_test/distribution_concept_check.cpp
+++ b/test/compile_test/distribution_concept_check.cpp
@@ -35,6 +35,7 @@ void instantiate(RealType)
    function_requires > >();
    function_requires > >();
    function_requires > >();
+   function_requires > >();
 }
 
 
diff --git a/test/compile_test/instantiate.hpp b/test/compile_test/instantiate.hpp
index e32caba5c..710f26697 100644
--- a/test/compile_test/instantiate.hpp
+++ b/test/compile_test/instantiate.hpp
@@ -30,6 +30,25 @@ BOOST_MATH_DECLARE_DISTRIBUTIONS(double, test_policy)
 
 }
 
+namespace boost{ namespace math{
+//
+// The non central beta doesn't define some properties,
+// define some stub methods here so that we can concept
+// check everything else:
+//
+template 
+inline T mean(const non_central_beta_distribution&){ return 0; }
+template 
+inline T variance(const non_central_beta_distribution&){ return 0; }
+template 
+inline T skewness(const non_central_beta_distribution&){ return 0; }
+template 
+inline T kurtosis_excess(const non_central_beta_distribution&){ return 0; }
+template 
+inline T kurtosis(const non_central_beta_distribution&){ return 0; }
+
+}} // namespaces
+
 template 
 void instantiate(RealType)
 {
@@ -56,6 +75,10 @@ void instantiate(RealType)
    function_requires > >();
    function_requires > >();
    function_requires > >();
+   function_requires > >();
+   function_requires > >();
+   function_requires > >();
+   function_requires > >();
 
    function_requires > >();
    function_requires > >();
@@ -67,6 +90,7 @@ void instantiate(RealType)
    function_requires > >();
    function_requires > >();
    function_requires > >();
+   function_requires > >();
    function_requires > >();
    function_requires > >();
    function_requires > >();
@@ -76,6 +100,10 @@ void instantiate(RealType)
    function_requires > >();
    function_requires > >();
    function_requires > >();
+   function_requires > >();
+   function_requires > >();
+   function_requires > >();
+   function_requires > >();
 
    function_requires >();
    function_requires >();
@@ -96,6 +124,10 @@ void instantiate(RealType)
    function_requires >();
    function_requires >();
    function_requires >();
+   function_requires >();
+   function_requires >();
+   function_requires >();
+   function_requires >();
 
    int i;
    RealType v1(0.5), v2(0.5), v3(0.5);
@@ -191,6 +223,29 @@ void instantiate(RealType)
    boost::math::sph_bessel(i, 1);
    boost::math::sph_neumann(i, v2);
    boost::math::sph_neumann(i, i);
+   boost::math::expint(v1);
+   boost::math::expint(i);
+   boost::math::expint(i, v2);
+   boost::math::expint(i, i);
+   boost::math::zeta(v1);
+   boost::math::zeta(i);
+   boost::math::trunc(v1);
+   boost::math::itrunc(v1);
+   boost::math::ltrunc(v1);
+   boost::math::round(v1);
+   boost::math::iround(v1);
+   boost::math::lround(v1);
+   boost::math::modf(v1, &v1);
+   boost::math::modf(v1, &i);
+   long l;
+   boost::math::modf(v1, &l);
+#ifdef BOOST_HAS_LONG_LONG
+   boost::math::lltrunc(v1);
+   boost::math::llround(v1);
+   long long ll;
+   boost::math::modf(v1, &ll);
+#endif
+   boost::math::pow<2>(v1);
    //
    // All over again, with a policy this time:
    //
@@ -286,6 +341,27 @@ void instantiate(RealType)
    boost::math::sph_bessel(i, 1, pol);
    boost::math::sph_neumann(i, v2, pol);
    boost::math::sph_neumann(i, i, pol);
+   boost::math::expint(v1, pol);
+   boost::math::expint(i, pol);
+   boost::math::expint(i, v2, pol);
+   boost::math::expint(i, i, pol);
+   boost::math::zeta(v1, pol);
+   boost::math::zeta(i, pol);
+   boost::math::trunc(v1, pol);
+   boost::math::itrunc(v1, pol);
+   boost::math::ltrunc(v1, pol);
+   boost::math::round(v1, pol);
+   boost::math::iround(v1, pol);
+   boost::math::lround(v1, pol);
+   boost::math::modf(v1, &v1, pol);
+   boost::math::modf(v1, &i, pol);
+   boost::math::modf(v1, &l, pol);
+#ifdef BOOST_HAS_LONG_LONG
+   boost::math::lltrunc(v1, pol);
+   boost::math::llround(v1, pol);
+   boost::math::modf(v1, &ll, pol);
+#endif
+   boost::math::pow<2>(v1, pol);
    //
    // All over again with the versions in test::
    //
@@ -380,6 +456,27 @@ void instantiate(RealType)
    test::sph_bessel(i, 1);
    test::sph_neumann(i, v2);
    test::sph_neumann(i, i);
+   test::expint(v1);
+   test::expint(i);
+   test::expint(i, v2);
+   test::expint(i, i);
+   test::zeta(v1);
+   test::zeta(i);
+   test::trunc(v1);
+   test::itrunc(v1);
+   test::ltrunc(v1);
+   test::round(v1);
+   test::iround(v1);
+   test::lround(v1);
+   test::modf(v1, &v1);
+   test::modf(v1, &i);
+   test::modf(v1, &l);
+#ifdef BOOST_HAS_LONG_LONG
+   test::lltrunc(v1);
+   test::llround(v1);
+   test::modf(v1, &ll);
+#endif
+   test::pow<2>(v1);
 }
 
 template 
diff --git a/test/compile_test/sf_expint_incl_test.cpp b/test/compile_test/sf_expint_incl_test.cpp
new file mode 100644
index 000000000..7db93a72b
--- /dev/null
+++ b/test/compile_test/sf_expint_incl_test.cpp
@@ -0,0 +1,28 @@
+//  Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void check()
+{
+   check_result(boost::math::expint(f));
+   check_result(boost::math::expint(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::expint(l));
+#endif
+   check_result(boost::math::expint(u, f));
+   check_result(boost::math::expint(u, d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::expint(u, l));
+#endif
+}
diff --git a/test/compile_test/sf_modf_incl_test.cpp b/test/compile_test/sf_modf_incl_test.cpp
new file mode 100644
index 000000000..b607127e9
--- /dev/null
+++ b/test/compile_test/sf_modf_incl_test.cpp
@@ -0,0 +1,48 @@
+//  Copyright John Maddock 2006.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+float ff;
+double dd;
+long double lldd;
+
+int ii;
+long ll;
+#ifdef BOOST_HAS_LONG_LONG
+long long llll;
+#endif
+
+void check()
+{
+   check_result(boost::math::modf(f, &ff));
+   check_result(boost::math::modf(d, &dd));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::modf(l, &lldd));
+#endif
+   check_result(boost::math::modf(f, &ii));
+   check_result(boost::math::modf(d, &ii));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::modf(l, &ii));
+#endif
+   check_result(boost::math::modf(f, &ll));
+   check_result(boost::math::modf(d, &ll));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::modf(l, &ll));
+#endif
+   check_result(boost::math::modf(f, &llll));
+   check_result(boost::math::modf(d, &llll));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::modf(l, &llll));
+#endif
+}
diff --git a/test/compile_test/sf_round_incl_test.cpp b/test/compile_test/sf_round_incl_test.cpp
new file mode 100644
index 000000000..4c89e9027
--- /dev/null
+++ b/test/compile_test/sf_round_incl_test.cpp
@@ -0,0 +1,40 @@
+//  Copyright John Maddock 2006.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void check()
+{
+   check_result(boost::math::round(f));
+   check_result(boost::math::round(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::round(l));
+#endif
+   check_result(boost::math::iround(f));
+   check_result(boost::math::iround(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::iround(l));
+#endif
+   check_result(boost::math::lround(f));
+   check_result(boost::math::lround(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::lround(l));
+#endif
+#ifdef BOOST_HAS_LONG_LONG
+   check_result(boost::math::llround(f));
+   check_result(boost::math::llround(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::llround(l));
+#endif
+#endif
+}
diff --git a/test/compile_test/sf_trunc_incl_test.cpp b/test/compile_test/sf_trunc_incl_test.cpp
new file mode 100644
index 000000000..3b0295468
--- /dev/null
+++ b/test/compile_test/sf_trunc_incl_test.cpp
@@ -0,0 +1,40 @@
+//  Copyright John Maddock 2006.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void check()
+{
+   check_result(boost::math::trunc(f));
+   check_result(boost::math::trunc(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::trunc(l));
+#endif
+   check_result(boost::math::itrunc(f));
+   check_result(boost::math::itrunc(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::itrunc(l));
+#endif
+   check_result(boost::math::ltrunc(f));
+   check_result(boost::math::ltrunc(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::ltrunc(l));
+#endif
+#ifdef BOOST_HAS_LONG_LONG
+   check_result(boost::math::lltrunc(f));
+   check_result(boost::math::lltrunc(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::lltrunc(l));
+#endif
+#endif
+}
diff --git a/test/compile_test/sf_zeta_incl_test.cpp b/test/compile_test/sf_zeta_incl_test.cpp
new file mode 100644
index 000000000..fe241ef6b
--- /dev/null
+++ b/test/compile_test/sf_zeta_incl_test.cpp
@@ -0,0 +1,23 @@
+//  Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Basic sanity check that header 
+// #includes all the files that it needs to.
+//
+#include 
+//
+// Note this header includes no other headers, this is
+// important if this test is to be meaningful:
+//
+#include "test_compile_result.hpp"
+
+void check()
+{
+   check_result(boost::math::zeta(f));
+   check_result(boost::math::zeta(d));
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   check_result(boost::math::zeta(l));
+#endif
+}
diff --git a/test/compile_test/test_compile_result.hpp b/test/compile_test/test_compile_result.hpp
index 9a3fd30ae..993d9dc43 100644
--- a/test/compile_test/test_compile_result.hpp
+++ b/test/compile_test/test_compile_result.hpp
@@ -22,6 +22,10 @@ inline void check_result_imp(float, float){}
 inline void check_result_imp(double, double){}
 inline void check_result_imp(long double, long double){}
 inline void check_result_imp(int, int){}
+inline void check_result_imp(long, long){}
+#ifdef BOOST_HAS_LONG_LONG
+inline void check_result_imp(long long, long long){}
+#endif
 inline void check_result_imp(bool, bool){}
 
 template 
diff --git a/test/expint_1_data.ipp b/test/expint_1_data.ipp
new file mode 100644
index 000000000..85f7a3682
--- /dev/null
+++ b/test/expint_1_data.ipp
@@ -0,0 +1,84 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 79> expint_1_data = {{
+      { SC_(1), SC_(0.1690093176520690576580818742513656616211e-8), SC_(19.62126651228390287899433646349668926594) }, 
+      { SC_(1), SC_(0.2114990849122477811761200428009033203125e-8), SC_(19.39699968832702671432639506875262488287) }, 
+      { SC_(1), SC_(0.7099628440698779741069301962852478027344e-8), SC_(18.18600772876256587669156181753338435097) }, 
+      { SC_(1), SC_(0.136718796284185373224318027496337890625e-7), SC_(17.53070904418311673532926624670363745081) }, 
+      { SC_(1), SC_(0.1679341288252089725574478507041931152344e-7), SC_(17.32506346964272541627765227695487661752) }, 
+      { SC_(1), SC_(0.586768322818898013792932033538818359375e-7), SC_(16.07400526183027268777222922688894197166) }, 
+      { SC_(1), SC_(0.1140460881288163363933563232421875e-6), SC_(15.40944763756462608330646107757571975159) }, 
+      { SC_(1), SC_(0.1455586016163579188287258148193359375e-6), SC_(15.16547155182818279856457574476936266928) }, 
+      { SC_(1), SC_(0.38918477685001562349498271942138671875e-6), SC_(14.18199632563439348037946938445484633991) }, 
+      { SC_(1), SC_(0.623782625552848912775516510009765625e-6), SC_(13.71024884463401352596363384090540526092) }, 
+      { SC_(1), SC_(0.104669607026153244078159332275390625e-5), SC_(13.19265733629451552935983109160182922456) }, 
+      { SC_(1), SC_(0.2951089072666945867240428924560546875e-5), SC_(12.15612356475179839693915983580837953116) }, 
+      { SC_(1), SC_(0.4877083483734168112277984619140625e-5), SC_(11.65375237571303028293100602849280330023) }, 
+      { SC_(1), SC_(0.9066634447663091123104095458984375e-5), SC_(11.033702828615680805096853068034765697) }, 
+      { SC_(1), SC_(0.2360353755648247897624969482421875e-4), SC_(10.07692189920168231695897773396921896378) }, 
+      { SC_(1), SC_(0.60817910707555711269378662109375e-4), SC_(9.130471380452133719689002203686010732863) }, 
+      { SC_(1), SC_(0.000119476739200763404369354248046875), SC_(8.455292664848407732192394706135617033129) }, 
+      { SC_(1), SC_(0.0002437086659483611583709716796875), SC_(7.742565066979092841621580079924528124121) }, 
+      { SC_(1), SC_(0.00047970912419259548187255859375), SC_(7.065594615713263713209655779382416164774) }, 
+      { SC_(1), SC_(0.000960788573138415813446044921875), SC_(6.371501073281348028486161198392483333344) }, 
+      { SC_(1), SC_(0.00113048148341476917266845703125), SC_(6.209026142656637951294057898954292515858) }, 
+      { SC_(1), SC_(0.0033707791008055210113525390625), SC_(5.118763649942589236114477763556608384932) }, 
+      { SC_(1), SC_(0.007697627879679203033447265625), SC_(4.297310240071577860879490194258146908042) }, 
+      { SC_(1), SC_(0.0154774188995361328125), SC_(3.606575234235758813120382950507615467416) }, 
+      { SC_(1), SC_(0.0305807329714298248291015625), SC_(2.940517962291826559900925068133667615931) }, 
+      { SC_(1), SC_(0.0346831791102886199951171875), SC_(2.818669547758849173655366691300656029988) }, 
+      { SC_(1), SC_(0.09283597767353057861328125), SC_(1.890430395046114091623024011625489238192) }, 
+      { SC_(1), SC_(0.22476322948932647705078125), SC_(1.128230840748073484651782346841079611668) }, 
+      { SC_(1), SC_(0.23917420208454132080078125), SC_(1.078947851117239985434642728998206006734) }, 
+      { SC_(1), SC_(0.4500701129436492919921875), SC_(0.6252319809071619975475212606569679083844) }, 
+      { SC_(1), SC_(1.785583972930908203125), SC_(0.06605196207880094390425879479033907552898) }, 
+      { SC_(1), SC_(4.8770198822021484375), SC_(0.001326894275438860249857941044254174502639) }, 
+      { SC_(1), SC_(5.4930877685546875), SC_(0.0006460832160891306352056104536312996827518) }, 
+      { SC_(1), SC_(5.623225688934326171875), SC_(0.0005557114466261269081523366304841856778567) }, 
+      { SC_(1), SC_(6.349340915679931640625), SC_(0.0002414929458653428650902712691508606087705) }, 
+      { SC_(1), SC_(6.77385044097900390625), SC_(0.0001491057337258556360697724884053639712183) }, 
+      { SC_(1), SC_(7.094316959381103515625), SC_(0.000103833853056272701038880940251981448874) }, 
+      { SC_(1), SC_(7.88065433502197265625), SC_(0.4302184733486055021456160704267900644151e-4) }, 
+      { SC_(1), SC_(9.41909885406494140625), SC_(0.785158179791932713400818863165202252408e-5) }, 
+      { SC_(1), SC_(10.5962162017822265625), SC_(0.2170821091221718858998745985121834633123e-5) }, 
+      { SC_(1), SC_(11.0517024993896484375), SC_(0.1323971054451696237675804650020934283271e-5) }, 
+      { SC_(1), SC_(13.9249114990234375), SC_(0.6030052082140414872763484176234936031379e-7) }, 
+      { SC_(1), SC_(14.85147190093994140625), SC_(0.2246847323452812310807076843921206699284e-7) }, 
+      { SC_(1), SC_(15.408351898193359375), SC_(0.1243451611444526471238603318210383094864e-7) }, 
+      { SC_(1), SC_(18.0646991729736328125), SC_(0.7506937540952249657080032497242314338058e-9) }, 
+      { SC_(1), SC_(19.9369258880615234375), SC_(0.1050756169313570044042540524516527996741e-9) }, 
+      { SC_(1), SC_(21.0880641937255859375), SC_(0.3149450286739813566149195966918766794019e-10) }, 
+      { SC_(1), SC_(24.2687816619873046875), SC_(0.1143540865960474355116790661840197166523e-11) }, 
+      { SC_(1), SC_(25.183135986328125), SC_(0.4422553437971115949495472179014784876379e-12) }, 
+      { SC_(1), SC_(27.344074249267578125), SC_(0.4706136215074688573466876839711291930065e-13) }, 
+      { SC_(1), SC_(27.3610286712646484375), SC_(0.4624246647932169908912545804468933517039e-13) }, 
+      { SC_(1), SC_(31.6179637908935546875), SC_(0.5694058988300047405430136315685981910904e-15) }, 
+      { SC_(1), SC_(31.98816680908203125), SC_(0.3888079168940721087324944469578712933197e-15) }, 
+      { SC_(1), SC_(32.7870330810546875), SC_(0.1707586829662679381480684070037630121613e-15) }, 
+      { SC_(1), SC_(33.936756134033203125), SC_(0.5230089477890500292647833806674719422967e-16) }, 
+      { SC_(1), SC_(34.0679779052734375), SC_(0.4569720316267919392435436312475469039788e-16) }, 
+      { SC_(1), SC_(36.2919464111328125), SC_(0.4648256808579637348536682966321094152884e-17) }, 
+      { SC_(1), SC_(39.6103668212890625), SC_(0.1545435668053719402464984966443581618056e-18) }, 
+      { SC_(1), SC_(39.89643096923828125), SC_(0.1152823764266388444276211386495818338284e-18) }, 
+      { SC_(1), SC_(39.905292510986328125), SC_(0.1142405282651606532309094911197076666306e-18) }, 
+      { SC_(1), SC_(40.0140228271484375), SC_(0.1021986300809498211588191270716148887523e-18) }, 
+      { SC_(1), SC_(40.73618316650390625), SC_(0.487782450682026156951156991212514994025e-19) }, 
+      { SC_(1), SC_(41.75042724609375), SC_(0.1727057820230415908617717666461962953748e-19) }, 
+      { SC_(1), SC_(42.4564666748046875), SC_(0.8386035754034782201062683833804929446885e-20) }, 
+      { SC_(1), SC_(43.92153167724609375), SC_(0.1874446514992257654186347034583264392481e-20) }, 
+      { SC_(1), SC_(45.2895965576171875), SC_(0.4631155735799306610393016753551769399309e-21) }, 
+      { SC_(1), SC_(45.668792724609375), SC_(0.3143839170407425907322861671102497142403e-21) }, 
+      { SC_(1), SC_(45.786777496337890625), SC_(0.278690825003829419502247825145190508394e-21) }, 
+      { SC_(1), SC_(46.6996612548828125), SC_(0.1097142494759480902665224812198017036116e-21) }, 
+      { SC_(1), SC_(47.858348846435546875), SC_(0.3362168462409445527866973776887649345695e-22) }, 
+      { SC_(1), SC_(47.87534332275390625), SC_(0.3304362677594583967844855615677058007508e-22) }, 
+      { SC_(1), SC_(47.974620819091796875), SC_(0.2986001918596063601815305407205441355782e-22) }, 
+      { SC_(1), SC_(48.244426727294921875), SC_(0.226739399060424385006440097684052080086e-22) }, 
+      { SC_(1), SC_(48.384746551513671875), SC_(0.1964943928572394204174413988519401201072e-22) }, 
+      { SC_(1), SC_(48.443389892578125), SC_(0.1850827201970609263420459500557652587842e-22) }, 
+      { SC_(1), SC_(48.52964019775390625), SC_(0.1694924366999538118474174187456764816795e-22) }, 
+      { SC_(1), SC_(49.055484771728515625), SC_(0.9912630736365412803849736897421968989741e-23) }, 
+      { SC_(1), SC_(49.64406585693359375), SC_(0.5438645188377533724985296541041944657958e-23) }, 
+      { SC_(1), SC_(49.82306671142578125), SC_(0.453125198123893560872142720624255521908e-23) }
+   }};
+#undef SC_
+
diff --git a/test/expint_data.ipp b/test/expint_data.ipp
new file mode 100644
index 000000000..f12e0cf86
--- /dev/null
+++ b/test/expint_data.ipp
@@ -0,0 +1,605 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 600> expint_data = {{
+      { SC_(0), SC_(4.8770198822021484375), SC_(0.001562365538135970995717852896857631808327) }, 
+      { SC_(0), SC_(5.4930877685546875), SC_(0.0007491447757702025944722131745633334937684) }, 
+      { SC_(0), SC_(6.349340915679931640625), SC_(0.0002752882216582873387067996572122917865872) }, 
+      { SC_(0), SC_(6.77385044097900390625), SC_(0.0001687790463104021974718191672246829394287) }, 
+      { SC_(0), SC_(7.88065433502197265625), SC_(0.47963738863754152769104622456952262715e-4) }, 
+      { SC_(0), SC_(9.41909885406494140625), SC_(0.8616442383363190691210027445652026531832e-5) }, 
+      { SC_(0), SC_(11.0517024993896484375), SC_(0.1435084267000391515109242970335955294949e-5) }, 
+      { SC_(0), SC_(13.9249114990234375), SC_(0.6437175227896219693144155889099646006989e-7) }, 
+      { SC_(0), SC_(14.85147190093994140625), SC_(0.2389561472425127015102225830183211311355e-7) }, 
+      { SC_(0), SC_(15.408351898193359375), SC_(0.1319719418545972741015149904348811051425e-7) }, 
+      { SC_(0), SC_(24.2687816619873046875), SC_(0.11889239267601390541015398133557006754e-11) }, 
+      { SC_(0), SC_(27.344074249267578125), SC_(0.4872549010302229290835986011540914041326e-13) }, 
+      { SC_(0), SC_(27.3610286712646484375), SC_(0.4787665585558497600241038034910791656316e-13) }, 
+      { SC_(0), SC_(31.6179637908935546875), SC_(0.5868929583967368539612302367590281628486e-15) }, 
+      { SC_(0), SC_(36.2919464111328125), SC_(0.4773068588658948995725058196271779063743e-17) }, 
+      { SC_(0), SC_(39.905292510986328125), SC_(0.1170364567486045719639244754262245531629e-18) }, 
+      { SC_(0), SC_(40.0140228271484375), SC_(0.1046931993792806191360983778308485111274e-18) }, 
+      { SC_(0), SC_(40.73618316650390625), SC_(0.4994822992740385189281065329903525138214e-19) }, 
+      { SC_(0), SC_(41.75042724609375), SC_(0.1767497897232480324288472314518314166362e-19) }, 
+      { SC_(0), SC_(45.2895965576171875), SC_(0.4731291164415236007530801800668192107248e-21) }, 
+      { SC_(0), SC_(45.668792724609375), SC_(0.32112623945754987507866272619248827473e-21) }, 
+      { SC_(0), SC_(47.858348846435546875), SC_(0.3431037557038677071409196944306329415725e-22) }, 
+      { SC_(0), SC_(47.87534332275390625), SC_(0.3372024134373767813623270201540442231994e-22) }, 
+      { SC_(0), SC_(48.244426727294921875), SC_(0.2313473555301647492330120635703080053112e-22) }, 
+      { SC_(0), SC_(48.384746551513671875), SC_(0.2004763256428269587290401533485854661334e-22) }, 
+      { SC_(0), SC_(48.443389892578125), SC_(0.1888289416818380641901072855471819672105e-22) }, 
+      { SC_(0), SC_(48.52964019775390625), SC_(0.1729171153596841734848571786533234373322e-22) }, 
+      { SC_(0), SC_(49.055484771728515625), SC_(0.1011081315291844758145446920376094243904e-22) }, 
+      { SC_(0), SC_(49.64406585693359375), SC_(0.554611404844874116390457034845700516171e-23) }, 
+      { SC_(0), SC_(49.82306671142578125), SC_(0.4620474736636545203207618442180434004238e-23) }, 
+      { SC_(1), SC_(4.8770198822021484375), SC_(0.001326894275438860249857941044254174502639) }, 
+      { SC_(1), SC_(5.4930877685546875), SC_(0.0006460832160891306352056104536312996827518) }, 
+      { SC_(1), SC_(6.349340915679931640625), SC_(0.0002414929458653428650902712691508606087705) }, 
+      { SC_(1), SC_(6.77385044097900390625), SC_(0.0001491057337258556360697724884053639712183) }, 
+      { SC_(1), SC_(7.88065433502197265625), SC_(0.4302184733486055021456160704267900644151e-4) }, 
+      { SC_(1), SC_(9.41909885406494140625), SC_(0.785158179791932713400818863165202252408e-5) }, 
+      { SC_(1), SC_(11.0517024993896484375), SC_(0.1323971054451696237675804650020934283271e-5) }, 
+      { SC_(1), SC_(13.9249114990234375), SC_(0.6030052082140414872763484176234936031379e-7) }, 
+      { SC_(1), SC_(14.85147190093994140625), SC_(0.2246847323452812310807076843921206699284e-7) }, 
+      { SC_(1), SC_(15.408351898193359375), SC_(0.1243451611444526471238603318210383094864e-7) }, 
+      { SC_(1), SC_(24.2687816619873046875), SC_(0.1143540865960474355116790661840197166523e-11) }, 
+      { SC_(1), SC_(27.344074249267578125), SC_(0.4706136215074688573466876839711291930065e-13) }, 
+      { SC_(1), SC_(27.3610286712646484375), SC_(0.4624246647932169908912545804468933517039e-13) }, 
+      { SC_(1), SC_(31.6179637908935546875), SC_(0.5694058988300047405430136315685981910904e-15) }, 
+      { SC_(1), SC_(36.2919464111328125), SC_(0.4648256808579637348536682966321094152884e-17) }, 
+      { SC_(1), SC_(39.905292510986328125), SC_(0.1142405282651606532309094911197076666306e-18) }, 
+      { SC_(1), SC_(40.0140228271484375), SC_(0.1021986300809498211588191270716148887523e-18) }, 
+      { SC_(1), SC_(40.73618316650390625), SC_(0.487782450682026156951156991212514994025e-19) }, 
+      { SC_(1), SC_(41.75042724609375), SC_(0.1727057820230415908617717666461962953748e-19) }, 
+      { SC_(1), SC_(45.2895965576171875), SC_(0.4631155735799306610393016753551769399309e-21) }, 
+      { SC_(1), SC_(45.668792724609375), SC_(0.3143839170407425907322861671102497142403e-21) }, 
+      { SC_(1), SC_(47.858348846435546875), SC_(0.3362168462409445527866973776887649345695e-22) }, 
+      { SC_(1), SC_(47.87534332275390625), SC_(0.3304362677594583967844855615677058007508e-22) }, 
+      { SC_(1), SC_(48.244426727294921875), SC_(0.226739399060424385006440097684052080086e-22) }, 
+      { SC_(1), SC_(48.384746551513671875), SC_(0.1964943928572394204174413988519401201072e-22) }, 
+      { SC_(1), SC_(48.443389892578125), SC_(0.1850827201970609263420459500557652587842e-22) }, 
+      { SC_(1), SC_(48.52964019775390625), SC_(0.1694924366999538118474174187456764816795e-22) }, 
+      { SC_(1), SC_(49.055484771728515625), SC_(0.9912630736365412803849736897421968989741e-23) }, 
+      { SC_(1), SC_(49.64406585693359375), SC_(0.5438645188377533724985296541041944657958e-23) }, 
+      { SC_(1), SC_(49.82306671142578125), SC_(0.453125198123893560872142720624255521908e-23) }, 
+      { SC_(2), SC_(4.8770198822021484375), SC_(0.001148398029861054199345012264954555516672) }, 
+      { SC_(2), SC_(5.4930877685546875), SC_(0.0005661261928922653194607642596729661834247) }, 
+      { SC_(2), SC_(6.349340915679931640625), SC_(0.0002145777273488298919718327983230556847796) }, 
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+      { SC_(19), SC_(6.77385044097900390625), SC_(0.4563629608692565947786319220663650516549e-4) }, 
+      { SC_(19), SC_(7.88065433502197265625), SC_(0.1443270554196663312646183655379321816718e-4) }, 
+      { SC_(19), SC_(9.41909885406494140625), SC_(0.29229375975083585076493105009646691193e-5) }, 
+      { SC_(19), SC_(11.0517024993896484375), SC_(0.5388187850716913097656101948535340106559e-6) }, 
+      { SC_(19), SC_(13.9249114990234375), SC_(0.2769774827344526024771822366860889367455e-7) }, 
+      { SC_(19), SC_(14.85147190093994140625), SC_(0.1065572314596267352295366530918149890449e-7) }, 
+      { SC_(19), SC_(15.408351898193359375), SC_(0.6003676313155847558727754397017594033951e-8) }, 
+      { SC_(19), SC_(24.2687816619873046875), SC_(0.673510094367160540559685869872164243268e-12) }, 
+      { SC_(19), SC_(27.344074249267578125), SC_(0.289993053831443280728704537691191408601e-13) }, 
+      { SC_(19), SC_(27.3610286712646484375), SC_(0.2850117596196444487754850323798614360794e-13) }, 
+      { SC_(19), SC_(31.6179637908935546875), SC_(0.36926858164899886274377174666388292089e-15) }, 
+      { SC_(19), SC_(36.2919464111328125), SC_(0.3152031486467603894636760424644054490708e-17) }, 
+      { SC_(19), SC_(39.905292510986328125), SC_(0.7971283471563883595647243305675430830003e-19) }, 
+      { SC_(19), SC_(40.0140228271484375), SC_(0.713670625520853508845859925787605624071e-19) }, 
+      { SC_(19), SC_(40.73618316650390625), SC_(0.3423968029396160381858047664609964057523e-19) }, 
+      { SC_(19), SC_(41.75042724609375), SC_(0.1220850361811720898162895334790244786434e-19) }, 
+      { SC_(19), SC_(45.2895965576171875), SC_(0.3348077781029727272690886420995939073007e-21) }, 
+      { SC_(19), SC_(45.668792724609375), SC_(0.2277906429392425943516822259098792365619e-21) }, 
+      { SC_(19), SC_(47.858348846435546875), SC_(0.2466258937525478225241536833849016808137e-22) }, 
+      { SC_(19), SC_(47.87534332275390625), SC_(0.2424079008386988642363753465963711935866e-22) }, 
+      { SC_(19), SC_(48.244426727294921875), SC_(0.1666655664849833148892461708398016166091e-22) }, 
+      { SC_(19), SC_(48.384746551513671875), SC_(0.1445416596516947735796394469778719792034e-22) }, 
+      { SC_(19), SC_(48.443389892578125), SC_(0.1361895170902993690500755665628455156467e-22) }, 
+      { SC_(19), SC_(48.52964019775390625), SC_(0.1247745693242413617880762275589768971805e-22) }, 
+      { SC_(19), SC_(49.055484771728515625), SC_(0.7317433348691693533972442490012924107111e-23) }, 
+      { SC_(19), SC_(49.64406585693359375), SC_(0.4026907655194597356087538417554343184765e-23) }, 
+      { SC_(19), SC_(49.82306671142578125), SC_(0.3358092679602377945368265530432149819446e-23) }
+   }};
+#undef SC_
+
diff --git a/test/expint_small_data.ipp b/test/expint_small_data.ipp
new file mode 100644
index 000000000..a8ec0db01
--- /dev/null
+++ b/test/expint_small_data.ipp
@@ -0,0 +1,385 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 380> expint_small_data = {{
+      { SC_(0), SC_(0.1730655412757187150418758392333984375e-5), SC_(577814.7758212256423775256378551874856003) }, 
+      { SC_(0), SC_(0.216575062950141727924346923828125e-5), SC_(461732.6762508792015318981937822200350918) }, 
+      { SC_(0), SC_(0.72700195232755504548549652099609375e-5), SC_(137550.2124589000541443257494936989244997) }, 
+      { SC_(0), SC_(0.14000004739500582218170166015625e-4), SC_(71427.54725445416496694480545527677490243) }, 
+      { SC_(0), SC_(0.17196454791701398789882659912109375e-4), SC_(58150.52089548332152905218845489376933772) }, 
+      { SC_(0), SC_(0.60085076256655156612396240234375e-4), SC_(16642.0678648645272946820823309167585461) }, 
+      { SC_(0), SC_(0.000116783194243907928466796875), SC_(8561.875962532232545332572615047016255041) }, 
+      { SC_(0), SC_(0.000149052008055150508880615234375), SC_(6708.067688223899497757367667879930968793) }, 
+      { SC_(0), SC_(0.0003985252114944159984588623046875), SC_(2508.25173755195584857212143870952023231) }, 
+      { SC_(0), SC_(0.00063875340856611728668212890625), SC_(1564.549694997861843953582226130571046846) }, 
+      { SC_(0), SC_(0.0010718167759478092193603515625), SC_(931.9958222627537459717559330883276580758) }, 
+      { SC_(0), SC_(0.00302191521041095256805419921875), SC_(329.9174784073144324156862883962096967334) }, 
+      { SC_(0), SC_(0.00499413348734378814697265625), SC_(199.2374290724703076159801092696400339127) }, 
+      { SC_(0), SC_(0.00928423367440700531005859375), SC_(106.7141098014748145666899963724983770114) }, 
+      { SC_(0), SC_(0.0241700224578380584716796875), SC_(40.38555342987263632091024457927399908981) }, 
+      { SC_(0), SC_(0.06227754056453704833984375), SC_(15.08765533838058040972104376703012409721) }, 
+      { SC_(0), SC_(0.12234418094158172607421875), SC_(7.232414021781513135268430322868745728174) }, 
+      { SC_(0), SC_(0.249557673931121826171875), SC_(3.122105326937778672022451656660829990212) }, 
+      { SC_(0), SC_(0.4912221431732177734375), SC_(1.245624088523070804276757644439503799036) }, 
+      { SC_(1), SC_(0.1730655412757187150418758392333984375e-5), SC_(12.68979643564902057445113029537557060384) }, 
+      { SC_(1), SC_(0.216575062950141727924346923828125e-5), SC_(12.46553004636203965518423078801621406614) }, 
+      { SC_(1), SC_(0.72700195232755504548549652099609375e-5), SC_(11.2545431860697943553517367149605754442) }, 
+      { SC_(1), SC_(0.14000004739500582218170166015625e-4), SC_(10.5992512248675236793183882919991723644) }, 
+      { SC_(1), SC_(0.17196454791701398789882659912109375e-4), SC_(10.39360884363072197965302323976810805946) }, 
+      { SC_(1), SC_(0.60085076256655156612396240234375e-4), SC_(9.142593481727702781399755039472990143275) }, 
+      { SC_(1), SC_(0.000116783194243907928466796875), SC_(8.478092497703841888257351897157795499674) }, 
+      { SC_(1), SC_(0.000149052008055150508880615234375), SC_(8.23414864712424722136034054262711272215) }, 
+      { SC_(1), SC_(0.0003985252114944159984588623046875), SC_(7.250922616359625879162196113845954202435) }, 
+      { SC_(1), SC_(0.00063875340856611728668212890625), SC_(6.779415066673595920390207059288727481393) }, 
+      { SC_(1), SC_(0.0010718167759478092193603515625), SC_(6.262256013645805034976972133526713777336) }, 
+      { SC_(1), SC_(0.00302191521041095256805419921875), SC_(5.227668441815221372703241290567350771159) }, 
+      { SC_(1), SC_(0.00499413348734378814697265625), SC_(4.727263598094615939046673594869014017738) }, 
+      { SC_(1), SC_(0.00928423367440700531005859375), SC_(4.111484685210341022101979530301768631054) }, 
+      { SC_(1), SC_(0.0241700224578380584716796875), SC_(3.169451246062171542238811993535958670845) }, 
+      { SC_(1), SC_(0.06227754056453704833984375), SC_(2.260259939322263892205804391830568328218) }, 
+      { SC_(1), SC_(0.12234418094158172607421875), SC_(1.642402990148853649294192107450058496557) }, 
+      { SC_(1), SC_(0.249557673931121826171875), SC_(1.045662095585737033852768372992425480117) }, 
+      { SC_(1), SC_(0.4912221431732177734375), SC_(0.570563675993986183667187214912446161025) }, 
+      { SC_(2), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.9999763076811966831897766561746894854348) }, 
+      { SC_(2), SC_(0.216575062950141727924346923828125e-5), SC_(0.9999708370221707573655426375521705456129) }, 
+      { SC_(2), SC_(0.72700195232755504548549652099609375e-5), SC_(0.999910909258214977122354162319349018702) }, 
+      { SC_(2), SC_(0.14000004739500582218170166015625e-4), SC_(0.9998376105258768057557573329394689665198) }, 
+      { SC_(2), SC_(0.17196454791701398789882659912109375e-4), SC_(0.9998040704684643561925140532604520761726) }, 
+      { SC_(2), SC_(0.60085076256655156612396240234375e-4), SC_(0.9993905833022821790211571622936164235556) }, 
+      { SC_(2), SC_(0.000116783194243907928466796875), SC_(0.9988931249016707081053405184509945116324) }, 
+      { SC_(2), SC_(0.000149052008055150508880615234375), SC_(0.9986236427091650503801677112391142850053) }, 
+      { SC_(2), SC_(0.0003985252114944159984588623046875), SC_(0.9967118787199152511223256805042743254983) }, 
+      { SC_(2), SC_(0.00063875340856611728668212890625), SC_(0.9950310760690411830694553942700458450716) }, 
+      { SC_(2), SC_(0.0010718167759478092193603515625), SC_(0.9922167663637865286439901988209755749909) }, 
+      { SC_(2), SC_(0.00302191521041095256805419921875), SC_(0.9811850754001837523201422600369909453641) }, 
+      { SC_(2), SC_(0.00499413348734378814697265625), SC_(0.9714097310243611715783408142596006996882) }, 
+      { SC_(2), SC_(0.00928423367440700531005859375), SC_(0.9525867471869806036208170870856088617673) }, 
+      { SC_(2), SC_(0.0241700224578380584716796875), SC_(0.899514025575894945250135338740921424329) }, 
+      { SC_(2), SC_(0.06227754056453704833984375), SC_(0.7988586373022102057246901625949836282736) }, 
+      { SC_(2), SC_(0.12234418094158172607421875), SC_(0.6839053211195040219693434236179451026624) }, 
+      { SC_(2), SC_(0.249557673931121826171875), SC_(0.5181923428662377685394762787685048866534) }, 
+      { SC_(2), SC_(0.4912221431732177734375), SC_(0.331604622613933458758263418893725943234) }, 
+      { SC_(3), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.4999982693658376543091737671690095008434) }, 
+      { SC_(3), SC_(0.216575062950141727924346923828125e-5), SC_(0.4999978342821229854793933090060882477432) }, 
+      { SC_(3), SC_(0.72700195232755504548549652099609375e-5), SC_(0.499992730317535704456607299984943350278) }, 
+      { SC_(3), SC_(0.14000004739500582218170166015625e-4), SC_(0.4999860011809870076130562371694389700641) }, 
+      { SC_(3), SC_(0.17196454791701398789882659912109375e-4), SC_(0.4999828053037840548845718384848723742553) }, 
+      { SC_(3), SC_(0.60085076256655156612396240234375e-4), SC_(0.4999399341347037428568024707226853352885) }, 
+      { SC_(3), SC_(0.000116783194243907928466796875), SC_(0.4998832848474067892057518818832512203809) }, 
+      { SC_(3), SC_(0.000149052008055150508880615234375), SC_(0.4998510561202031850646246064500000857424) }, 
+      { SC_(3), SC_(0.0003985252114944159984588623046875), SC_(0.4996021696884318821443832438164013431266) }, 
+      { SC_(3), SC_(0.00063875340856611728668212890625), SC_(0.4993629355297475610790650823685848821969) }, 
+      { SC_(3), SC_(0.0010718167759478092193603515625), SC_(0.4989326414194633805099515586523952746467) }, 
+      { SC_(3), SC_(0.00302191521041095256805419921875), SC_(0.4970087940379552304612639268845472514031) }, 
+      { SC_(3), SC_(0.00499413348734378814697265625), SC_(0.4950834832977331977677179906437250733682) }, 
+      { SC_(3), SC_(0.00928423367440700531005859375), SC_(0.4909573468985959698257136388230010783411) }, 
+      { SC_(3), SC_(0.0241700224578380584716796875), SC_(0.4771892295864653755887373794289668954978) }, 
+      { SC_(3), SC_(0.06227754056453704833984375), SC_(0.4449355580849156787345354284758576392931) }, 
+      { SC_(3), SC_(0.12234418094158172607421875), SC_(0.400585966685657543850238947546362051285) }, 
+      { SC_(3), SC_(0.249557673931121826171875), SC_(0.3249132337119700131594392776225790919829) }, 
+      { SC_(3), SC_(0.4912221431732177734375), SC_(0.2244933004729631534551199436414075158278) }, 
+      { SC_(4), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.3333324680071245262715865645284048381042) }, 
+      { SC_(4), SC_(0.216575062950141727924346923828125e-5), SC_(0.3333322504603637963103582665303151431887) }, 
+      { SC_(4), SC_(0.72700195232755504548549652099609375e-5), SC_(0.3333296983499974493372224529199642401407) }, 
+      { SC_(4), SC_(0.14000004739500582218170166015625e-4), SC_(0.3333263334289579635589330888999452889502) }, 
+      { SC_(4), SC_(0.17196454791701398789882659912109375e-4), SC_(0.3333247352537861483970485437943510891261) }, 
+      { SC_(4), SC_(0.60085076256655156612396240234375e-4), SC_(0.3333032925999163851950867018863045026453) }, 
+      { SC_(4), SC_(0.000116783194243907928466796875), SC_(0.3332749485526314189805479992822408219843) }, 
+      { SC_(4), SC_(0.000149052008055150508880615234375), SC_(0.3332588184320001054426253340418943955967) }, 
+      { SC_(4), SC_(0.0003985252114944159984588623046875), SC_(0.3331341500429304879323886027889306418722) }, 
+      { SC_(4), SC_(0.00063875340856611728668212890625), SC_(0.333014160257927408406635357113451451623) }, 
+      { SC_(4), SC_(0.0010718167759478092193603515625), SC_(0.3327979976797836072508267743048393663433) }, 
+      { SC_(4), SC_(0.00302191521041095256805419921875), SC_(0.3318269092483597307661485853343450609366) }, 
+      { SC_(4), SC_(0.00499413348734378814697265625), SC_(0.3308486011533795870796983158583450430641) }, 
+      { SC_(4), SC_(0.00928423367440700531005859375), SC_(0.3287335230068152237322561573905418455842) }, 
+      { SC_(4), SC_(0.0241700224578380584716796875), SC_(0.321528686325499046761296643527534796266) }, 
+      { SC_(4), SC_(0.06227754056453704833984375), SC_(0.3039708583641707588487204824261130758999) }, 
+      { SC_(4), SC_(0.12234418094158172607421875), SC_(0.2786114692448072420299674008584420739148) }, 
+      { SC_(4), SC_(0.249557673931121826171875), SC_(0.2326869174413194941490162582911016352083) }, 
+      { SC_(4), SC_(0.4912221431732177734375), SC_(0.1672006847220435577039399872043804888457) }, 
+      { SC_(5), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.2499994231156112054464478225868175766528) }, 
+      { SC_(5), SC_(0.216575062950141727924346923828125e-5), SC_(0.2499992780842961167818165530973580904202) }, 
+      { SC_(5), SC_(0.72700195232755504548549652099609375e-5), SC_(0.2499975766733721400779896480513000531392) }, 
+      { SC_(5), SC_(0.14000004739500582218170166015625e-4), SC_(0.2499953333807530756689397632193171572859) }, 
+      { SC_(5), SC_(0.17196454791701398789882659912109375e-4), SC_(0.2499942679223314330462557114927736244578) }, 
+      { SC_(5), SC_(0.60085076256655156612396240234375e-4), SC_(0.2499799725437657315484048809036607807089) }, 
+      { SC_(5), SC_(0.000116783194243907928466796875), SC_(0.2499610756778986060072655969409855563922) }, 
+      { SC_(5), SC_(0.000149052008055150508880615234375), SC_(0.2499503215508885359803723774515238310774) }, 
+      { SC_(5), SC_(0.0003985252114944159984588623046875), SC_(0.2498671979578819359594098594467548202963) }, 
+      { SC_(5), SC_(0.00063875340856611728668212890625), SC_(0.2497871841552494748465221110450611975769) }, 
+      { SC_(5), SC_(0.0010718167759478092193603515625), SC_(0.2496430147343942808033948163209649673697) }, 
+      { SC_(5), SC_(0.00302191521041095256805419921875), SC_(0.2489949733488023051271180731389395708097) }, 
+      { SC_(5), SC_(0.00499413348734378814697265625), SC_(0.2483415035962114594950005069148420510374) }, 
+      { SC_(5), SC_(0.00928423367440700531005859375), SC_(0.2469266732272532034223040397507562406243) }, 
+      { SC_(5), SC_(0.0241700224578380584716796875), SC_(0.2420870944507284922750390337420489762581) }, 
+      { SC_(5), SC_(0.06227754056453704833984375), SC_(0.2301728774743846881561522041544016024552) }, 
+      { SC_(5), SC_(0.12234418094158172607421875), SC_(0.2126893194298959031515617592899204600847) }, 
+      { SC_(5), SC_(0.249557673931121826171875), SC_(0.1802691343219245000486413064752883220342) }, 
+      { SC_(5), SC_(0.4912221431732177734375), SC_(0.1324363639158242626230482022654728761494) }, 
+      { SC_(6), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.1999995673366460049641967287178764376758) }, 
+      { SC_(6), SC_(0.216575062950141727924346923828125e-5), SC_(0.1999994585631243697640119955956215158009) }, 
+      { SC_(6), SC_(0.72700195232755504548549652099609375e-5), SC_(0.1999981825039280130703307389527539339626) }, 
+      { SC_(6), SC_(0.14000004739500582218170166015625e-4), SC_(0.1999965000314815849734869604432305581943) }, 
+      { SC_(6), SC_(0.17196454791701398789882659912109375e-4), SC_(0.1999957009355879937792673172585206209907) }, 
+      { SC_(6), SC_(0.60085076256655156612396240234375e-4), SC_(0.1999849793326204915379339620663404213245) }, 
+      { SC_(6), SC_(0.000116783194243907928466796875), SC_(0.1999708064743587132406006868918039255621) }, 
+      { SC_(6), SC_(0.000149052008055150508880615234375), SC_(0.1999627407004604659688373925079291930869) }, 
+      { SC_(6), SC_(0.0003985252114944159984588623046875), SC_(0.1999003951622435866430026938266496921632) }, 
+      { SC_(6), SC_(0.00063875340856611728668212890625), SC_(0.1998403796271336271407932741008590942797) }, 
+      { SC_(6), SC_(0.0010718167759478092193603515625), SC_(0.1997322371686603290924085933634566379327) }, 
+      { SC_(6), SC_(0.00302191521041095256805419921875), SC_(0.1992460408964423756244108293541117608605) }, 
+      { SC_(6), SC_(0.00499413348734378814697265625), SC_(0.1987556131687399264370086252838978909125) }, 
+      { SC_(6), SC_(0.00928423367440700531005859375), SC_(0.1976932413637066757394817471625577237966) }, 
+      { SC_(6), SC_(0.0241700224578380584716796875), SC_(0.1940536965725227157665771390371888397218) }, 
+      { SC_(6), SC_(0.06227754056453704833984375), SC_(0.1850574933291966669077136179077438196585) }, 
+      { SC_(6), SC_(0.12234418094158172607421875), SC_(0.1717644938289194367486550307278864140087) }, 
+      { SC_(6), SC_(0.249557673931121826171875), SC_(0.1468315594631200476064231753398882300411) }, 
+      { SC_(6), SC_(0.4912221431732177734375), SC_(0.1093644919671378757189796182413879395249) }, 
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+      { SC_(15), SC_(0.17196454791701398789882659912109375e-4), SC_(0.07142724863667819098544040349933483459537) }, 
+      { SC_(15), SC_(0.60085076256655156612396240234375e-4), SC_(0.07142394965005100519504785729035742912749) }, 
+      { SC_(15), SC_(0.000116783194243907928466796875), SC_(0.07141958867417625278045171566133804924267) }, 
+      { SC_(15), SC_(0.000149052008055150508880615234375), SC_(0.07141710681512763831624656689212439533833) }, 
+      { SC_(15), SC_(0.0003985252114944159984588623046875), SC_(0.07139792225971062733216224219889843492458) }, 
+      { SC_(15), SC_(0.00063875340856611728668212890625), SC_(0.07137945354728793815621837897126096496695) }, 
+      { SC_(15), SC_(0.0010718167759478092193603515625), SC_(0.07134617183191733372828052493089770600179) }, 
+      { SC_(15), SC_(0.00302191521041095256805419921875), SC_(0.07119649649342545512786733526338407058593) }, 
+      { SC_(15), SC_(0.00499413348734378814697265625), SC_(0.07104544465318913130029520977272205803238) }, 
+      { SC_(15), SC_(0.00928423367440700531005859375), SC_(0.07071797905446335190765005167612134211414) }, 
+      { SC_(15), SC_(0.0241700224578380584716796875), SC_(0.06959346765795077653558839105295821251784) }, 
+      { SC_(15), SC_(0.06227754056453704833984375), SC_(0.0667959972998317143729966269635932436109) }, 
+      { SC_(15), SC_(0.12234418094158172607421875), SC_(0.06261431370954492875982416200591991469247) }, 
+      { SC_(15), SC_(0.249557673931121826171875), SC_(0.05460660412773958169800526198387768453117) }, 
+      { SC_(15), SC_(0.4912221431732177734375), SC_(0.0421188330888019402635824495314924339382) }, 
+      { SC_(16), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.06666654304853809699945783166277385282533) }, 
+      { SC_(16), SC_(0.216575062950141727924346923828125e-5), SC_(0.06666651197037353362502658679389514469466) }, 
+      { SC_(16), SC_(0.72700195232755504548549652099609375e-5), SC_(0.0666661473815906706976833386950951600242) }, 
+      { SC_(16), SC_(0.14000004739500582218170166015625e-4), SC_(0.0666656666738665594423295905799989143287) }, 
+      { SC_(16), SC_(0.17196454791701398789882659912109375e-4), SC_(0.06666543835984096023360798850623321457013) }, 
+      { SC_(16), SC_(0.60085076256655156612396240234375e-4), SC_(0.06666237501435694077352966293019493851952) }, 
+      { SC_(16), SC_(0.000116783194243907928466796875), SC_(0.06665832553446339453823619449641153525662) }, 
+      { SC_(16), SC_(0.000149052008055150508880615234375), SC_(0.06665602094909754909286909682461902922413) }, 
+      { SC_(16), SC_(0.0003985252114944159984588623046875), SC_(0.06663820668780405347821578869651693922563) }, 
+      { SC_(16), SC_(0.00063875340856611728668212890625), SC_(0.06662105711211390111652234096260015918844) }, 
+      { SC_(16), SC_(0.0010718167759478092193603515625), SC_(0.06659015249270820342229697822760925298911) }, 
+      { SC_(16), SC_(0.00302191521041095256805419921875), SC_(0.0664511664269206027424005742189069408551) }, 
+      { SC_(16), SC_(0.00499413348734378814697265625), SC_(0.06631090040192273720685590565904807744936) }, 
+      { SC_(16), SC_(0.00928423367440700531005859375), SC_(0.06600681130071304531237155750190562009028) }, 
+      { SC_(16), SC_(0.0241700224578380584716796875), SC_(0.06496251051306859685686412141792258653208) }, 
+      { SC_(16), SC_(0.06227754056453704833984375), SC_(0.06236414512855743773641213229896183548994) }, 
+      { SC_(16), SC_(0.12234418094158172607421875), SC_(0.05847888485328378106294664079191164865064) }, 
+      { SC_(16), SC_(0.249557673931121826171875), SC_(0.05103452307007735926554556327773818214919) }, 
+      { SC_(16), SC_(0.4912221431732177734375), SC_(0.0394125620596434965123587499491500472372) }, 
+      { SC_(17), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.06249988462307945307908017581791268977313) }, 
+      { SC_(17), SC_(0.216575062950141727924346923828125e-5), SC_(0.06249985561679221676774980550769608140614) }, 
+      { SC_(17), SC_(0.72700195232755504548549652099609375e-5), SC_(0.06249951533391939041337864186116416893234) }, 
+      { SC_(17), SC_(0.14000004739500582218170166015625e-4), SC_(0.06249906667335066952129732040559092146342) }, 
+      { SC_(17), SC_(0.17196454791701398789882659912109375e-4), SC_(0.06249885358024184723716755518368815597862) }, 
+      { SC_(17), SC_(0.60085076256655156612396240234375e-4), SC_(0.06249599445718307493973764409020902900864) }, 
+      { SC_(17), SC_(0.000116783194243907928466796875), SC_(0.06249221494077931309495003783005590817055) }, 
+      { SC_(17), SC_(0.000149052008055150508880615234375), SC_(0.06249006399286700569832074698786566925701) }, 
+      { SC_(17), SC_(0.0003985252114944159984588623046875), SC_(0.06247343732398223434411132037030316052086) }, 
+      { SC_(17), SC_(0.00063875340856611728668212890625), SC_(0.06245743100772817456409663607219418267563) }, 
+      { SC_(17), SC_(0.0010718167759478092193603515625), SC_(0.06242858656074609674340793412520265769202) }, 
+      { SC_(17), SC_(0.00302191521041095256805419921875), SC_(0.0622988647743072145354092596903005273557) }, 
+      { SC_(17), SC_(0.00499413348734378814697265625), SC_(0.0621679469359271011639958295023269764062) }, 
+      { SC_(17), SC_(0.00928423367440700531005859375), SC_(0.06188411931831255179325908903786178409114) }, 
+      { SC_(17), SC_(0.0241700224578380584716796875), SC_(0.0609093492521388775469551843749806027059) }, 
+      { SC_(17), SC_(0.06227754056453704833984375), SC_(0.0584836363613583832127398530378980108328) }, 
+      { SC_(17), SC_(0.12234418094158172607421875), SC_(0.05485557615346988551034803028047672930453) }, 
+      { SC_(17), SC_(0.249557673931121826171875), SC_(0.04790058039318774966694255640723585925481) }, 
+      { SC_(17), SC_(0.4912221431732177734375), SC_(0.03703236319685020300958697194277916844504) }, 
+      { SC_(18), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.05882342124590124743503668917708420145518) }, 
+      { SC_(18), SC_(0.216575062950141727924346923828125e-5), SC_(0.05882339405250671111581257451611106191635) }, 
+      { SC_(18), SC_(0.72700195232755504548549652099609375e-5), SC_(0.05882307503730626938175588111928585498593) }, 
+      { SC_(18), SC_(0.14000004739500582218170166015625e-4), SC_(0.05882265441800179218625554918997835286824) }, 
+      { SC_(18), SC_(0.17196454791701398789882659912109375e-4), SC_(0.05882245464319743258599789131069371575228) }, 
+      { SC_(18), SC_(0.60085076256655156612396240234375e-4), SC_(0.05881977421483662888664297358478870305647) }, 
+      { SC_(18), SC_(0.000116783194243907928466796875), SC_(0.0588162309167159831370507751429249096136) }, 
+      { SC_(18), SC_(0.000149052008055150508880615234375), SC_(0.05881421440177187580343423242512009971648) }, 
+      { SC_(18), SC_(0.0003985252114944159984588623046875), SC_(0.05879862687937101718003654785828567378979) }, 
+      { SC_(18), SC_(0.00063875340856611728668212890625), SC_(0.05878362092082452731016712169968859340322) }, 
+      { SC_(18), SC_(0.0010718167759478092193603515625), SC_(0.05875657914165397869174629461513706700597) }, 
+      { SC_(18), SC_(0.00302191521041095256805419921875), SC_(0.05863496378190809879409693964081298572753) }, 
+      { SC_(18), SC_(0.00499413348734378814697265625), SC_(0.05851222596691027379082269719377427641588) }, 
+      { SC_(18), SC_(0.00928423367440700531005859375), SC_(0.05824612853698429641923284472585223102581) }, 
+      { SC_(18), SC_(0.0241700224578380584716796875), SC_(0.05733220900193670301704905656625237704967) }, 
+      { SC_(18), SC_(0.06227754056453704833984375), SC_(0.05505763825434673012796407470855753202628) }, 
+      { SC_(18), SC_(0.12234418094158172607421875), SC_(0.0516548534818056121546604299679736700432) }, 
+      { SC_(18), SC_(0.249557673931121826171875), SC_(0.04512890504327541405581236239109694591622) }, 
+      { SC_(18), SC_(0.4912221431732177734375), SC_(0.03492276573742135444124721201053141343969) }, 
+      { SC_(19), SC_(0.1730655412757187150418758392333984375e-5), SC_(0.05555545375238958055070296836154042278148) }, 
+      { SC_(19), SC_(0.216575062950141727924346923828125e-5), SC_(0.05555542815860627978655071793595712560455) }, 
+      { SC_(19), SC_(0.72700195232755504548549652099609375e-5), SC_(0.05555512790899996177912196960367217844985) }, 
+      { SC_(19), SC_(0.14000004739500582218170166015625e-4), SC_(0.05555473203198997035603620704636908809792) }, 
+      { SC_(19), SC_(0.17196454791701398789882659912109375e-4), SC_(0.0555545440086324706169620903193223815888) }, 
+      { SC_(19), SC_(0.60085076256655156612396240234375e-4), SC_(0.05555202125212201603991344567350516412012) }, 
+      { SC_(19), SC_(0.000116783194243907928466796875), SC_(0.05554868638207377961222457350655311699087) }, 
+      { SC_(19), SC_(0.000149052008055150508880615234375), SC_(0.0555467884846047083384104067993782562285) }, 
+      { SC_(19), SC_(0.0003985252114944159984588623046875), SC_(0.05553211785855094070193498404565764766408) }, 
+      { SC_(19), SC_(0.00063875340856611728668212890625), SC_(0.05551799457292957769783835164124369758407) }, 
+      { SC_(19), SC_(0.0010718167759478092193603515625), SC_(0.05549254339595949030608724637993842293557) }, 
+      { SC_(19), SC_(0.00302191521041095256805419921875), SC_(0.05537808090503200278730106215360027103479) }, 
+      { SC_(19), SC_(0.00499413348734378814697265625), SC_(0.05526256103311035590358747232544709551335) }, 
+      { SC_(19), SC_(0.00928423367440700531005859375), SC_(0.05501210894918067939819530617078899142577) }, 
+      { SC_(19), SC_(0.0241700224578380584716796875), SC_(0.05415188958850589857220572747127058337905) }, 
+      { SC_(19), SC_(0.06227754056453704833984375), SC_(0.05201073405888765875221070931942632402262) }, 
+      { SC_(19), SC_(0.12234418094158172607421875), SC_(0.04880689438802118463144973826036250259302) }, 
+      { SC_(19), SC_(0.249557673931121826171875), SC_(0.04266017103271657719951582163012671039402) }, 
+      { SC_(19), SC_(0.4912221431732177734375), SC_(0.03304018325118980221254092304969558212594) }
+   }};
+#undef SC_
+
diff --git a/test/expinti_data.ipp b/test/expinti_data.ipp
new file mode 100644
index 000000000..da876b5eb
--- /dev/null
+++ b/test/expinti_data.ipp
@@ -0,0 +1,342 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 337> expinti_data = {{
+      { SC_(-49.689971923828125), SC_(-0.5189914452467706181911213069148082266893e-23) }, 
+      { SC_(-49.490234375), SC_(-0.6362401135264284153452455085506782750647e-23) }, 
+      { SC_(-49.47381591796875), SC_(-0.6469829627301154800340680350229540167762e-23) }, 
+      { SC_(-49.109668731689453125), SC_(-0.937965617499186961883342318134168114907e-23) }, 
+      { SC_(-48.69077301025390625), SC_(-0.1438002258908106326351299430868912629378e-22) }, 
+      { SC_(-48.5106964111328125), SC_(-0.1728000132640339028589502655738823027867e-22) }, 
+      { SC_(-48.044872283935546875), SC_(-0.2779439615740334951105570945539716295032e-22) }, 
+      { SC_(-46.498386383056640625), SC_(-0.1347452831431197364179115494975704338441e-21) }, 
+      { SC_(-46.225093841552734375), SC_(-0.1781193691784135039948913637371768811083e-21) }, 
+      { SC_(-46.21092987060546875), SC_(-0.1807144449606719884758204680891841205212e-21) }, 
+      { SC_(-46.07171630859375), SC_(-0.2083224907084183832424058026703771220474e-21) }, 
+      { SC_(-45.99146270751953125), SC_(-0.2261161370639941533874318532661368660359e-21) }, 
+      { SC_(-45.54817962646484375), SC_(-0.3556041033058530933762241390777221084271e-21) }, 
+      { SC_(-45.04344940185546875), SC_(-0.5955350514558786142053309726857087311429e-21) }, 
+      { SC_(-44.921146392822265625), SC_(-0.6748061149415831787816898069300771337011e-21) }, 
+      { SC_(-44.366191864013671875), SC_(-0.1189810693892140146725035626514689534384e-20) }, 
+      { SC_(-44.065486907958984375), SC_(-0.1617943260346693355541238773884456402131e-20) }, 
+      { SC_(-42.564510345458984375), SC_(-0.7508521784292956555049663090063210339236e-20) }, 
+      { SC_(-41.65602874755859375), SC_(-0.1902237115363634179207156972256911270036e-19) }, 
+      { SC_(-41.643665313720703125), SC_(-0.1926460223216498626564145997341831122167e-19) }, 
+      { SC_(-41.46872711181640625), SC_(-0.2304209021566303248261300380232548536606e-19) }, 
+      { SC_(-41.400691986083984375), SC_(-0.2470393735589908561748312777657558449938e-19) }, 
+      { SC_(-40.7796478271484375), SC_(-0.4665489090348590088892832574733877627252e-19) }, 
+      { SC_(-40.712055206298828125), SC_(-0.4999841334502210157248794528480866083337e-19) }, 
+      { SC_(-39.510929107666015625), SC_(-0.1711205236582734104034468188313993053133e-18) }, 
+      { SC_(-39.3155059814453125), SC_(-0.2090623264737543134488804288570287187466e-18) }, 
+      { SC_(-39.270557403564453125), SC_(-0.2189181301371969956898734656820283591514e-18) }, 
+      { SC_(-38.26819610595703125), SC_(-0.6117321854640996737992349893398315143733e-18) }, 
+      { SC_(-37.9152069091796875), SC_(-0.8785955246457078845733834215638759432102e-18) }, 
+      { SC_(-37.628902435302734375), SC_(-0.1178529325141498446240403317681089430123e-17) }, 
+      { SC_(-36.91025543212890625), SC_(-0.2463830668835851637664366500894910731401e-17) }, 
+      { SC_(-36.849811553955078125), SC_(-0.26215321484857982843437445475200392826e-17) }, 
+      { SC_(-36.434917449951171875), SC_(-0.4013604158054956102381643294616861600937e-17) }, 
+      { SC_(-36.22989654541015625), SC_(-0.4954070919347881798661389820765284703293e-17) }, 
+      { SC_(-36.151371002197265625), SC_(-0.5370115748619942846995056236200542722029e-17) }, 
+      { SC_(-36.0314483642578125), SC_(-0.607395305918129149416531788551080247298e-17) }, 
+      { SC_(-35.710315704345703125), SC_(-0.8447444058571321223562848170132272760574e-17) }, 
+      { SC_(-35.3704376220703125), SC_(-0.1197781809600591211033914907221945799548e-16) }, 
+      { SC_(-35.097530364990234375), SC_(-0.1585533750794002114788183801172421930711e-16) }, 
+      { SC_(-35.032459259033203125), SC_(-0.1695197166162417180772352306691754347417e-16) }, 
+      { SC_(-34.819854736328125), SC_(-0.2109244705480778173400075610148135850665e-16) }, 
+      { SC_(-34.751312255859375), SC_(-0.2263224452346398759852695717206224969765e-16) }, 
+      { SC_(-34.3925018310546875), SC_(-0.3272986079708841109973691119640729899672e-16) }, 
+      { SC_(-34.054973602294921875), SC_(-0.4631254422748072673716271830348503655722e-16) }, 
+      { SC_(-33.990711212158203125), SC_(-0.4947724616135280674694624593161655499417e-16) }, 
+      { SC_(-33.597461700439453125), SC_(-0.7414940191228214696888223680604909022873e-16) }, 
+      { SC_(-33.57765960693359375), SC_(-0.756757300887760805540854651208858682068e-16) }, 
+      { SC_(-33.2384185791015625), SC_(-0.107294068831277583736449351876748813907e-15) }, 
+      { SC_(-33.01177215576171875), SC_(-0.1354864993921957916546792647862260697468e-15) }, 
+      { SC_(-32.66255950927734375), SC_(-0.1941093737430240934530108031230878545462e-15) }, 
+      { SC_(-32.613666534423828125), SC_(-0.204132772872516639905834010047613657569e-15) }, 
+      { SC_(-32.159946441650390625), SC_(-0.3257412136825485821320656994134128511202e-15) }, 
+      { SC_(-32.11270904541015625), SC_(-0.3419855833378806479533913787891698469742e-15) }, 
+      { SC_(-31.7786407470703125), SC_(-0.4825063941260257502369727213840286372208e-15) }, 
+      { SC_(-31.169464111328125), SC_(-0.9041208285654553216232000743485732341508e-15) }, 
+      { SC_(-30.8748321533203125), SC_(-0.1225142484842369432707212786481995255584e-14) }, 
+      { SC_(-29.9968280792236328125), SC_(-0.3031462122352020681576569789998943438361e-14) }, 
+      { SC_(-29.7701435089111328125), SC_(-0.3830838750986454571203218948391228454923e-14) }, 
+      { SC_(-29.4440135955810546875), SC_(-0.5364965948171210691720366951042121092755e-14) }, 
+      { SC_(-29.2779827117919921875), SC_(-0.6368731799234152625106787139014919307596e-14) }, 
+      { SC_(-28.374523162841796875), SC_(-0.1620330664359454781224975910217836859007e-13) }, 
+      { SC_(-28.049365997314453125), SC_(-0.2268099668304392203466560599584613615573e-13) }, 
+      { SC_(-27.112514495849609375), SC_(-0.5981365620673597072402185048412869627752e-13) }, 
+      { SC_(-26.877002716064453125), SC_(-0.7633855292124147317951832423188187154848e-13) }, 
+      { SC_(-26.688323974609375), SC_(-0.9282018389970155561367076378137998442654e-13) }, 
+      { SC_(-26.1038379669189453125), SC_(-0.1701256502901405065500817349298173344176e-12) }, 
+      { SC_(-25.6862545013427734375), SC_(-0.2623518232936666267503379731452152909371e-12) }, 
+      { SC_(-25.3806858062744140625), SC_(-0.3602510949927852845512603205232949953593e-12) }, 
+      { SC_(-24.812534332275390625), SC_(-0.6498766587291270315525780335102007560594e-12) }, 
+      { SC_(-24.6828327178955078125), SC_(-0.7436238775678827344102896240858028195429e-12) }, 
+      { SC_(-23.609222412109375), SC_(-0.2270985496456140144232209569165697838238e-11) }, 
+      { SC_(-23.6052227020263671875), SC_(-0.2280458712546087199917148252497757574451e-11) }, 
+      { SC_(-23.212253570556640625), SC_(-0.3433205132674812376797712986415901957608e-11) }, 
+      { SC_(-22.38077545166015625), SC_(-0.8166398479320291904581660909155149328026e-11) }, 
+      { SC_(-22.17484283447265625), SC_(-0.1012326926235613489340088549168765113258e-10) }, 
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+      { SC_(37.337249755859375), SC_(452229579706005.3198360961998657288335433) }, 
+      { SC_(37.371295928955078125), SC_(467452657592235.4557742032788566543129601) }, 
+      { SC_(37.47199249267578125), SC_(515545372809301.8307905963516087180550462) }, 
+      { SC_(37.700786590576171875), SC_(644036634222999.9230954385992851671021201) }, 
+      { SC_(37.77214813232421875), SC_(690331189582367.0242854882027008973993238) }, 
+      { SC_(37.7916412353515625), SC_(703546341004539.6440063503740195080075798) }, 
+      { SC_(38.007534027099609375), SC_(867977923035967.2387116719471097584367879) }, 
+      { SC_(38.030849456787109375), SC_(887892682109427.8216437485269424411635003) }, 
+      { SC_(38.232257843017578125), SC_(1080118946394155.640540236541909448482468) }, 
+      { SC_(38.828411102294921875), SC_(1929604067639860.142261254221961073466133) }, 
+      { SC_(38.8993072509765625), SC_(2067490868399521.448714428128264044795958) }, 
+      { SC_(39.070796966552734375), SC_(2443188466949830.286454990607186034125934) }, 
+      { SC_(39.57132720947265625), SC_(3977896133471904.309030036870273146195475) }, 
+      { SC_(39.619602203369140625), SC_(4169413741026091.435196275993524526107061) }, 
+      { SC_(39.903354644775390625), SC_(5496968390256242.123534199929484292088181) }, 
+      { SC_(40.292484283447265625), SC_(8031404394724528.542925073441994364789595) }, 
+      { SC_(40.337055206298828125), SC_(8387940643235804.328777240761144315540951) }, 
+      { SC_(40.40936279296875), SC_(9000350988468569.862069911874242513693811) }, 
+      { SC_(40.486545562744140625), SC_(9703503769049494.903270793598303590559637) }, 
+      { SC_(40.58036041259765625), SC_(10632608216710854.46031088764839485644682) }, 
+      { SC_(40.839870452880859375), SC_(13693091147862452.41874314869980290347395) }, 
+      { SC_(41.391147613525390625), SC_(23439146134369609.98587928723498036090512) }, 
+      { SC_(41.850940704345703125), SC_(36703294479064600.3832020868783140575162) }, 
+      { SC_(42.4788970947265625), SC_(67731301681578920.49039567895447521625383) }, 
+      { SC_(43.331455230712890625), SC_(155669602636333053.4786944018929963653098) }, 
+      { SC_(43.404224395751953125), SC_(167132241928819035.0710856728527709620153) }, 
+      { SC_(43.8334197998046875), SC_(254143262583491699.1980601913565298527589) }, 
+      { SC_(43.9896087646484375), SC_(296024739641759806.6894125116837989457761) }, 
+      { SC_(44.14626312255859375), SC_(344969417880314064.475422911828132537173) }, 
+      { SC_(44.89459991455078125), SC_(716642754835341877.2986625908564001827266) }, 
+      { SC_(45.55641937255859375), SC_(1368424686960668756.908114295234155840218) }, 
+      { SC_(45.622142791748046875), SC_(1459228779377576203.085179194127347039233) }, 
+      { SC_(45.96717071533203125), SC_(2044647179130784910.065675826506375503182) }, 
+      { SC_(46.443317413330078125), SC_(3257069147351952822.406316784082908654148) }, 
+      { SC_(46.62737274169921875), SC_(3899455212627022627.757193164190203742303) }, 
+      { SC_(47.999355316162109375), SC_(14926880987843627550.42423425846631056877) }, 
+      { SC_(49.637111663818359375), SC_(74190413685387077283.04485547837473387867) }, 
+      { SC_(49.81011962890625), SC_(87890252389194795154.44680392696975525721) }, 
+      { SC_(50.171234130859375), SC_(125189140534515913902.5259763391614688736) }, 
+      { SC_(50.383525848388671875), SC_(154131408309808097686.7891755712917358669) }, 
+      { SC_(50.46710968017578125), SC_(167284637436075321503.8911970981891929543) }, 
+      { SC_(50.471343994140625), SC_(167980083475835196141.8258748379299905807) }, 
+      { SC_(50.7309112548828125), SC_(216626578190231872367.3411388285205467896) }, 
+      { SC_(50.891300201416015625), SC_(253494280682248147653.5031137670581769109) }, 
+      { SC_(51.29622650146484375), SC_(376974396494639297221.5916323256511307768) }, 
+      { SC_(52.0242156982421875), SC_(769533307813336085464.2719431240758770955) }, 
+      { SC_(52.21900177001953125), SC_(931463445412117009569.997805462678793371) }, 
+      { SC_(52.4724273681640625), SC_(1194213241460405145426.923208285103882948) }, 
+      { SC_(52.739253997802734375), SC_(1551371845141512428417.754279321277408047) }, 
+      { SC_(52.741176605224609375), SC_(1554299590225018307998.020329038078465699) }, 
+      { SC_(53.40814208984375), SC_(2989698064310689472929.903511572929914131) }, 
+      { SC_(54.5244293212890625), SC_(8938496865444328223663.418183347060066178) }, 
+      { SC_(55.05193328857421875), SC_(15000102942849475726352.24634597020497441) }, 
+      { SC_(55.28836822509765625), SC_(18918195096476420185424.79716369248547301) }, 
+      { SC_(55.32575225830078125), SC_(19625295432594734639694.04077946718413513) }, 
+      { SC_(55.522052764892578125), SC_(23795829974930383969706.74411638885122467) }, 
+      { SC_(55.544170379638671875), SC_(24318128427099146738245.91342763630756375) }, 
+      { SC_(55.57183837890625), SC_(24987672558936599326235.83821092811506408) }, 
+      { SC_(55.808788299560546875), SC_(31531809737095643566486.71781327383155317) }, 
+      { SC_(56.137737274169921875), SC_(43552095758129714470140.32600682101217921) }, 
+      { SC_(56.146297454833984375), SC_(43919686479374955504528.98148221455056972) }, 
+      { SC_(56.446441650390625), SC_(58972731376406161145451.87899710728216492) }, 
+      { SC_(56.5754547119140625), SC_(66937712106290641632239.78290159424299056) }, 
+      { SC_(56.765209197998046875), SC_(80648977731394081623112.8051042421861491) }, 
+      { SC_(57.47022247314453125), SC_(161184177439288421438465.5484877575634735) }, 
+      { SC_(57.791820526123046875), SC_(221066403776152634685122.7495432888528563) }, 
+      { SC_(57.92206573486328125), SC_(251241864908534403966454.9934420615252414) }, 
+      { SC_(58.059658050537109375), SC_(287606300821348197823323.3455461108172774) }, 
+      { SC_(58.620555877685546875), SC_(499047878771232722946891.2015515727402121) }, 
+      { SC_(58.721736907958984375), SC_(551216418687710616233343.712210604071037) }, 
+      { SC_(58.73737335205078125), SC_(559751492456295202734141.0778013286664605) }, 
+      { SC_(59.21694183349609375), SC_(896756596017748427943431.7704197691518272) }, 
+      { SC_(59.3475341796875), SC_(1019568455497745443792447.961272554810421) }, 
+      { SC_(59.574817657470703125), SC_(1274778904679711262832523.146694528881756) }, 
+      { SC_(59.610748291015625), SC_(1320604762679106118330023.701104305685706) }, 
+      { SC_(114.701263427734375), SC_(0.5733168299717727201285049464972941664115e48) }
+   }};
+#undef SC_
+
diff --git a/test/expinti_data_double.ipp b/test/expinti_data_double.ipp
new file mode 100644
index 000000000..6a6b9ed11
--- /dev/null
+++ b/test/expinti_data_double.ipp
@@ -0,0 +1,105 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 100> expinti_data_double = {{
+      { SC_(102.87009429931640625), SC_(4654899469800805764672952463660041015404000.0) }, 
+      { SC_(119.09970855712890625), SC_(0.4488787864805080932333174640972770490538e50) }, 
+      { SC_(120.6676483154296875), SC_(0.2124946028694675872596376925084081671409e51) }, 
+      { SC_(121.42700958251953125), SC_(0.4512183727732527195281492082353068494556e51) }, 
+      { SC_(121.86475372314453125), SC_(0.6964992423126020624418128987604728390362e51) }, 
+      { SC_(127.7028350830078125), SC_(0.2279700329256221183052489611729485531343e54) }, 
+      { SC_(130.7298583984375), SC_(0.4594543786954020597612997101862332382815e55) }, 
+      { SC_(158.2790679931640625), SC_(0.3491987572497265283430495639424245161776e67) }, 
+      { SC_(158.5242462158203125), SC_(0.4455287145500353654763437019012245914284e67) }, 
+      { SC_(165.91705322265625), SC_(0.6912119996498744776551301234337228896794e70) }, 
+      { SC_(167.4787139892578125), SC_(0.326391223691365039787070460177842703726e71) }, 
+      { SC_(175.1096649169921875), SC_(0.6432100430305357924660611042288806557127e74) }, 
+      { SC_(175.5379791259765625), SC_(0.984691477953540716615977148580851612426e74) }, 
+      { SC_(176.1920928955078125), SC_(0.1886920114953374654886114337300975535295e75) }, 
+      { SC_(181.2862091064453125), SC_(0.2989862847852351506449654279623175818276e77) }, 
+      { SC_(185.131805419921875), SC_(0.1369637565311070319468869408302175020227e79) }, 
+      { SC_(189.4683837890625), SC_(0.1022933561959569428116028573369712959689e81) }, 
+      { SC_(194.5678558349609375), SC_(0.1632768521286416542097135533095455177471e83) }, 
+      { SC_(202.712005615234375), SC_(0.5394913535503452815798780947886876429896e86) }, 
+      { SC_(204.3191070556640625), SC_(0.266988871270822922902591264774139389463e87) }, 
+      { SC_(212.123565673828125), SC_(0.6303288415421386740517895306336947600047e90) }, 
+      { SC_(213.0291748046875), SC_(0.1552420011212288898683659113258420389942e91) }, 
+      { SC_(226.1254425048828125), SC_(0.7122229519086770010493744714810456037758e96) }, 
+      { SC_(227.15460205078125), SC_(0.1984236104811331566958586895971472749551e97) }, 
+      { SC_(232.62042236328125), SC_(0.4581388566249763831986535890804413533361e99) }, 
+      { SC_(266.153778076171875), SC_(0.1464284823232428349504366357670506664606e114) }, 
+      { SC_(267.09893798828125), SC_(0.3754550321478881080837201630749628066915e114) }, 
+      { SC_(278.2176513671875), SC_(0.2429828209076613873458952686349499170143e119) }, 
+      { SC_(281.147857666015625), SC_(0.4503824419536589690469228449149704329645e120) }, 
+      { SC_(284.900238037109375), SC_(0.1894265905804735697510091486272554808834e122) }, 
+      { SC_(289.930267333984375), SC_(0.2846606517420129071955201585454115986331e124) }, 
+      { SC_(290.259674072265625), SC_(0.39526840660281511332137740213452297475e124) }, 
+      { SC_(316.776397705078125), SC_(0.1188136226285138671097715211294885613261e136) }, 
+      { SC_(328.93505859375), SC_(0.2182212639027467806212909144237589962574e141) }, 
+      { SC_(335.336212158203125), SC_(0.1289694992441169816466607238785447573694e144) }, 
+      { SC_(339.243133544921875), SC_(0.6341554830794841647273380024739218173519e145) }, 
+      { SC_(345.23870849609375), SC_(0.2502707079015256413360729708739472586996e148) }, 
+      { SC_(353.0567626953125), SC_(0.6081275380494346069537610386054436827084e151) }, 
+      { SC_(353.252593994140625), SC_(0.7392674930634857604064928936832561047528e151) }, 
+      { SC_(363.246612548828125), SC_(0.1573977048026212180539326023109084395454e156) }, 
+      { SC_(367.351715087890625), SC_(0.9439039533362185936065067145525348987048e157) }, 
+      { SC_(374.793487548828125), SC_(0.1578028673470190623900612461257603840414e161) }, 
+      { SC_(384.855224609375), SC_(0.3600276754143745485244589154691966465381e165) }, 
+      { SC_(391.225372314453125), SC_(0.2068748707894393683497591012649949622203e168) }, 
+      { SC_(392.541351318359375), SC_(0.7687196958833528385591120302020777152611e168) }, 
+      { SC_(393.858642578125), SC_(0.2860234483451614302230860963468500787004e169) }, 
+      { SC_(394.353424072265625), SC_(0.468528356426515701193951809153160635264e169) }, 
+      { SC_(402.1976318359375), SC_(0.1171808089560200191770907797339877928134e173) }, 
+      { SC_(428.12890625), SC_(0.2011244899732843068179501387740539518665e184) }, 
+      { SC_(428.332366943359375), SC_(0.2463882456108220623335396182335238049978e184) }, 
+      { SC_(479.415557861328125), SC_(0.3370760755402075136867387081832481381884e206) }, 
+      { SC_(483.858001708984375), SC_(0.2838197444669518328148323406487783086905e208) }, 
+      { SC_(487.787811279296875), SC_(0.143290343327313200442365090263240144269e210) }, 
+      { SC_(493.2867431640625), SC_(0.3463332679043421510270870135017998699304e212) }, 
+      { SC_(493.44439697265625), SC_(0.4053436082306786060312645931633934496659e212) }, 
+      { SC_(498.163299560546875), SC_(0.4498573166263689115195724188943233736555e214) }, 
+      { SC_(507.2410888671875), SC_(0.3869458554978062751502315639584587941431e218) }, 
+      { SC_(508.815704345703125), SC_(0.1862722954440262359736876867660438647055e219) }, 
+      { SC_(516.89715576171875), SC_(0.5929539458008759668618166365480530357574e222) }, 
+      { SC_(523.627685546875), SC_(0.490256757720855085525310071865504294369e225) }, 
+      { SC_(525.618896484375), SC_(0.357720625670250295507690509025554576924e226) }, 
+      { SC_(535.50335693359375), SC_(0.6889759236100754327282718895680993386846e230) }, 
+      { SC_(544.38836669921875), SC_(0.4895023821578599017471211778436380380851e234) }, 
+      { SC_(545.87945556640625), SC_(0.2168384886985358923425414610198222504761e235) }, 
+      { SC_(552.81201171875), SC_(0.2194908907077200735474576859355376276996e238) }, 
+      { SC_(554.64410400390625), SC_(0.1366609803311340085634888162278346794975e239) }, 
+      { SC_(558.25), SC_(0.4998570812776135939052842271424771438308e240) }, 
+      { SC_(559.31011962890625), SC_(0.1440205702121135197609975402434930330836e241) }, 
+      { SC_(575.32440185546875), SC_(0.1261993396536182845635950097162949293812e248) }, 
+      { SC_(576.385009765625), SC_(0.3638077665497671657713912984804072342658e248) }, 
+      { SC_(577.11993408203125), SC_(0.7576893430265850749719869973928888261581e248) }, 
+      { SC_(578.367919921875), SC_(0.2633569534665923102825640510310718246757e249) }, 
+      { SC_(578.7572021484375), SC_(0.3884321712516615414225859937380556292439e249) }, 
+      { SC_(578.863525390625), SC_(0.4319275188177097667628494729863878264458e249) }, 
+      { SC_(580.16827392578125), SC_(0.1588826507174073600934477712203698999436e250) }, 
+      { SC_(584.51861572265625), SC_(0.1222238450958130847374075209904594309916e252) }, 
+      { SC_(588.834228515625), SC_(0.9082441109422063046992881078366160444507e253) }, 
+      { SC_(593.1419677734375), SC_(0.6696671407396550532370011475709646515434e255) }, 
+      { SC_(594.07470703125), SC_(0.1699256492240263485176709898640795327905e256) }, 
+      { SC_(601.005126953125), SC_(0.1718131816979918101950016705556617558037e259) }, 
+      { SC_(609.47760009765625), SC_(0.8100561951389239245138612767305143306984e262) }, 
+      { SC_(623.457275390625), SC_(0.9331382282084315894480060552801462030494e268) }, 
+      { SC_(627.05841064453125), SC_(0.3399333946028564608617370823657507561735e270) }, 
+      { SC_(643.47515869140625), SC_(0.4465348678487959522963305527404292744891e277) }, 
+      { SC_(648.0255126953125), SC_(0.4197434532469066342906967841224435165556e279) }, 
+      { SC_(649.44134521484375), SC_(0.1725531471297453891677758589012301168234e280) }, 
+      { SC_(652.52484130859375), SC_(0.3749798510829081836112102781820076672405e281) }, 
+      { SC_(660.39593505859375), SC_(0.970879214993044630543023552485120399286e284) }, 
+      { SC_(670.13323974609375), SC_(0.1620527966055446945578211401048814814567e289) }, 
+      { SC_(674.3001708984375), SC_(0.1039047983324197139199069164254061321298e291) }, 
+      { SC_(674.50408935546875), SC_(0.1273692969308263916056410711840867769624e291) }, 
+      { SC_(675.69549560546875), SC_(0.418522040928659237731709573433592942673e291) }, 
+      { SC_(678.93310546875), SC_(0.1061000019714235158838961951634579077223e293) }, 
+      { SC_(680.616943359375), SC_(0.5700586451271579571730049808881026675533e293) }, 
+      { SC_(681.3206787109375), SC_(0.1151061266572356641000638910442083400077e294) }, 
+      { SC_(682.35565185546875), SC_(0.3235350762276795224692901027817771950219e294) }, 
+      { SC_(688.66583251953125), SC_(0.1763576946849989630024915426356908693227e297) }, 
+      { SC_(695.728759765625), SC_(0.2038669812824068591196373014464478923157e300) }, 
+      { SC_(696.44110107421875), SC_(0.4152099129072985415211360691072606219165e300) }, 
+      { SC_(697.87677001953125), SC_(0.174130632289273126035703061440352012941e301) }
+   }};
+#undef SC_
+
diff --git a/test/expinti_data_long.ipp b/test/expinti_data_long.ipp
new file mode 100644
index 000000000..6d4a63930
--- /dev/null
+++ b/test/expinti_data_long.ipp
@@ -0,0 +1,105 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 100> expinti_data_long = {{
+      { SC_(850.51361083984375), SC_(0.27809823533792637952061836944224670902e367) }, 
+      { SC_(1136.15478515625), SC_(0.2348005093803919554840423708437417479629e491) }, 
+      { SC_(1163.7506103515625), SC_(0.2213003663371766101124862788858798209669e503) }, 
+      { SC_(1177.1153564453125), SC_(0.1393972678294381321914138715599921955926e509) }, 
+      { SC_(1184.819580078125), SC_(0.3071287487721510514525001455932125917587e512) }, 
+      { SC_(1287.56982421875), SC_(0.1188602460855659524267859866086060607259e557) }, 
+      { SC_(1340.845458984375), SC_(0.1565775363947514543544059577542317926535e580) }, 
+      { SC_(1825.7115478515625), SC_(0.4317742008433835384506876651615126974963e790) }, 
+      { SC_(1830.026611328125), SC_(0.3222842941582302836955227140289123449271e792) }, 
+      { SC_(1960.14013671875), SC_(0.9682326984764871443713708725009118516667e848) }, 
+      { SC_(1987.625244140625), SC_(0.8252010696701409604448632584198026007861e860) }, 
+      { SC_(2121.929931640625), SC_(0.1644122120004322809189630355750827856571e919) }, 
+      { SC_(2129.468505859375), SC_(0.3078607683726664945534741803554577395453e922) }, 
+      { SC_(2140.980712890625), SC_(0.3059846959258757487477467065245238848267e927) }, 
+      { SC_(2230.63720703125), SC_(0.2542119875349999176355379625196504093816e966) }, 
+      { SC_(2298.31982421875), SC_(0.6114992506410978259391244796777268178912e995) }, 
+      { SC_(2374.6435546875), SC_(0.830188785884719427191192371811470577614e1028) }, 
+      { SC_(2464.39404296875), SC_(0.7606769935221277835214875514322852420595e1067) }, 
+      { SC_(2607.7314453125), SC_(0.1280208651710915937668281576410585595382e1130) }, 
+      { SC_(2636.01611328125), SC_(0.2434831958141217397564034109022725860803e1142) }, 
+      { SC_(2773.374755859375), SC_(0.1043520151961041658604037267493948608009e1202) }, 
+      { SC_(2789.313720703125), SC_(0.8673924117610746105433718703338830121224e1208) }, 
+      { SC_(3019.807861328125), SC_(0.1014040167380916647540036248296427121987e1309) }, 
+      { SC_(3037.9208984375), SC_(0.7410529098571197987076032731629101798719e1316) }, 
+      { SC_(3134.11962890625), SC_(0.4314033621612001130684487653920208910505e1358) }, 
+      { SC_(3724.306640625), SC_(0.7497114876830077572608496589486939616531e1614) }, 
+      { SC_(3740.94140625), SC_(0.1251252881668710692336811165448253472824e1622) }, 
+      { SC_(3936.630859375), SC_(0.1153573278500689879003545458843117005296e1707) }, 
+      { SC_(3988.202392578125), SC_(0.2841996613630984591213735017628358662044e1729) }, 
+      { SC_(4054.243896484375), SC_(0.1342609828695717510201743140807115713194e1758) }, 
+      { SC_(4142.7724609375), SC_(0.3681572481442059810190451103963992112454e1796) }, 
+      { SC_(4148.5703125), SC_(0.121171581000799833633456183949328398278e1799) }, 
+      { SC_(4615.2646484375), SC_(0.5246465971256288730180022026676777543742e2001) }, 
+      { SC_(4829.25732421875), SC_(0.4325309705481133900503845562540831591495e2094) }, 
+      { SC_(4941.91748046875), SC_(0.357836144515945182929963672150715372631e2143) }, 
+      { SC_(5010.6787109375), SC_(0.2572200946506254896455407953607460924114e2173) }, 
+      { SC_(5116.201171875), SC_(0.1694628673308089036903938764581354437254e2219) }, 
+      { SC_(5253.798828125), SC_(0.9450381302497917822730309088983075713142e2278) }, 
+      { SC_(5257.24560546875), SC_(0.2965383255217071801210759810882002854358e2280) }, 
+      { SC_(5433.140625), SC_(0.7047285278346101208658057139925849862554e2356) }, 
+      { SC_(5505.39013671875), SC_(0.1659005813598457669810325988575538660018e2388) }, 
+      { SC_(5636.36572265625), SC_(0.123483589653905750755240300669656546009e2445) }, 
+      { SC_(5813.45166015625), SC_(0.9674253782674757458616517516767150594778e2521) }, 
+      { SC_(5925.56689453125), SC_(0.465959154348727474260042419560482730271e2570) }, 
+      { SC_(5948.7275390625), SC_(0.5311210417035456841299141336297429192824e2580) }, 
+      { SC_(5971.912109375), SC_(0.6200616140526457518581489641316743841867e2590) }, 
+      { SC_(5980.62060546875), SC_(0.3748467021497618776363280710356423632891e2594) }, 
+      { SC_(6118.67822265625), SC_(0.3323548513925888198554192040808784242521e2654) }, 
+      { SC_(6575.06884765625), SC_(0.4992113296799401332170302610613651749985e2852) }, 
+      { SC_(6578.6494140625), SC_(0.1790887030753559149862073840512717626631e2854) }, 
+      { SC_(7477.7138671875), SC_(0.453063439997264160754767400139975001266e3244) }, 
+      { SC_(7555.90087890625), SC_(0.4053486713272468063037722021443381630624e3278) }, 
+      { SC_(7625.0654296875), SC_(0.4381811161168660111987981480837499404122e3308) }, 
+      { SC_(7721.84619140625), SC_(0.4650783679722625981733974952858145989039e3350) }, 
+      { SC_(7724.62158203125), SC_(0.7459451366176179637703427587587394395181e3351) }, 
+      { SC_(7807.67431640625), SC_(0.8657770283993666196881334661703905178512e3387) }, 
+      { SC_(7967.44287109375), SC_(0.2066376033881102222399296966624611161435e3457) }, 
+      { SC_(7995.15673828125), SC_(0.2237075980936927860568603957470382881289e3469) }, 
+      { SC_(8137.39013671875), SC_(0.1297781899952190216559462644235208641515e3531) }, 
+      { SC_(8255.8466796875), SC_(0.3564079826420461256934314917221024535487e3582) }, 
+      { SC_(8290.892578125), SC_(0.589315461709375088751076327530039211034e3597) }, 
+      { SC_(8464.859375), SC_(0.2061333287437003593390952585665220300663e3673) }, 
+      { SC_(8621.2353515625), SC_(0.1657376800782722410304770650822997699241e3741) }, 
+      { SC_(8647.478515625), SC_(0.4124415895621698868851529362785050121075e3752) }, 
+      { SC_(8769.4912109375), SC_(0.3969329427154640956668041611282529236515e3805) }, 
+      { SC_(8801.736328125), SC_(0.3990244136134911987900607765723496356083e3819) }, 
+      { SC_(8865.2001953125), SC_(0.1445061203725423928848837944828607819372e3847) }, 
+      { SC_(8883.857421875), SC_(0.1826853197788422299249942076987355766608e3855) }, 
+      { SC_(9165.708984375), SC_(0.4515605271244922649573310924321143987289e3977) }, 
+      { SC_(9184.3759765625), SC_(0.5765062048528042160801422542318948604069e3985) }, 
+      { SC_(9197.3115234375), SC_(0.238797240985925516325017189407703419842e3991) }, 
+      { SC_(9219.275390625), SC_(0.8237200206643906423722827693221290304098e4000) }, 
+      { SC_(9226.1259765625), SC_(0.7773715903123152522709440763956473274495e4003) }, 
+      { SC_(9227.998046875), SC_(0.5053244921662419600389850256151955782088e4004) }, 
+      { SC_(9250.9619140625), SC_(0.4737744487728344772209960864307761252156e4014) }, 
+      { SC_(9327.52734375), SC_(0.839334799085535932104716295994462739704e4047) }, 
+      { SC_(9403.482421875), SC_(0.8077630243130543392122877176716464625234e4080) }, 
+      { SC_(9479.298828125), SC_(0.6767729229089682203216741035877315937008e4113) }, 
+      { SC_(9495.71484375), SC_(0.9100734532106930249198078682510663631931e4120) }, 
+      { SC_(9617.6904296875), SC_(0.8449998576157010058160975375848278518588e4173) }, 
+      { SC_(9766.8056640625), SC_(0.4787377238207901984222005262457964596487e4238) }, 
+      { SC_(10012.8486328125), SC_(0.3344992068689187467671400212667671782847e4345) }, 
+      { SC_(10076.2275390625), SC_(0.11136885577784012567387295792753442916e4373) }, 
+      { SC_(10365.1630859375), SC_(0.3293047656065511164747161575530322956908e4498) }, 
+      { SC_(10445.2490234375), SC_(0.1973039455254220882950372775604517375325e4533) }, 
+      { SC_(10470.1669921875), SC_(0.1305681315488859113163146324068469579781e4544) }, 
+      { SC_(10524.4375), SC_(0.4819186831856610440931487751621965500502e4567) }, 
+      { SC_(10662.96875), SC_(0.6928694779347995167937115115212504365928e4627) }, 
+      { SC_(10834.3447265625), SC_(0.1825438577646410483210158166935577469757e4702) }, 
+      { SC_(10907.68359375), SC_(0.1285589751375311174300431256570906461288e4734) }, 
+      { SC_(10911.2724609375), SC_(0.4651411212288175929735371788790669615768e4735) }, 
+      { SC_(10932.240234375), SC_(0.5928423151111867954833915596799084326543e4744) }, 
+      { SC_(10989.22265625), SC_(0.3294826635257870726228138790579703502685e4769) }, 
+      { SC_(11018.8583984375), SC_(0.2439507354669304579499512829726839932215e4782) }, 
+      { SC_(11031.244140625), SC_(0.5832754259182122887134092147181083406225e4787) }, 
+      { SC_(11049.4599609375), SC_(0.474446561495313567373051850934536721701e4795) }, 
+      { SC_(11160.5185546875), SC_(0.8016374991446073482862383560024456346995e4843) }, 
+      { SC_(11284.826171875), SC_(0.7678551455742636373830825128178952778616e4897) }, 
+      { SC_(11297.36328125), SC_(0.2135966594384904628860134271820875984946e4903) }, 
+      { SC_(11322.6318359375), SC_(0.2007326162507306591356341202787380118764e4914) }
+   }};
+#undef SC_
+
diff --git a/test/functor.hpp b/test/functor.hpp
index cde300100..8da3b5c77 100644
--- a/test/functor.hpp
+++ b/test/functor.hpp
@@ -3,6 +3,8 @@
 //  Boost Software License, Version 1.0. (See accompanying file
 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
 
+#include 
+
 
 #ifndef BOOST_MATH_TEST_FUNCTOR_HPP
 #define BOOST_MATH_TEST_FUNCTOR_HPP
@@ -121,7 +123,7 @@ struct row_binder2_i1
    template 
    typename S::value_type operator()(const S& row)
    {
-      return f(boost::math::tools::real_cast(row[m_i]), row[m_j]);
+      return f(boost::math::itrunc(row[m_i]), row[m_j]);
    }
 
 private:
@@ -144,8 +146,8 @@ struct row_binder3_i2
    typename S::value_type operator()(const S& row)
    {
       return f(
-         boost::math::tools::real_cast(row[m_i]), 
-         boost::math::tools::real_cast(row[m_j]),
+         boost::math::itrunc(row[m_i]), 
+         boost::math::itrunc(row[m_j]),
          row[m_k]);
    }
 
@@ -169,8 +171,8 @@ struct row_binder4_i2
    typename S::value_type operator()(const S& row)
    {
       return f(
-         boost::math::tools::real_cast(row[m_i]), 
-         boost::math::tools::real_cast(row[m_j]),
+         boost::math::itrunc(row[m_i]), 
+         boost::math::itrunc(row[m_j]),
          row[m_k],
          row[m_l]);
    }
diff --git a/test/ncbeta.ipp b/test/ncbeta.ipp
new file mode 100644
index 000000000..3e54ab9d7
--- /dev/null
+++ b/test/ncbeta.ipp
@@ -0,0 +1,3005 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 3000> ncbeta = {{
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000e-1), SC_(5.940588760375976562500000000000000000000e1), SC_(9.976066350936889648437500000000000000000e-1), SC_(2.759834870217354705236013708534509068967e-1), SC_(7.240165129782645294763986291465490931033e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000e-1), SC_(1.451677856445312500000000000000000000000e2), SC_(9.990068674087524414062500000000000000000e-1), SC_(2.757975665000284929998400439182434398680e-1), SC_(7.242024334999715070001599560817565601320e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000e-1), SC_(1.929777069091796875000000000000000000000e2), SC_(9.992512464523315429687500000000000000000e-1), SC_(2.757802819095769722518059796277858159202e-1), SC_(7.242197180904230277481940203722141840798e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(3.635762631893157958984375000000000000000e-1), SC_(6.038262176513671875000000000000000000000e1), SC_(9.961022734642028808593750000000000000000e-1), SC_(4.949484084085013882284839924844591052030e-1), SC_(5.050515915914986117715160075155408947970e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(3.635762631893157958984375000000000000000e-1), SC_(1.481294555664062500000000000000000000000e2), SC_(9.983823299407958984375000000000000000000e-1), SC_(4.946201811284367289305268285202655846240e-1), SC_(5.053798188715632710694731714797344153760e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(3.635762631893157958984375000000000000000e-1), SC_(1.935389862060546875000000000000000000000e2), SC_(9.987584948539733886718750000000000000000e-1), SC_(4.945965085725495633413346642780624277086e-1), SC_(5.054034914274504366586653357219375722914e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(7.271525263786315917968750000000000000000e-1), SC_(6.163340759277343750000000000000000000000e1), SC_(9.943350553512573242187500000000000000000e-1), SC_(7.067242511174509034733895807356551147428e-1), SC_(2.932757488825490965266104192643448852572e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(7.271525263786315917968750000000000000000e-1), SC_(1.486264953613281250000000000000000000000e2), SC_(9.975933432579040527343750000000000000000e-1), SC_(7.063204046711177968479175758665909815947e-1), SC_(2.936795953288822031520824241334090184053e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(7.271525263786315917968750000000000000000e-1), SC_(1.937735595703125000000000000000000000000e2), SC_(9.981468915939331054687500000000000000000e-1), SC_(7.062805762166387906359787891104213355210e-1), SC_(2.937194237833612093640212108895786644790e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.090728759765625000000000000000000000000), SC_(7.225879669189453125000000000000000000000e1), SC_(9.942231774330139160156250000000000000000e-1), SC_(8.372920335940658618578320877705617571936e-1), SC_(1.627079664059341381421679122294382428064e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.090728759765625000000000000000000000000), SC_(1.515480346679687500000000000000000000000e2), SC_(9.971802234649658203125000000000000000000e-1), SC_(8.370187919390128563087545041366727719913e-1), SC_(1.629812080609871436912454958633272280087e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.090728759765625000000000000000000000000), SC_(1.941185607910156250000000000000000000000e2), SC_(9.977884292602539062500000000000000000000e-1), SC_(8.369846256186989556701034949935290540605e-1), SC_(1.630153743813010443298965050064709459395e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.308874487876892089843750000000000000000), SC_(9.566968083381652832031250000000000000000e-1), SC_(5.778348073363304138183593750000000000000e-2), SC_(1.409704128923593153631527182055535438009e-2), SC_(9.859029587107640684636847281794446456199e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.308874487876892089843750000000000000000), SC_(7.844540405273437500000000000000000000000e1), SC_(9.681322425603866577148437500000000000000e-2), SC_(2.569096227285625192995992565780836758662e-17), SC_(9.999999999999999743090377271437480700401e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.308874487876892089843750000000000000000), SC_(1.584414672851562500000000000000000000000e2), SC_(9.838468581438064575195312500000000000000e-2), SC_(7.148747906745571900269746100091585733876e-33), SC_(9.999999999999999999999999999999928512521e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.308874487876892089843750000000000000000), SC_(1.962219390869140625000000000000000000000e2), SC_(9.868995845317840576171875000000000000000e-2), SC_(3.133324157161160812982715199693443151905e-40), SC_(9.999999999999999999999999999999999999997e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.439761996269226074218750000000000000000), SC_(7.142335891723632812500000000000000000000), SC_(1.895702630281448364257812500000000000000e-1), SC_(8.246187378326890920818812693938620222737e-3), SC_(9.917538126216731090791811873060613797773e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.439761996269226074218750000000000000000), SC_(7.974770355224609375000000000000000000000e1), SC_(2.414003908634185791015625000000000000000e-1), SC_(2.743306172427076308949349814705500897953e-14), SC_(9.999999999999725669382757292369105065019e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.439761996269226074218750000000000000000), SC_(1.595857238769531250000000000000000000000e2), SC_(2.455961406230926513671875000000000000000e-1), SC_(3.615587311674064774434229582160414432976e-27), SC_(9.999999999999999999999999963844126883259e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.439761996269226074218750000000000000000), SC_(1.985762634277343750000000000000000000000e2), SC_(2.464439719915390014648437500000000000000e-1), SC_(1.769432346388276500700335757818980807043e-33), SC_(9.999999999999999999999999999999982305677e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.452850818634033203125000000000000000000), SC_(1.950807952880859375000000000000000000000e1), SC_(4.391348361968994140625000000000000000000e-1), SC_(2.673764091042295518866919574008896029552e-3), SC_(9.973262359089577044811330804259911039704e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.452850818634033203125000000000000000000), SC_(8.435225677490234375000000000000000000000e1), SC_(4.835526645183563232421875000000000000000e-1), SC_(4.197372846541376004107385263233562496292e-10), SC_(9.999999995802627153458623995892614736766e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.452850818634033203125000000000000000000), SC_(1.596211700439453125000000000000000000000e2), SC_(4.911155700683593750000000000000000000000e-1), SC_(3.695059050069457866849050715946269539742e-18), SC_(9.999999999999999963049409499305421331509e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.452850818634033203125000000000000000000), SC_(1.992922668457031250000000000000000000000e2), SC_(4.928494989871978759765625000000000000000e-1), SC_(2.004823756718951621438737650562766380258e-22), SC_(9.999999999999999999997995176243281048379e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000), SC_(2.197235107421875000000000000000000000000e1), SC_(6.670339703559875488281250000000000000000e-1), SC_(2.938827902133597908162529714537893342335e-2), SC_(9.706117209786640209183747028546210665767e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000), SC_(8.441753387451171875000000000000000000000e1), SC_(7.253233790397644042968750000000000000000e-1), SC_(1.828399814138725196172294345445724389776e-5), SC_(9.999817160018586127480382770565455427561e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454305052757263183593750000000000000000), SC_(1.600560913085937500000000000000000000000e2), SC_(7.366956472396850585937500000000000000000e-1), SC_(1.838909377742473059089666873575275698077e-9), SC_(9.999999981610906222575269409103331264247e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454450488090515136718750000000000000000), SC_(2.249290275573730468750000000000000000000e1), SC_(8.023343086242675781250000000000000000000e-1), SC_(1.444816643582166349744437266238358383054e-1), SC_(8.555183356417833650255562733761641616946e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454450488090515136718750000000000000000), SC_(9.495173645019531250000000000000000000000e1), SC_(8.735338449478149414062500000000000000000e-1), SC_(5.297391880242822813440890445530785806678e-3), SC_(9.947026081197571771865591095544692141933e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.454450488090515136718750000000000000000), SC_(1.629447326660156250000000000000000000000e2), SC_(8.843094706535339355468750000000000000000e-1), SC_(2.109987510023566218907025733718046851867e-4), SC_(9.997890012489976433781092974266281953148e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.455759406089782714843750000000000000000), SC_(2.539736366271972656250000000000000000000e1), SC_(8.928544521331787109375000000000000000000e-1), SC_(3.547407387217092519571701060719919695556e-1), SC_(6.452592612782907480428298939280080304444e-1) }, 
+      { SC_(1.454305052757263183593750000000000000000), SC_(1.455759406089782714843750000000000000000), SC_(9.707512664794921875000000000000000000000e1), SC_(9.614732861518859863281250000000000000000e-1), SC_(2.611091095508861765371680541840956899457e-1), SC_(7.388908904491138234628319458159043100543e-1) }, 
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+      { SC_(1.992940368652343750000000000000000000000e2), SC_(3.985880737304687500000000000000000000000e2), SC_(1.481294555664062500000000000000000000000e2), SC_(4.606534242630004882812500000000000000000e-1), SC_(9.957282424377606356346329644628312528585e-1), SC_(4.271757562239364365367035537168747141534e-3) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(3.985880737304687500000000000000000000000e2), SC_(1.935389862060546875000000000000000000000e2), SC_(4.782629907131195068359375000000000000000e-1), SC_(9.945960851426927928055493135079582151791e-1), SC_(5.403914857307207194450686492041784820904e-3) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(5.978820800781250000000000000000000000000e2), SC_(6.163340759277343750000000000000000000000e1), SC_(3.982345759868621826171875000000000000000e-1), SC_(9.999999999983652719310843670759144107488e-1), SC_(1.634728068915632924085589251240883044304e-12) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(5.978820800781250000000000000000000000000e2), SC_(1.486264953613281250000000000000000000000e2), SC_(4.282388091087341308593750000000000000000e-1), SC_(9.999999999441405803165315291403807033859e-1), SC_(5.585941968346847085961929661413163659822e-11) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(5.978820800781250000000000000000000000000e2), SC_(1.937735595703125000000000000000000000000e2), SC_(4.426617622375488281250000000000000000000e-1), SC_(9.999999997983110564053295602949830922408e-1), SC_(2.016889435946704397050169077592286063336e-10) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(7.971761474609375000000000000000000000000e2), SC_(7.225879669189453125000000000000000000000e1), SC_(4.061267971992492675781250000000000000000e-1), SC_(9.999999999999999999999999999997290246639e-1), SC_(2.709753361367076002320691695420448945649e-31) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(7.971761474609375000000000000000000000000e2), SC_(1.515480346679687500000000000000000000000e2), SC_(4.280660748481750488281250000000000000000e-1), SC_(9.999999999999999999999999991303421392948e-1), SC_(8.696578607051932204338673773133285372742e-28) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(7.971761474609375000000000000000000000000e2), SC_(1.941185607910156250000000000000000000000e2), SC_(4.391900300979614257812500000000000000000e-1), SC_(9.999999999999999999999999789782532523897e-1), SC_(2.102174674761034080045110832943420015762e-26) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964702148437500000000000000000000000000e2), SC_(9.566968083381652832031250000000000000000e-1), SC_(4.446664154529571533203125000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(6.723822936759331715719218974775798182259e-93) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964702148437500000000000000000000000000e2), SC_(7.844540405273437500000000000000000000000e1), SC_(4.620748460292816162109375000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.547617018541288535048352060726128288630e-80) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964702148437500000000000000000000000000e2), SC_(1.584414672851562500000000000000000000000e2), SC_(4.789382815361022949218750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.016791451093890693491633506946470794739e-72) }, 
+      { SC_(1.992940368652343750000000000000000000000e2), SC_(9.964702148437500000000000000000000000000e2), SC_(1.962219390869140625000000000000000000000e2), SC_(4.865405857563018798828125000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(1.362436549196397892011134548818387099631e-69) }
+   }};
+#undef SC_
+
diff --git a/test/ncbeta_big.ipp b/test/ncbeta_big.ipp
new file mode 100644
index 000000000..21f52a790
--- /dev/null
+++ b/test/ncbeta_big.ipp
@@ -0,0 +1,77 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 72> ncbeta_big = {{
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.090561676025390625000000000000000000000e2), SC_(2.322846374511718750000000000000000000000e2), SC_(6.248598918318748474121093750000000000000e-2), SC_(5.822794103663371475941613559141512048716e-200), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.299617919921875000000000000000000000000e2), SC_(2.906821289062500000000000000000000000000e2), SC_(1.553418934345245361328125000000000000000e-1), SC_(2.376427035888773394585864365564861664654e-112), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.320523529052734375000000000000000000000e2), SC_(9.757655029296875000000000000000000000000e2), SC_(3.780863285064697265625000000000000000000e-1), SC_(9.534309971409020993977308030456117404144e-89), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.322846374511718750000000000000000000000e2), SC_(1.879048828125000000000000000000000000000e3), SC_(6.258654594421386718750000000000000000000e-1), SC_(8.273529404980685686135545983154559305766e-53), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.323078765869140625000000000000000000000e2), SC_(2.308069091796875000000000000000000000000e3), SC_(7.707736492156982421875000000000000000000e-1), SC_(6.642746074306700324296888792472255191709e-16), SC_(9.999999999999993357253925693299675703111e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.325169372558593750000000000000000000000e2), SC_(8.064482421875000000000000000000000000000e3), SC_(9.388024210929870605468750000000000000000e-1), SC_(3.784012698595881643945309133853831952949e-3), SC_(9.962159873014041183560546908661461680471e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.346074829101562500000000000000000000000e2), SC_(1.567437500000000000000000000000000000000e4), SC_(9.707729816436767578125000000000000000000e-1), SC_(2.935931059732195123761306546780042425559e-1), SC_(7.064068940267804876238693453219957574441e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.555131072998046875000000000000000000000e2), SC_(2.000542187500000000000000000000000000000e4), SC_(9.756411910057067871093750000000000000000e-1), SC_(4.916958930557002818402814932631962599797e-1), SC_(5.083041069442997181597185067368037400203e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(2.787415771484375000000000000000000000000e2), SC_(5.348914843750000000000000000000000000000e4), SC_(9.897736907005310058593750000000000000000e-1), SC_(4.926920140457373120750763227119217556742e-1), SC_(5.073079859542626879249236772880782443258e-1) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(2.906821250915527343750000000000000000000e1), SC_(1.567437500000000000000000000000000000000e4), SC_(9.982179403305053710937500000000000000000e-1), SC_(9.994919920744164088096546647236384815783e-1), SC_(5.080079255835911903453352763615184216904e-4) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(7.267053222656250000000000000000000000000e1), SC_(2.000542187500000000000000000000000000000e4), SC_(9.976629614830017089843750000000000000000e-1), SC_(9.999999999999983875164826739274160375349e-1), SC_(1.612483517326072583962465078546376039408e-15) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(1.453410644531250000000000000000000000000e2), SC_(5.348914843750000000000000000000000000000e4), SC_(9.986631274223327636718750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(3.010804490077860063798231369313535930122e-42) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(3.778867492675781250000000000000000000000e2), SC_(2.322846374511718750000000000000000000000e2), SC_(5.188288092613220214843750000000000000000e-1), SC_(5.089321557957671134199777152425169214951e-1), SC_(4.910678442042328865800222847574830785049e-1) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(4.360231933593750000000000000000000000000e2), SC_(2.906821289062500000000000000000000000000e2), SC_(5.048558712005615234375000000000000000000e-1), SC_(6.058697905723221366664491586322735988918e-1), SC_(3.941302094276778633335508413677264011082e-1) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(5.813642578125000000000000000000000000000e2), SC_(9.757655029296875000000000000000000000000e2), SC_(6.112647652626037597656250000000000000000e-1), SC_(9.955089747240769047271157763291403354685e-1), SC_(4.491025275923095272884223670859664531545e-3) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(8.720463867187500000000000000000000000000e2), SC_(1.879048828125000000000000000000000000000e3), SC_(6.542472243309020996093750000000000000000e-1), SC_(9.999999972226024110911179121134729543583e-1), SC_(2.777397588908882087886527045641662997938e-9) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(1.162728515625000000000000000000000000000e3), SC_(2.308069091796875000000000000000000000000e3), SC_(6.569214463233947753906250000000000000000e-1), SC_(9.999999999999999999995533478732255838241e-1), SC_(4.466521267744161758750286812848432918534e-22) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(1.453410644531250000000000000000000000000e3), SC_(8.064482421875000000000000000000000000000e3), SC_(8.322365880012512207031250000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(1.724098253290586949046235121920786188871e-50) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(7.318240966796875000000000000000000000000e2), SC_(2.322846374511718750000000000000000000000e2), SC_(9.197415113449096679687500000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.098029526746715772059557152803443778923e-305) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(8.781889038085937500000000000000000000000e2), SC_(2.906821289062500000000000000000000000000e2), SC_(5.607348680496215820312500000000000000000e-2), SC_(4.137966307189253467290003067675414259896e-745), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(9.660078735351562500000000000000000000000e2), SC_(9.757655029296875000000000000000000000000e2), SC_(1.505941897630691528320312500000000000000e-1), SC_(2.312581255996761321216691130907918725012e-439), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(9.747897338867187500000000000000000000000e2), SC_(1.879048828125000000000000000000000000000e3), SC_(3.313369452953338623046875000000000000000e-1), SC_(1.822938095440314319524488179659476739600e-219), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(9.757655029296875000000000000000000000000e2), SC_(2.308069091796875000000000000000000000000e3), SC_(5.143225789070129394531250000000000000000e-1), SC_(1.421828425120214003942552400693765508326e-67), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(9.758630981445312500000000000000000000000e2), SC_(8.064482421875000000000000000000000000000e3), SC_(7.532094120979309082031250000000000000000e-1), SC_(1.278959916011845843611062944857639073496e-47), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(9.767413330078125000000000000000000000000e2), SC_(1.567437500000000000000000000000000000000e4), SC_(8.912172317504882812500000000000000000000e-1), SC_(2.728322119200344826952604570486340362225e-3), SC_(9.972716778807996551730473954295136596378e-1) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(9.855231323242187500000000000000000000000e2), SC_(2.000542187500000000000000000000000000000e4), SC_(9.167025685310363769531250000000000000000e-1), SC_(3.589860146897613099118333082236256051011e-1), SC_(6.410139853102386900881666917763743948989e-1) }, 
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(1.073342041015625000000000000000000000000e3), SC_(5.348914843750000000000000000000000000000e4), SC_(9.627218246459960937500000000000000000000e-1), SC_(4.959666475640454900645452407891567289414e-1), SC_(5.040333524359545099354547592108432710586e-1) }, 
+      { SC_(1.879048828125000000000000000000000000000e3), SC_(1.879048919677734375000000000000000000000e2), SC_(2.000542187500000000000000000000000000000e4), SC_(9.922152757644653320312500000000000000000e-1), SC_(9.999999999999999906525997974104688623475e-1), SC_(9.347400202589531137652505012008628236569e-18) }, 
+      { SC_(1.879048828125000000000000000000000000000e3), SC_(4.697622070312500000000000000000000000000e2), SC_(5.348914843750000000000000000000000000000e4), SC_(9.946175813674926757812500000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(1.812197155304730289100502335815782533179e-90) }, 
+      { SC_(1.879048828125000000000000000000000000000e3), SC_(2.254858642578125000000000000000000000000e3), SC_(2.322846374511718750000000000000000000000e2), SC_(4.695008695125579833984375000000000000000e-1), SC_(5.029136707270802745099779711341809125434e-1), SC_(4.970863292729197254900220288658190874566e-1) }, 
+      { SC_(1.879048828125000000000000000000000000000e3), SC_(2.442763427734375000000000000000000000000e3), SC_(2.906821289062500000000000000000000000000e2), SC_(4.537145793437957763671875000000000000000e-1), SC_(5.289819531087712125353700747589292943748e-1), SC_(4.710180468912287874646299252410707056252e-1) }, 
+      { SC_(1.879048828125000000000000000000000000000e3), SC_(2.818573242187500000000000000000000000000e3), SC_(9.757655029296875000000000000000000000000e2), SC_(4.618234336376190185546875000000000000000e-1), SC_(7.697208318278162838782020353802049561352e-1), SC_(2.302791681721837161217979646197950438648e-1) }, 
+      { SC_(1.879048828125000000000000000000000000000e3), SC_(3.758097656250000000000000000000000000000e3), SC_(1.879048828125000000000000000000000000000e3), SC_(4.805082082748413085937500000000000000000e-1), SC_(9.999999999999968174474902410920896815627e-1), SC_(3.182552509758907910318437261362448122236e-15) }, 
+      { SC_(1.879048828125000000000000000000000000000e3), SC_(5.637146484375000000000000000000000000000e3), SC_(2.308069091796875000000000000000000000000e3), SC_(4.581811428070068359375000000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(1.102182053081964421449952586342158942845e-77) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(1.154034545898437500000000000000000000000e3), SC_(2.322846374511718750000000000000000000000e2), SC_(9.193707704544067382812500000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.009973732211367743382389112086731774944e-373) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(1.731051757812500000000000000000000000000e3), SC_(2.906821289062500000000000000000000000000e2), SC_(9.172621965408325195312500000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(1.026038931560756120296233644557392281345e-728) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(2.077262207031250000000000000000000000000e3), SC_(9.757655029296875000000000000000000000000e2), SC_(5.737299844622611999511718750000000000000e-2), SC_(1.179438847006603499209184718675810235937e-1792), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(2.284988525390625000000000000000000000000e3), SC_(1.879048828125000000000000000000000000000e3), SC_(1.467453837394714355468750000000000000000e-1), SC_(2.170603560826971624886942881463485578948e-993), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(2.305760986328125000000000000000000000000e3), SC_(2.308069091796875000000000000000000000000e3), SC_(3.001131117343902587890625000000000000000e-1), SC_(8.489166704175388964892782203557684023722e-396), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(2.308069091796875000000000000000000000000e3), SC_(8.064482421875000000000000000000000000000e3), SC_(5.498300790786743164062500000000000000000e-1), SC_(1.254458591955832602131382517483326851816e-213), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(2.308300048828125000000000000000000000000e3), SC_(1.567437500000000000000000000000000000000e4), SC_(7.331741452217102050781250000000000000000e-1), SC_(1.826182635021394060381579011272045655768e-85), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(2.310377197265625000000000000000000000000e3), SC_(2.000542187500000000000000000000000000000e4), SC_(8.335568308830261230468750000000000000000e-1), SC_(4.781961640340889428050915411134222276392e-3), SC_(9.952180383596591105719490845888657777236e-1) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(2.331149658203125000000000000000000000000e3), SC_(5.348914843750000000000000000000000000000e4), SC_(9.247934818267822265625000000000000000000e-1), SC_(2.711435846327258761421995177897213919361e-1), SC_(7.288564153672741238578004822102786080639e-1) }, 
+      { SC_(8.064482421875000000000000000000000000000e3), SC_(8.064482421875000000000000000000000000000e2), SC_(5.348914843750000000000000000000000000000e4), SC_(9.886781573295593261718750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(3.572832953557009007878032183153866412857e-70) }, 
+      { SC_(8.064482421875000000000000000000000000000e3), SC_(8.870930664062500000000000000000000000000e3), SC_(2.322846374511718750000000000000000000000e2), SC_(4.797580540180206298828125000000000000000e-1), SC_(5.000745572327812933893269721471576983968e-1), SC_(4.999254427672187066106730278528423016032e-1) }, 
+      { SC_(8.064482421875000000000000000000000000000e3), SC_(9.677378906250000000000000000000000000000e3), SC_(2.906821289062500000000000000000000000000e2), SC_(4.590313434600830078125000000000000000000e-1), SC_(5.059188813196472021413131958200680825291e-1), SC_(4.940811186803527978586868041799319174709e-1) }, 
+      { SC_(8.064482421875000000000000000000000000000e3), SC_(1.048382714843750000000000000000000000000e4), SC_(9.757655029296875000000000000000000000000e2), SC_(4.498181641101837158203125000000000000000e-1), SC_(5.598900959283613304893371453709487210277e-1), SC_(4.401099040716386695106628546290512789723e-1) }, 
+      { SC_(8.064482421875000000000000000000000000000e3), SC_(1.209672363281250000000000000000000000000e4), SC_(1.879048828125000000000000000000000000000e3), SC_(4.323903024196624755859375000000000000000e-1), SC_(9.472136011791436975079346659925488874113e-1), SC_(5.278639882085630249206533400745111258868e-2) }, 
+      { SC_(8.064482421875000000000000000000000000000e3), SC_(1.612896484375000000000000000000000000000e4), SC_(2.308069091796875000000000000000000000000e3), SC_(4.215314388275146484375000000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(8.780570835430068597846932288933646184057e-74) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(3.918593750000000000000000000000000000000e3), SC_(2.322846374511718750000000000000000000000e2), SC_(9.337261915206909179687500000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(6.669886156648541481539239127712633559563e-822) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(7.837187500000000000000000000000000000000e3), SC_(2.906821289062500000000000000000000000000e2), SC_(9.171786308288574218750000000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.537328853966596437961665214743068422061e-2547) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(1.175578125000000000000000000000000000000e4), SC_(9.757655029296875000000000000000000000000e2), SC_(9.157835841178894042968750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.578246188050503138375491350089200688257e-4975) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(1.410693750000000000000000000000000000000e4), SC_(1.879048828125000000000000000000000000000e3), SC_(5.408018454909324645996093750000000000000e-2), SC_(8.129170124843363135273982574840676966496e-11622), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(1.551763183593750000000000000000000000000e4), SC_(2.308069091796875000000000000000000000000e3), SC_(1.300653219223022460937500000000000000000e-1), SC_(9.360587609330494354572770355536264481673e-5810), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(1.565870117187500000000000000000000000000e4), SC_(8.064482421875000000000000000000000000000e3), SC_(2.786142826080322265625000000000000000000e-1), SC_(1.261773771265826023398263693589020602527e-2297), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(1.567437500000000000000000000000000000000e4), SC_(1.567437500000000000000000000000000000000e4), SC_(4.499984383583068847656250000000000000000e-1), SC_(1.100181469524262372222569926548005371912e-657), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(1.567594238281250000000000000000000000000e4), SC_(2.000542187500000000000000000000000000000e4), SC_(5.588295459747314453125000000000000000000e-1), SC_(2.560684482889387137691472255137878939473e-124), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(1.569004980468750000000000000000000000000e4), SC_(5.348914843750000000000000000000000000000e4), SC_(7.226873636245727539062500000000000000000e-1), SC_(1.364294949865959215854400373254240620072e-4), SC_(9.998635705050134040784145599626745759380e-1) }, 
+      { SC_(2.000542187500000000000000000000000000000e4), SC_(2.020547656250000000000000000000000000000e4), SC_(2.322846374511718750000000000000000000000e2), SC_(4.984606206417083740234375000000000000000e-1), SC_(4.207010290007294561360169037428775918686e-1), SC_(5.792989709992705438639830962571224081314e-1) }, 
+      { SC_(2.000542187500000000000000000000000000000e4), SC_(2.200596484375000000000000000000000000000e4), SC_(2.906821289062500000000000000000000000000e2), SC_(4.779963195323944091796875000000000000000e-1), SC_(5.000532054426537105845574884793934312647e-1), SC_(4.999467945573462894154425115206065687353e-1) }, 
+      { SC_(2.000542187500000000000000000000000000000e4), SC_(2.400650781250000000000000000000000000000e4), SC_(9.757655029296875000000000000000000000000e2), SC_(4.605794548988342285156250000000000000000e-1), SC_(5.091425099452637143386757843925728266261e-1), SC_(4.908574900547362856613242156074271733739e-1) }, 
+      { SC_(2.000542187500000000000000000000000000000e4), SC_(2.600704687500000000000000000000000000000e4), SC_(1.879048828125000000000000000000000000000e3), SC_(4.466459453105926513671875000000000000000e-1), SC_(5.942780802025344552207236227109420873466e-1), SC_(4.057219197974655447792763772890579126534e-1) }, 
+      { SC_(2.000542187500000000000000000000000000000e4), SC_(3.000813281250000000000000000000000000000e4), SC_(2.308069091796875000000000000000000000000e3), SC_(4.193387329578399658203125000000000000000e-1), SC_(9.956380547431874873496935745113045362901e-1), SC_(4.361945256812512650306425488695463709880e-3) }, 
+      { SC_(2.000542187500000000000000000000000000000e4), SC_(4.001084375000000000000000000000000000000e4), SC_(8.064482421875000000000000000000000000000e3), SC_(4.320940375328063964843750000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.312959578619525129783342844601108813625e-171) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.348915039062500000000000000000000000000e3), SC_(2.322846374511718750000000000000000000000e2), SC_(9.546350240707397460937500000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(2.237637941712600702639280257134814673880e-479) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(1.337228710937500000000000000000000000000e4), SC_(2.906821289062500000000000000000000000000e2), SC_(9.334779381752014160156250000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(7.697670330139327953085651655652971629062e-2801) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(2.674457421875000000000000000000000000000e4), SC_(9.757655029296875000000000000000000000000e2), SC_(9.171703457832336425781250000000000000000e-1), SC_(1.000000000000000000000000000000000000000), SC_(4.351032154164457022358781300987678516698e-8686) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(4.814023046875000000000000000000000000000e4), SC_(2.308069091796875000000000000000000000000e3), SC_(5.316342040896415710449218750000000000000e-2), SC_(7.149393115066689998913230513163359568986e-39230), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.295425781250000000000000000000000000000e4), SC_(8.064482421875000000000000000000000000000e3), SC_(1.301675438880920410156250000000000000000e-1), SC_(8.209475494274670414553430270177931678225e-19833), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.343566015625000000000000000000000000000e4), SC_(1.567437500000000000000000000000000000000e4), SC_(2.671890854835510253906250000000000000000e-1), SC_(9.106575025886434917832830930013038223616e-7308), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.348914843750000000000000000000000000000e4), SC_(2.000542187500000000000000000000000000000e4), SC_(4.070649147033691406250000000000000000000e-1), SC_(8.116577402645222335506750742438163224103e-1745), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(5.349450000000000000000000000000000000000e4), SC_(5.348914843750000000000000000000000000000e4), SC_(5.399778485298156738281250000000000000000e-1), SC_(4.303272623463637069485056374998013097226e-372), SC_(1.000000000000000000000000000000000000000) }
+   }};
+#undef SC_
+
diff --git a/test/nccs.ipp b/test/nccs.ipp
new file mode 100644
index 000000000..4195e9acb
--- /dev/null
+++ b/test/nccs.ipp
@@ -0,0 +1,3205 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 3200> nccs = {{
+      { SC_(1.951913356781005859375000000000000000000), SC_(9.566968083381652832031250000000000000000e-1), SC_(2.908610105514526367187500000000000000000e-1), SC_(9.191713210042786241188236234883914114395e-2), SC_(9.080828678995721375881176376511608588560e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(6.366568565368652343750000000000000000000), SC_(2.079620361328125000000000000000000000000), SC_(8.979177306921986952474050864260945461537e-2), SC_(9.102082269307801304752594913573905453846e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(6.889215946197509765625000000000000000000), SC_(4.420564651489257812500000000000000000000), SC_(2.322522640917811378036214577533389504074e-1), SC_(7.677477359082188621963785422466610495926e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(7.142335891723632812500000000000000000000), SC_(6.820687294006347656250000000000000000000), SC_(4.029439026943616888034033394094687890419e-1), SC_(5.970560973056383111965966605905312109581e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(9.234277725219726562500000000000000000000), SC_(1.006757259368896484375000000000000000000e1), SC_(4.912552959077002677485496881218430896094e-1), SC_(5.087447040922997322514503118781569103906e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.942635536193847656250000000000000000000e1), SC_(2.116448593139648437500000000000000000000e1), SC_(5.344158171377402637365393278378581649496e-1), SC_(4.655841828622597362634606721621418350504e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.950807952880859375000000000000000000000e1), SC_(2.143853378295898437500000000000000000000e1), SC_(5.427110898702781884985658638646815339571e-1), SC_(4.572889101297218115014341361353184660429e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(2.197235107421875000000000000000000000000e1), SC_(2.392426490783691406250000000000000000000e1), SC_(5.412751121814981951824612055009695852890e-1), SC_(4.587248878185018048175387944990304147110e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(2.249290275573730468750000000000000000000e1), SC_(2.444726181030273437500000000000000000000e1), SC_(5.409219532207546156929103529206929272982e-1), SC_(4.590780467792453843070896470793070727018e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(2.503655242919921875000000000000000000000e1), SC_(2.701545524597167968750000000000000000000e1), SC_(5.398488681606659449009007854898639088100e-1), SC_(4.601511318393340550990992145101360911900e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(2.539736366271972656250000000000000000000e1), SC_(2.762277030944824218750000000000000000000e1), SC_(5.489826827593184212047987802360330000285e-1), SC_(4.510173172406815787952012197639669999715e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(2.709540176391601562500000000000000000000e1), SC_(3.195204734802246093750000000000000000000e1), SC_(6.402283129477376083547421708583723034402e-1), SC_(3.597716870522623916452578291416276965598e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(2.837726783752441406250000000000000000000e1), SC_(3.639501953125000000000000000000000000000e1), SC_(7.328503378322701372366867357591531160795e-1), SC_(2.671496621677298627633132642408468839205e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(2.982279586791992187500000000000000000000e1), SC_(4.130712127685546875000000000000000000000e1), SC_(8.120315212974665140882026008610420369286e-1), SC_(1.879684787025334859117973991389579630714e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(3.152261734008789062500000000000000000000e1), SC_(5.021179199218750000000000000000000000000e1), SC_(9.186319322366888176750588602864877172835e-1), SC_(8.136806776331118232494113971351228271646e-2) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(3.423733520507812500000000000000000000000e1), SC_(7.237849426269531250000000000000000000000e1), SC_(9.951873088673392922733292174972560412168e-1), SC_(4.812691132660707726670782502743958783235e-3) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(3.477303314208984375000000000000000000000e1), SC_(1.101748352050781250000000000000000000000e2), SC_(9.999971837793305211473087127894649237140e-1), SC_(2.816220669478852691287210535076286027043e-6) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(3.767639541625976562500000000000000000000e1), SC_(1.585132293701171875000000000000000000000e2), SC_(9.999999999217985889295034646019210191196e-1), SC_(7.820141107049653539807898088039446209823e-11) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(4.238486480712890625000000000000000000000e1), SC_(2.216838836669921875000000000000000000000e2), SC_(9.999999999999999601293913998035171348369e-1), SC_(3.987060860019648286516310053058333358666e-17) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(4.420680999755859375000000000000000000000e1), SC_(4.615872383117675781250000000000000000000), SC_(1.905661027512242706659103721587818984333e-6), SC_(9.999980943389724877572933408962784121810e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(5.538459396362304687500000000000000000000e1), SC_(1.433412647247314453125000000000000000000e1), SC_(9.034581449355297571199439006101212682858e-5), SC_(9.999096541855064470242880056099389878732e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(5.569964599609375000000000000000000000000e1), SC_(2.882577896118164062500000000000000000000e1), SC_(1.502491024742726900721768573150553664461e-2), SC_(9.849750897525727309927823142684944633554e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(5.940588760375976562500000000000000000000e1), SC_(4.601834869384765625000000000000000000000e1), SC_(1.611280641977754491265049708566642649071e-1), SC_(8.388719358022245508734950291433357350929e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(6.038262176513671875000000000000000000000e1), SC_(5.610107803344726562500000000000000000000e1), SC_(3.657521178731620226395103904384252292498e-1), SC_(6.342478821268379773604896095615747707502e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(6.163340759277343750000000000000000000000e1), SC_(6.294946670532226562500000000000000000000e1), SC_(5.091374904325356692615510556985159084002e-1), SC_(4.908625095674643307384489443014840915998e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(6.331008529663085937500000000000000000000e1), SC_(6.519673919677734375000000000000000000000e1), SC_(5.231859749752328120091326913983730165168e-1), SC_(4.768140250247671879908673086016269834832e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(6.341989517211914062500000000000000000000e1), SC_(6.537181091308593750000000000000000000000e1), SC_(5.247798390357895659922652920258981413362e-1), SC_(4.752201609642104340077347079741018586638e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(7.225879669189453125000000000000000000000e1), SC_(7.421813201904296875000000000000000000000e1), SC_(5.234172204634461348973050395185083796154e-1), SC_(4.765827795365538651026949604814916203846e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(7.844540405273437500000000000000000000000e1), SC_(8.047771453857421875000000000000000000000e1), SC_(5.241166012332058450099735584802403396666e-1), SC_(4.758833987667941549900264415197596603334e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(7.974770355224609375000000000000000000000e1), SC_(8.251660919189453125000000000000000000000e1), SC_(5.401275541463796727029721715244411607698e-1), SC_(4.598724458536203272970278284755588392302e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(8.435225677490234375000000000000000000000e1), SC_(9.493458557128906250000000000000000000000e1), SC_(6.945150702027718064387971840673098423325e-1), SC_(3.054849297972281935612028159326901576675e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(8.441753387451171875000000000000000000000e1), SC_(1.036433410644531250000000000000000000000e2), SC_(8.272511071589428500718069542694108681095e-1), SC_(1.727488928410571499281930457305891318905e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(9.495173645019531250000000000000000000000e1), SC_(1.259747390747070312500000000000000000000e2), SC_(9.242119719038375857308175896733646764492e-1), SC_(7.578802809616241426918241032663532355085e-2) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(9.707512664794921875000000000000000000000e1), SC_(1.485405578613281250000000000000000000000e2), SC_(9.890367746031278342312969412157252380369e-1), SC_(1.096322539687216576870305878427476196306e-2) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(9.811781311035156250000000000000000000000e1), SC_(2.001394500732421875000000000000000000000e2), SC_(9.999867471525884221223495220849233657771e-1), SC_(1.325284741157787765047791507663422291772e-5) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.007325439453125000000000000000000000000e2), SC_(3.080533752441406250000000000000000000000e2), SC_(9.999999999999626856367701345315672334662e-1), SC_(3.731436322986546843276653379798110295426e-14) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.093762969970703125000000000000000000000e2), SC_(4.453128356933593750000000000000000000000e2), SC_(9.999999999999999999999999869957388503105e-1), SC_(1.300426114968953210370021710236260945941e-26) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.094441146850585937500000000000000000000e2), SC_(5.569801025390625000000000000000000000000e2), SC_(9.999999999999999999999999999999999999985e-1), SC_(1.454780177561926332042209107700037715461e-39) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.264718551635742187500000000000000000000e2), SC_(1.284237670898437500000000000000000000000e1), SC_(5.222989929752465381367695253781868498622e-15), SC_(9.999999999999947770100702475346186323047e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.279526672363281250000000000000000000000e2), SC_(3.247614669799804687500000000000000000000e1), SC_(7.092987538615312696053198552453967755005e-9), SC_(9.999999929070124613846873039468014475460e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.310955810546875000000000000000000000000e2), SC_(6.652375030517578125000000000000000000000e1), SC_(4.149921419238204980392051630305258887363e-4), SC_(9.995850078580761795019607948369694741113e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.311481323242187500000000000000000000000e2), SC_(9.982504272460937500000000000000000000000e1), SC_(6.612715986899804491611660635109993003519e-2), SC_(9.338728401310019550838833936489000699648e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.327210998535156250000000000000000000000e2), SC_(1.212057113647460937500000000000000000000e2), SC_(2.899836628432815307947437260175033162688e-1), SC_(7.100163371567184692052562739824966837312e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.357470245361328125000000000000000000000e2), SC_(1.363219604492187500000000000000000000000e2), SC_(4.935330558490911252185725134753965026552e-1), SC_(5.064669441509088747814274865246034973448e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.362719116210937500000000000000000000000e2), SC_(1.380856018066406250000000000000000000000e2), SC_(5.146537665673362067255846059601319698069e-1), SC_(4.853462334326637932744153940398680301931e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.389657287597656250000000000000000000000e2), SC_(1.409176483154296875000000000000000000000e2), SC_(5.168378642075320211457630901833535233871e-1), SC_(4.831621357924679788542369098166464766129e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.412092285156250000000000000000000000000e2), SC_(1.431754608154296875000000000000000000000e2), SC_(5.169436664301119716716053496901880183243e-1), SC_(4.830563335698880283283946503098119816757e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.451677856445312500000000000000000000000e2), SC_(1.472668304443359375000000000000000000000e2), SC_(5.188981985493474256932176544847754096874e-1), SC_(4.811018014506525743067823455152245903126e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.481294555664062500000000000000000000000e2), SC_(1.515821838378906250000000000000000000000e2), SC_(5.406622878092400357690536608444921680034e-1), SC_(4.593377121907599642309463391555078319966e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.486264953613281250000000000000000000000e2), SC_(1.656362609863281250000000000000000000000e2), SC_(7.391397189328775581384348958477215460740e-1), SC_(2.608602810671224418615651041522784539260e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.515480346679687500000000000000000000000e2), SC_(1.841999511718750000000000000000000000000e2), SC_(8.896558084407117967808474192131987138874e-1), SC_(1.103441915592882032191525807868012861126e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.527500000000000000000000000000000000000e2), SC_(2.011124877929687500000000000000000000000e2), SC_(9.629705966174118390791283637763410295302e-1), SC_(3.702940338258816092087163622365897046984e-2) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.584414672851562500000000000000000000000e2), SC_(2.405900878906250000000000000000000000000e2), SC_(9.980712396528729011573908230977135787903e-1), SC_(1.928760347127098842609176902286421209744e-3) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.594559783935546875000000000000000000000e2), SC_(3.228157958984375000000000000000000000000e2), SC_(9.999999445917227847846508437559823409047e-1), SC_(5.540827721521534915624401765909528966399e-8) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.595857238769531250000000000000000000000e2), SC_(4.846129150390625000000000000000000000000e2), SC_(9.999999999999999999957405096393651479609e-1), SC_(4.259490360634852039115781052649444943445e-21) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.596211700439453125000000000000000000000e2), SC_(6.462923583984375000000000000000000000000e2), SC_(9.999999999999999999999999999999999998666e-1), SC_(1.334240896327898129861145777016715981703e-37) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.600560913085937500000000000000000000000e2), SC_(8.100400390625000000000000000000000000000e2), SC_(1.000000000000000000000000000000000000000), SC_(1.959033484704693563237887368387876094125e-56) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.629447326660156250000000000000000000000e2), SC_(1.648966598510742187500000000000000000000e1), SC_(9.167717762926751639562323741092713671023e-19), SC_(9.999999999999999990832282237073248360438e-1) }, 
+      { SC_(1.951913356781005859375000000000000000000), SC_(1.643806610107421875000000000000000000000e2), SC_(4.158314514160156250000000000000000000000e1), SC_(6.635104828532394976511689206464619299402e-11), SC_(9.999999999336489517146760502348831079354e-1) }, 
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+      { SC_(1.992958068847656250000000000000000000000e2), SC_(2.837726783752441406250000000000000000000e1), SC_(6.830192260742187500000000000000000000000e2), SC_(1.000000000000000000000000000000000000000), SC_(1.596173863478020974160494704614658560640e-42) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(2.982279586791992187500000000000000000000e1), SC_(9.164744262695312500000000000000000000000e2), SC_(1.000000000000000000000000000000000000000), SC_(7.455957003768529406461545771049812165338e-75) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(3.152261734008789062500000000000000000000e1), SC_(1.154092041015625000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(1.693222372366514029556108319256273073032e-110) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(3.423733520507812500000000000000000000000e1), SC_(2.335331535339355468750000000000000000000e1), SC_(3.103182379472903797601940814985594672749e-63), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(3.477303314208984375000000000000000000000e1), SC_(5.851721191406250000000000000000000000000e1), SC_(7.420641678914550895308006723734516551112e-30), SC_(9.999999999999999999999999999925793583211e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(3.767639541625976562500000000000000000000e1), SC_(1.184860992431640625000000000000000000000e2), SC_(2.383139839135143731922234253494684226556e-10), SC_(9.999999997616860160864856268077765746505e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(4.238486480712890625000000000000000000000e1), SC_(1.812604980468750000000000000000000000000e2), SC_(3.027357340450312671247602441976583838184e-3), SC_(9.969726426595496873287523975580234161618e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(4.420680999755859375000000000000000000000e1), SC_(2.191523590087890625000000000000000000000e2), SC_(1.544004671524164671894090930806851592772e-1), SC_(8.455995328475835328105909069193148407228e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(5.538459396362304687500000000000000000000e1), SC_(2.521336059570312500000000000000000000000e2), SC_(4.717010394632957111000217685075435347177e-1), SC_(5.282989605367042888999782314924564652823e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(5.569964599609375000000000000000000000000e1), SC_(2.547404632568359375000000000000000000000e2), SC_(5.085064634043854272643008119337915428271e-1), SC_(4.914935365956145727356991880662084571729e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(5.940588760375976562500000000000000000000e1), SC_(2.587016906738281250000000000000000000000e2), SC_(5.125169162440256991403526062617440053744e-1), SC_(4.874830837559743008596473937382559946256e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(6.038262176513671875000000000000000000000e1), SC_(2.597044067382812500000000000000000000000e2), SC_(5.129080861569142407257142135128426031641e-1), SC_(4.870919138430857592742857864871573968359e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(6.163340759277343750000000000000000000000e1), SC_(2.611901550292968750000000000000000000000e2), SC_(5.165684159239572039760357165390752194857e-1), SC_(4.834315840760427960239642834609247805143e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(6.331008529663085937500000000000000000000e1), SC_(2.652319641113281250000000000000000000000e2), SC_(5.531745854351384031064771924275531720248e-1), SC_(4.468254145648615968935228075724468279752e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(6.341989517211914062500000000000000000000e1), SC_(2.889872741699218750000000000000000000000e2), SC_(8.480809538563064598505202795459528835631e-1), SC_(1.519190461436935401494797204540471164369e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(7.225879669189453125000000000000000000000e1), SC_(3.258655395507812500000000000000000000000e2), SC_(9.762916737191814395013111152174334518554e-1), SC_(2.370832628081856049868888478256654814462e-2) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(7.844540405273437500000000000000000000000e1), SC_(3.610635681152343750000000000000000000000e2), SC_(9.981151164217188367115242273673616021111e-1), SC_(1.884883578281163288475772632638397888942e-3) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(7.974770355224609375000000000000000000000e1), SC_(4.185652770996093750000000000000000000000e2), SC_(9.999977834200703695571672244148127730619e-1), SC_(2.216579929630442832775585187226938128851e-6) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(8.435225677490234375000000000000000000000e1), SC_(5.672961425781250000000000000000000000000e2), SC_(9.999999999999999582156647231511972583150e-1), SC_(4.178433527684880274168501371346571094419e-17) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(8.441753387451171875000000000000000000000e1), SC_(8.511400146484375000000000000000000000000e2), SC_(1.000000000000000000000000000000000000000), SC_(3.925070158959466953812479298717915302202e-47) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(9.495173645019531250000000000000000000000e1), SC_(1.176990234375000000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(1.483287238711652862667480704405226065147e-85) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(9.707512664794921875000000000000000000000e1), SC_(1.481854736328125000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(1.514425769807175623558095528529580391211e-127) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(9.811781311035156250000000000000000000000e1), SC_(2.974136352539062500000000000000000000000e1), SC_(7.951503824873234670315135566997042985015e-66), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.007325439453125000000000000000000000000e2), SC_(7.500708770751953125000000000000000000000e1), SC_(1.351138180982215102176233383969144843736e-31), SC_(9.999999999999999999999999999998648861819e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.093762969970703125000000000000000000000e2), SC_(1.543360595703125000000000000000000000000e2), SC_(3.842311051911953531699511314150830125915e-11), SC_(9.999999999615768894808804646830048868585e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.094441146850585937500000000000000000000e2), SC_(2.315549468994140625000000000000000000000e2), SC_(1.977771601141785005040394981394662386973e-3), SC_(9.980222283988582149949596050186053376130e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.264718551635742187500000000000000000000e2), SC_(2.931908874511718750000000000000000000000e2), SC_(1.379394613924815578740312961727573956301e-1), SC_(8.620605386075184421259687038272426043699e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.279526672363281250000000000000000000000e2), SC_(3.239759826660156250000000000000000000000e2), SC_(4.679501016162186391406519275639482219570e-1), SC_(5.320498983837813608593480724360517780430e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.310955810546875000000000000000000000000e2), SC_(3.300610046386718750000000000000000000000e2), SC_(5.069084021374822564265958345673588983285e-1), SC_(4.930915978625177435734041654326411016715e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.311481323242187500000000000000000000000e2), SC_(3.304439392089843750000000000000000000000e2), SC_(5.112441754093731192770461370966518166597e-1), SC_(4.887558245906268807229538629033481833403e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.327210998535156250000000000000000000000e2), SC_(3.320501098632812500000000000000000000000e2), SC_(5.116528911763111280094804346204772872348e-1), SC_(4.883471088236888719905195653795227127652e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.357470245361328125000000000000000000000e2), SC_(3.353778991699218750000000000000000000000e2), SC_(5.155208220685295000915831311905315735513e-1), SC_(4.844791779314704999084168688094684264487e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.362719116210937500000000000000000000000e2), SC_(3.389234008789062500000000000000000000000e2), SC_(5.544203142815802710390962198185787464169e-1), SC_(4.455796857184197289609037801814212535831e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.389657287597656250000000000000000000000e2), SC_(3.720877075195312500000000000000000000000e2), SC_(8.622908847894982566097825610829691392981e-1), SC_(1.377091152105017433902174389170308607019e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.412092285156250000000000000000000000000e2), SC_(4.086060485839843750000000000000000000000e2), SC_(9.821607322117884979495654377827711966550e-1), SC_(1.783926778821150205043456221722880334497e-2) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.451677856445312500000000000000000000000e2), SC_(4.478026428222656250000000000000000000000e2), SC_(9.989298174363830482551903570127157560119e-1), SC_(1.070182563616951744809642987284243988141e-3) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.481294555664062500000000000000000000000e2), SC_(5.211378784179687500000000000000000000000e2), SC_(9.999994797904691860176751277865619206758e-1), SC_(5.202095308139823248722134380793241867631e-7) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.486264953613281250000000000000000000000e2), SC_(6.958446044921875000000000000000000000000e2), SC_(9.999999999999999996045263399197254490884e-1), SC_(3.954736600802745509115943800189889355831e-19) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.515480346679687500000000000000000000000e2), SC_(1.052531494140625000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(6.601257805885150289909120658456231227750e-54) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.527500000000000000000000000000000000000e2), SC_(1.408183227539062500000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(1.000237582081951046145742432553355955693e-96) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.584414672851562500000000000000000000000e2), SC_(1.788686401367187500000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(5.957827315427703908759646403474290650064e-146) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.594559783935546875000000000000000000000e2), SC_(3.587517929077148437500000000000000000000e1), SC_(1.356176082172300107520771145977600912607e-69), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.595857238769531250000000000000000000000e2), SC_(8.972038269042968750000000000000000000000e1), SC_(8.216070643082009610897966985030390252065e-34), SC_(9.999999999999999999999999999999991783929e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.596211700439453125000000000000000000000e2), SC_(1.794584960937500000000000000000000000000e2), SC_(7.166324162989548688114040163345096606824e-12), SC_(9.999999999928336758370104513118859598367e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.600560913085937500000000000000000000000e2), SC_(2.695139160156250000000000000000000000000e2), SC_(1.327523249276128325865905450265666297728e-3), SC_(9.986724767507238716741340945497343337023e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.629447326660156250000000000000000000000e2), SC_(3.260164794921875000000000000000000000000e2), SC_(1.301004072687408931880643785374331713448e-1), SC_(8.698995927312591068119356214625668286552e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.643806610107421875000000000000000000000e2), SC_(3.600397033691406250000000000000000000000e2), SC_(4.660182128381547289926298172432381841274e-1), SC_(5.339817871618452710073701827567618158726e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.646915740966796875000000000000000000000e2), SC_(3.636233825683593750000000000000000000000e2), SC_(5.062665303560026040030081445813429265462e-1), SC_(4.937334696439973959969918554186570734538e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.670017089843750000000000000000000000000e2), SC_(3.662975158691406250000000000000000000000e2), SC_(5.106973005574084169848510356025972361947e-1), SC_(4.893026994425915830151489643974027638053e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.698258666992187500000000000000000000000e2), SC_(3.691585998535156250000000000000000000000e2), SC_(5.111052702424046835457855804537903702324e-1), SC_(4.888947297575953164542144195462096297676e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.744857635498046875000000000000000000000e2), SC_(3.741553649902343750000000000000000000000e2), SC_(5.150887834143480940075807657281644704146e-1), SC_(4.849112165856519059924192342718355295854e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.756861267089843750000000000000000000000e2), SC_(3.787317504882812500000000000000000000000e2), SC_(5.553201941675350167646371773361318286268e-1), SC_(4.446798058324649832353628226638681713732e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.811583862304687500000000000000000000000e2), SC_(4.184996337890625000000000000000000000000e2), SC_(8.705310827199552808744555344825350400779e-1), SC_(1.294689172800447191255444655174649599221e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.826751708984375000000000000000000000000e2), SC_(4.583652038574218750000000000000000000000e2), SC_(9.852368357723595013366611071898316886584e-1), SC_(1.476316422764049866333889281016831134165e-2) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.831471099853515625000000000000000000000e2), SC_(4.971757812500000000000000000000000000000e2), SC_(9.992475277030363823098749022492933911247e-1), SC_(7.524722969636176901250977507066088753398e-4) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.867986450195312500000000000000000000000e2), SC_(5.791416625976562500000000000000000000000e2), SC_(9.999997868073928052689964204548628458249e-1), SC_(2.131926071947310035795451371541751186443e-7) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.900444183349609375000000000000000000000e2), SC_(7.786804199218750000000000000000000000000e2), SC_(9.999999999999999999842890448735225215767e-1), SC_(1.571095512647747842332431001488736906025e-20) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.914333953857421875000000000000000000000e2), SC_(1.172187500000000000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(3.535476598966853255870979872762898186893e-58) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.915013732910156250000000000000000000000e2), SC_(1.563188720703125000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(1.503818272229840966678812511638176571203e-104) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.918984832763671875000000000000000000000e2), SC_(1.955971435546875000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(2.310477211914576555408738212352063615286e-156) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.929777069091796875000000000000000000000e2), SC_(3.922735214233398437500000000000000000000e1), SC_(5.529022449107786967054709588291909745351e-72), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.935389862060546875000000000000000000000e2), SC_(9.820869445800781250000000000000000000000e1), SC_(3.003464474651918107665338937597739013444e-35), SC_(9.999999999999999999999999999999999699654e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.937735595703125000000000000000000000000e2), SC_(1.965346832275390625000000000000000000000e2), SC_(2.080463495775573742672052667674087592048e-12), SC_(9.999999999979195365042244262573279473323e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.941185607910156250000000000000000000000e2), SC_(2.950607910156250000000000000000000000000e2), SC_(9.973915776745850702522937113932704987176e-4), SC_(9.990026084223254149297477062886067295013e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.962219390869140625000000000000000000000e2), SC_(3.559659729003906250000000000000000000000e2), SC_(1.231238558149305651892248029845975246239e-1), SC_(8.768761441850694348107751970154024753761e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.985762634277343750000000000000000000000e2), SC_(3.938933410644531250000000000000000000000e2), SC_(4.642429596210990429025849224204611903317e-1), SC_(5.357570403789009570974150775795388096683e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.988137054443359375000000000000000000000e2), SC_(3.977113952636718750000000000000000000000e2), SC_(5.056692632383849664727396199463872273040e-1), SC_(4.943307367616150335272603800536127726960e-1) }, 
+      { SC_(1.992958068847656250000000000000000000000e2), SC_(1.992922668457031250000000000000000000000e2), SC_(3.985880737304687500000000000000000000000e2), SC_(5.102581793845303603671068481454659458711e-1), SC_(4.897418206154696396328931518545340541289e-1) }
+   }};
+#undef SC_
+
diff --git a/test/nccs_big.ipp b/test/nccs_big.ipp
new file mode 100644
index 000000000..616de2441
--- /dev/null
+++ b/test/nccs_big.ipp
@@ -0,0 +1,240 @@
+// Copyright John Maddock 2008.
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+//
+// Some of these tests have been commented out: 
+// the current algorithm may underflow to zero
+// prematurely in these cases.
+//
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 216> nccs_big = {{
+      { SC_(1.018147201538085937500000000000000000000e2), SC_(1.814723730087280273437500000000000000000), SC_(1.036294460296630859375000000000000000000e1), SC_(6.015496565199092654771842521716269252752e-33), SC_(9.999999999999999999999999999999939845034e-1) }, 
+      { SC_(1.018147201538085937500000000000000000000e2), SC_(2.270954132080078125000000000000000000000), SC_(2.602141952514648437500000000000000000000e1), SC_(6.271325708033427466636203558887430713942e-16), SC_(9.999999999999993728674291966572533363796e-1) }, 
+      { SC_(1.018147201538085937500000000000000000000e2), SC_(7.623167991638183593750000000000000000000), SC_(5.471894454956054687500000000000000000000e1), SC_(5.592130493491734836774684682197361443348e-6), SC_(9.999944078695065082651632253153178026386e-1) }, 
+      { SC_(1.018147201538085937500000000000000000000e2), SC_(1.468006896972656250000000000000000000000e1), SC_(8.737109375000000000000000000000000000000e1), SC_(2.710350845630041378510514217949405178637e-2), SC_(9.728964915436995862148948578205059482136e-1) }, 
+      { SC_(1.018147201538085937500000000000000000000e2), SC_(1.803178977966308593750000000000000000000e1), SC_(1.078618545532226562500000000000000000000e2), SC_(2.416865577598000489309403624290209365410e-1), SC_(7.583134422401999510690596375709790634590e-1) }, 
+      { SC_(1.018147201538085937500000000000000000000e2), SC_(6.300376892089843750000000000000000000000e1), SC_(1.631703033447265625000000000000000000000e2), SC_(4.850524327039212486399364362407790060498e-1), SC_(5.149475672960787513600635637592209939502e-1) }, 
+      { SC_(1.018147201538085937500000000000000000000e2), SC_(1.224560546875000000000000000000000000000e2), SC_(2.240465087890625000000000000000000000000e2), SC_(5.102803820072670629735512094460263022259e-1), SC_(4.897196179927329370264487905539736977741e-1) }, 
+      { SC_(1.018147201538085937500000000000000000000e2), SC_(1.562923583984375000000000000000000000000e2), SC_(2.581070861816406250000000000000000000000e2), SC_(5.127291899610524813372367620548767727485e-1), SC_(4.872708100389475186627632379451232272515e-1) }, 
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+      { SC_(3.268707763671875000000000000000000000000e3), SC_(6.697814941406250000000000000000000000000e2), SC_(2.953866943359375000000000000000000000000e3), SC_(1.407565789077463347175673837791022925398e-29), SC_(9.999999999999999999999999999859243421092e-1) }, 
+      { SC_(3.268707763671875000000000000000000000000e3), SC_(1.123881347656250000000000000000000000000e3), SC_(3.953329833984375000000000000000000000000e3), SC_(7.940374169384573883003159947702418665259e-6), SC_(9.999920596258306154261169968400522975813e-1) }, 
+      { SC_(3.268707763671875000000000000000000000000e3), SC_(3.168707763671875000000000000000000000000e3), SC_(6.373041503906250000000000000000000000000e3), SC_(3.229699874048570325644015283488133243419e-1), SC_(6.770300125951429674355984716511866756581e-1) }, 
+      { SC_(3.268707763671875000000000000000000000000e3), SC_(5.236728515625000000000000000000000000000e3), SC_(8.496931640625000000000000000000000000000e3), SC_(4.817511189518640281763605885755537488723e-1), SC_(5.182488810481359718236394114244462511277e-1) }, 
+      { SC_(3.268707763671875000000000000000000000000e3), SC_(9.735224609375000000000000000000000000000e3), SC_(1.300393261718750000000000000000000000000e4), SC_(5.017815537703105249703557002638167692452e-1), SC_(4.982184462296894750296442997361832307548e-1) }, 
+      { SC_(3.268707763671875000000000000000000000000e3), SC_(2.534410546875000000000000000000000000000e4), SC_(2.861567382812500000000000000000000000000e4), SC_(5.046636709131849599417788658424494463632e-1), SC_(4.953363290868150400582211341575505536368e-1) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(1.814723730087280273437500000000000000000), SC_(5.343882324218750000000000000000000000000e3), SC_(5.231641912991815247310768938116631968187e-1), SC_(4.768358087008184752689231061883368031813e-1) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(2.270954132080078125000000000000000000000), SC_(5.392389648437500000000000000000000000000e3), SC_(6.989209785829823642527285557816442705306e-1), SC_(3.010790214170176357472714442183557294694e-1) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(7.623167991638183593750000000000000000000), SC_(5.878786621093750000000000000000000000000e3), SC_(9.999997267631334862144092371181640867755e-1), SC_(2.732368665137855907628818359132245077050e-7) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(1.468006896972656250000000000000000000000e1), SC_(6.421690917968750000000000000000000000000e3), SC_(9.999999999999999999998755436517077779140e-1), SC_(1.244563482922220859843457033640238937977e-22) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(1.803178977966308593750000000000000000000e1), SC_(6.961187988281250000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(6.213904209645332170491444002733911787382e-46) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(6.300376892089843750000000000000000000000e1), SC_(8.099598632812500000000000000000000000000e3), SC_(1.000000000000000000000000000000000000000), SC_(4.129578759179570039501223721133554053649e-112) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(1.224560546875000000000000000000000000000e2), SC_(1.091836914062500000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(1.013122398540403737571759044585873714869e-358) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(1.562923583984375000000000000000000000000e2), SC_(1.647906250000000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(1.798378318681131842856599937421909755127e-1049) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(4.178839721679687500000000000000000000000e2), SC_(2.301844921875000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(1.245637974066302551841972589921559293779e-1895) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(6.697814941406250000000000000000000000000e2), SC_(3.003254882812500000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(1.964762684623637286574646116911226588649e-2854) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(1.123881347656250000000000000000000000000e3), SC_(6.460609741210937500000000000000000000000e2), SC_(5.434554874828800376020528413555687226962e-1646), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(3.168707763671875000000000000000000000000e3), SC_(2.126359130859375000000000000000000000000e3), SC_(4.014044471242827936794218405164185178313e-811), SC_(1.000000000000000000000000000000000000000) }, 
+      //{ SC_(5.336728515625000000000000000000000000000e3), SC_(5.236728515625000000000000000000000000000e3), SC_(5.286728515625000000000000000000000000000e3), SC_(4.230486062225304643326517333533191913791e-285), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(9.735224609375000000000000000000000000000e3), SC_(1.130396484375000000000000000000000000000e4), SC_(4.137926192929096684247217099159206422184e-75), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(5.336728515625000000000000000000000000000e3), SC_(2.534410546875000000000000000000000000000e4), SC_(2.761275000000000000000000000000000000000e4), SC_(2.272437242751958256048797820399249083167e-21), SC_(9.999999999999999999977275627572480417440e-1) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(1.814723730087280273437500000000000000000), SC_(9.738668945312500000000000000000000000000e3), SC_(2.423226533318444691190816122183650790120e-1), SC_(7.576773466681555308809183877816349209880e-1) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(2.270954132080078125000000000000000000000), SC_(9.827658203125000000000000000000000000000e3), SC_(4.739300204447159138057411608874372469320e-1), SC_(5.260699795552840861942588391125627530680e-1) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(7.623167991638183593750000000000000000000), SC_(9.842847656250000000000000000000000000000e3), SC_(5.018959763803816158049482480448946260966e-1), SC_(4.981040236196183841950517519551053739034e-1) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(1.468006896972656250000000000000000000000e1), SC_(9.850889648437500000000000000000000000000e3), SC_(5.046936613055142674404951702442208480020e-1), SC_(4.953063386944857325595048297557791519980e-1) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(1.803178977966308593750000000000000000000e1), SC_(9.863110351562500000000000000000000000000e3), SC_(5.298370953450929796710290002338201784199e-1), SC_(4.701629046549070203289709997661798215801e-1) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(6.300376892089843750000000000000000000000e1), SC_(9.997210937500000000000000000000000000000e3), SC_(7.591896468371765812280509666823008804623e-1), SC_(2.408103531628234187719490333176991195377e-1) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(1.224560546875000000000000000000000000000e2), SC_(1.095344921875000000000000000000000000000e4), SC_(9.999999999946528610317823181276409224358e-1), SC_(5.347138968217681872359077564224414898729e-12) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(1.562923583984375000000000000000000000000e2), SC_(1.198982031250000000000000000000000000000e4), SC_(9.999999999999999999999999999999999999995e-1), SC_(4.844117509934818729605680780365877081835e-40) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(4.178839721679687500000000000000000000000e2), SC_(1.332904003906250000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(5.501985290758226024441004905328583091016e-83) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(6.697814941406250000000000000000000000000e2), SC_(1.575750878906250000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(1.281917879913831434997572136980170169938e-205) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(1.123881347656250000000000000000000000000e3), SC_(2.191821093750000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(1.655478781768704897040723830687178230050e-668) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(3.168707763671875000000000000000000000000e3), SC_(3.901179687500000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(3.472631147339733657827714586706936341515e-2118) }, 
+      //{ SC_(9.835224609375000000000000000000000000000e3), SC_(5.236728515625000000000000000000000000000e3), SC_(6.028781250000000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(9.212326594397207246241789680223342444637e-4200) }, 
+      { SC_(9.835224609375000000000000000000000000000e3), SC_(9.735224609375000000000000000000000000000e3), SC_(9.785225000000000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(3.538077281516414493897074365065585126946e-7667) }, 
+      //{ SC_(9.835224609375000000000000000000000000000e3), SC_(2.534410546875000000000000000000000000000e4), SC_(3.517932861328125000000000000000000000000e3), SC_(1.099992559780263385542867064735840160345e-4822), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(1.814723730087280273437500000000000000000), SC_(6.361479980468750000000000000000000000000e3), SC_(1.181726713955470992474919794090175086526e-3518), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(2.270954132080078125000000000000000000000), SC_(1.272318847656250000000000000000000000000e4), SC_(4.884425625229736252928233330384214577613e-1070), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(7.623167991638183593750000000000000000000), SC_(1.908879687500000000000000000000000000000e4), SC_(8.962370551702060333750421105332120391485e-211), SC_(1.000000000000000000000000000000000000000) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(1.468006896972656250000000000000000000000e1), SC_(2.291290625000000000000000000000000000000e4), SC_(8.474346197209301705276834960187638277086e-32), SC_(9.999999999999999999999999999999152565380e-1) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(1.803178977966308593750000000000000000000e1), SC_(2.520751562500000000000000000000000000000e4), SC_(1.295024406285843621340357720924586110287e-1), SC_(8.704975593714156378659642279075413889713e-1) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(6.300376892089843750000000000000000000000e1), SC_(2.548160351562500000000000000000000000000e4), SC_(4.562568770648142018768727830933913267766e-1), SC_(5.437431229351857981231272169066086732234e-1) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(1.224560546875000000000000000000000000000e2), SC_(2.556656250000000000000000000000000000000e4), SC_(5.011806692322517737217772574781293569349e-1), SC_(4.988193307677482262782227425218706430651e-1) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(1.562923583984375000000000000000000000000e2), SC_(2.560295898437500000000000000000000000000e4), SC_(5.056803760816591586262668258627004583009e-1), SC_(4.943196239183408413737331741372995416991e-1) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(4.178839721679687500000000000000000000000e2), SC_(2.588785351562500000000000000000000000000e4), SC_(5.460676224635753887770522516056576743617e-1), SC_(4.539323775364246112229477483943423256383e-1) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(6.697814941406250000000000000000000000000e2), SC_(2.637502539062500000000000000000000000000e4), SC_(8.702351059685343076476037133703416750345e-1), SC_(1.297648940314656923523962866296583249655e-1) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(1.123881347656250000000000000000000000000e3), SC_(2.922478515625000000000000000000000000000e4), SC_(9.999999999999999999999999996167282036646e-1), SC_(3.832717963354218502430822356853389506342e-28) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(3.168707763671875000000000000000000000000e3), SC_(3.433537500000000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(1.698150074923070488658872407738404871525e-101) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(5.236728515625000000000000000000000000000e3), SC_(3.988508203125000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(1.092452334181002182656298507096893396391e-217) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(9.735224609375000000000000000000000000000e3), SC_(5.276899218750000000000000000000000000000e4), SC_(1.000000000000000000000000000000000000000), SC_(3.597661166334420937810823788802336702587e-576) }, 
+      { SC_(2.544410546875000000000000000000000000000e4), SC_(2.534410546875000000000000000000000000000e4), SC_(1.015764218750000000000000000000000000000e5), SC_(1.000000000000000000000000000000000000000), SC_(2.563248488880158240698244894381770231093e-2382) }
+   }};
+#undef SC_
+
diff --git a/test/nct.ipp b/test/nct.ipp
new file mode 100644
index 000000000..3281d2324
--- /dev/null
+++ b/test/nct.ipp
@@ -0,0 +1,228 @@
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 209-7> nct = {{
+      { SC_(5.637862086296081542968750000000000000000e-1), SC_(-5.074075460433959960937500000000000000000e-1), SC_(-3.162277862429618835449218750000000000000e-2), SC_(6.862274577179818450132372470056769938949e-1), SC_(3.137725422820181549867627529943230061051e-1) }, 
+      { SC_(9.567963480949401855468750000000000000000e-1), SC_(-9.472283720970153808593750000000000000000e-1), SC_(-7.905694097280502319335937500000000000000e-2), SC_(8.115615601997266002916301508229723403909e-1), SC_(1.884384398002733997083698491770276596091e-1) }, 
+      { SC_(2.380512714385986328125000000000000000000), SC_(-2.378132343292236328125000000000000000000), SC_(-6.344355583190917968750000000000000000000), SC_(1.181983559218041139443788725932712768639e-1), SC_(8.818016440781958860556211274067287231361e-1) }, 
+      { SC_(2.707923889160156250000000000000000000000), SC_(2.707923889160156250000000000000000000000), SC_(6.967820167541503906250000000000000000000), SC_(8.962869141158998144131448676176096050228e-1), SC_(1.037130858841001855868551323823903949772e-1) }, 
+      { SC_(3.554877519607543945312500000000000000000), SC_(3.555233001708984375000000000000000000000), SC_(7.444825649261474609375000000000000000000), SC_(8.868528863556108953156241536058758129831e-1), SC_(1.131471136443891046843758463941241870169e-1) }, 
+      { SC_(6.366665840148925781250000000000000000000), SC_(-6.373032569885253906250000000000000000000), SC_(-1.003813362121582031250000000000000000000e1), SC_(1.297164612941840729663335994423583046378e-1), SC_(8.702835387058159270336664005576416953622e-1) }, 
+      { SC_(6.889312267303466796875000000000000000000), SC_(6.958205223083496093750000000000000000000), SC_(1.067599391937255859375000000000000000000e1), SC_(8.692923253313482797187029403902244593628e-1), SC_(1.307076746686517202812970596097755406372e-1) }, 
+      { SC_(7.142432212829589843750000000000000000000), SC_(-7.856675624847412109375000000000000000000), SC_(-1.186992073059082031250000000000000000000e1), SC_(1.313759752665446453920643109581266741211e-1), SC_(8.686240247334553546079356890418733258789e-1) }, 
+      { SC_(7.288346767425537109375000000000000000000), SC_(-8.746016502380371093750000000000000000000), SC_(-1.308834171295166015625000000000000000000e1), SC_(1.317487167403902234213465542239538177641e-1), SC_(8.682512832596097765786534457760461822359e-1) }, 
+      { SC_(9.234373092651367187500000000000000000000), SC_(-1.200468444824218750000000000000000000000e1), SC_(-1.678483200073242187500000000000000000000e1), SC_(1.371773284108319849485042712205994589836e-1), SC_(8.628226715891680150514957287794005410164e-1) }, 
+      { SC_(1.024338054656982421875000000000000000000e1), SC_(-1.536507034301757812500000000000000000000e1), SC_(-2.095777320861816406250000000000000000000e1), SC_(1.376443537392091127705735460070325295078e-1), SC_(8.623556462607908872294264539929674704922e-1) }, 
+      { SC_(1.079011821746826171875000000000000000000e1), SC_(2.158023643493652343750000000000000000000e1), SC_(2.953773117065429687500000000000000000000e1), SC_(8.756990872254366689422087613232016840613e-1), SC_(1.243009127745633310577912386767983159387e-1) }, 
+      { SC_(1.351916885375976562500000000000000000000e1), SC_(4.055750656127929687500000000000000000000e1), SC_(5.393296432495117187500000000000000000000e1), SC_(8.875082903101746924904055764230529369583e-1), SC_(1.124917096898253075095944235769470630417e-1) }, 
+      { SC_(1.517095088958740234375000000000000000000e1), SC_(6.068380355834960937500000000000000000000e1), SC_(8.029798126220703125000000000000000000000e1), SC_(8.999784514511157146615339407607497230611e-1), SC_(1.000215485488842853384660592392502769389e-1) }, 
+      { SC_(1.942644500732421875000000000000000000000e1), SC_(-9.713222503662109375000000000000000000000e1), SC_(-1.270076446533203125000000000000000000000e2), SC_(7.762632640481949429728015088679192552401e-2), SC_(9.223736735951805057027198491132080744760e-1) }, 
+      { SC_(1.950817108154296875000000000000000000000e1), SC_(-1.950817108154296875000000000000000000000), SC_(-4.251358509063720703125000000000000000000), SC_(3.051855543632768793517707982155241831073e-2), SC_(9.694814445636723120648229201784475816893e-1) }, 
+      { SC_(2.197244071960449218750000000000000000000e1), SC_(5.493110179901123046875000000000000000000), SC_(9.847434997558593750000000000000000000000), SC_(9.929860655432502813979005205517475638750e-1), SC_(7.013934456749718602099479448252436125022e-3) }, 
+      { SC_(2.249299240112304687500000000000000000000e1), SC_(-1.124649620056152343750000000000000000000e1), SC_(-2.007061576843261718750000000000000000000e1), SC_(1.741152139887334291426335869016989927262e-3), SC_(9.982588478601126657085736641309830100727e-1) }, 
+      { SC_(2.379962348937988281250000000000000000000e1), SC_(1.784971809387207031250000000000000000000e1), SC_(3.341829299926757812500000000000000000000e1), SC_(9.996211766573392792339813291721999010055e-1), SC_(3.788233426607207660186708278000989945169e-4) }, 
+      { SC_(2.503664016723632812500000000000000000000e1), SC_(-2.253297615051269531250000000000000000000e1), SC_(-2.359688377380371093750000000000000000000e1), SC_(4.134518081460681240313822521036373281691e-1), SC_(5.865481918539318759686177478963626718309e-1) }, 
+      { SC_(2.517941474914550781250000000000000000000e1), SC_(2.492761993408203125000000000000000000000e1), SC_(2.668598747253417968750000000000000000000e1), SC_(6.429374782181830684645655350039514639861e-1), SC_(3.570625217818169315354344649960485360139e-1) }, 
+      { SC_(2.539745140075683593750000000000000000000e1), SC_(2.537205505371093750000000000000000000000e1), SC_(2.814428710937500000000000000000000000000e1), SC_(7.259483462797133090367177861426920725105e-1), SC_(2.740516537202866909632822138573079274895e-1) }, 
+      { SC_(2.598132896423339843750000000000000000000e1), SC_(-2.598132896423339843750000000000000000000e1), SC_(-2.977846527099609375000000000000000000000e1), SC_(2.056285524153440036454579324861282902585e-1), SC_(7.943714475846559963545420675138717097415e-1) }, 
+      { SC_(2.709548759460449218750000000000000000000e1), SC_(2.709819793701171875000000000000000000000e1), SC_(3.155788612365722656250000000000000000000e1), SC_(8.284319294492629884981570706960038439140e-1), SC_(1.715680705507370115018429293039961560860e-1) }, 
+      { SC_(2.772497558593750000000000000000000000000e1), SC_(-2.775270271301269531250000000000000000000e1), SC_(-3.262088012695312500000000000000000000000e1), SC_(1.533040128385550877036403158398526326095e-1), SC_(8.466959871614449122963596841601473673905e-1) }, 
+      { SC_(2.837735366821289062500000000000000000000e1), SC_(-2.866112709045410156250000000000000000000e1), SC_(-3.364639282226562500000000000000000000000e1), SC_(1.517071461091471563002300276017556302873e-1), SC_(8.482928538908528436997699723982443697127e-1) }, 
+      { SC_(2.982288169860839843750000000000000000000e1), SC_(-3.280517196655273437500000000000000000000e1), SC_(-3.830894470214843750000000000000000000000e1), SC_(1.518216968394176742712403142990093487196e-1), SC_(8.481783031605823257287596857009906512804e-1) }, 
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+      { SC_(1.841749572753906250000000000000000000000e2), SC_(1.860167083740234375000000000000000000000e2), SC_(1.966119689941406250000000000000000000000e2), SC_(8.423069271382795700398439101444273937711e-1), SC_(1.576930728617204299601560898555726062289e-1) }, 
+      { SC_(1.858527374267578125000000000000000000000e2), SC_(-2.044380187988281250000000000000000000000e2), SC_(-2.160265808105468750000000000000000000000e2), SC_(1.574804038174927854751974225084637112666e-1), SC_(8.425195961825072145248025774915362887334e-1) }, 
+      { SC_(1.867986450195312500000000000000000000000e2), SC_(2.241583862304687500000000000000000000000e2), SC_(2.368225402832031250000000000000000000000e2), SC_(8.425392206438456186820694371845737047599e-1), SC_(1.574607793561543813179305628154262952401e-1) }, 
+      { SC_(1.868021392822265625000000000000000000000e2), SC_(-2.428427734375000000000000000000000000000e2), SC_(-2.565665283203125000000000000000000000000e2), SC_(1.572680326600672177070073925543010532140e-1), SC_(8.427319673399327822929926074456989467860e-1) }, 
+      { SC_(1.880148162841796875000000000000000000000e2), SC_(-2.820222167968750000000000000000000000000e2), SC_(-2.980253295898437500000000000000000000000e2), SC_(1.552789395983287090937623733357006268049e-1), SC_(8.447210604016712909062376266642993731951e-1) }, 
+      { SC_(1.900444183349609375000000000000000000000e2), SC_(-3.800888366699218750000000000000000000000e2), SC_(-4.032850341796875000000000000000000000000e2), SC_(1.363857890620788955477380353547122412928e-1), SC_(8.636142109379211044522619646452877587072e-1) }, 
+      { SC_(1.910035247802734375000000000000000000000e2), SC_(5.730105590820312500000000000000000000000e2), SC_(6.108234252929687500000000000000000000000e2), SC_(8.825546776651612915449270809923133302827e-1), SC_(1.174453223348387084550729190076866697173e-1) }, 
+      { SC_(1.914333953857421875000000000000000000000e2), SC_(7.657335815429687500000000000000000000000e2), SC_(8.201442260742187500000000000000000000000e2), SC_(8.994307655353378788627687172889911875494e-1), SC_(1.005692344646621211372312827110088124506e-1) }, 
+      { SC_(1.915013732910156250000000000000000000000e2), SC_(-9.575068359375000000000000000000000000000e2), SC_(-1.035407836914062500000000000000000000000e3), SC_(7.254550295882910100884475499526303225815e-2), SC_(9.274544970411708989911552450047369677418e-1) }, 
+      { SC_(1.918582763671875000000000000000000000000e2), SC_(1.918582725524902343750000000000000000000e1), SC_(2.208179092407226562500000000000000000000e1), SC_(9.721242618485546393356290361951045322104e-1), SC_(2.787573815144536066437096380489546778959e-2) }, 
+      { SC_(1.918984985351562500000000000000000000000e2), SC_(-4.797462463378906250000000000000000000000e1), SC_(-5.617157363891601562500000000000000000000e1), SC_(3.221111566392305522573892879121826455479e-3), SC_(9.967788884336076944774261071208781735445e-1) }, 
+      { SC_(1.919488067626953125000000000000000000000e2), SC_(-9.597440338134765625000000000000000000000e1), SC_(-1.165421524047851562500000000000000000000e2), SC_(2.481260732563524200219933878692461610213e-4), SC_(9.997518739267436475799780066121307538390e-1) }, 
+      { SC_(1.929777069091796875000000000000000000000e2), SC_(-1.447332763671875000000000000000000000000e2), SC_(-1.828341522216796875000000000000000000000e2), SC_(1.358098637444654191572655104301270829943e-5), SC_(9.999864190136255534580842734489569872917e-1) }, 
+      { SC_(1.929932708740234375000000000000000000000e2), SC_(-1.736939392089843750000000000000000000000e2), SC_(-1.752710113525390625000000000000000000000e2), SC_(4.434359641618019366789276090072593648763e-1), SC_(5.565640358381980633210723909927406351237e-1) }, 
+      { SC_(1.935389862060546875000000000000000000000e2), SC_(1.916035919189453125000000000000000000000e2), SC_(1.948214416503906250000000000000000000000e2), SC_(6.142723104748303441684413193877427660393e-1), SC_(3.857276895251696558315586806122572339607e-1) }, 
+      { SC_(1.937735595703125000000000000000000000000e2), SC_(1.935797882080078125000000000000000000000e2), SC_(1.993231201171875000000000000000000000000e2), SC_(7.031303801855181023960454440247304541731e-1), SC_(2.968696198144818976039545559752695458269e-1) }, 
+      { SC_(1.941185607910156250000000000000000000000e2), SC_(1.941185607910156250000000000000000000000e2), SC_(2.023715820312500000000000000000000000000e2), SC_(7.797728872340829673174837038355921015185e-1), SC_(2.202271127659170326825162961644078984815e-1) }, 
+      { SC_(1.962219390869140625000000000000000000000e2), SC_(-1.962415618896484375000000000000000000000e2), SC_(-2.060424804687500000000000000000000000000e2), SC_(1.809237828594511737114522040101156011652e-1), SC_(8.190762171405488262885477959898843988348e-1) }, 
+      { SC_(1.974919281005859375000000000000000000000e2), SC_(-1.976894226074218750000000000000000000000e2), SC_(-2.084357757568359375000000000000000000000e2), SC_(1.597848828006174813168828984223774741925e-1), SC_(8.402151171993825186831171015776225258075e-1) }, 
+      { SC_(1.977043151855468750000000000000000000000e2), SC_(1.996813507080078125000000000000000000000e2), SC_(2.106204223632812500000000000000000000000e2), SC_(8.422293832834955684228336504298493504347e-1), SC_(1.577706167165044315771663495701506495653e-1) }, 
+      { SC_(1.985762634277343750000000000000000000000e2), SC_(-2.184338989257812500000000000000000000000e2), SC_(-2.303740386962890625000000000000000000000e2), SC_(1.575531385245673058508978138666145574355e-1), SC_(8.424468614754326941491021861333854425645e-1) }, 
+      { SC_(1.988137054443359375000000000000000000000e2), SC_(2.385764617919921875000000000000000000000e2), SC_(2.516024322509765625000000000000000000000e2), SC_(8.424688825000982079679215138264048043475e-1), SC_(1.575311174999017920320784861735951956525e-1) }, 
+      { SC_(1.992922668457031250000000000000000000000e2), SC_(-2.590799255371093750000000000000000000000e2), SC_(-2.732116088867187500000000000000000000000e2), SC_(1.573382255153084153679636715700757369509e-1), SC_(8.426617744846915846320363284299242630491e-1) }, 
+      { SC_(2.322846374511718750000000000000000000000e2), SC_(3.484269409179687500000000000000000000000e2), SC_(3.660482482910156250000000000000000000000e2), SC_(8.445224219835303698101085035756072755625e-1), SC_(1.554775780164696301898914964243927244375e-1) }, 
+      { SC_(2.906821289062500000000000000000000000000e2), SC_(5.813642578125000000000000000000000000000e2), SC_(6.095877075195312500000000000000000000000e2), SC_(8.635682877769042305180745412047783757853e-1), SC_(1.364317122230957694819254587952216242147e-1) }, 
+      /*
+      //
+      // These last few values are commented out, the complexity of the implementation
+      // depends upon the square of the non-centrality parameter, so these both take
+      // a long time to evaluate and are rather hard to evaluate accurately also.
+      //
+      { SC_(9.757655029296875000000000000000000000000e2), SC_(-2.927296386718750000000000000000000000000e3), SC_(-3.009226074218750000000000000000000000000e3), SC_(1.164317566424995639445047413284130115370e-1), SC_(8.835682433575004360554952586715869884630e-1) }, 
+      { SC_(1.879048828125000000000000000000000000000e3), SC_(7.516195312500000000000000000000000000000e3), SC_(7.678772949218750000000000000000000000000e3), SC_(9.017566036730798342611358387622429767684e-1), SC_(9.824339632692016573886416123775702323164e-2) }, 
+      { SC_(2.308069091796875000000000000000000000000e3), SC_(-1.154034570312500000000000000000000000000e4), SC_(-1.179905078125000000000000000000000000000e4), SC_(6.872608129209766834994044970484572985093e-2), SC_(9.312739187079023316500595502951542701491e-1) }, 
+      { SC_(8.064482421875000000000000000000000000000e3), SC_(-8.064482421875000000000000000000000000000e2), SC_(-8.193711547851562500000000000000000000000e2), SC_(2.389575887949156628152767472787355181112e-2), SC_(9.761042411205084337184723252721264481889e-1) }, 
+      { SC_(1.567437500000000000000000000000000000000e4), SC_(-3.918593750000000000000000000000000000000e3), SC_(-3.985162353515625000000000000000000000000e3), SC_(1.542392032294953892149510464673239432939e-3), SC_(9.984576079677050461078504895353267605671e-1) }, 
+      { SC_(2.000542187500000000000000000000000000000e4), SC_(-1.000271093750000000000000000000000000000e4), SC_(-1.020245312500000000000000000000000000000e4), SC_(4.337531004895530778641649516506912837255e-5), SC_(9.999566246899510446922135835048349308716e-1) }, 
+      { SC_(5.348914843750000000000000000000000000000e4), SC_(-4.011685937500000000000000000000000000000e4), SC_(-4.073089843750000000000000000000000000000e4), SC_(3.883382003866549840825255916580316551597e-7), SC_(9.999996116617996133450159174744083419683e-1) }
+      */
+   }};
+#undef SC_
+
diff --git a/test/pow_test.cpp b/test/pow_test.cpp
new file mode 100644
index 000000000..0e9406f5d
--- /dev/null
+++ b/test/pow_test.cpp
@@ -0,0 +1,186 @@
+//  Boost pow_test.cpp test file
+//  Tests the pow function
+
+//  (C) Copyright Bruno Lalande 2008.
+//  Distributed under the Boost Software License, Version 1.0.
+//  (See accompanying file LICENSE_1_0.txt or copy at
+//  http://www.boost.org/LICENSE_1_0.txt)
+
+
+#include 
+#include 
+#include 
+
+#include 
+#include 
+#include 
+
+#include 
+#include 
+#include 
+
+#include 
+
+#include BOOST_TYPEOF_INCREMENT_REGISTRATION_GROUP()
+BOOST_TYPEOF_REGISTER_TYPE(boost::math::concepts::real_concept)
+
+using namespace boost;
+using namespace boost::math;
+
+template 
+void test_pow(T base)
+{
+    typedef typename tools::promote_args::type result_type;
+
+    BOOST_MATH_STD_USING
+
+    if ((base == 0) && N < 0)
+    {
+       BOOST_CHECK_THROW(math::pow(base), std::overflow_error);
+    }
+    else
+    {
+       BOOST_CHECK_CLOSE(math::pow(base),
+              pow(static_cast(base), static_cast(N)),
+              boost::math::tools::epsilon() * 100 * 200); // 200 eps as a %
+    }
+}
+
+template 
+void test_with_big_bases()
+{
+    for (T base = T(); base < T(1000); ++base)
+        test_pow(base);
+}
+
+template 
+void test_with_small_bases()
+{
+    T base = 0.9f;
+    for (int i = 0; i < 10; ++i)
+    {
+        base += base/50;
+        test_pow(base);
+    }
+}
+
+template 
+void test_with_small_exponents()
+{
+    test_with_big_bases<0, T>();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+    test_with_big_bases();
+}
+
+template 
+void test_with_big_exponents()
+{
+    test_with_small_bases();
+    test_with_small_bases();
+    test_with_small_bases();
+    test_with_small_bases();
+    test_with_small_bases();
+    test_with_small_bases();
+    test_with_small_bases();
+    test_with_small_bases();
+    test_with_small_bases();
+    test_with_small_bases();
+}
+
+
+void test_return_types()
+{
+    BOOST_STATIC_ASSERT((is_same('\1')), double>::value));
+    BOOST_STATIC_ASSERT((is_same(L'\2')), double>::value));
+    BOOST_STATIC_ASSERT((is_same(3)), double>::value));
+    BOOST_STATIC_ASSERT((is_same(4u)), double>::value));
+    BOOST_STATIC_ASSERT((is_same(5ul)), double>::value));
+    BOOST_STATIC_ASSERT((is_same(6.0f)), float>::value));
+    BOOST_STATIC_ASSERT((is_same(7.0)), double>::value));
+    BOOST_STATIC_ASSERT((is_same(7.0l)), long double>::value));
+};
+
+
+namespace boost { namespace math { namespace policies {
+template 
+T user_overflow_error(const char*, const char*, const T&)
+{ return 123.456; }
+}}}
+
+
+void test_error_policy()
+{
+    using namespace policies;
+
+    BOOST_CHECK(pow<-2>(
+                    0.0,
+                    policy< ::boost::math::policies::overflow_error >()
+                )
+                == 123.456);
+}
+
+int test_main(int, char* [])
+{
+    using namespace std;
+
+    cout << "Testing with integral bases and positive small exponents" << endl;
+    test_with_small_exponents();
+    cout << "Testing with integral bases and negative small exponents" << endl;
+    test_with_small_exponents();
+
+    cout << "Testing with float precision bases and positive small exponents" << endl;
+    test_with_small_exponents();
+    cout << "Testing with float precision bases and negative small exponents" << endl;
+    test_with_small_exponents();
+
+    cout << "Testing with float precision bases and positive big exponents" << endl;
+    test_with_big_exponents();
+    cout << "Testing with float precision bases and negative big exponents" << endl;
+    test_with_big_exponents();
+
+     cout << "Testing with double precision bases and positive small exponents" << endl;
+    test_with_small_exponents();
+    cout << "Testing with double precision bases and negative small exponents" << endl;
+    test_with_small_exponents();
+
+    cout << "Testing with double precision bases and positive big exponents" << endl;
+    test_with_big_exponents();
+    cout << "Testing with double precision bases and negative big exponents" << endl;
+    test_with_big_exponents();
+
+    cout << "Testing with long double precision bases and positive small exponents" << endl;
+    test_with_small_exponents();
+    cout << "Testing with long double precision bases and negative small exponents" << endl;
+    test_with_small_exponents();
+
+    cout << "Testing with long double precision bases and positive big exponents" << endl;
+    test_with_big_exponents();
+    cout << "Testing with long double precision bases and negative big exponents" << endl;
+    test_with_big_exponents();
+
+    cout << "Testing with concepts::real_concept precision bases and positive small exponents" << endl;
+    test_with_small_exponents();
+    cout << "Testing with concepts::real_concept precision bases and negative small exponents" << endl;
+    test_with_small_exponents();
+
+    cout << "Testing with concepts::real_concept precision bases and positive big exponents" << endl;
+    test_with_big_exponents();
+    cout << "Testing with concepts::real_concept precision bases and negative big exponents" << endl;
+    test_with_big_exponents();
+
+    test_return_types();
+
+    test_error_policy();
+
+    return 0;
+}
+
diff --git a/test/test_bernoulli.cpp b/test/test_bernoulli.cpp
index e86389b27..63dc39301 100644
--- a/test/test_bernoulli.cpp
+++ b/test/test_bernoulli.cpp
@@ -13,12 +13,12 @@
 // Default domain error policy is
 // #define BOOST_MATH_DOMAIN_ERROR_POLICY throw_on_error
 
-#include  // for bernoulli_distribution
-using boost::math::bernoulli_distribution;
-
 #include  // for real_concept
 using ::boost::math::concepts::real_concept;
 
+#include  // for bernoulli_distribution
+using boost::math::bernoulli_distribution;
+
 #include  // for test_main
 #include  // for BOOST_CHECK_CLOSE_FRACTION, BOOST_CHECK_EQUAL...
 
diff --git a/test/test_bessel_i.cpp b/test/test_bessel_i.cpp
index 0a49128e0..461ba1881 100644
--- a/test/test_bessel_i.cpp
+++ b/test/test_bessel_i.cpp
@@ -8,6 +8,7 @@
 #include 
 #include 
 #include 
+#include 
 #include 
 #include 
 #include "functor.hpp"
@@ -103,7 +104,7 @@ T cyl_bessel_i_int_wrapper(T v, T x)
 {
    return static_cast(
       boost::math::cyl_bessel_i(
-      boost::math::tools::real_cast(v), x));
+      boost::math::itrunc(v), x));
 }
 
 template 
diff --git a/test/test_bessel_j.cpp b/test/test_bessel_j.cpp
index 3955e18cc..548e68511 100644
--- a/test/test_bessel_j.cpp
+++ b/test/test_bessel_j.cpp
@@ -334,7 +334,7 @@ void do_test_cyl_bessel_j(const T& data, const char* type_name, const char* test
 template 
 T cyl_bessel_j_int_wrapper(T v, T x)
 {
-   return static_cast(boost::math::cyl_bessel_j(boost::math::tools::real_cast(v), x));
+   return static_cast(boost::math::cyl_bessel_j(boost::math::itrunc(v), x));
 }
 
 
diff --git a/test/test_bessel_k.cpp b/test/test_bessel_k.cpp
index 3f7c286cb..73714410c 100644
--- a/test/test_bessel_k.cpp
+++ b/test/test_bessel_k.cpp
@@ -100,7 +100,7 @@ T cyl_bessel_k_int_wrapper(T v, T x)
 {
    return static_cast(
       boost::math::cyl_bessel_k(
-      boost::math::tools::real_cast(v), x));
+      boost::math::itrunc(v), x));
 }
 
 template 
diff --git a/test/test_bessel_y.cpp b/test/test_bessel_y.cpp
index 138d1daa2..910bdb075 100644
--- a/test/test_bessel_y.cpp
+++ b/test/test_bessel_y.cpp
@@ -293,7 +293,7 @@ void do_test_cyl_neumann_y(const T& data, const char* type_name, const char* tes
 template 
 T cyl_neumann_int_wrapper(T v, T x)
 {
-   return static_cast(boost::math::cyl_neumann(boost::math::tools::real_cast(v), x));
+   return static_cast(boost::math::cyl_neumann(boost::math::itrunc(v), x));
 }
 
 template 
diff --git a/test/test_beta_dist.cpp b/test/test_beta_dist.cpp
index 5256e4a31..ae9899f09 100644
--- a/test/test_beta_dist.cpp
+++ b/test/test_beta_dist.cpp
@@ -30,13 +30,13 @@
 #  pragma warning(disable: 4127) // conditional expression is constant.
 #endif
 
+#include  // for real_concept
+using ::boost::math::concepts::real_concept;
+
 #include  // for beta_distribution
 using boost::math::beta_distribution;
 using boost::math::beta;
 
-#include  // for real_concept
-using ::boost::math::concepts::real_concept;
-
 #include  // for test_main
 #include  // for BOOST_CHECK_CLOSE_FRACTION
 
diff --git a/test/test_beta_hooks.hpp b/test/test_beta_hooks.hpp
index ff2909eb3..4f512cd53 100644
--- a/test/test_beta_hooks.hpp
+++ b/test/test_beta_hooks.hpp
@@ -68,6 +68,47 @@ inline long double ibeta(long double a, long double b, long double x)
 #define TEST_OTHER
 #endif
 
+#ifdef TEST_BRATIO
+namespace other{
+extern "C" int bratio_(double*a, double*b, double*x, double*y, double*w, double*w1, int*ierr);
+
+inline float ibeta(float a, float b, float x)
+{
+   double a_ = a;
+   double b_ = b;
+   double x_ = x;
+   double y_ = 1-x_;
+   double w, w1;
+   int ierr = 0;
+   bratio_(&a_, &b_, &x_, &y_, &w, &w1, &ierr); 
+   return w;
+}
+inline double ibeta(double a, double b, double x)
+{ 
+   double a_ = a;
+   double b_ = b;
+   double x_ = x;
+   double y_ = 1-x_;
+   double w, w1;
+   int ierr = 0;
+   bratio_(&a_, &b_, &x_, &y_, &w, &w1, &ierr); 
+   return w;
+}
+inline long double ibeta(long double a, long double b, long double x)
+{
+   double a_ = a;
+   double b_ = b;
+   double x_ = x;
+   double y_ = 1-x_;
+   double w, w1;
+   int ierr = 0;
+   bratio_(&a_, &b_, &x_, &y_, &w, &w1, &ierr); 
+   return w;
+}
+}
+#define TEST_OTHER
+#endif
+
 #ifdef TEST_OTHER
 namespace other{
    boost::math::concepts::real_concept beta(boost::math::concepts::real_concept, boost::math::concepts::real_concept){ return 0; }
diff --git a/test/test_binomial.cpp b/test/test_binomial.cpp
index cfe9e5f1b..33239bb8c 100644
--- a/test/test_binomial.cpp
+++ b/test/test_binomial.cpp
@@ -23,12 +23,12 @@
 #  pragma warning(disable: 4127) // conditional expression is constant.
 #endif
 
-#include  // for binomial_distribution
-using boost::math::binomial_distribution;
-
 #include  // for real_concept
 using ::boost::math::concepts::real_concept;
 
+#include  // for binomial_distribution
+using boost::math::binomial_distribution;
+
 #include  // for test_main
 #include  // for BOOST_CHECK_CLOSE
 
diff --git a/test/test_binomial_coeff.cpp b/test/test_binomial_coeff.cpp
index f8557a4f8..41bc22013 100644
--- a/test/test_binomial_coeff.cpp
+++ b/test/test_binomial_coeff.cpp
@@ -7,6 +7,7 @@
 #include 
 #include 
 #include 
+#include 
 #include 
 #include "functor.hpp"
 #include 
@@ -94,8 +95,8 @@ template 
 T binomial_wrapper(T n, T k)
 {
    return boost::math::binomial_coefficient(
-      boost::math::tools::real_cast(n),
-      boost::math::tools::real_cast(k));
+      boost::math::itrunc(n),
+      boost::math::itrunc(k));
 }
 
 template 
diff --git a/test/test_classify.cpp b/test/test_classify.cpp
index ab457b597..66394fcb3 100644
--- a/test/test_classify.cpp
+++ b/test/test_classify.cpp
@@ -7,8 +7,8 @@
 #include 
 #include 
 #include 
-#include 
 #include 
+#include 
 #include 
 
 #ifdef _MSC_VER
diff --git a/test/test_error_handling.cpp b/test/test_error_handling.cpp
index 04d31a314..a34678b8d 100644
--- a/test/test_error_handling.cpp
+++ b/test/test_error_handling.cpp
@@ -55,9 +55,9 @@ T user_evaluation_error(const char* , const char* , const T& )
 
 }}} // namespaces
 
+#include 
 #include 
 #include 
-#include 
 #include  // for test_main
 //
 // Define some policies:
diff --git a/test/test_expint.cpp b/test/test_expint.cpp
new file mode 100644
index 000000000..0ee1d3a11
--- /dev/null
+++ b/test/test_expint.cpp
@@ -0,0 +1,326 @@
+//  (C) Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include "functor.hpp"
+
+#include "handle_test_result.hpp"
+#include "test_expint_hooks.hpp"
+
+//
+// DESCRIPTION:
+// ~~~~~~~~~~~~
+//
+// This file tests the expint functions. There are two sets of tests:
+// 1) Sanity checks: comparison to test values created with the
+// online calculator at functions.wolfram.com
+// 2) Accuracy tests use values generated with NTL::RR at 
+// 1000-bit precision and our generic versions of these functions.
+//
+// Note that when this file is first run on a new platform many of
+// these tests will fail: the default accuracy is 1 epsilon which
+// is too tight for most platforms.  In this situation you will 
+// need to cast a human eye over the error rates reported and make
+// a judgement as to whether they are acceptable.  Either way please
+// report the results to the Boost mailing list.  Acceptable rates of
+// error are marked up below as a series of regular expressions that
+// identify the compiler/stdlib/platform/data-type/test-data/test-function
+// along with the maximum expected peek and RMS mean errors for that
+// test.
+//
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   const char* largest_type;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   if(boost::math::policies::digits >() == boost::math::policies::digits >())
+   {
+      largest_type = "(long\\s+)?double";
+   }
+   else
+   {
+      largest_type = "long double";
+   }
+#else
+   largest_type = "(long\\s+)?double";
+#endif
+
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      "float|double|long double",    // test type(s)
+      ".*E1.*",                      // test data group
+      ".*", 2, 1);                   // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      "float|double|long double",    // test type(s)
+      ".*Ei.*",                      // test data group
+      ".*", 6, 3);                   // test function
+   if(std::numeric_limits::digits > 100)
+   {
+      add_expected_result(
+         ".*",                          // compiler
+         ".*",                          // stdlib
+         ".*",                          // platform
+         "real_concept",                // test type(s)
+         ".*Ei.*",                      // test data group
+         ".*", 150, 50);                // test function
+   }
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      "real_concept",                // test type(s)
+      ".*Ei.*",                      // test data group
+      ".*", 50, 20);                 // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      ".*",                          // test type(s)
+      ".*",                          // test data group
+      ".*", 25, 5);                   // test function
+
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+template 
+T expint_wrapper(T n, T z)
+{
+   return boost::math::expint(
+      boost::math::itrunc(n), z);
+}
+
+#ifdef TEST_OTHER
+template 
+T other_expint_wrapper(T n, T z)
+{
+   return other::expint(
+      boost::math::itrunc(n), z);
+}
+#endif
+template 
+void do_test_expint(const T& data, const char* type_name, const char* test_name)
+{
+   //
+   // test En(T) against data:
+   //
+   using namespace std;
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   std::cout << test_name << " with type " << type_name << std::endl;
+
+   typedef value_type (*pg)(value_type, value_type);
+   pg funcp = expint_wrapper;
+
+   boost::math::tools::test_result result;
+   //
+   // test expint against data:
+   //
+   result = boost::math::tools::test(
+      data,
+      bind_func(funcp, 0, 1),
+      extract_result(2));
+   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::expint", test_name);
+#ifdef TEST_OTHER
+   if(boost::is_floating_point::value && other::expint(2u, 2.0))
+   {
+      funcp = other_expint_wrapper;
+      //
+      // test expint against data:
+      //
+      result = boost::math::tools::test(
+         data,
+         bind_func(funcp, 0, 1),
+         extract_result(2));
+      handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::expint", test_name);
+   }
+#endif
+   std::cout << std::endl;
+}
+
+template 
+void do_test_expint_Ei(const T& data, const char* type_name, const char* test_name)
+{
+   //
+   // test Ei(T) against data:
+   //
+   using namespace std;
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   std::cout << test_name << " with type " << type_name << std::endl;
+
+   typedef value_type (*pg)(value_type);
+   pg funcp = boost::math::expint;
+
+   boost::math::tools::test_result result;
+   //
+   // test expint against data:
+   //
+   result = boost::math::tools::test(
+      data,
+      bind_func(funcp, 0),
+      extract_result(1));
+   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::expint", test_name);
+#ifdef TEST_OTHER
+   if(boost::is_floating_point::value && other::expint(2.0))
+   {
+      funcp = other::expint;
+      //
+      // test expint against data:
+      //
+      result = boost::math::tools::test(
+         data,
+         bind_func(funcp, 0),
+         extract_result(1));
+      handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::expint", test_name);
+   }
+#endif
+}
+
+template 
+void test_expint(T, const char* name)
+{
+   //
+   // The actual test data is rather verbose, so it's in a separate file
+   //
+#include "expint_data.ipp"
+   do_test_expint(expint_data, name, "Exponential Integral En");
+#include "expint_small_data.ipp"
+   do_test_expint(expint_small_data, name, "Exponential Integral En: small z values");
+#include "expint_1_data.ipp"
+   do_test_expint(expint_1_data, name, "Exponential Integral E1");
+#include "expinti_data.ipp"
+   do_test_expint_Ei(expinti_data, name, "Exponential Integral Ei");
+
+   if(boost::math::tools::log_max_value() > 100)
+   {
+#include "expinti_data_double.ipp"
+      do_test_expint_Ei(expinti_data_double, name, "Exponential Integral Ei: double exponent range");
+   }
+#if defined(LDBL_MAX_10_EXP) && (LDBL_MAX_10_EXP > 2000)
+   if(boost::math::tools::log_max_value() > 1000)
+   {
+#include "expinti_data_long.ipp"
+      do_test_expint_Ei(expinti_data_long, name, "Exponential Integral Ei: long exponent range");
+   }
+#endif
+}
+
+template 
+void test_spots(T, const char* t)
+{
+   std::cout << "Testing basic sanity checks for type " << t << std::endl;
+   //
+   // Basic sanity checks, tolerance is 100 epsilon 
+   // expressed as a percentage:
+   //
+   T tolerance = boost::math::tools::epsilon() * 100 *
+      (boost::is_floating_point::value ? 500 : 500);
+   //
+   // En:
+   //
+   BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast(1)/1024), static_cast(1023.0004881223430781283448725609773366468629307172L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast(0.125F)), static_cast(7.0599752206767632229191371458324058897760385999252L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast(0.5F)), static_cast(1.2130613194252668472075990699823609068838362709744L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast(1.5F)), static_cast(0.14875344009895321928885364717600834756144775290739L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast(4.5F)), static_cast(0.0024686658973871792213651409526512283936753927790603L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(0, static_cast(50.0F)), static_cast(3.8574996959278355660346856330540251495056653024605e-24L), tolerance);
+
+   BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast(1)/1024), static_cast(6.3552324648310718026144555193580322129376300855378L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast(0.125F)), static_cast(1.6234256405841687914563069246244088736331060573721L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast(0.5F)), static_cast(0.55977359477616081174679593931508523522684689031635L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast(1.5F)), static_cast(0.10001958240663265190190933991166697826173000614035L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast(4.5F)), static_cast(0.0020734007547146144328855938695797884889319725701443L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(1, static_cast(50.0F)), static_cast(3.7832640295504590186989678540212857803028931862511e-24L), tolerance);
+
+   BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast(1)/1024), static_cast(0.99281763247803906867747111039220635198625517639812L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast(0.125F)), static_cast(0.67956869751157430393285377765099962701786656781914L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast(0.5F)), static_cast(0.32664386232455301773040156533363783582849469032901L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast(1.5F)), static_cast(0.073100786538480851080416460896512053949576620150553L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast(4.5F)), static_cast(0.0017786931420265415481579618738214795713453909401220L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(2, static_cast(50.0F)), static_cast(3.7117833188688273667858889516369684601386058104706e-24L), tolerance);
+
+   BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast(1)/1024), static_cast(0.24967471743034509414923673526350536071348482068601L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast(0.125F)), static_cast(0.21195078838966585733668853784460504343264488743527L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast(0.5F)), static_cast(0.13097731169586484777931864012654136046214618229236L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast(1.5F)), static_cast(0.038529924425495155395971538166055731456940831714065L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast(4.5F)), static_cast(0.0012311157382296328534406162790653865883418172939975L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(5, static_cast(50.0F)), static_cast(3.5124400631332394056901125740903320085753990490695e-24L), tolerance);
+
+   BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast(1)/1024), static_cast(0.047570244582119027573000641518739337055625638422014L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast(0.125F)), static_cast(0.041762730174712898120606793100375713866392079558609L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast(0.5F)), static_cast(0.028178840877963713109230354192609362941651630844684L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast(1.5F)), static_cast(0.0098864453561701486668317763826728620676449196215016L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast(4.5F)), static_cast(0.00043257793497205419001613830279995985617548506505159L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(22, static_cast(50.0F)), static_cast(2.6900194251201629500599598206345018300567305625080e-24L), tolerance);
+   //
+   // Ei:
+   //
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(1)/1024), static_cast(-6.35327933972759151358547423727042905862963067106751711596065L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(0.125)), static_cast(-1.37320852494298333781545045921206470808223543321810480716122L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(0.5)), static_cast(0.454219904863173579920523812662802365281405554352642045162818L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(1)), static_cast(1.89511781635593675546652093433163426901706058173270759164623L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(50.5)), static_cast(1.72763195602911805201155668940185673806099654090456049881069e20L), tolerance);
+
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(-1)/1024), static_cast(-6.35523246483107180261445551935803221293763008553775821607264L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(-0.125)), static_cast(-1.62342564058416879145630692462440887363310605737209536579267L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(-0.5)), static_cast(-0.559773594776160811746795939315085235226846890316353515248293L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(-1)), static_cast(-0.219383934395520273677163775460121649031047293406908207577979L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::expint(static_cast(-50.5)), static_cast(-2.27237132932219350440719707268817831250090574830769670186618e-24L), tolerance);
+}
+
+int test_main(int, char* [])
+{
+   expected_results();
+   BOOST_MATH_CONTROL_FP;
+
+   boost::math::expint(114.7);
+
+   test_spots(0.0f, "float");
+   test_spots(0.0, "double");
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   test_spots(0.0L, "long double");
+   test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
+#else
+   std::cout << "The long double tests have been disabled on this platform "
+      "either because the long double overloads of the usual math functions are "
+      "not available at all, or because they are too inaccurate for these tests "
+      "to pass." << std::cout;
+#endif
+
+   test_expint(0.1F, "float");
+   test_expint(0.1, "double");
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   test_expint(0.1L, "long double");
+   test_expint(boost::math::concepts::real_concept(0.1), "real_concept");
+#else
+   std::cout << "The long double tests have been disabled on this platform "
+      "either because the long double overloads of the usual math functions are "
+      "not available at all, or because they are too inaccurate for these tests "
+      "to pass." << std::cout;
+#endif
+   return 0;
+}
+
diff --git a/test/test_expint_hooks.hpp b/test/test_expint_hooks.hpp
new file mode 100644
index 000000000..89b5fc89a
--- /dev/null
+++ b/test/test_expint_hooks.hpp
@@ -0,0 +1,94 @@
+//  (C) Copyright John Maddock 2006.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_TEST_ZETA_OTHER_HOOKS_HPP
+#define BOOST_MATH_TEST_ZETA_OTHER_HOOKS_HPP
+
+
+#ifdef TEST_CEPHES
+namespace other{
+extern "C" {
+   double expn(int, double);
+   float expnf(int, float);
+   long double expnl(int, long double);
+}
+inline float expint(unsigned n, float a)
+{ return expnf(n, a); }
+inline double expint(unsigned n, double a)
+{ return expn(n, a); }
+inline long double expint(unsigned n, long double a)
+{
+#ifdef BOOST_MSVC
+   return expn(n, (double)a); 
+#else
+   return expnl(n, a); 
+#endif
+}
+// Ei is not supported:
+template 
+inline T expint(T){ return 0; }
+}
+#define TEST_OTHER
+#endif
+
+#ifdef TEST_GSL
+#include 
+
+namespace other{
+inline float expint(float a)
+{ return (float)gsl_sf_expint_Ei(a); }
+inline double expint(double a)
+{ return gsl_sf_expint_Ei(a); }
+inline long double expint(long double a)
+{ return gsl_sf_expint_Ei(a); }
+// En is not supported:
+template 
+inline T expint(unsigned, T){ return 0; }
+}
+#define TEST_OTHER
+#endif
+
+#ifdef TEST_SPECFUN
+namespace other{
+extern "C" int calcei_(double *arg, double *result, int*);
+inline float expint(float a)
+{ 
+   double r, a_(a);
+   int v = 1;
+   calcei_(&a_, &r, &v); 
+   return (float)r;
+}
+inline double expint(double a)
+{ 
+   double r, a_(a);
+   int v = 1;
+   calcei_(&a_, &r, &v); 
+   return r;
+}
+inline long double expint(long double a)
+{ 
+   double r, a_(a);
+   int v = 1;
+   calcei_(&a_, &r, &v); 
+   return r;
+}
+// En is not supported:
+template 
+inline T expint(unsigned, T){ return 0; }
+}
+#define TEST_OTHER
+#endif
+
+#ifdef TEST_OTHER
+namespace other{
+   boost::math::concepts::real_concept expint(unsigned, boost::math::concepts::real_concept){ return 0; }
+   boost::math::concepts::real_concept expint(boost::math::concepts::real_concept){ return 0; }
+}
+#endif
+
+
+#endif
+
+
diff --git a/test/test_find_location.cpp b/test/test_find_location.cpp
index 7f1a8b61f..94ff4b2e8 100644
--- a/test/test_find_location.cpp
+++ b/test/test_find_location.cpp
@@ -13,6 +13,7 @@
 // Default domain error policy is
 // #define BOOST_MATH_DOMAIN_ERROR_POLICY throw_on_error
 
+#include  // for real_concept
 #include  // for normal_distribution
   using boost::math::normal; // Default type double.
   using boost::math::normal_distribution; // All floating-point types.
@@ -28,7 +29,6 @@
 
 #include  // for test_main
 #include  // for BOOST_CHECK_CLOSE_FRACTION, BOOST_CHECK_EQUAL...
-#include  // for real_concept
 
 #include 
   using std::cout; using std::endl; using std::fixed;
diff --git a/test/test_find_scale.cpp b/test/test_find_scale.cpp
index 4312253a4..e5b488708 100644
--- a/test/test_find_scale.cpp
+++ b/test/test_find_scale.cpp
@@ -13,6 +13,7 @@
 // Default distribution domain error policy is
 // #define BOOST_MATH_DOMAIN_ERROR_POLICY throw_on_error
 
+#include  // for real_concept
 #include  // for normal_distribution
   using boost::math::normal; // Default type double.
   using boost::math::normal_distribution; // All floating-point types.
@@ -28,7 +29,6 @@
 
 #include  // for test_main
 #include  // for BOOST_CHECK_CLOSE_FRACTION, BOOST_CHECK_EQUAL...
-#include  // for real_concept
 
 #include 
   using std::cout; using std::endl; using std::fixed;
diff --git a/test/test_gamma_dist.cpp b/test/test_gamma_dist.cpp
index 0023de948..430bce904 100644
--- a/test/test_gamma_dist.cpp
+++ b/test/test_gamma_dist.cpp
@@ -94,7 +94,7 @@ void test_spots(RealType)
    // The first tests use values generated by MathCAD,
    // and should be accurate to around double precision.
    //
-   RealType tolerance = (std::max)(5e-14f, boost::math::tools::real_cast(std::numeric_limits::epsilon() * 20)) * 100; 
+   RealType tolerance = (std::max)(RealType(5e-14f), std::numeric_limits::epsilon() * 20) * 100; 
    cout << "Tolerance for type " << typeid(RealType).name()  << " is " << tolerance << " %" << endl;
 
    check_gamma(
diff --git a/test/test_igamma_inva.cpp b/test/test_igamma_inva.cpp
index e16f9e24a..66673b5f4 100644
--- a/test/test_igamma_inva.cpp
+++ b/test/test_igamma_inva.cpp
@@ -305,3 +305,4 @@ int test_main(int, char* [])
 
 
 
+
diff --git a/test/test_nc_beta.cpp b/test/test_nc_beta.cpp
new file mode 100644
index 000000000..88a0f16a5
--- /dev/null
+++ b/test/test_nc_beta.cpp
@@ -0,0 +1,445 @@
+// test_nc_beta.cpp
+
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifdef _MSC_VER
+#pragma warning (disable:4127 4512)
+#endif
+
+#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
+#  define TEST_FLOAT
+#  define TEST_DOUBLE
+#  define TEST_LDOUBLE
+#  define TEST_REAL_CONCEPT
+#endif
+
+#include  // for real_concept
+#include  // for chi_squared_distribution
+#include  // for chi_squared_distribution
+#include  // for test_main
+#include  // for BOOST_CHECK_CLOSE
+
+#include "functor.hpp"
+#include "handle_test_result.hpp"
+#include "test_ncbeta_hooks.hpp"
+
+#include 
+using std::cout;
+using std::endl;
+#include 
+using std::numeric_limits;
+
+#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK_CLOSE(a, b, prec); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+#define BOOST_CHECK_EX(a, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK(a); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   const char* largest_type;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   if(boost::math::policies::digits >() == boost::math::policies::digits >())
+   {
+      largest_type = "(long\\s+)?double|real_concept";
+   }
+   else
+   {
+      largest_type = "long double|real_concept";
+   }
+#else
+   largest_type = "(long\\s+)?double|real_concept";
+#endif
+
+   if(boost::math::tools::digits() == 64)
+   {
+      //
+      // Allow a small amount of error leakage from long double to double:
+      //
+      add_expected_result(
+         "[^|]*",                          // compiler
+         "[^|]*",                          // stdlib
+         "[^|]*",                          // platform
+         "double",                         // test type(s)
+         "[^|]*large[^|]*",                // test data group
+         "[^|]*", 5, 5);                   // test function
+   }
+
+   if(boost::math::tools::digits() == 64)
+   {
+      add_expected_result(
+         "[^|]*",                          // compiler
+         "[^|]*",                          // stdlib
+         "[^|]*",                          // platform
+         largest_type,                     // test type(s)
+         "[^|]*medium[^|]*",               // test data group
+         "[^|]*", 900, 500);               // test function
+      add_expected_result(
+         "[^|]*",                          // compiler
+         "[^|]*",                          // stdlib
+         "[^|]*",                          // platform
+         largest_type,                     // test type(s)
+         "[^|]*large[^|]*",                // test data group
+         "[^|]*", 40000, 5500);            // test function
+   }
+   //
+   // Catch all cases come last:
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      largest_type,                     // test type(s)
+      "[^|]*medium[^|]*",               // test data group
+      "[^|]*", 700, 500);               // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      "real_concept",                   // test type(s)
+      "[^|]*large[^|]*",                // test data group
+      "[^|]*", 30000, 4000);             // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      largest_type,                     // test type(s)
+      "[^|]*large[^|]*",                // test data group
+      "[^|]*", 10000, 2000);             // test function
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+template 
+RealType naive_pdf(RealType a, RealType b, RealType lam, RealType x)
+{
+   using namespace boost::math;
+
+   RealType term = pdf(poisson_distribution(lam/2), 0)
+      * ibeta_derivative(a, b, x);
+   RealType sum = term;
+
+   int i = 1;
+   while(term / sum > tools::epsilon())
+   {
+      term = pdf(poisson_distribution(lam/2), i)
+      * ibeta_derivative(a + i, b, x);
+      ++i;
+      sum += term;
+   }
+   return sum;
+}
+
+template 
+void test_spot(
+     RealType a,     // alpha
+     RealType b,     // beta
+     RealType ncp,   // non-centrality param
+     RealType cs,    // Chi Square statistic
+     RealType P,     // CDF
+     RealType Q,     // Complement of CDF
+     RealType D,     // PDF
+     RealType tol)   // Test tolerance
+{
+   boost::math::non_central_beta_distribution dist(a, b, ncp);
+   BOOST_CHECK_CLOSE(
+      cdf(dist, cs), P, tol);
+   //
+   // Sanity checking using the naive PDF calculation above fails at
+   // float precision:
+   //
+   if(!boost::is_same::value)
+   {
+      BOOST_CHECK_CLOSE(
+         pdf(dist, cs), naive_pdf(dist.alpha(), dist.beta(), ncp, cs), tol);
+   }
+   BOOST_CHECK_CLOSE(
+      pdf(dist, cs), D, tol);
+
+   if((P < 0.99) && (Q < 0.99))
+   {
+      //
+      // We can only check this if P is not too close to 1,
+      // so that we can guarentee Q is reasonably free of error:
+      //
+      BOOST_CHECK_CLOSE(
+         cdf(complement(dist, cs)), Q, tol);
+      BOOST_CHECK_CLOSE(
+            quantile(dist, P), cs, tol * 10);
+      BOOST_CHECK_CLOSE(
+            quantile(complement(dist, Q)), cs, tol * 10);
+   }
+}
+
+template  // Any floating-point type RealType.
+void test_spots(RealType)
+{
+   RealType tolerance = (std::max)(
+      boost::math::tools::epsilon() * 100,
+      (RealType)1e-6) * 100;
+
+   cout << "Tolerance = " << tolerance << "%." << endl;
+
+   //
+   // Spot tests use values computed by the R statistical
+   // package and the pbeta and dbeta functions:
+   //
+   test_spot(
+     RealType(2),                   // alpha
+     RealType(5),                   // beta
+     RealType(1),                   // non-centrality param
+     RealType(0.25),                // Chi Square statistic
+     RealType(0.3658349),           // CDF
+     RealType(1-0.3658349),         // Complement of CDF
+     RealType(2.184465),            // PDF
+     RealType(tolerance));
+   test_spot(
+     RealType(20),                  // alpha
+     RealType(15),                  // beta
+     RealType(35),                  // non-centrality param
+     RealType(0.75),                // Chi Square statistic
+     RealType(0.6994175),           // CDF
+     RealType(1-0.6994175),         // Complement of CDF
+     RealType(5.576146),            // PDF
+     RealType(tolerance));
+   test_spot(
+     RealType(100),                 // alpha
+     RealType(3),                   // beta
+     RealType(63),                  // non-centrality param
+     RealType(0.95),                // Chi Square statistic
+     RealType(0.03529306),          // CDF
+     RealType(1-0.03529306),        // Complement of CDF
+     RealType(3.637894),            // PDF
+     RealType(tolerance));
+   test_spot(
+     RealType(0.25),                // alpha
+     RealType(0.75),                // beta
+     RealType(150),                 // non-centrality param
+     RealType(0.975),               // Chi Square statistic
+     RealType(0.09752216),          // CDF
+     RealType(1-0.09752216),        // Complement of CDF
+     RealType(8.020935),            // PDF
+     RealType(tolerance));
+
+} // template void test_spots(RealType)
+
+template 
+T nc_beta_cdf(T a, T b, T nc, T x)
+{
+   return cdf(boost::math::non_central_beta_distribution(a, b, nc), x);
+}
+
+template 
+T nc_beta_ccdf(T a, T b, T nc, T x)
+{
+   return cdf(complement(boost::math::non_central_beta_distribution(a, b, nc), x));
+}
+
+template 
+void do_test_nc_chi_squared(T& data, const char* type_name, const char* test)
+{
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+   value_type (*fp1)(value_type, value_type, value_type, value_type) = nc_beta_cdf;
+   boost::math::tools::test_result result;
+
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2, 3),
+      extract_result(4));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "CDF", test);
+
+   fp1 = nc_beta_ccdf;
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2, 3),
+      extract_result(5));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "CCDF", test);
+
+#ifdef TEST_OTHER
+   fp1 = other::ncbeta_cdf;
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2, 3),
+      extract_result(4));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "Other::CDF", test);
+#endif
+   std::cout << std::endl;
+
+}
+
+template 
+void quantile_sanity_check(T& data, const char* type_name, const char* test)
+{
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   //
+   // Tests with type real_concept take rather too long to run, so
+   // for now we'll disable them:
+   //
+   if(!boost::is_floating_point::value)
+      return;
+
+   std::cout << "Testing: " << type_name << " quantile sanity check, with tests " << test << std::endl;
+
+   //
+   // These sanity checks test for a round trip accuracy of one half
+   // of the bits in T, unless T is type float, in which case we check
+   // for just one decimal digit.  The problem here is the sensitivity
+   // of the functions, not their accuracy.  This test data was generated
+   // for the forward functions, which means that when it is used as
+   // the input to the inverses then it is necessarily inexact.  This rounding
+   // of the input is what makes the data unsuitable for use as an accuracy check,
+   // and also demonstrates that you can't in general round-trip these functions.
+   // It is however a useful sanity check.
+   //
+   value_type precision = static_cast(ldexp(1.0, 1-boost::math::policies::digits >()/2)) * 100;
+   if(boost::math::policies::digits >() < 50)
+      precision = 1;   // 1% or two decimal digits, all we can hope for when the input is truncated to float
+
+   for(unsigned i = 0; i < data.size(); ++i)
+   {
+      //
+      // Test case 493 fails at float precision: not enough bits to get
+      // us back where we started:
+      //
+      if((i == 493) && boost::is_same::value)
+         continue;
+
+      if(data[i][4] == 0)
+      {
+         BOOST_CHECK(0 == quantile(boost::math::non_central_beta_distribution(data[i][0], data[i][1], data[i][2]), data[i][4]));
+      }
+      else if(data[i][4] < 0.9999f)
+      {
+         value_type p = quantile(boost::math::non_central_beta_distribution(data[i][0], data[i][1], data[i][2]), data[i][4]);
+         value_type pt = data[i][3];
+         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
+      }
+      if(data[i][5] == 0)
+      {
+         BOOST_CHECK(1 == quantile(complement(boost::math::non_central_beta_distribution(data[i][0], data[i][1], data[i][2]), data[i][5])));
+      }
+      else if(data[i][5] < 0.9999f)
+      {
+         value_type p = quantile(complement(boost::math::non_central_beta_distribution(data[i][0], data[i][1], data[i][2]), data[i][5]));
+         value_type pt = data[i][3];
+         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
+      }
+      if(boost::math::tools::digits() > 50)
+      {
+         //
+         // Sanity check mode, accuracy of
+         // the mode is at *best* the square root of the accuracy of the PDF:
+         //
+         value_type m = mode(boost::math::non_central_beta_distribution(data[i][0], data[i][1], data[i][2]));
+         if((m == 1) || (m == 0))
+            break;
+         value_type p = pdf(boost::math::non_central_beta_distribution(data[i][0], data[i][1], data[i][2]), m);
+         if(m * (1 + sqrt(precision) * 10) < 1)
+         {
+            BOOST_CHECK_EX(pdf(boost::math::non_central_beta_distribution(data[i][0], data[i][1], data[i][2]), m * (1 + sqrt(precision) * 10)) <= p, i);
+         }
+         if(m * (1 - sqrt(precision)) * 10 > boost::math::tools::min_value())
+         {
+            BOOST_CHECK_EX(pdf(boost::math::non_central_beta_distribution(data[i][0], data[i][1], data[i][2]), m * (1 - sqrt(precision)) * 10) <= p, i);
+         }
+      }
+   }
+}
+
+template 
+void test_accuracy(T, const char* type_name)
+{
+#include "ncbeta.ipp"
+    do_test_nc_chi_squared(ncbeta, type_name, "Non Central Beta, medium parameters");
+    quantile_sanity_check(ncbeta, type_name, "Non Central Beta, medium parameters");
+
+#include "ncbeta_big.ipp"
+    do_test_nc_chi_squared(ncbeta_big, type_name, "Non Central Beta, large parameters");
+    // Takes too long to run:
+    // quantile_sanity_check(ncbeta_big, type_name, "Non Central Beta, large parameters");
+}
+
+int test_main(int, char* [])
+{
+   BOOST_MATH_CONTROL_FP;
+   // Basic sanity-check spot values.
+   expected_results();
+   // (Parameter value, arbitrarily zero, only communicates the floating point type).
+#ifdef TEST_FLOAT
+   test_spots(0.0F); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+   test_spots(0.0); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+#ifdef TEST_LDOUBLE
+   test_spots(0.0L); // Test long double.
+#endif
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+#ifdef TEST_REAL_CONCEPT
+   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+#endif
+#endif
+#endif
+
+#ifdef TEST_FLOAT
+   test_accuracy(0.0F, "float"); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+   test_accuracy(0.0, "double"); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+#ifdef TEST_LDOUBLE
+   test_accuracy(0.0L, "long double"); // Test long double.
+#endif
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+#ifdef TEST_REAL_CONCEPT
+   test_accuracy(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept.
+#endif
+#endif
+#endif
+   return 0;
+} // int test_main(int, char* [])
+
diff --git a/test/test_nc_chi_squared.cpp b/test/test_nc_chi_squared.cpp
new file mode 100644
index 000000000..be139b531
--- /dev/null
+++ b/test/test_nc_chi_squared.cpp
@@ -0,0 +1,541 @@
+// test_nc_chi_squared.cpp
+
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifdef _MSC_VER
+#pragma warning (disable:4127 4512)
+#endif
+
+#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
+#  define TEST_FLOAT
+#  define TEST_DOUBLE
+#  define TEST_LDOUBLE
+#  define TEST_REAL_CONCEPT
+#endif
+
+#include  // for real_concept
+#include  // for chi_squared_distribution
+#include  // for chi_squared_distribution
+#include  // for test_main
+#include  // for BOOST_CHECK_CLOSE
+
+#include "functor.hpp"
+#include "handle_test_result.hpp"
+#include "test_nccs_hooks.hpp"
+
+#include 
+using std::cout;
+using std::endl;
+#include 
+using std::numeric_limits;
+
+#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK_CLOSE(a, b, prec); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+#define BOOST_CHECK_EX(a, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK(a); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   const char* largest_type;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   if(boost::math::policies::digits >() == boost::math::policies::digits >())
+   {
+      largest_type = "(long\\s+)?double|real_concept";
+   }
+   else
+   {
+      largest_type = "long double|real_concept";
+   }
+#else
+   largest_type = "(long\\s+)?double|real_concept";
+#endif
+
+   //
+   // Catch all cases come last:
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      largest_type,                     // test type(s)
+      "[^|]*medium[^|]*",                   // test data group
+      "[^|]*", 350, 100);                  // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      largest_type,                     // test type(s)
+      "[^|]*large[^|]*",                   // test data group
+      "[^|]*", 15000, 3000);                  // test function
+
+   //
+   // Allow some long double error to creep into
+   // the double results:
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      "double",                         // test type(s)
+      "[^|]*",                   // test data group
+      "[^|]*", 3, 2);                  // test function
+
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+template 
+RealType naive_pdf(RealType v, RealType lam, RealType x)
+{
+   // Formula direct from 
+   // http://mathworld.wolfram.com/NoncentralChi-SquaredDistribution.html
+   // with no simplification:
+   RealType sum, term, prefix(1);
+   RealType eps = boost::math::tools::epsilon();
+   term = sum = pdf(boost::math::chi_squared_distribution(v), x);
+   for(int i = 1;; ++i)
+   {
+      prefix *= lam / (2 * i);
+      term = prefix * pdf(boost::math::chi_squared_distribution(v + 2 * i), x);
+      sum += term;
+      if(term / sum < eps)
+         break;
+   }
+   return sum * exp(-lam/2);
+}
+
+template 
+void test_spot(
+     RealType df,    // Degrees of freedom
+     RealType ncp,   // non-centrality param
+     RealType cs,    // Chi Square statistic
+     RealType P,     // CDF
+     RealType Q,     // Complement of CDF
+     RealType tol)   // Test tolerance
+{
+   boost::math::non_central_chi_squared_distribution dist(df, ncp);
+   BOOST_CHECK_CLOSE(
+      cdf(dist, cs), P, tol);
+   try{
+      BOOST_CHECK_CLOSE(
+         pdf(dist, cs), naive_pdf(dist.degrees_of_freedom(), ncp, cs), tol * 50);
+   }
+   catch(const std::overflow_error&)
+   {}
+   if((P < 0.99) && (Q < 0.99))
+   {
+      //
+      // We can only check this if P is not too close to 1,
+      // so that we can guarentee Q is reasonably free of error:
+      //
+      BOOST_CHECK_CLOSE(
+         cdf(complement(dist, cs)), Q, tol);
+      BOOST_CHECK_CLOSE(
+            quantile(dist, P), cs, tol * 10);
+      BOOST_CHECK_CLOSE(
+            quantile(complement(dist, Q)), cs, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_degrees_of_freedom(ncp, cs, P), df, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_degrees_of_freedom(boost::math::complement(ncp, cs, Q)), df, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_non_centrality(df, cs, P), ncp, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_non_centrality(boost::math::complement(df, cs, Q)), ncp, tol * 10);
+   }
+}
+
+template  // Any floating-point type RealType.
+void test_spots(RealType)
+{
+   RealType tolerance = (std::max)(
+      boost::math::tools::epsilon(),
+      (RealType)boost::math::tools::epsilon() * 5) * 100;
+   //
+   // At float precision we need to up the tolerance, since 
+   // the input values are rounded off to inexact quantities
+   // the results get thrown off by a noticeable amount.
+   //
+   if(boost::math::tools::digits() < 50)
+      tolerance *= 50;
+   if(boost::is_floating_point::value != 1)
+      tolerance *= 20; // real_concept special functions are less accurate
+
+   cout << "Tolerance = " << tolerance << "%." << endl;
+
+   using boost::math::chi_squared_distribution;
+   using  ::boost::math::chi_squared;
+   using  ::boost::math::cdf;
+   using  ::boost::math::pdf;
+   //
+   // Test against the data from Table 6 of:
+   //
+   // "Self-Validating Computations of Probabilities for Selected 
+   // Central and Noncentral Univariate Probability Functions."
+   // Morgan C. Wang; William J. Kennedy
+   // Journal of the American Statistical Association, 
+   // Vol. 89, No. 427. (Sep., 1994), pp. 878-887.
+   //
+   test_spot(
+      static_cast(1),   // degrees of freedom
+      static_cast(6),   // non centrality
+      static_cast(0.00393),   // Chi Squared statistic
+      static_cast(0.2498463724258039e-2),       // Probability of result (CDF), P
+      static_cast(1-0.2498463724258039e-2),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(5),   // degrees of freedom
+      static_cast(1),   // non centrality
+      static_cast(9.23636),   // Chi Squared statistic
+      static_cast(0.8272918751175548),       // Probability of result (CDF), P
+      static_cast(1-0.8272918751175548),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(11),   // degrees of freedom
+      static_cast(21),   // non centrality
+      static_cast(24.72497),   // Chi Squared statistic
+      static_cast(0.2539481822183126),       // Probability of result (CDF), P
+      static_cast(1-0.2539481822183126),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(31),   // degrees of freedom
+      static_cast(6),   // non centrality
+      static_cast(44.98534),   // Chi Squared statistic
+      static_cast(0.8125198785064969),       // Probability of result (CDF), P
+      static_cast(1-0.8125198785064969),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(51),   // degrees of freedom
+      static_cast(1),   // non centrality
+      static_cast(38.56038),   // Chi Squared statistic
+      static_cast(0.8519497361859118e-1),       // Probability of result (CDF), P
+      static_cast(1-0.8519497361859118e-1),           // Q = 1 - P
+      tolerance * 2);
+   test_spot(
+      static_cast(100),   // degrees of freedom
+      static_cast(16),   // non centrality
+      static_cast(82.35814),   // Chi Squared statistic
+      static_cast(0.1184348822747824e-1),       // Probability of result (CDF), P
+      static_cast(1-0.1184348822747824e-1),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(300),   // degrees of freedom
+      static_cast(16),   // non centrality
+      static_cast(331.78852),   // Chi Squared statistic
+      static_cast(0.7355956710306709),       // Probability of result (CDF), P
+      static_cast(1-0.7355956710306709),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(500),   // degrees of freedom
+      static_cast(21),   // non centrality
+      static_cast(459.92612),   // Chi Squared statistic
+      static_cast(0.2797023600800060e-1),       // Probability of result (CDF), P
+      static_cast(1-0.2797023600800060e-1),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(1),   // degrees of freedom
+      static_cast(1),   // non centrality
+      static_cast(0.00016),   // Chi Squared statistic
+      static_cast(0.6121428929881423e-2),       // Probability of result (CDF), P
+      static_cast(1-0.6121428929881423e-2),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(1),   // degrees of freedom
+      static_cast(1),   // non centrality
+      static_cast(0.00393),   // Chi Squared statistic
+      static_cast(0.3033814229753780e-1),       // Probability of result (CDF), P
+      static_cast(1-0.3033814229753780e-1),           // Q = 1 - P
+      tolerance);
+
+   RealType tol2 = boost::math::tools::epsilon() * 5 * 100; // 5 eps as a percentage
+   boost::math::non_central_chi_squared_distribution dist(static_cast(8), static_cast(12));
+   RealType x = 7;
+   using namespace std; // ADL of std names.
+   // mean:
+   BOOST_CHECK_CLOSE(
+      mean(dist)
+      , static_cast(8+12), tol2);
+   // variance:
+   BOOST_CHECK_CLOSE(
+      variance(dist)
+      , static_cast(64), tol2);
+   // std deviation:
+   BOOST_CHECK_CLOSE(
+      standard_deviation(dist)
+      , static_cast(8), tol2);
+   // hazard:
+   BOOST_CHECK_CLOSE(
+      hazard(dist, x)
+      , pdf(dist, x) / cdf(complement(dist, x)), tol2);
+   // cumulative hazard:
+   BOOST_CHECK_CLOSE(
+      chf(dist, x)
+      , -log(cdf(complement(dist, x))), tol2);
+   // coefficient_of_variation:
+   BOOST_CHECK_CLOSE(
+      coefficient_of_variation(dist)
+      , standard_deviation(dist) / mean(dist), tol2);
+   // mode:
+   BOOST_CHECK_CLOSE(
+      mode(dist)
+      , static_cast(17.184201184730857030170788677340294070728990862663L), sqrt(tolerance * 10));
+   BOOST_CHECK_CLOSE(
+      median(dist), 
+      quantile(
+      boost::math::non_central_chi_squared_distribution(
+         static_cast(8),
+         static_cast(12)),
+      static_cast(0.5)), static_cast(tol2));
+   // skewness:
+   BOOST_CHECK_CLOSE(
+      skewness(dist)
+      , static_cast(0.6875), tol2);
+   // kurtosis:
+   BOOST_CHECK_CLOSE(
+      kurtosis(dist)
+      , static_cast(3.65625), tol2);
+   // kurtosis excess:
+   BOOST_CHECK_CLOSE(
+      kurtosis_excess(dist)
+      , static_cast(0.65625), tol2);
+} // template void test_spots(RealType)
+
+template 
+T nccs_cdf(T df, T nc, T x)
+{
+   return cdf(boost::math::non_central_chi_squared_distribution(df, nc), x);
+}
+
+template 
+T nccs_ccdf(T df, T nc, T x)
+{
+   return cdf(complement(boost::math::non_central_chi_squared_distribution(df, nc), x));
+}
+
+template 
+void do_test_nc_chi_squared(T& data, const char* type_name, const char* test)
+{
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+   value_type (*fp1)(value_type, value_type, value_type) = nccs_cdf;
+   boost::math::tools::test_result result;
+
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2),
+      extract_result(3));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "CDF", test);
+
+   fp1 = nccs_ccdf;
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2),
+      extract_result(4));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "CCDF", test);
+
+#ifdef TEST_OTHER
+   fp1 = other::nccs_cdf;
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2),
+      extract_result(3));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "other::CDF", test);
+#endif
+
+   std::cout << std::endl;
+
+}
+
+template 
+void quantile_sanity_check(T& data, const char* type_name, const char* test)
+{
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   //
+   // Tests with type real_concept take rather too long to run, so
+   // for now we'll disable them:
+   //
+   if(!boost::is_floating_point::value)
+      return;
+
+   std::cout << "Testing: " << type_name << " quantile sanity check, with tests " << test << std::endl;
+
+   //
+   // These sanity checks test for a round trip accuracy of one half
+   // of the bits in T, unless T is type float, in which case we check
+   // for just one decimal digit.  The problem here is the sensitivity
+   // of the functions, not their accuracy.  This test data was generated
+   // for the forward functions, which means that when it is used as
+   // the input to the inverses then it is necessarily inexact.  This rounding
+   // of the input is what makes the data unsuitable for use as an accuracy check,
+   // and also demonstrates that you can't in general round-trip these functions.
+   // It is however a useful sanity check.
+   //
+   value_type precision = static_cast(ldexp(1.0, 1-boost::math::policies::digits >()/2)) * 100;
+   if(boost::math::policies::digits >() < 50)
+      precision = 1;   // 1% or two decimal digits, all we can hope for when the input is truncated to float
+
+   for(unsigned i = 0; i < data.size(); ++i)
+   {
+      if(data[i][3] == 0)
+      {
+         BOOST_CHECK(0 == quantile(boost::math::non_central_chi_squared_distribution(data[i][0], data[i][1]), data[i][3]));
+      }
+      else if(data[i][3] < 0.9999f)
+      {
+         value_type p = quantile(boost::math::non_central_chi_squared_distribution(data[i][0], data[i][1]), data[i][3]);
+         value_type pt = data[i][2];
+         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
+      }
+      if(data[i][4] == 0)
+      {
+         BOOST_CHECK(0 == quantile(complement(boost::math::non_central_chi_squared_distribution(data[i][0], data[i][1]), data[i][3])));
+      }
+      else if(data[i][4] < 0.9999f)
+      {
+         value_type p = quantile(complement(boost::math::non_central_chi_squared_distribution(data[i][0], data[i][1]), data[i][4]));
+         value_type pt = data[i][2];
+         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
+      }
+      if(boost::math::tools::digits() > 50)
+      {
+         //
+         // Sanity check mode, the accuracy of
+         // the mode is at *best* the square root of the accuracy of the PDF:
+         //
+         try{
+            value_type m = mode(boost::math::non_central_chi_squared_distribution(data[i][0], data[i][1]));
+            value_type p = pdf(boost::math::non_central_chi_squared_distribution(data[i][0], data[i][1]), m);
+            BOOST_CHECK_EX(pdf(boost::math::non_central_chi_squared_distribution(data[i][0], data[i][1]), m * (1 + sqrt(precision) * 50)) <= p, i);
+            BOOST_CHECK_EX(pdf(boost::math::non_central_chi_squared_distribution(data[i][0], data[i][1]), m * (1 - sqrt(precision)) * 50) <= p, i);
+         }
+         catch(const boost::math::evaluation_error& ) {}
+         //
+         // Sanity check degrees-of-freedom finder, don't bother at float
+         // precision though as there's not enough data in the probability
+         // values to get back to the correct degrees of freedom or 
+         // non-cenrality parameter:
+         //
+         try{
+            if((data[i][3] < 0.99) && (data[i][3] != 0))
+            {
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_chi_squared_distribution::find_degrees_of_freedom(data[i][1], data[i][2], data[i][3]),
+                  data[i][0], precision, i);
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_chi_squared_distribution::find_non_centrality(data[i][0], data[i][2], data[i][3]),
+                  data[i][1], precision, i);
+            }
+            if((data[i][4] < 0.99) && (data[i][4] != 0))
+            {
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_chi_squared_distribution::find_degrees_of_freedom(boost::math::complement(data[i][1], data[i][2], data[i][4])),
+                  data[i][0], precision, i);
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_chi_squared_distribution::find_non_centrality(boost::math::complement(data[i][0], data[i][2], data[i][4])),
+                  data[i][1], precision, i);
+            }
+         }
+         catch(const std::exception& e)
+         {
+            BOOST_ERROR(e.what());
+         }
+      }
+   }
+}
+
+template 
+void test_accuracy(T, const char* type_name)
+{
+#include "nccs.ipp"
+    do_test_nc_chi_squared(nccs, type_name, "Non Central Chi Squared, medium parameters");
+    quantile_sanity_check(nccs, type_name, "Non Central Chi Squared, medium parameters");
+
+#include "nccs_big.ipp"
+    do_test_nc_chi_squared(nccs_big, type_name, "Non Central Chi Squared, large parameters");
+    quantile_sanity_check(nccs_big, type_name, "Non Central Chi Squared, large parameters");
+}
+
+int test_main(int, char* [])
+{
+   BOOST_MATH_CONTROL_FP;
+   // Basic sanity-check spot values.
+   expected_results();
+   // (Parameter value, arbitrarily zero, only communicates the floating point type).
+#ifdef TEST_FLOAT
+   test_spots(0.0F); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+   test_spots(0.0); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+#ifdef TEST_LDOUBLE
+   test_spots(0.0L); // Test long double.
+#endif
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+#ifdef TEST_REAL_CONCEPT
+   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+#endif
+#endif
+#endif
+
+#ifdef TEST_FLOAT
+   test_accuracy(0.0F, "float"); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+   test_accuracy(0.0, "double"); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+#ifdef TEST_LDOUBLE
+   test_accuracy(0.0L, "long double"); // Test long double.
+#endif
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+#ifdef TEST_REAL_CONCEPT
+   test_accuracy(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept.
+#endif
+#endif
+#endif
+   return 0;
+} // int test_main(int, char* [])
+
diff --git a/test/test_nc_f.cpp b/test/test_nc_f.cpp
new file mode 100644
index 000000000..09d792511
--- /dev/null
+++ b/test/test_nc_f.cpp
@@ -0,0 +1,300 @@
+// test_nc_beta.cpp
+
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifdef _MSC_VER
+#pragma warning (disable:4127 4512)
+#endif
+
+#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
+#  define TEST_FLOAT
+#  define TEST_DOUBLE
+#  define TEST_LDOUBLE
+#  define TEST_REAL_CONCEPT
+#endif
+
+#include  // for real_concept
+#include  // for chi_squared_distribution
+#include  // for test_main
+#include  // for BOOST_CHECK_CLOSE
+
+#include "functor.hpp"
+#include "handle_test_result.hpp"
+
+#include 
+using std::cout;
+using std::endl;
+#include 
+using std::numeric_limits;
+
+#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK_CLOSE(a, b, prec); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+#define BOOST_CHECK_EX(a, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK(a); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   const char* largest_type;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   if(boost::math::policies::digits >() == boost::math::policies::digits >())
+   {
+      largest_type = "(long\\s+)?double|real_concept";
+   }
+   else
+   {
+      largest_type = "long double|real_concept";
+   }
+#else
+   largest_type = "(long\\s+)?double|real_concept";
+#endif
+
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+template 
+RealType naive_pdf(RealType v1, RealType v2, RealType l, RealType f)
+{
+   BOOST_MATH_STD_USING
+   RealType sum = 0;
+   for(int i = 0; ; ++i)
+   {
+      RealType term = -l/2 + log(l/2) * i;
+      term += boost::math::lgamma(v2/2 + v1/2+i) - (boost::math::lgamma(v2/2) + boost::math::lgamma(v1/2+i));
+      term -= boost::math::lgamma(RealType(i+1));
+      term += log(v1/v2) * (v1/2+i) + log(v2 / (v2 + v1 * f)) * ((v1 + v2) / 2 + i);
+      term += log(f) * (v1/2 - 1 + i);
+      term = exp(term);
+      sum += term;
+      if((term/sum < boost::math::tools::epsilon()) || (term == 0))
+         break;
+   }
+   return sum;
+}
+
+template 
+void test_spot(
+     RealType a,     // df1
+     RealType b,     // df2
+     RealType ncp,   // non-centrality param
+     RealType x,     // F statistic
+     RealType P,     // CDF
+     RealType Q,     // Complement of CDF
+     RealType D,     // PDF
+     RealType tol)   // Test tolerance
+{
+   boost::math::non_central_f_distribution dist(a, b, ncp);
+   BOOST_CHECK_CLOSE(
+      cdf(dist, x), P, tol);
+   BOOST_CHECK_CLOSE(
+      pdf(dist, x), D, tol);
+   if(boost::math::tools::digits() > 50)
+   {
+      //
+      // The "naive" pdf calculation fails at float precision.
+      //
+      BOOST_CHECK_CLOSE(
+         pdf(dist, x), naive_pdf(a, b, ncp, x), tol);
+   }
+
+   if((P < 0.99) && (Q < 0.99))
+   {
+      //
+      // We can only check this if P is not too close to 1,
+      // so that we can guarentee Q is reasonably free of error:
+      //
+      BOOST_CHECK_CLOSE(
+         cdf(complement(dist, x)), Q, tol);
+      BOOST_CHECK_CLOSE(
+            quantile(dist, P), x, tol * 10);
+      BOOST_CHECK_CLOSE(
+            quantile(complement(dist, Q)), x, tol * 10);
+   }
+   if(boost::math::tools::digits() > 50)
+   {
+      //
+      // Sanity check mode:
+      //
+      RealType m = mode(dist);
+      RealType p = pdf(dist, m);
+      BOOST_CHECK(pdf(dist, m * (1 + sqrt(tol) * 10)) <= p);
+      BOOST_CHECK(pdf(dist, m * (1 - sqrt(tol)) * 10) <= p);
+   }
+}
+
+template  // Any floating-point type RealType.
+void test_spots(RealType)
+{
+   RealType tolerance = (std::max)(
+      boost::math::tools::epsilon() * 100,
+      (RealType)1e-6) * 100;
+
+   cout << "Tolerance = " << tolerance << "%." << endl;
+
+   //
+   // Spot tests use values computed by the R statistical
+   // package and the pbeta and dbeta functions:
+   //
+   test_spot(
+     RealType(2),                   // alpha
+     RealType(5),                   // beta
+     RealType(1),                   // non-centrality param
+     RealType(2),                   // F statistic
+     RealType(0.6493871),           // CDF
+     RealType(1-0.6493871),         // Complement of CDF
+     RealType(0.1551262),           // PDF
+     RealType(tolerance));
+   test_spot(
+     RealType(100),                 // alpha
+     RealType(5),                   // beta
+     RealType(15),                  // non-centrality param
+     RealType(105),                 // F statistic
+     RealType(0.999962),            // CDF
+     RealType(1-0.999962),          // Complement of CDF
+     RealType(8.95623e-07),         // PDF
+     RealType(tolerance));
+   test_spot(
+     RealType(100),                 // alpha
+     RealType(5),                   // beta
+     RealType(15),                  // non-centrality param
+     RealType(1.5),                 // F statistic
+     RealType(0.5759232),           // CDF
+     RealType(1-0.5759232),         // Complement of CDF
+     RealType(0.3674375),           // PDF
+     RealType(tolerance));
+   test_spot(
+     RealType(5),                   // alpha
+     RealType(100),                 // beta
+     RealType(102),                 // non-centrality param
+     RealType(25),                  // F statistic
+     RealType(0.7499338),           // CDF
+     RealType(1-0.7499338),         // Complement of CDF
+     RealType(0.0544676),           // PDF
+     RealType(tolerance));
+   test_spot(
+     RealType(85),                  // alpha
+     RealType(100),                 // beta
+     RealType(245),                 // non-centrality param
+     RealType(3.5),                 // F statistic
+     RealType(0.2697244),           // CDF
+     RealType(1-0.2697244),         // Complement of CDF
+     RealType(0.5435237),           // PDF
+     RealType(tolerance));
+   test_spot(
+     RealType(85),                  // alpha
+     RealType(100),                 // beta
+     RealType(0.5),                 // non-centrality param
+     RealType(1.25),                // F statistic
+     RealType(0.8522862),           // CDF
+     RealType(1-0.8522862),         // Complement of CDF
+     RealType(0.8851028),           // PDF
+     RealType(tolerance));
+
+   BOOST_MATH_STD_USING
+
+   //
+   // 2 eps expressed as a persentage, otherwise the limit of the test data:
+   //
+   RealType tol2 = (std::max)(boost::math::tools::epsilon() * 200, RealType(1e-25));
+   RealType x = 2;
+   
+   boost::math::non_central_f_distribution dist(20, 15, 30);
+   // mean:
+   BOOST_CHECK_CLOSE(
+      mean(dist)
+      , static_cast(2.8846153846153846153846153846154L), tol2);
+   // variance:
+   BOOST_CHECK_CLOSE(
+      variance(dist)
+      , static_cast(2.1422807961269499731038192576654L), tol2);
+   // std deviation:
+   BOOST_CHECK_CLOSE(
+      standard_deviation(dist)
+      , sqrt(variance(dist)), tol2);
+   // hazard:
+   BOOST_CHECK_CLOSE(
+      hazard(dist, x)
+      , pdf(dist, x) / cdf(complement(dist, x)), tol2);
+   // cumulative hazard:
+   BOOST_CHECK_CLOSE(
+      chf(dist, x)
+      , -log(cdf(complement(dist, x))), tol2);
+   // coefficient_of_variation:
+   BOOST_CHECK_CLOSE(
+      coefficient_of_variation(dist)
+      , standard_deviation(dist) / mean(dist), tol2);
+   BOOST_CHECK_CLOSE(
+      median(dist), 
+      quantile(
+      dist,
+      static_cast(0.5)), static_cast(tol2));
+   // mode:
+   BOOST_CHECK_CLOSE(
+      mode(dist)
+      , static_cast(2.070019130232759428074835788815387743293972985542L), sqrt(tolerance));
+   // skewness:
+   BOOST_CHECK_CLOSE(
+      skewness(dist)
+      , static_cast(2.1011821125804540669752380228510691320707051692719L), tol2);
+   // kurtosis:
+   BOOST_CHECK_CLOSE(
+      kurtosis(dist)
+      , 3 + kurtosis_excess(dist), tol2);
+   // kurtosis excess:
+   BOOST_CHECK_CLOSE(
+      kurtosis_excess(dist)
+      , static_cast(13.225781681053154767604638331440974359675882226873L), tol2);
+} // template void test_spots(RealType)
+
+int test_main(int, char* [])
+{
+   BOOST_MATH_CONTROL_FP;
+   // Basic sanity-check spot values.
+   expected_results();
+   // (Parameter value, arbitrarily zero, only communicates the floating point type).
+   test_spots(0.0F); // Test float.
+   test_spots(0.0); // Test double.
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   test_spots(0.0L); // Test long double.
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+#endif
+#endif
+
+   return 0;
+} // int test_main(int, char* [])
+
diff --git a/test/test_nc_t.cpp b/test/test_nc_t.cpp
new file mode 100644
index 000000000..79525b99f
--- /dev/null
+++ b/test/test_nc_t.cpp
@@ -0,0 +1,523 @@
+// test_nc_t.cpp
+
+// Copyright John Maddock 2008.
+
+// Use, modification and distribution are subject to the
+// Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifdef _MSC_VER
+#pragma warning (disable:4127 4512)
+#endif
+
+#if !defined(TEST_FLOAT) && !defined(TEST_DOUBLE) && !defined(TEST_LDOUBLE) && !defined(TEST_REAL_CONCEPT)
+#  define TEST_FLOAT
+#  define TEST_DOUBLE
+#  define TEST_LDOUBLE
+#  define TEST_REAL_CONCEPT
+#endif
+
+#include  // for real_concept
+#include  // for chi_squared_distribution
+#include  // for test_main
+#include  // for BOOST_CHECK_CLOSE
+
+#include "functor.hpp"
+#include "handle_test_result.hpp"
+
+#include 
+using std::cout;
+using std::endl;
+#include 
+using std::numeric_limits;
+
+#define BOOST_CHECK_CLOSE_EX(a, b, prec, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK_CLOSE(a, b, prec); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+#define BOOST_CHECK_EX(a, i) \
+   {\
+      unsigned int failures = boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed;\
+      BOOST_CHECK(a); \
+      if(failures != boost::unit_test::results_collector.results( boost::unit_test::framework::current_test_case().p_id ).p_assertions_failed)\
+      {\
+         std::cerr << "Failure was at row " << i << std::endl;\
+         std::cerr << std::setprecision(35); \
+         std::cerr << "{ " << data[i][0] << " , " << data[i][1] << " , " << data[i][2];\
+         std::cerr << " , " << data[i][3] << " , " << data[i][4] << " } " << std::endl;\
+      }\
+   }
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   const char* largest_type;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   if(boost::math::policies::digits >() == boost::math::policies::digits >())
+   {
+      largest_type = "(long\\s+)?double|real_concept";
+   }
+   else
+   {
+      largest_type = "long double|real_concept";
+   }
+#else
+   largest_type = "(long\\s+)?double|real_concept";
+#endif
+
+   //
+   // Catch all cases come last:
+   //
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      "real_concept",                   // test type(s)
+      "[^|]*",                          // test data group
+      "[^|]*", 300000, 100000);                // test function
+   add_expected_result(
+      "[^|]*",                          // compiler
+      "[^|]*",                          // stdlib
+      "[^|]*",                          // platform
+      largest_type,                     // test type(s)
+      "[^|]*",                          // test data group
+      "[^|]*", 250, 50);                // test function
+
+   //
+   // Finish off by printing out the compiler/stdlib/platform names,
+   // we do this to make it easier to mark up expected error rates.
+   //
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+template 
+RealType naive_pdf(RealType v, RealType delta, RealType x)
+{
+}
+
+template 
+RealType naive_mean(RealType v, RealType delta)
+{
+   using boost::math::tgamma;
+   return delta * sqrt(v / 2) * tgamma((v-1)/2) / tgamma(v/2);
+}
+
+float naive_mean(float v, float delta)
+{
+   return (float)naive_mean((double)v, (double)delta);
+}
+
+template 
+RealType naive_variance(RealType v, RealType delta)
+{
+   using boost::math::tgamma;
+   RealType r = tgamma((v-1)/2) / tgamma(v/2);
+   r *= r;
+   r *= -delta * delta * v / 2;
+   r += (1 + delta * delta) * v / (v - 2);
+   return r;
+}
+
+float naive_variance(float v, float delta)
+{
+   return (float)naive_variance((double)v, (double)delta);
+}
+
+template 
+RealType naive_skewness(RealType v, RealType delta)
+{
+   using boost::math::tgamma;
+   RealType tgr = tgamma((v-1)/2) / tgamma(v / 2);
+   RealType r = delta * sqrt(v) * tgamma((v-1)/2)
+      * (v * (-3 + delta * delta + 2 * v) / ((-3 + v) * (-2 + v)) 
+         - 2 * ((1 + delta * delta) * v / (-2 + v) - delta * delta * v * tgr * tgr / 2));
+   r /= boost::math::constants::root_two()
+      * pow(((1+delta*delta) * v / (-2+v) - delta*delta*v*tgr*tgr/2), RealType(1.5f))
+      * tgamma(v/2);
+   return r;
+}
+
+float naive_skewness(float v, float delta)
+{
+   return (float)naive_skewness((double)v, (double)delta);
+}
+
+template 
+RealType naive_kurtosis_excess(RealType v, RealType delta)
+{
+   using boost::math::tgamma;
+   RealType tgr = tgamma((v-1)/2) / tgamma(v / 2);
+   RealType r = -delta * delta * v * tgr * tgr / 2;
+   r *= v * (delta * delta * (1 + v) + 3 * (-5 + 3 * v)) / ((-3 + v)*(-2+v))
+      - 3 * ((1 + delta * delta) * v / (-2 + v) - delta * delta * v * tgr * tgr / 2);
+   r += (3 + 6 * delta * delta + delta * delta * delta * delta)* v * v 
+      / ((-4+v) * (-2+v));
+   r /= (1+delta*delta)*v / (-2+v) - delta*delta*v *tgr*tgr/2;
+   r /= (1+delta*delta)*v / (-2+v) - delta*delta*v *tgr*tgr/2;
+   return r;
+}
+
+float naive_kurtosis_excess(float v, float delta)
+{
+   return (float)naive_kurtosis_excess((double)v, (double)delta);
+}
+
+template 
+void test_spot(
+     RealType df,    // Degrees of freedom
+     RealType ncp,   // non-centrality param
+     RealType t,     // T statistic
+     RealType P,     // CDF
+     RealType Q,     // Complement of CDF
+     RealType tol)   // Test tolerance
+{
+   boost::math::non_central_t_distribution dist(df, ncp);
+   BOOST_CHECK_CLOSE(
+      cdf(dist, t), P, tol);
+   try{
+      BOOST_CHECK_CLOSE(
+         mean(dist), naive_mean(df, ncp), tol);
+      BOOST_CHECK_CLOSE(
+         variance(dist), naive_variance(df, ncp), tol);
+      BOOST_CHECK_CLOSE(
+         skewness(dist), naive_skewness(df, ncp), tol * 10);
+      BOOST_CHECK_CLOSE(
+         kurtosis_excess(dist), naive_kurtosis_excess(df, ncp), tol * 50);
+      BOOST_CHECK_CLOSE(
+         kurtosis(dist), 3 + naive_kurtosis_excess(df, ncp), tol * 50);
+   }
+   catch(const std::domain_error&)
+   {
+   }
+   /*
+   BOOST_CHECK_CLOSE(
+      pdf(dist, t), naive_pdf(dist.degrees_of_freedom(), ncp, t), tol * 50);
+   */
+   if((P < 0.99) && (Q < 0.99))
+   {
+      //
+      // We can only check this if P is not too close to 1,
+      // so that we can guarentee Q is reasonably free of error:
+      //
+      BOOST_CHECK_CLOSE(
+         cdf(complement(dist, t)), Q, tol);
+      BOOST_CHECK_CLOSE(
+            quantile(dist, P), t, tol * 10);
+      BOOST_CHECK_CLOSE(
+            quantile(complement(dist, Q)), t, tol * 10);
+      /*
+      BOOST_CHECK_CLOSE(
+         dist.find_degrees_of_freedom(ncp, t, P), df, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_degrees_of_freedom(boost::math::complement(ncp, t, Q)), df, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_non_centrality(df, t, P), ncp, tol * 10);
+      BOOST_CHECK_CLOSE(
+         dist.find_non_centrality(boost::math::complement(df, t, Q)), ncp, tol * 10);
+         */
+   }
+}
+
+template  // Any floating-point type RealType.
+void test_spots(RealType)
+{
+   //
+   // Approx limit of test data is 12 digits expressed here as a persentage:
+   //
+   RealType tolerance = (std::max)(
+      boost::math::tools::epsilon(),
+      (RealType)5e-12f) * 100;
+   //
+   // At float precision we need to up the tolerance, since 
+   // the input values are rounded off to inexact quantities
+   // the results get thrown off by a noticeable amount.
+   //
+   if(boost::math::tools::digits() < 50)
+      tolerance *= 50;
+   if(boost::is_floating_point::value != 1)
+      tolerance *= 20; // real_concept special functions are less accurate
+
+   cout << "Tolerance = " << tolerance << "%." << endl;
+
+   //
+   // Test data is taken from:
+   //
+   // Computing discrete mixtures of continuous
+   // distributions: noncentral chisquare, noncentral t
+   // and the distribution of the square of the sample
+   // multiple correlation coeficient.
+   // Denise Benton, K. Krishnamoorthy.
+   // Computational Statistics & Data Analysis 43 (2003) 249 – 267
+   //
+   test_spot(
+      static_cast(3),   // degrees of freedom
+      static_cast(1),   // non centrality
+      static_cast(2.34),   // T
+      static_cast(0.801888999613917),       // Probability of result (CDF), P
+      static_cast(1-0.801888999613917),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(126),   // degrees of freedom
+      static_cast(-2),   // non centrality
+      static_cast(-4.33),   // T
+      static_cast(1.252846196792878e-2),       // Probability of result (CDF), P
+      static_cast(1-1.252846196792878e-2),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(20),   // degrees of freedom
+      static_cast(23),   // non centrality
+      static_cast(23),   // T
+      static_cast(0.460134400391924),       // Probability of result (CDF), P
+      static_cast(1-0.460134400391924),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(20),   // degrees of freedom
+      static_cast(33),   // non centrality
+      static_cast(34),   // T
+      static_cast(0.532008386378725),       // Probability of result (CDF), P
+      static_cast(1-0.532008386378725),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(12),   // degrees of freedom
+      static_cast(38),   // non centrality
+      static_cast(39),   // T
+      static_cast(0.495868184917805),       // Probability of result (CDF), P
+      static_cast(1-0.495868184917805),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(12),   // degrees of freedom
+      static_cast(39),   // non centrality
+      static_cast(39),   // T
+      static_cast(0.446304024668836),       // Probability of result (CDF), P
+      static_cast(1-0.446304024668836),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(200),   // degrees of freedom
+      static_cast(38),   // non centrality
+      static_cast(39),   // T
+      static_cast(0.666194209961795),       // Probability of result (CDF), P
+      static_cast(1-0.666194209961795),           // Q = 1 - P
+      tolerance);
+   test_spot(
+      static_cast(200),   // degrees of freedom
+      static_cast(42),   // non centrality
+      static_cast(40),   // T
+      static_cast(0.179292265426085),       // Probability of result (CDF), P
+      static_cast(1-0.179292265426085),           // Q = 1 - P
+      tolerance);
+
+   boost::math::non_central_t_distribution dist(static_cast(8), static_cast(12));
+   BOOST_CHECK_CLOSE(pdf(dist, 12), static_cast(1.235329715425894935157684607751972713457e-1L), tolerance);
+   BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution(126, -2), -4), static_cast(5.797932289365814702402873546466798025787e-2L), tolerance);
+   BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution(126, 2), 4), static_cast(5.797932289365814702402873546466798025787e-2L), tolerance);
+   BOOST_CHECK_CLOSE(pdf(boost::math::non_central_t_distribution(126, 2), 0), static_cast(5.388394890639957139696546086044839573749e-2L), tolerance);
+} // template void test_spots(RealType)
+
+template 
+T nct_cdf(T df, T nc, T x)
+{
+   return cdf(boost::math::non_central_t_distribution(df, nc), x);
+}
+
+template 
+T nct_ccdf(T df, T nc, T x)
+{
+   return cdf(complement(boost::math::non_central_t_distribution(df, nc), x));
+}
+
+template 
+void do_test_nc_t(T& data, const char* type_name, const char* test)
+{
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   std::cout << "Testing: " << test << std::endl;
+
+   value_type (*fp1)(value_type, value_type, value_type) = nct_cdf;
+   boost::math::tools::test_result result;
+
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2),
+      extract_result(3));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "CDF", test);
+
+   fp1 = nct_ccdf;
+   result = boost::math::tools::test(
+      data,
+      bind_func(fp1, 0, 1, 2),
+      extract_result(4));
+   handle_test_result(result, data[result.worst()], result.worst(),
+      type_name, "CCDF", test);
+
+   std::cout << std::endl;
+
+}
+
+template 
+void quantile_sanity_check(T& data, const char* type_name, const char* test)
+{
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   //
+   // Tests with type real_concept take rather too long to run, so
+   // for now we'll disable them:
+   //
+   if(!boost::is_floating_point::value)
+      return;
+
+   std::cout << "Testing: " << type_name << " quantile sanity check, with tests " << test << std::endl;
+
+   //
+   // These sanity checks test for a round trip accuracy of one half
+   // of the bits in T, unless T is type float, in which case we check
+   // for just one decimal digit.  The problem here is the sensitivity
+   // of the functions, not their accuracy.  This test data was generated
+   // for the forward functions, which means that when it is used as
+   // the input to the inverses then it is necessarily inexact.  This rounding
+   // of the input is what makes the data unsuitable for use as an accuracy check,
+   // and also demonstrates that you can't in general round-trip these functions.
+   // It is however a useful sanity check.
+   //
+   value_type precision = static_cast(ldexp(1.0, 1-boost::math::policies::digits >()/2)) * 100;
+   if(boost::math::policies::digits >() < 50)
+      precision = 1;   // 1% or two decimal digits, all we can hope for when the input is truncated to float
+
+   for(unsigned i = 0; i < data.size(); ++i)
+   {
+      if(data[i][3] == 0)
+      {
+         BOOST_CHECK(0 == quantile(boost::math::non_central_t_distribution(data[i][0], data[i][1]), data[i][3]));
+      }
+      else if(data[i][3] < 0.9999f)
+      {
+         value_type p = quantile(boost::math::non_central_t_distribution(data[i][0], data[i][1]), data[i][3]);
+         value_type pt = data[i][2];
+         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
+      }
+      if(data[i][4] == 0)
+      {
+         BOOST_CHECK(0 == quantile(complement(boost::math::non_central_t_distribution(data[i][0], data[i][1]), data[i][3])));
+      }
+      else if(data[i][4] < 0.9999f)
+      {
+         value_type p = quantile(complement(boost::math::non_central_t_distribution(data[i][0], data[i][1]), data[i][4]));
+         value_type pt = data[i][2];
+         BOOST_CHECK_CLOSE_EX(pt, p, precision, i);
+      }
+      if(boost::math::tools::digits() > 50)
+      {
+         //
+         // Sanity check mode, the accuracy of
+         // the mode is at *best* the square root of the accuracy of the PDF:
+         //
+         try{
+            value_type m = mode(boost::math::non_central_t_distribution(data[i][0], data[i][1]));
+            value_type p = pdf(boost::math::non_central_t_distribution(data[i][0], data[i][1]), m);
+            BOOST_CHECK_EX(pdf(boost::math::non_central_t_distribution(data[i][0], data[i][1]), m * (1 + sqrt(precision) * 100)) <= p, i);
+            BOOST_CHECK_EX(pdf(boost::math::non_central_t_distribution(data[i][0], data[i][1]), m * (1 - sqrt(precision)) * 100) <= p, i);
+         }
+         catch(const boost::math::evaluation_error& ) {}
+#if 0
+         //
+         // Sanity check degrees-of-freedom finder, don't bother at float
+         // precision though as there's not enough data in the probability
+         // values to get back to the correct degrees of freedom or 
+         // non-cenrality parameter:
+         //
+         try{
+            if((data[i][3] < 0.99) && (data[i][3] != 0))
+            {
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_t_distribution::find_degrees_of_freedom(data[i][1], data[i][2], data[i][3]),
+                  data[i][0], precision, i);
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_t_distribution::find_non_centrality(data[i][0], data[i][2], data[i][3]),
+                  data[i][1], precision, i);
+            }
+            if((data[i][4] < 0.99) && (data[i][4] != 0))
+            {
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_t_distribution::find_degrees_of_freedom(boost::math::complement(data[i][1], data[i][2], data[i][4])),
+                  data[i][0], precision, i);
+               BOOST_CHECK_CLOSE_EX(
+                  boost::math::non_central_t_distribution::find_non_centrality(boost::math::complement(data[i][0], data[i][2], data[i][4])),
+                  data[i][1], precision, i);
+            }
+         }
+         catch(const std::exception& e)
+         {
+            BOOST_ERROR(e.what());
+         }
+#endif
+      }
+   }
+}
+
+template 
+void test_accuracy(T, const char* type_name)
+{
+#include "nct.ipp"
+    do_test_nc_t(nct, type_name, "Non Central T");
+    quantile_sanity_check(nct, type_name, "Non Central T");
+}
+
+int test_main(int, char* [])
+{
+   BOOST_MATH_CONTROL_FP;
+   // Basic sanity-check spot values.
+   expected_results();
+
+   // (Parameter value, arbitrarily zero, only communicates the floating point type).
+#ifdef TEST_FLOAT
+   test_spots(0.0F); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+   test_spots(0.0); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+#ifdef TEST_LDOUBLE
+   test_spots(0.0L); // Test long double.
+#endif
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+#ifdef TEST_REAL_CONCEPT
+   test_spots(boost::math::concepts::real_concept(0.)); // Test real concept.
+#endif
+#endif
+#endif
+
+#ifdef TEST_FLOAT
+   test_accuracy(0.0F, "float"); // Test float.
+#endif
+#ifdef TEST_DOUBLE
+   test_accuracy(0.0, "double"); // Test double.
+#endif
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+#ifdef TEST_LDOUBLE
+   test_accuracy(0.0L, "long double"); // Test long double.
+#endif
+#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x582))
+#ifdef TEST_REAL_CONCEPT
+   test_accuracy(boost::math::concepts::real_concept(0.), "real_concept"); // Test real concept.
+#endif
+#endif
+#endif
+   return 0;
+} // int test_main(int, char* [])
+
diff --git a/test/test_ncbeta_hooks.hpp b/test/test_ncbeta_hooks.hpp
new file mode 100644
index 000000000..e81555508
--- /dev/null
+++ b/test/test_ncbeta_hooks.hpp
@@ -0,0 +1,39 @@
+//  (C) Copyright John Maddock 2008.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_TEST_NCBETA_OTHER_HOOKS_HPP
+#define BOOST_MATH_TEST_NCBETA_OTHER_HOOKS_HPP
+
+
+#ifdef TEST_R
+#define MATHLIB_STANDALONE
+#include 
+namespace other{
+inline float ncbeta_cdf(float a, float b, float nc, float x)
+{ 
+   return (float)pnbeta(x, a, b, nc, 1, 0);
+}
+inline double ncbeta_cdf(double a, double b, double nc, double x)
+{
+   return pnbeta(x, a, b, nc, 1, 0);
+}
+inline long double ncbeta_cdf(long double a, long double b, long double nc, long double x)
+{ 
+   return pnbeta((double)x, (double)a, (double)b, (double)nc, 1, 0);
+}
+}
+#define TEST_OTHER
+#endif
+
+#ifdef TEST_OTHER
+namespace other{
+   boost::math::concepts::real_concept ncbeta_cdf(boost::math::concepts::real_concept, boost::math::concepts::real_concept, boost::math::concepts::real_concept){ return 0; }
+}
+#endif
+
+
+#endif
+
+
diff --git a/test/test_nccs_hooks.hpp b/test/test_nccs_hooks.hpp
new file mode 100644
index 000000000..11225fa56
--- /dev/null
+++ b/test/test_nccs_hooks.hpp
@@ -0,0 +1,61 @@
+//  (C) Copyright John Maddock 2008.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_TEST_NCCS_OTHER_HOOKS_HPP
+#define BOOST_MATH_TEST_NCCS_OTHER_HOOKS_HPP
+
+
+#ifdef TEST_R
+#define MATHLIB_STANDALONE
+#include 
+namespace other{
+inline float nccs_cdf(float df, float nc, float x)
+{ 
+   return (float)pnchisq(x, df, nc, 1, 0);
+}
+inline double nccs_cdf(double df, double nc, double x)
+{
+   return pnchisq(x, df, nc, 1, 0);
+}
+inline long double nccs_cdf(long double df, long double nc, long double x)
+{ 
+   return pnchisq((double)x, (double)df, (double)nc, 1, 0);
+}
+}
+#define TEST_OTHER
+#endif
+
+#ifdef TEST_CDFLIB
+#include 
+namespace other{
+inline double nccs_cdf(double df, double nc, double x)
+{
+   int kind(1), status(0);
+   double p, q, bound(0);
+   cdfchn(&kind, &p, &q, &x, &df, &nc, &status, &bound);
+   return p;
+}
+inline float nccs_cdf(float df, float nc, float x)
+{ 
+   return (double)nccs_cdf((double)df, (double)nc, (double)x);
+}
+inline long double nccs_cdf(long double df, long double nc, long double x)
+{ 
+   return nccs_cdf((double)df, (double)nc, (double)x);
+}
+}
+#define TEST_OTHER
+#endif
+
+#ifdef TEST_OTHER
+namespace other{
+   boost::math::concepts::real_concept nccs_cdf(boost::math::concepts::real_concept, boost::math::concepts::real_concept, boost::math::concepts::real_concept){ return 0; }
+}
+#endif
+
+
+#endif
+
+
diff --git a/test/test_negative_binomial.cpp b/test/test_negative_binomial.cpp
index 64417d28c..71471935c 100644
--- a/test/test_negative_binomial.cpp
+++ b/test/test_negative_binomial.cpp
@@ -26,15 +26,15 @@
 #  define TEST_REAL_CONCEPT
 #endif
 
+#include  // for real_concept
+using ::boost::math::concepts::real_concept;
+
 #include  // for negative_binomial_distribution
 using boost::math::negative_binomial_distribution;
 
 #include 
   using boost::math::lgamma;  // log gamma
 
-#include  // for real_concept
-using ::boost::math::concepts::real_concept;
-
 #include  // for test_main
 #include  // for BOOST_CHECK_CLOSE
 
diff --git a/test/test_poisson.cpp b/test/test_poisson.cpp
index 361637cd7..69751a96c 100644
--- a/test/test_poisson.cpp
+++ b/test/test_poisson.cpp
@@ -26,9 +26,9 @@
 #include  // Boost.Test
 #include 
 
+#include  // for real_concept
 #include 
     using boost::math::poisson_distribution;
-#include  // for real_concept
 #include  // for real_concept
 
 #include  // for (incomplete) gamma.
diff --git a/test/test_round.cpp b/test/test_round.cpp
new file mode 100644
index 000000000..9b682274d
--- /dev/null
+++ b/test/test_round.cpp
@@ -0,0 +1,237 @@
+//  (C) Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+boost::mt19937 rng;
+
+template 
+T get_random()
+{
+   //
+   // Fill all the bits in T with random values, 
+   // likewise set the exponent to a random value
+   // that will still fit inside a T, and always
+   // have a remainder as well as an integer part.
+   //
+   int bits = boost::math::tools::digits();
+   int shift = 0;
+   int exponent = rng() % (bits - 4);
+   T result = 0;
+   while(bits > 0)
+   {
+      result += ldexp(static_cast(rng()), shift);
+      shift += std::numeric_limits::digits;
+      bits -= std::numeric_limits::digits;
+   }
+   return rng() & 1u ? -ldexp(frexp(result, &bits), exponent) : ldexp(frexp(result, &bits), exponent);
+}
+
+template 
+void check_within_half(T a, U u)
+{
+   if(fabs(a-u) > 0.5f)
+   {
+      BOOST_ERROR("Rounded result differed by more than 0.5 from the original");
+      std::cerr << "Values were: " << std::setprecision(35) << std::setw(40)
+         << std::left << a << u << std::endl;
+   }
+}
+
+//
+// We may not have an abs overload for long long so provide a fall back:
+//
+template 
+inline T safe_abs(T const& v ...)
+{
+   return v < 0 ? -v : v;
+}
+
+template 
+void check_trunc_result(T a, U u)
+{
+   BOOST_MATH_STD_USING
+   using ::abs;
+   if(fabs(a-u) >= 1)
+   {
+      BOOST_ERROR("Rounded result differed by more than 1 from the original");
+      std::cerr << "Values were: " << std::setprecision(35) << std::setw(40)
+         << std::left << a << u << std::endl;
+   }
+   if(abs(a) < safe_abs(u))
+   {
+      BOOST_ERROR("Truncated result had larger absolute value than the original");
+      std::cerr << "Values were: " << std::setprecision(35) << std::setw(40)
+         << std::left << a << u << std::endl;
+   }
+}
+
+template 
+void check_modf_result(T a, T fract, U ipart)
+{
+   BOOST_MATH_STD_USING
+   if(fract + ipart != a)
+   {
+      BOOST_ERROR("Fractional and integer results do not add up to the original value");
+      std::cerr << "Values were: " << std::setprecision(35) << " "
+         << std::left << a << ipart << " " << fract << std::endl;
+   }
+   if((boost::math::sign(a) != boost::math::sign(fract)) && boost::math::sign(fract))
+   {
+      BOOST_ERROR("Original and fractional parts have differing signs");
+      std::cerr << "Values were: " << std::setprecision(35) << " "
+         << std::left << a << ipart << " " << fract << std::endl;
+   }
+   if((boost::math::sign(a) != boost::math::sign(ipart)) && boost::math::sign(ipart))
+   {
+      BOOST_ERROR("Original and integer parts have differing signs");
+      std::cerr << "Values were: " << std::setprecision(35) << " "
+         << std::left << a << ipart << " " << ipart << std::endl;
+   }
+   if(fabs(a-ipart) >= 1)
+   {
+      BOOST_ERROR("Rounded result differed by more than 1 from the original");
+      std::cerr << "Values were: " << std::setprecision(35) << std::setw(40)
+         << std::left << a << ipart << std::endl;
+   }
+}
+
+template 
+void test_round(T, const char* name)
+{
+   BOOST_MATH_STD_USING
+
+   for(int i = 0; i < 1000; ++i)
+   {
+      T arg = get_random();
+      T r = boost::math::round(arg);
+      check_within_half(arg, r);
+      r = boost::math::trunc(arg);
+      check_trunc_result(arg, r);
+      T frac = boost::math::modf(arg, &r);
+      check_modf_result(arg, frac, r);
+
+      if(abs(r) < (std::numeric_limits::max)())
+      {
+         int i = boost::math::iround(arg);
+         check_within_half(arg, i);
+         i = boost::math::itrunc(arg);
+         check_trunc_result(arg, i);
+         r = boost::math::modf(arg, &i);
+         check_modf_result(arg, r, i);
+      }
+      
+      if(abs(r) < (std::numeric_limits::max)())
+      {
+         long l = boost::math::lround(arg);
+         check_within_half(arg, l);
+         l = boost::math::ltrunc(arg);
+         check_trunc_result(arg, l);
+         r = boost::math::modf(arg, &l);
+         check_modf_result(arg, r, l);
+      }
+
+#ifdef BOOST_HAS_LONG_LONG
+      if(abs(r) < (std::numeric_limits::max)())
+      {
+         long long ll = boost::math::llround(arg);
+         check_within_half(arg, ll);
+         ll = boost::math::lltrunc(arg);
+         check_trunc_result(arg, ll);
+         r = boost::math::modf(arg, &ll);
+         check_modf_result(arg, r, ll);
+      }
+#endif
+   }
+   //
+   // Finish off by testing the error handlers:
+   //
+   BOOST_CHECK_THROW(boost::math::iround(static_cast(1e20)), boost::math::rounding_error);
+   BOOST_CHECK_THROW(boost::math::iround(static_cast(-1e20)), boost::math::rounding_error);
+   BOOST_CHECK_THROW(boost::math::lround(static_cast(1e20)), boost::math::rounding_error);
+   BOOST_CHECK_THROW(boost::math::lround(static_cast(-1e20)), boost::math::rounding_error);
+#ifdef BOOST_HAS_LONG_LONG
+   BOOST_CHECK_THROW(boost::math::llround(static_cast(1e20)), boost::math::rounding_error);
+   BOOST_CHECK_THROW(boost::math::llround(static_cast(-1e20)), boost::math::rounding_error);
+#endif
+   if(std::numeric_limits::has_infinity)
+   {
+      BOOST_CHECK_THROW(boost::math::round(std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::iround(std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::iround(-std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::lround(std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::lround(-std::numeric_limits::infinity()), boost::math::rounding_error);
+   #ifdef BOOST_HAS_LONG_LONG
+      BOOST_CHECK_THROW(boost::math::llround(std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::llround(-std::numeric_limits::infinity()), boost::math::rounding_error);
+   #endif
+   }
+   if(std::numeric_limits::has_quiet_NaN)
+   {
+      BOOST_CHECK_THROW(boost::math::round(std::numeric_limits::quiet_NaN()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::iround(std::numeric_limits::quiet_NaN()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::lround(std::numeric_limits::quiet_NaN()), boost::math::rounding_error);
+   #ifdef BOOST_HAS_LONG_LONG
+      BOOST_CHECK_THROW(boost::math::llround(std::numeric_limits::quiet_NaN()), boost::math::rounding_error);
+   #endif
+   }
+   BOOST_CHECK_THROW(boost::math::itrunc(static_cast(1e20)), boost::math::rounding_error);
+   BOOST_CHECK_THROW(boost::math::itrunc(static_cast(-1e20)), boost::math::rounding_error);
+   BOOST_CHECK_THROW(boost::math::ltrunc(static_cast(1e20)), boost::math::rounding_error);
+   BOOST_CHECK_THROW(boost::math::ltrunc(static_cast(-1e20)), boost::math::rounding_error);
+#ifdef BOOST_HAS_LONG_LONG
+   BOOST_CHECK_THROW(boost::math::lltrunc(static_cast(1e20)), boost::math::rounding_error);
+   BOOST_CHECK_THROW(boost::math::lltrunc(static_cast(-1e20)), boost::math::rounding_error);
+#endif
+   if(std::numeric_limits::has_infinity)
+   {
+      BOOST_CHECK_THROW(boost::math::trunc(std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::itrunc(std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::itrunc(-std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::ltrunc(std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::ltrunc(-std::numeric_limits::infinity()), boost::math::rounding_error);
+   #ifdef BOOST_HAS_LONG_LONG
+      BOOST_CHECK_THROW(boost::math::lltrunc(std::numeric_limits::infinity()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::lltrunc(-std::numeric_limits::infinity()), boost::math::rounding_error);
+   #endif
+   }
+   if(std::numeric_limits::has_quiet_NaN)
+   {
+      BOOST_CHECK_THROW(boost::math::trunc(std::numeric_limits::quiet_NaN()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::itrunc(std::numeric_limits::quiet_NaN()), boost::math::rounding_error);
+      BOOST_CHECK_THROW(boost::math::ltrunc(std::numeric_limits::quiet_NaN()), boost::math::rounding_error);
+   #ifdef BOOST_HAS_LONG_LONG
+      BOOST_CHECK_THROW(boost::math::lltrunc(std::numeric_limits::quiet_NaN()), boost::math::rounding_error);
+   #endif
+   }
+}
+
+int test_main(int, char* [])
+{
+   test_round(0.1F, "float");
+   test_round(0.1, "double");
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   test_round(0.1L, "long double");
+   //test_round(boost::math::concepts::real_concept(0.1), "real_concept");
+#else
+   std::cout << "The long double tests have been disabled on this platform "
+      "either because the long double overloads of the usual math functions are "
+      "not available at all, or because they are too inaccurate for these tests "
+      "to pass." << std::cout;
+#endif
+   return 0;
+}
+
+
+
+
+
diff --git a/test/test_students_t.cpp b/test/test_students_t.cpp
index 153f360c7..1f9db1dde 100644
--- a/test/test_students_t.cpp
+++ b/test/test_students_t.cpp
@@ -17,9 +17,9 @@
 #include  // Boost.Test
 #include 
 
+#include  // for real_concept
 #include 
     using boost::math::students_t_distribution;
-#include  // for real_concept
 #include  // for real_concept
 
 #include 
diff --git a/test/test_zeta.cpp b/test/test_zeta.cpp
new file mode 100644
index 000000000..6414a3c42
--- /dev/null
+++ b/test/test_zeta.cpp
@@ -0,0 +1,219 @@
+//  (C) Copyright John Maddock 2006.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+#include "functor.hpp"
+
+#include "handle_test_result.hpp"
+#include "test_zeta_hooks.hpp"
+
+//
+// DESCRIPTION:
+// ~~~~~~~~~~~~
+//
+// This file tests the zeta function. There are two sets of tests:
+// 1) Sanity checks: comparison to test values created with the
+// online calculator at functions.wolfram.com
+// 2) Accuracy tests use values generated with NTL::RR at 
+// 1000-bit precision and our generic versions of these functions.
+//
+// Note that when this file is first run on a new platform many of
+// these tests will fail: the default accuracy is 1 epsilon which
+// is too tight for most platforms.  In this situation you will 
+// need to cast a human eye over the error rates reported and make
+// a judgement as to whether they are acceptable.  Either way please
+// report the results to the Boost mailing list.  Acceptable rates of
+// error are marked up below as a series of regular expressions that
+// identify the compiler/stdlib/platform/data-type/test-data/test-function
+// along with the maximum expected peek and RMS mean errors for that
+// test.
+//
+
+void expected_results()
+{
+   //
+   // Define the max and mean errors expected for
+   // various compilers and platforms.
+   //
+   const char* largest_type;
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   if(boost::math::policies::digits >() == boost::math::policies::digits >())
+   {
+      largest_type = "(long\\s+)?double";
+   }
+   else
+   {
+      largest_type = "long double";
+   }
+#else
+   largest_type = "(long\\s+)?double";
+#endif
+
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      largest_type,                  // test type(s)
+      ".*Random values less than 1", // test data group
+      ".*", 1200, 500);              // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      "real_concept",                // test type(s)
+      ".*Random values less than 1", // test data group
+      ".*", 1200, 500);              // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      largest_type,                  // test type(s)
+      ".*",                          // test data group
+      ".*", 2, 1);                   // test function
+   add_expected_result(
+      ".*",                          // compiler
+      ".*",                          // stdlib
+      ".*",                          // platform
+      "real_concept",                // test type(s)
+      ".*",                          // test data group
+      ".*", 10, 5);                  // test function
+
+   std::cout << "Tests run with " << BOOST_COMPILER << ", " 
+      << BOOST_STDLIB << ", " << BOOST_PLATFORM << std::endl;
+}
+
+template 
+void do_test_zeta(const T& data, const char* type_name, const char* test_name)
+{
+   //
+   // test zeta(T) against data:
+   //
+   using namespace std;
+   typedef typename T::value_type row_type;
+   typedef typename row_type::value_type value_type;
+
+   std::cout << test_name << " with type " << type_name << std::endl;
+
+   typedef value_type (*pg)(value_type);
+   pg funcp = boost::math::zeta;
+
+   boost::math::tools::test_result result;
+   //
+   // test zeta against data:
+   //
+   result = boost::math::tools::test(
+      data,
+      bind_func(funcp, 0),
+      extract_result(1));
+   handle_test_result(result, data[result.worst()], result.worst(), type_name, "boost::math::zeta", test_name);
+#ifdef TEST_OTHER
+   if(boost::is_floating_point::value)
+   {
+      funcp = other::zeta;
+
+      result = boost::math::tools::test(
+         data,
+         bind_func(funcp, 0),
+         extract_result(1));
+      handle_test_result(result, data[result.worst()], result.worst(), type_name, "other::zeta", test_name);
+   }
+#endif
+   std::cout << std::endl;
+}
+template 
+void test_zeta(T, const char* name)
+{
+   //
+   // The actual test data is rather verbose, so it's in a separate file
+   //
+#include "zeta_data.ipp"
+   do_test_zeta(zeta_data, name, "Zeta: Random values greater than 1");
+#include "zeta_neg_data.ipp"
+   do_test_zeta(zeta_neg_data, name, "Zeta: Random values less than 1");
+#include "zeta_1_up_data.ipp"
+   do_test_zeta(zeta_1_up_data, name, "Zeta: Values close to and greater than 1");
+#include "zeta_1_below_data.ipp"
+   do_test_zeta(zeta_1_below_data, name, "Zeta: Values close to and less than 1");
+}
+
+extern "C" double zetac(double);
+
+template 
+void test_spots(T, const char* t)
+{
+   std::cout << "Testing basic sanity checks for type " << t << std::endl;
+   //
+   // Basic sanity checks, tolerance is either 2 or 10 epsilon 
+   // expressed as a percentage:
+   //
+   T tolerance = boost::math::tools::epsilon() * 100 *
+      (boost::is_floating_point::value ? 2 : 10);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(0.125)), static_cast(-0.63277562349869525529352526763564627152686379131122L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(1023) / static_cast(1024)), static_cast(-1023.4228554489429786541032870895167448906103303056L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(1025) / static_cast(1024)), static_cast(1024.5772867695045940578681624248887776501597556226L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(0.5)), static_cast(-1.46035450880958681288949915251529801246722933101258149054289L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(1.125)), static_cast(8.5862412945105752999607544082693023591996301183069L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(2)), static_cast(1.6449340668482264364724151666460251892189499012068L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(3.5)), static_cast(1.1267338673170566464278124918549842722219969574036L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(4)), static_cast(1.08232323371113819151600369654116790277475095191872690768298L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(4 + static_cast(1) / 1024), static_cast(1.08225596856391369799036835439238249195298434901488518878804L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(4.5)), static_cast(1.05470751076145426402296728896028011727249383295625173068468L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(6.5)), static_cast(1.01200589988852479610078491680478352908773213619144808841031L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(7.5)), static_cast(1.00582672753652280770224164440459408011782510096320822989663L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(8.125)), static_cast(1.0037305205308161603183307711439385250181080293472L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(16.125)), static_cast(1.0000140128224754088474783648500235958510030511915L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(0)), static_cast(-0.5L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-0.125)), static_cast(-0.39906966894504503550986928301421235400280637468895L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-1)), static_cast(-0.083333333333333333333333333333333333333333333333333L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-2)), static_cast(0L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-2.5)), static_cast(0.0085169287778503305423585670283444869362759902200745L), tolerance * 3);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-3)), static_cast(0.0083333333333333333333333333333333333333333333333333L), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-4)), static_cast(0), tolerance);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-20)), static_cast(0), tolerance * 100);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-21)), static_cast(-281.46014492753623188405797101449275362318840579710L), tolerance * 100);
+   BOOST_CHECK_CLOSE(::boost::math::zeta(static_cast(-30.125)), static_cast(2.2762941726834511267740045451463455513839970804578e7L), tolerance * 100);
+}
+
+int test_main(int, char* [])
+{
+   expected_results();
+   BOOST_MATH_CONTROL_FP;
+
+   test_spots(0.0f, "float");
+   test_spots(0.0, "double");
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   test_spots(0.0L, "long double");
+   test_spots(boost::math::concepts::real_concept(0.1), "real_concept");
+#else
+   std::cout << "The long double tests have been disabled on this platform "
+      "either because the long double overloads of the usual math functions are "
+      "not available at all, or because they are too inaccurate for these tests "
+      "to pass." << std::cout;
+#endif
+
+   test_zeta(0.1F, "float");
+   test_zeta(0.1, "double");
+#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
+   test_zeta(0.1L, "long double");
+   test_zeta(boost::math::concepts::real_concept(0.1), "real_concept");
+#else
+   std::cout << "The long double tests have been disabled on this platform "
+      "either because the long double overloads of the usual math functions are "
+      "not available at all, or because they are too inaccurate for these tests "
+      "to pass." << std::cout;
+#endif
+   return 0;
+}
+
+
+
diff --git a/test/test_zeta_hooks.hpp b/test/test_zeta_hooks.hpp
new file mode 100644
index 000000000..087d87d3e
--- /dev/null
+++ b/test/test_zeta_hooks.hpp
@@ -0,0 +1,56 @@
+//  (C) Copyright John Maddock 2006.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef BOOST_MATH_TEST_ZETA_OTHER_HOOKS_HPP
+#define BOOST_MATH_TEST_ZETA_OTHER_HOOKS_HPP
+
+
+#ifdef TEST_CEPHES
+namespace other{
+extern "C" {
+   double zetac(double);
+   float zetacf(float);
+   long double zetacl(long double);
+}
+inline float zeta(float a)
+{ return 1 + zetac(a); }
+inline double zeta(double a)
+{ return 1 + zetac(a); }
+inline long double zeta(long double a)
+{
+#ifdef BOOST_MSVC
+   return 1 + zetac((double)a); 
+#else
+   return zetacl(a); 
+#endif
+}
+}
+#define TEST_OTHER
+#endif
+
+#ifdef TEST_GSL
+#include 
+
+namespace other{
+inline float zeta(float a)
+{ return (float)gsl_sf_zeta(a); }
+inline double zeta(double a)
+{ return gsl_sf_zeta(a); }
+inline long double zeta(long double a)
+{ return gsl_sf_zeta(a); }
+}
+#define TEST_OTHER
+#endif
+
+#ifdef TEST_OTHER
+namespace other{
+   boost::math::concepts::real_concept zeta(boost::math::concepts::real_concept){ return 0; }
+}
+#endif
+
+
+#endif
+
+
diff --git a/test/zeta_1_below_data.ipp b/test/zeta_1_below_data.ipp
new file mode 100644
index 000000000..31b85ca53
--- /dev/null
+++ b/test/zeta_1_below_data.ipp
@@ -0,0 +1,29 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 24> zeta_1_below_data = {{
+      { SC_(0.02141654491424560546875), SC_(-0.5201506602793944998316548018699690797681) }, 
+      { SC_(0.50472259521484375), SC_(-1.479059796502255763615575236860218694317) }, 
+      { SC_(0.753675937652587890625), SC_(-3.500701844470537839375475836745309608254) }, 
+      { SC_(0.892135083675384521484375), SC_(-8.701549551111914711016864206105707387913) }, 
+      { SC_(0.963824570178985595703125), SC_(-27.06849649507583530629721672895651369373) }, 
+      { SC_(0.969254791736602783203125), SC_(-31.95042124075855399021415469463730656365) }, 
+      { SC_(0.98464930057525634765625), SC_(-64.56751477719026237096105864334609394117) }, 
+      { SC_(0.992201328277587890625), SC_(-127.6503167276133070149448420866102648888) }, 
+      { SC_(0.99617671966552734375), SC_(-260.9785629260130820484322508586172549118) }, 
+      { SC_(0.998053848743438720703125), SC_(-513.2576018780070294737373079904789166413) }, 
+      { SC_(0.99924468994140625), SC_(-1323.382435295998941597319533493165885945) }, 
+      { SC_(0.9997098445892333984375), SC_(-3445.851729045998047072816129417437104917) }, 
+      { SC_(0.99984395503997802734375), SC_(-6407.832268577823258975422770409768729774) }, 
+      { SC_(0.99990558624267578125), SC_(-10591.09955888672689821582177914203224971) }, 
+      { SC_(0.99996650218963623046875), SC_(-29852.12029567107244043543924323873276124) }, 
+      { SC_(0.999980032444000244140625), SC_(-50080.66457683383099069439395050656417597) }, 
+      { SC_(0.999987542629241943359375), SC_(-80273.18355079243243774478653269383556504) }, 
+      { SC_(0.99999535083770751953125), SC_(-215091.9356051864517678048611890100788117) }, 
+      { SC_(0.999996364116668701171875), SC_(-275035.7506534523074664329441741330074557) }, 
+      { SC_(0.9999980926513671875), SC_(-524287.4227844739836880964361309795525948) }, 
+      { SC_(0.999999463558197021484375), SC_(-1864134.533895485271043081470070250144498) }, 
+      { SC_(0.999999582767486572265625), SC_(-2396744.56564150833674906851990450393092) }, 
+      { SC_(0.9999997615814208984375), SC_(-4194303.422784352459117831107301957279448) }, 
+      { SC_(0.999999940395355224609375), SC_(-16777215.42278433943862976068131370725545) }
+   }};
+#undef SC_
+
diff --git a/test/zeta_1_up_data.ipp b/test/zeta_1_up_data.ipp
new file mode 100644
index 000000000..676fdb859
--- /dev/null
+++ b/test/zeta_1_up_data.ipp
@@ -0,0 +1,29 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 24> zeta_1_up_data = {{
+      { SC_(1.00000011920928955078125), SC_(8388608.57721567358185799990090564625463) }, 
+      { SC_(1.0000002384185791015625), SC_(4194304.577215682262183001486952251646755) }, 
+      { SC_(1.000000476837158203125), SC_(2097152.577215699622832591533990692770612) }, 
+      { SC_(1.00000059604644775390625), SC_(1677722.177215708303157179994975569843472) }, 
+      { SC_(1.0000019073486328125), SC_(524288.577215803786718564313226471202153) }, 
+      { SC_(1.00000369548797607421875), SC_(270600.8352804501205804024002567735033821) }, 
+      { SC_(1.00000464916229248046875), SC_(215093.0900365162546240716837932060406643) }, 
+      { SC_(1.00001239776611328125), SC_(80660.26952425996230208837588346956460766) }, 
+      { SC_(1.00001990795135498046875), SC_(50231.76284585702889240460092067814586596) }, 
+      { SC_(1.00003349781036376953125), SC_(29853.27472700086463256814366228500539722) }, 
+      { SC_(1.00009441375732421875), SC_(10592.253990216443584450690925565465553) }, 
+      { SC_(1.00015604496002197265625), SC_(6408.986699907390364066670889074476433249) }, 
+      { SC_(1.0002901554107666015625), SC_(3447.006160374985279544507526117209600704) }, 
+      { SC_(1.00075531005859375), SC_(1324.536866620273720254607350418328040857) }, 
+      { SC_(1.0019462108612060546875), SC_(514.3962964770573413079586126451916678814) }, 
+      { SC_(1.00382328033447265625), SC_(262.1329941141675715333591367272474762968) }, 
+      { SC_(1.007798671722412109375), SC_(128.8047474680561710562008547158197319238) }, 
+      { SC_(1.01535069942474365234375), SC_(65.72194382352840743913691516911618095535) }, 
+      { SC_(1.0307452678680419921875), SC_(33.1047803593638190816111616860939640546) }, 
+      { SC_(1.03617537021636962890625), SC_(28.22296068581747567698336482012316769919) }, 
+      { SC_(1.10786497592926025390625), SC_(9.855863042654116305734265296224764929693) }, 
+      { SC_(1.246324062347412109375), SC_(4.654545919478261756646025472315043204481) }, 
+      { SC_(1.49527740478515625), SC_(2.631125733364186076058384433696635480314) }, 
+      { SC_(1.97858345508575439453125), SC_(1.665479359458163559316085149303802250507) }
+   }};
+#undef SC_
+
diff --git a/test/zeta_data.ipp b/test/zeta_data.ipp
new file mode 100644
index 000000000..7deb75325
--- /dev/null
+++ b/test/zeta_data.ipp
@@ -0,0 +1,205 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 200> zeta_data = {{
+      { SC_(1.16628754138946533203125), SC_(6.602868183069916948720755731837247651904) }, 
+      { SC_(1.28222560882568359375), SC_(4.140637712279411074557164685415721499333) }, 
+      { SC_(1.7022221088409423828125), SC_(2.049914055577335303673424130546639695977) }, 
+      { SC_(1.79880845546722412109375), SC_(1.884017213259316830925461356827163589705) }, 
+      { SC_(2.048659801483154296875), SC_(1.601558368429615698519833097274473510457) }, 
+      { SC_(2.8781378269195556640625), SC_(1.228101328930692778618914405979886894909) }, 
+      { SC_(3.032318592071533203125), SC_(1.195776877916973414012665761751705560617) }, 
+      { SC_(3.1069891452789306640625), SC_(1.182159242558432231709092493922425008201) }, 
+      { SC_(3.1500339508056640625), SC_(1.174833816740130223224455066511517932084) }, 
+      { SC_(3.724112033843994140625), SC_(1.104091496679991538723159196605198807097) }, 
+      { SC_(4.021769046783447265625), SC_(1.080838392415394466528941224431751600289) }, 
+      { SC_(4.18305683135986328125), SC_(1.070728699189787267711417808282208201243) }, 
+      { SC_(4.988127231597900390625), SC_(1.037268683773212337925891820825986369163) }, 
+      { SC_(5.475403308868408203125), SC_(1.025677237452222708699509051024184979758) }, 
+      { SC_(6.73077487945556640625), SC_(1.010147799135311596739412446000395677634) }, 
+      { SC_(6.75488376617431640625), SC_(1.009971613405573851873574290566390329028) }, 
+      { SC_(7.481843471527099609375), SC_(1.005903033995481747047683253211887943379) }, 
+      { SC_(7.635406494140625), SC_(1.005288494073193869275365293603878222362) }, 
+      { SC_(8.020862579345703125), SC_(1.004017268583341130595381689022448999632) }, 
+      { SC_(8.38578319549560546875), SC_(1.003100201571479771794633384423398597856) }, 
+      { SC_(8.42790126800537109375), SC_(1.003009041836055382568010141093226826892) }, 
+      { SC_(8.492221832275390625), SC_(1.002875040229932893183945988160370427031) }, 
+      { SC_(8.66446590423583984375), SC_(1.002545196845709311376898921088902444564) }, 
+      { SC_(8.9931430816650390625), SC_(1.002018125856127423319731400168443258982) }, 
+      { SC_(9.1788425445556640625), SC_(1.001770614157242715970257755765969939378) }, 
+      { SC_(9.3712940216064453125), SC_(1.001546356501243682890096399666391078865) }, 
+      { SC_(9.79772472381591796875), SC_(1.001146130957712750505516168299351687689) }, 
+      { SC_(9.808345794677734375), SC_(1.00113762301831987584969089187780050217) }, 
+      { SC_(10.11186695098876953125), SC_(1.000919597225029357674089436218492816592) }, 
+      { SC_(10.29917240142822265625), SC_(1.000806567139600490049263928993429525886) }, 
+      { SC_(10.325397491455078125), SC_(1.000791898339491638031859012162073442552) }, 
+      { SC_(10.59409236907958984375), SC_(1.000656217007150362893379421381526735049) }, 
+      { SC_(11.10001468658447265625), SC_(1.000460863347090913162269206213828518989) }, 
+      { SC_(11.258045196533203125), SC_(1.000412744570371150451037951828092883018) }, 
+      { SC_(12.02548313140869140625), SC_(1.000241757815894734629418410369301746079) }, 
+      { SC_(12.114536285400390625), SC_(1.000227221507799340331471780559564457085) }, 
+      { SC_(12.59912014007568359375), SC_(1.000162173028028771481952241164711193704) }, 
+      { SC_(13.27601528167724609375), SC_(1.000101287979535386768777024448093303828) }, 
+      { SC_(13.40233516693115234375), SC_(1.000092774524593217714357153624534009066) }, 
+      { SC_(13.50353527069091796875), SC_(1.000086474027947163401202419199584993912) }, 
+      { SC_(13.81703281402587890625), SC_(1.00006954876715640831942977005349491939) }, 
+      { SC_(14.04100894927978515625), SC_(1.000059528194484375589465960959559392027) }, 
+      { SC_(14.2049045562744140625), SC_(1.000053123725822614470754551602877776071) }, 
+      { SC_(14.57920742034912109375), SC_(1.000040965134201953746630782215943808799) }, 
+      { SC_(15.36797332763671875), SC_(1.000023694259291145619969142932513875694) }, 
+      { SC_(15.8139476776123046875), SC_(1.000017387917474363833490985179130947483) }, 
+      { SC_(16.0026493072509765625), SC_(1.000015254196094267783311053302032549741) }, 
+      { SC_(16.0506114959716796875), SC_(1.000014754970384001823203354717544204648) }, 
+      { SC_(16.1929874420166015625), SC_(1.000013367248015505858617397050136565041) }, 
+      { SC_(17.285480499267578125), SC_(1.000006265375288782355276787853647834027) }, 
+      { SC_(17.3384552001953125), SC_(1.000006039370585766187763904743838901712) }, 
+      { SC_(17.431396484375), SC_(1.000005662382433471779572282335717605371) }, 
+      { SC_(17.864501953125), SC_(1.00000419335137039446528405523273417847) }, 
+      { SC_(18.5247364044189453125), SC_(1.000002653000473253577578493409620982871) }, 
+      { SC_(18.69007110595703125), SC_(1.000002365653327425220021887287461178979) }, 
+      { SC_(18.81287384033203125), SC_(1.000002172565731416793616844762261244142) }, 
+      { SC_(19.1818561553955078125), SC_(1.000001682165061320587705723061871112821) }, 
+      { SC_(19.67647552490234375), SC_(1.00000119382334998635578076483569134487) }, 
+      { SC_(19.70886993408203125), SC_(1.000001167310591227212167384387209403708) }, 
+      { SC_(20.61444854736328125), SC_(1.000000623066938898373480079125184673916) }, 
+      { SC_(20.89023590087890625), SC_(1.000000514640103638265544723138844382034) }, 
+      { SC_(21.0827579498291015625), SC_(1.000000450341377189234015911832375901699) }, 
+      { SC_(21.6490421295166015625), SC_(1.000000304127710718113360167907484415053) }, 
+      { SC_(21.7479114532470703125), SC_(1.000000283981940559836806790957987649415) }, 
+      { SC_(21.8129825592041015625), SC_(1.000000271456777007108293719830577426366) }, 
+      { SC_(22.024364471435546875), SC_(1.000000234457016042858052978953659230864) }, 
+      { SC_(22.31634521484375), SC_(1.000000191496938987028342073327362804024) }, 
+      { SC_(23.4463043212890625), SC_(1.000000087496653103497740447812661569997) }, 
+      { SC_(23.5119476318359375), SC_(1.000000083604563844903851348021422245475) }, 
+      { SC_(23.8504581451416015625), SC_(1.000000066118672757144002036583533060251) }, 
+      { SC_(23.9256191253662109375), SC_(1.000000062762118335210507369548667805974) }, 
+      { SC_(24.1413936614990234375), SC_(1.000000054043162442589559272614572137384) }, 
+      { SC_(24.1469058990478515625), SC_(1.000000053837061982953069368273926175689) }, 
+      { SC_(24.2995853424072265625), SC_(1.000000048430482721838693416022261315822) }, 
+      { SC_(24.52557373046875), SC_(1.00000004140831046897333530316265610171) }, 
+      { SC_(24.8483028411865234375), SC_(1.000000033108065641575998984551968709104) }, 
+      { SC_(25.115139007568359375), SC_(1.000000027517326675188465672935455696634) }, 
+      { SC_(25.347324371337890625), SC_(1.000000023426640017082892404381467024384) }, 
+      { SC_(25.883914947509765625), SC_(1.000000016150174569147643163428466835474) }, 
+      { SC_(25.903171539306640625), SC_(1.000000015936036497475570766824085170722) }, 
+      { SC_(25.9667415618896484375), SC_(1.000000015249075980692704336912033740583) }, 
+      { SC_(26.88591766357421875), SC_(1.000000008063810840808460735890647313959) }, 
+      { SC_(27.289585113525390625), SC_(1.000000006095693351337655085514196913602) }, 
+      { SC_(27.9059352874755859375), SC_(1.000000003976323567324742280069738235563) }, 
+      { SC_(28.0213603973388671875), SC_(1.000000003670583049284047356311447119736) }, 
+      { SC_(28.6940479278564453125), SC_(1.000000002302686016920949834610470007565) }, 
+      { SC_(28.924041748046875), SC_(1.000000001963357304099298248229398455341) }, 
+      { SC_(29.0107631683349609375), SC_(1.000000001848815070266702493862791862422) }, 
+      { SC_(29.6371631622314453125), SC_(1.000000001197643401744885528390587608634) }, 
+      { SC_(29.7665653228759765625), SC_(1.000000001094897489879537307636075154625) }, 
+      { SC_(29.896099090576171875), SC_(1.000000001000874865523017090100762703195) }, 
+      { SC_(29.9447536468505859375), SC_(1.000000000967683322176361378042505764603) }, 
+      { SC_(30.40348052978515625), SC_(1.000000000704112916637256444040895840462) }, 
+      { SC_(30.716098785400390625), SC_(1.000000000566936750566018696285006521506) }, 
+      { SC_(30.851467132568359375), SC_(1.000000000516160286455123973861824307492) }, 
+      { SC_(32.114917755126953125), SC_(1.000000000215004429998345753311603463246) }, 
+      { SC_(32.31705474853515625), SC_(1.000000000186895151300205581521237835124) }, 
+      { SC_(33.2660064697265625), SC_(1.000000000096813254374934769090357620442) }, 
+      { SC_(33.285717010498046875), SC_(1.000000000095499555541792141940005023127) }, 
+      { SC_(33.286014556884765625), SC_(1.000000000095479861400139003020181708444) }, 
+      { SC_(33.43369293212890625), SC_(1.000000000086189849924727332774207599423) }, 
+      { SC_(34.13188934326171875), SC_(1.000000000053122428800090015460135314565) }, 
+      { SC_(34.501476287841796875), SC_(1.000000000041116970445658244297262938037) }, 
+      { SC_(34.5605926513671875), SC_(1.000000000039466198914643412779159907251) }, 
+      { SC_(34.85152435302734375), SC_(1.000000000032258642822020209836223179965) }, 
+      { SC_(35.2764434814453125), SC_(1.000000000024028830747846719836544655561) }, 
+      { SC_(35.530582427978515625), SC_(1.000000000020147871220182569297544208725) }, 
+      { SC_(35.530796051025390625), SC_(1.000000000020144888100208513063984898063) }, 
+      { SC_(35.9766082763671875), SC_(1.000000000014789788630980767807649535379) }, 
+      { SC_(36.075710296630859375), SC_(1.000000000013807952318212484703393304569) }, 
+      { SC_(37.346637725830078125), SC_(1.000000000005721921857809586500408112553) }, 
+      { SC_(38.30919647216796875), SC_(1.000000000002936181040773097124904210497) }, 
+      { SC_(38.746036529541015625), SC_(1.00000000000216910640536046429265717688) }, 
+      { SC_(38.9936981201171875), SC_(1.000000000001826952613666734849972430403) }, 
+      { SC_(39.13246917724609375), SC_(1.000000000001659407425313111065810951635) }, 
+      { SC_(39.650783538818359375), SC_(1.000000000001158576855480162680056752427) }, 
+      { SC_(39.67319488525390625), SC_(1.000000000001140718173333054850436397748) }, 
+      { SC_(39.688701629638671875), SC_(1.000000000001128522871078350064987157044) }, 
+      { SC_(40.1527252197265625), SC_(1.00000000000081813568920259864182340915) }, 
+      { SC_(41.04537200927734375), SC_(1.000000000000440668358431418275080044096) }, 
+      { SC_(41.102458953857421875), SC_(1.000000000000423571747277636883518004963) }, 
+      { SC_(41.10936737060546875), SC_(1.00000000000042154830144392988490289401) }, 
+      { SC_(41.2002105712890625), SC_(1.000000000000395822807194682529407123307) }, 
+      { SC_(41.9948883056640625), SC_(1.000000000000228180734060750744420949622) }, 
+      { SC_(42.01873779296875), SC_(1.000000000000224439639108525255752196646) }, 
+      { SC_(42.245525360107421875), SC_(1.000000000000191791651936161940112696305) }, 
+      { SC_(42.640682220458984375), SC_(1.000000000000145839655420702994396584213) }, 
+      { SC_(42.656719207763671875), SC_(1.000000000000144227479936645019793391633) }, 
+      { SC_(42.8525238037109375), SC_(1.000000000000125922969766185468474101667) }, 
+      { SC_(42.93152618408203125), SC_(1.000000000000119212795161526838438039263) }, 
+      { SC_(43.824497222900390625), SC_(1.000000000000064196566283314196661109382) }, 
+      { SC_(43.89032745361328125), SC_(1.000000000000061333101268165345810372718) }, 
+      { SC_(44.2351226806640625), SC_(1.00000000000004829489412268436483221931) }, 
+      { SC_(44.69818878173828125), SC_(1.000000000000035035186258816984623517723) }, 
+      { SC_(44.844814300537109375), SC_(1.000000000000031649419666232107485326247) }, 
+      { SC_(45.324756622314453125), SC_(1.000000000000022692832892549255237158092) }, 
+      { SC_(45.4700164794921875), SC_(1.000000000000020519233831913348485253367) }, 
+      { SC_(45.52651214599609375), SC_(1.000000000000019731234145578672796054892) }, 
+      { SC_(45.67481231689453125), SC_(1.000000000000017803748480318501874295268) }, 
+      { SC_(45.706668853759765625), SC_(1.000000000000017414927749921329025278045) }, 
+      { SC_(45.942142486572265625), SC_(1.000000000000014792345774484033646200826) }, 
+      { SC_(46.061252593994140625), SC_(1.000000000000013620132568841259892936442) }, 
+      { SC_(46.165493011474609375), SC_(1.000000000000012670735995557404974141305) }, 
+      { SC_(46.66110992431640625), SC_(1.000000000000008986824993086497939810961) }, 
+      { SC_(46.95496368408203125), SC_(1.000000000000007330734455050719634274445) }, 
+      { SC_(46.970867156982421875), SC_(1.000000000000007250368259197024518158727) }, 
+      { SC_(47.740230560302734375), SC_(1.000000000000004253619155993815373574244) }, 
+      { SC_(47.82225799560546875), SC_(1.00000000000000401851769095578631160734) }, 
+      { SC_(47.844524383544921875), SC_(1.000000000000003956972517068642986534164) }, 
+      { SC_(47.916797637939453125), SC_(1.000000000000003763627354737768001799664) }, 
+      { SC_(48.03951263427734375), SC_(1.000000000000003456732091224533384587416) }, 
+      { SC_(48.077789306640625), SC_(1.000000000000003366226193065923102690805) }, 
+      { SC_(48.088245391845703125), SC_(1.000000000000003341917308946400199448992) }, 
+      { SC_(48.21654510498046875), SC_(1.000000000000003057550491069862425535113) }, 
+      { SC_(48.644329071044921875), SC_(1.000000000000002272991605673625823218911) }, 
+      { SC_(48.682353973388671875), SC_(1.000000000000002213865312361618938196866) }, 
+      { SC_(48.7743377685546875), SC_(1.000000000000002077118692813712217229131) }, 
+      { SC_(49.042804718017578125), SC_(1.000000000000001724426584048478072980917) }, 
+      { SC_(49.068695068359375), SC_(1.00000000000000169375635354541860333178) }, 
+      { SC_(49.429607391357421875), SC_(1.000000000000001318880667089529421391478) }, 
+      { SC_(49.453510284423828125), SC_(1.000000000000001297209182880660183342645) }, 
+      { SC_(49.4922943115234375), SC_(1.000000000000001262800830493712288542346) }, 
+      { SC_(49.584011077880859375), SC_(1.000000000000001185019129246615676129004) }, 
+      { SC_(50.018886566162109375), SC_(1.000000000000000876626902724624554021734) }, 
+      { SC_(50.265506744384765625), SC_(1.000000000000000738881381594389232226354) }, 
+      { SC_(50.60231781005859375), SC_(1.000000000000000585038557479300395348451) }, 
+      { SC_(51.059597015380859375), SC_(1.000000000000000426117855101476521328968) }, 
+      { SC_(51.098628997802734375), SC_(1.000000000000000414743830855801205190555) }, 
+      { SC_(52.473300933837890625), SC_(1.000000000000000159941972488386163451755) }, 
+      { SC_(52.728687286376953125), SC_(1.000000000000000133993427096920945462604) }, 
+      { SC_(52.8274078369140625), SC_(1.00000000000000012513121114750147039425) }, 
+      { SC_(53.563289642333984375), SC_(1.000000000000000075135148894081185552722) }, 
+      { SC_(54.441722869873046875), SC_(1.000000000000000040870354119536041226567) }, 
+      { SC_(54.534519195556640625), SC_(1.000000000000000038324272820380003916252) }, 
+      { SC_(54.8891754150390625), SC_(1.00000000000000002997172663898867687923) }, 
+      { SC_(55.0283966064453125), SC_(1.000000000000000027214603309398090046137) }, 
+      { SC_(55.1144256591796875), SC_(1.000000000000000025639212561447923551389) }, 
+      { SC_(55.33161163330078125), SC_(1.000000000000000022055920618207215687506) }, 
+      { SC_(55.826557159423828125), SC_(1.000000000000000015650626977085832472044) }, 
+      { SC_(56.10559844970703125), SC_(1.000000000000000012898284202740849648306) }, 
+      { SC_(56.106632232666015625), SC_(1.000000000000000012889045070538182553024) }, 
+      { SC_(56.464366912841796875), SC_(1.000000000000000010058468799404521129717) }, 
+      { SC_(57.06310272216796875), SC_(1.000000000000000006641932153342522535343) }, 
+      { SC_(57.346035003662109375), SC_(1.000000000000000005459128681570429564283) }, 
+      { SC_(57.472850799560546875), SC_(1.000000000000000004999746361816983875868) }, 
+      { SC_(57.4929046630859375), SC_(1.000000000000000004930729282248733593481) }, 
+      { SC_(57.598194122314453125), SC_(1.000000000000000004583696701999359539209) }, 
+      { SC_(57.61005401611328125), SC_(1.000000000000000004546170184327776041529) }, 
+      { SC_(57.6248931884765625), SC_(1.00000000000000000449964916454958377241) }, 
+      { SC_(57.9284210205078125), SC_(1.000000000000000003645924503223314003083) }, 
+      { SC_(57.933013916015625), SC_(1.000000000000000003634335967038469182822) }, 
+      { SC_(58.09400177001953125), SC_(1.000000000000000003250595270157055505909) }, 
+      { SC_(58.16320037841796875), SC_(1.000000000000000003098361177564293540649) }, 
+      { SC_(58.26497650146484375), SC_(1.000000000000000002887316391786182139852) }, 
+      { SC_(58.885471343994140625), SC_(1.00000000000000000187804855653649070089) }, 
+      { SC_(59.2601165771484375), SC_(1.000000000000000001448529565053139975957) }, 
+      { SC_(59.322772979736328125), SC_(1.000000000000000001386966294498092563052) }, 
+      { SC_(59.579998016357421875), SC_(1.000000000000000001160468764851974345628) }, 
+      { SC_(59.650043487548828125), SC_(1.000000000000000001105471797878708756365) }, 
+      { SC_(59.791217803955078125), SC_(1.000000000000000001002420555691430478745) }
+   }};
+#undef SC_
+
diff --git a/test/zeta_neg_data.ipp b/test/zeta_neg_data.ipp
new file mode 100644
index 000000000..86476509a
--- /dev/null
+++ b/test/zeta_neg_data.ipp
@@ -0,0 +1,205 @@
+#define SC_(x) static_cast(BOOST_JOIN(x, L))
+   static const boost::array, 200> zeta_neg_data = {{
+      { SC_(-29.912628173828125), SC_(-11411595.03734503626230312380285630491992) }, 
+      { SC_(-29.851711273193359375), SC_(-17491128.83255653477666248263741824395945) }, 
+      { SC_(-29.6310367584228515625), SC_(-29338557.80907609522626540806232745245856) }, 
+      { SC_(-29.580287933349609375), SC_(-30306395.15877987544763078130380383514834) }, 
+      { SC_(-29.449008941650390625), SC_(-30679896.21366776808601886434072241922978) }, 
+      { SC_(-29.0131816864013671875), SC_(-20461364.43945172423472081418662644617911) }, 
+      { SC_(-28.932170867919921875), SC_(-17954718.78416694210282615237096201590328) }, 
+      { SC_(-28.8929386138916015625), SC_(-16756279.89114728919232419374363852845816) }, 
+      { SC_(-28.8703212738037109375), SC_(-16073970.93038052754961877241558169058995) }, 
+      { SC_(-28.56868743896484375), SC_(-8043912.797659222132349302164106524597545) }, 
+      { SC_(-28.4122905731201171875), SC_(-4903635.075080145389499851622270349855906) }, 
+      { SC_(-28.3275470733642578125), SC_(-3515000.607629881325886083145603311677359) }, 
+      { SC_(-27.9045429229736328125), SC_(561872.9101127770815302245082844482980385) }, 
+      { SC_(-27.648517608642578125), SC_(1342198.470655673842508718473103589634627) }, 
+      { SC_(-26.98891448974609375), SC_(958967.3644061210965186556335814069245902) }, 
+      { SC_(-26.9762477874755859375), SC_(940695.8288692367233401584802662854004146) }, 
+      { SC_(-26.5942859649658203125), SC_(431764.3905797650182797008420936167894022) }, 
+      { SC_(-26.513599395751953125), SC_(344789.2311643767144853652064583290283269) }, 
+      { SC_(-26.3110713958740234375), SC_(166950.9217712466990407178286461519015362) }, 
+      { SC_(-26.119335174560546875), SC_(50216.50838488570401977081704289833643882) }, 
+      { SC_(-26.0972042083740234375), SC_(39696.07667360741023132228278408445173572) }, 
+      { SC_(-26.06340789794921875), SC_(24717.59361206202031383049563915428563206) }, 
+      { SC_(-25.97290802001953125), SC_(-9283.102630861689329279837111548500337322) }, 
+      { SC_(-25.800212860107421875), SC_(-52573.91752584962621396048551282302169873) }, 
+      { SC_(-25.7026424407958984375), SC_(-66701.3515681932512045823224337761059857) }, 
+      { SC_(-25.60152435302734375), SC_(-75127.68961892726687631489083928203368082) }, 
+      { SC_(-25.3774662017822265625), SC_(-77369.49762740646964459716518117457943474) }, 
+      { SC_(-25.3718852996826171875), SC_(-77211.18174801304523919999376682789300922) }, 
+      { SC_(-25.2124080657958984375), SC_(-69818.92283651854238898648172800794135819) }, 
+      { SC_(-25.113994598388671875), SC_(-63308.57776529969909975415070544651202913) }, 
+      { SC_(-25.1002140045166015625), SC_(-62323.27853183353019086156608655701085742) }, 
+      { SC_(-24.9590358734130859375), SC_(-51664.42535000520168097529147316913191884) }, 
+      { SC_(-24.6932125091552734375), SC_(-31670.01281816867446841516400384736191327) }, 
+      { SC_(-24.610179901123046875), SC_(-26064.93805025958872153777775894298753194) }, 
+      { SC_(-24.2069492340087890625), SC_(-5837.615323910213540582720536747728255397) }, 
+      { SC_(-24.1601581573486328125), SC_(-4267.760146707777974801177862963289435484) }, 
+      { SC_(-23.905548095703125), SC_(1791.561198109913837096109939891110951525) }, 
+      { SC_(-23.5498905181884765625), SC_(4871.416521314878510824761013567411455181) }, 
+      { SC_(-23.4835186004638671875), SC_(4975.227974192317781212488271510561925245) }, 
+      { SC_(-23.4303455352783203125), SC_(4984.336960568300045015617894873870024567) }, 
+      { SC_(-23.2656269073486328125), SC_(4689.056669026157611801515942421136275408) }, 
+      { SC_(-23.147945404052734375), SC_(4269.09697487404379106734373164284895236) }, 
+      { SC_(-23.0618305206298828125), SC_(3895.967523742781467049009764795714670535) }, 
+      { SC_(-22.865161895751953125), SC_(2953.311728747392678575675862332538485112) }, 
+      { SC_(-22.450725555419921875), SC_(1144.061952511390247866794452177364720154) }, 
+      { SC_(-22.216400146484375), SC_(433.4964624209467744240111502742949136417) }, 
+      { SC_(-22.117252349853515625), SC_(209.670669847220366780433535101515157212) }, 
+      { SC_(-22.0920505523681640625), SC_(159.7249542805152560864294822534577696243) }, 
+      { SC_(-22.0172443389892578125), SC_(27.28537205103064323405309172342888102988) }, 
+      { SC_(-21.4432220458984375), SC_(-374.2415260535891625043607900493959621482) }, 
+      { SC_(-21.4153881072998046875), SC_(-374.303271908688039818985907313585954208) }, 
+      { SC_(-21.36655426025390625), SC_(-371.7545846369976735832217959234696992869) }, 
+      { SC_(-21.1389904022216796875), SC_(-326.1669603491139591285009725186578239647) }, 
+      { SC_(-20.792087554931640625), SC_(-206.625063426231189233571547577406886055) }, 
+      { SC_(-20.7052173614501953125), SC_(-175.5791090488241874023715949426197745063) }, 
+      { SC_(-20.64069366455078125), SC_(-153.3071708461727420185632819734936375388) }, 
+      { SC_(-20.4468212127685546875), SC_(-92.67534368527936634847943709898214630585) }, 
+      { SC_(-20.1869373321533203125), SC_(-30.43108614924854718139530495549243305713) }, 
+      { SC_(-20.1699161529541015625), SC_(-27.17316397712932041916821790643340800192) }, 
+      { SC_(-19.694103240966796875), SC_(27.1714136640721528789798045585951196151) }, 
+      { SC_(-19.549198150634765625), SC_(32.29909704565499257138194367283757692887) }, 
+      { SC_(-19.4480419158935546875), SC_(33.67605769729398309956337071678460455377) }, 
+      { SC_(-19.1505031585693359375), SC_(30.51834489947975739023200586922515652717) }, 
+      { SC_(-19.0985546112060546875), SC_(29.23410383834503370501000988892387173246) }, 
+      { SC_(-19.064365386962890625), SC_(28.3146818846773107926880125501905809413) }, 
+      { SC_(-18.95330047607421875), SC_(25.02711851332149330549031951636533097105) }, 
+      { SC_(-18.7998867034912109375), SC_(20.07798417651821829598839554245992618286) }, 
+      { SC_(-18.2061786651611328125), SC_(3.48259567016902798768190885417275768286) }, 
+      { SC_(-18.171688079833984375), SC_(2.808091309863074171772985422170099249644) }, 
+      { SC_(-17.99382781982421875), SC_(-0.08425805633923885570999830270532256204479) }, 
+      { SC_(-17.9543361663818359375), SC_(-0.5968706969826661560508135615534999329391) }, 
+      { SC_(-17.840961456298828125), SC_(-1.822852247678475212693660825685951918909) }, 
+      { SC_(-17.83806610107421875), SC_(-1.849579792577253331534678618823864608689) }, 
+      { SC_(-17.7578449249267578125), SC_(-2.504689097176022370085233310047718350241) }, 
+      { SC_(-17.6391048431396484375), SC_(-3.193024470338536865812887315255732910235) }, 
+      { SC_(-17.46953582763671875), SC_(-3.679429462928429733583422830868284984109) }, 
+      { SC_(-17.329334259033203125), SC_(-3.730955850518545451525056518679296419855) }, 
+      { SC_(-17.2073383331298828125), SC_(-3.582528563068304439407127816770249435282) }, 
+      { SC_(-16.9253997802734375), SC_(-2.810296984266164459897058245930083917242) }, 
+      { SC_(-16.915283203125), SC_(-2.77589555245432113406083575136508432266) }, 
+      { SC_(-16.8818817138671875), SC_(-2.660508806128033733833130593715903076036) }, 
+      { SC_(-16.3989238739013671875), SC_(-0.9776305321380423960622625495871224063825) }, 
+      { SC_(-16.18682861328125), SC_(-0.3914840091082085155017628868619033070834) }, 
+      { SC_(-15.86298274993896484375), SC_(0.2113095736867095471658768228963977110005) }, 
+      { SC_(-15.8023357391357421875), SC_(0.2852756275882561377493711146849722900443) }, 
+      { SC_(-15.44889068603515625), SC_(0.5095766448261500611629872324946933071932) }, 
+      { SC_(-15.32804584503173828125), SC_(0.5204935020247384500134730244597097470842) }, 
+      { SC_(-15.28248119354248046875), SC_(0.518000024039102855822688087754595443758) }, 
+      { SC_(-14.95335483551025390625), SC_(0.4238642347557435114933888974408451377203) }, 
+      { SC_(-14.88536357879638671875), SC_(0.3933692627692705652205577653029677414393) }, 
+      { SC_(-14.81730365753173828125), SC_(0.3608573293373039084524243522210581723643) }, 
+      { SC_(-14.79173946380615234375), SC_(0.3482722720977891877868480924645011434135) }, 
+      { SC_(-14.5507144927978515625), SC_(0.2263366094050870980047656705259818867826) }, 
+      { SC_(-14.38645648956298828125), SC_(0.147084896053585110709304360793633346003) }, 
+      { SC_(-14.31533050537109375), SC_(0.1152816347651253287394552787556741727121) }, 
+      { SC_(-13.65148448944091796875), SC_(-0.07251231425417656377649950152568494966249) }, 
+      { SC_(-13.545276641845703125), SC_(-0.08375031877772358984694147296792966961615) }, 
+      { SC_(-13.04667377471923828125), SC_(-0.08613748015144290972450792644674564697467) }, 
+      { SC_(-13.03631877899169921875), SC_(-0.08554589764966609410422566041830102984647) }, 
+      { SC_(-13.0361614227294921875), SC_(-0.08553676925262460195666037008963074921075) }, 
+      { SC_(-12.95856761932373046875), SC_(-0.08056765309761383957595558846249995931279) }, 
+      { SC_(-12.5917186737060546875), SC_(-0.04916757520124342761036750118646514054843) }, 
+      { SC_(-12.39752960205078125), SC_(-0.03115114084163494465794707790061004080063) }, 
+      { SC_(-12.36646747589111328125), SC_(-0.02836586465940004481089358385830546327083) }, 
+      { SC_(-12.21360492706298828125), SC_(-0.01539036046556130908669688029744711232684) }, 
+      { SC_(-11.99034214019775390625), SC_(0.0006069904308788892543024610864850846763506) }, 
+      { SC_(-11.8568134307861328125), SC_(0.008147201960813915155871421057182351090437) }, 
+      { SC_(-11.856700897216796875), SC_(0.008152875868653809905975061985964214000197) }, 
+      { SC_(-11.62246036529541015625), SC_(0.01746194346204194142446845779680149340516) }, 
+      { SC_(-11.5703887939453125), SC_(0.01886566756877059520362077789879963609155) }, 
+      { SC_(-10.902614593505859375), SC_(0.0196626059012350652716117019088095189095) }, 
+      { SC_(-10.39686298370361328125), SC_(0.008689980413332084843117426575282850372437) }, 
+      { SC_(-10.16733551025390625), SC_(0.003416813948098911896742939961274332301015) }, 
+      { SC_(-10.0372104644775390625), SC_(0.0007176193820913189364411980055213424358445) }, 
+      { SC_(-9.9642963409423828125), SC_(-0.0006632811340011981503362639124151757266767) }, 
+      { SC_(-9.6919612884521484375), SC_(-0.004807940796456133525623000987469972333747) }, 
+      { SC_(-9.6801853179931640625), SC_(-0.004948106664919310929639531491612686942336) }, 
+      { SC_(-9.672039031982421875), SC_(-0.005043104323545521915854009513305224121704) }, 
+      { SC_(-9.42822933197021484375), SC_(-0.007140216297724451093935994631687254893686) }, 
+      { SC_(-8.95921039581298828125), SC_(-0.007434519412310381781780546556040051757663) }, 
+      { SC_(-8.9292163848876953125), SC_(-0.007313912761229121731761666014703562188579) }, 
+      { SC_(-8.92558765411376953125), SC_(-0.00729839292833941319530973378448137863064) }, 
+      { SC_(-8.87785434722900390625), SC_(-0.00707633883068269537335294544211513278741) }, 
+      { SC_(-8.46031284332275390625), SC_(-0.004074256641827071875084784818914263298709) }, 
+      { SC_(-8.447780609130859375), SC_(-0.003964973936847219963439195813913605287177) }, 
+      { SC_(-8.32862186431884765625), SC_(-0.002903415969312147961289161209278260789382) }, 
+      { SC_(-8.120998382568359375), SC_(-0.00103823391856569843811586237609042444109) }, 
+      { SC_(-8.11257076263427734375), SC_(-0.0009641405242205096512409518786467984036622) }, 
+      { SC_(-8.00969028472900390625), SC_(-0.8081897555380671288572993901221806428558e-4) }, 
+      { SC_(-7.96818065643310546875), SC_(0.000261996231792748327532018167663538399616) }, 
+      { SC_(-7.498992443084716796875), SC_(0.003273417189465077929314372888310860553978) }, 
+      { SC_(-7.46440410614013671875), SC_(0.003417551297097495653085939986968115182729) }, 
+      { SC_(-7.28324031829833984375), SC_(0.003973224858687943569640790429796668774442) }, 
+      { SC_(-7.03993511199951171875), SC_(0.004188064885842535489566897798831477388136) }, 
+      { SC_(-6.96289348602294921875), SC_(0.00413307218623721479271246253687857536289) }, 
+      { SC_(-6.710720539093017578125), SC_(0.003579650425628445602269416395217624438872) }, 
+      { SC_(-6.6343975067138671875), SC_(0.003311914606322736219077651823305971579526) }, 
+      { SC_(-6.604713916778564453125), SC_(0.003196837407418412428928538915252495489608) }, 
+      { SC_(-6.5267925262451171875), SC_(0.00286808681065953969739400100637205637184) }, 
+      { SC_(-6.5100555419921875), SC_(0.002792769359155893317313951562112124642491) }, 
+      { SC_(-6.38633251190185546875), SC_(0.002191129317123186105010600162934947438173) }, 
+      { SC_(-6.323749542236328125), SC_(0.001861047805191740695151906651937619919389) }, 
+      { SC_(-6.268978595733642578125), SC_(0.001560903697471362240875092595942452538086) }, 
+      { SC_(-6.00856876373291015625), SC_(0.5056493923745302784537384920689241524123e-4) }, 
+      { SC_(-5.854171276092529296875), SC_(-0.000850699827548195177814512570253393816845) }, 
+      { SC_(-5.8458156585693359375), SC_(-0.0008984756388001563233098481127032455383618) }, 
+      { SC_(-5.441573619842529296875), SC_(-0.002915026968595680785713416510699222417991) }, 
+      { SC_(-5.398475170135498046875), SC_(-0.003081263239844393794556192268338493619238) }, 
+      { SC_(-5.38677501678466796875), SC_(-0.003124321716617199710687253202017509643958) }, 
+      { SC_(-5.348802089691162109375), SC_(-0.003257740949901305827723740216599368435532) }, 
+      { SC_(-5.284323215484619140625), SC_(-0.003461160844402030020337003403034416960299) }, 
+      { SC_(-5.26421260833740234375), SC_(-0.003518393964166156715278378770334015232501) }, 
+      { SC_(-5.258718967437744140625), SC_(-0.003533499841767076804949459388722993177251) }, 
+      { SC_(-5.19130611419677734375), SC_(-0.003699890777792053165830070855367893096293) }, 
+      { SC_(-4.966538906097412109375), SC_(-0.003982393105088701410063296824875351251516) }, 
+      { SC_(-4.946559429168701171875), SC_(-0.00398600239489331055969397480564266110296) }, 
+      { SC_(-4.8982295989990234375), SC_(-0.003979612855119401843972374236087226591403) }, 
+      { SC_(-4.757171154022216796875), SC_(-0.003836405057552962242456530288751158127348) }, 
+      { SC_(-4.743566036224365234375), SC_(-0.003812665437930484329367028055222166144102) }, 
+      { SC_(-4.553936004638671875), SC_(-0.003299286445112839390501564610822343063568) }, 
+      { SC_(-4.54137516021728515625), SC_(-0.003253340207436420485572929378617465360415) }, 
+      { SC_(-4.5209980010986328125), SC_(-0.003175691140094301576675103590991471527218) }, 
+      { SC_(-4.4728069305419921875), SC_(-0.002976858185863617245397173014294301888612) }, 
+      { SC_(-4.24431324005126953125), SC_(-0.00175551877458019938328423578132053906906) }, 
+      { SC_(-4.114734649658203125), SC_(-0.0008756602845971692915754872652644095998698) }, 
+      { SC_(-3.9377651214599609375), SC_(0.0005075394336783163996239897113119062326783) }, 
+      { SC_(-3.69749927520751953125), SC_(0.002622130552658735330754289390878800389753) }, 
+      { SC_(-3.676990985870361328125), SC_(0.002810112977938437719471179582479423269376) }, 
+      { SC_(-2.9547061920166015625), SC_(0.00856184012269561519081119026118342931302) }, 
+      { SC_(-2.8205192089080810546875), SC_(0.009037989206198579118042330714986772360851) }, 
+      { SC_(-2.7686493396759033203125), SC_(0.009128821249400912985786171301727546611781) }, 
+      { SC_(-2.3819997310638427734375), SC_(0.007528500554786901983716620452938789863242) }, 
+      { SC_(-1.9204499721527099609375), SC_(-0.002637408450550919969361055380236527200873) }, 
+      { SC_(-1.87169349193572998046875), SC_(-0.004478507698442871056456977520107815363936) }, 
+      { SC_(-1.6853485107421875), SC_(-0.01331301401933966559224964767883365698475) }, 
+      { SC_(-1.6121981143951416015625), SC_(-0.01766825358627221799677465200009125172091) }, 
+      { SC_(-1.5669968128204345703125), SC_(-0.02064343048265733044842029728400047740426) }, 
+      { SC_(-1.4528820514678955078125), SC_(-0.02922143297753860874334243356099190516151) }, 
+      { SC_(-1.192826747894287109375), SC_(-0.05566943732471789169546884977433587458236) }, 
+      { SC_(-1.04621016979217529296875), SC_(-0.07595018260277478359527480657330720805406) }, 
+      { SC_(-1.0456688404083251953125), SC_(-0.07603371990103121884396103918441800305874) }, 
+      { SC_(-0.857705175876617431640625), SC_(-0.1096023911883116703076955371201458249853) }, 
+      { SC_(-0.543115675449371337890625), SC_(-0.1928664573137838612762872432285532859205) }, 
+      { SC_(-0.394455432891845703125), SC_(-0.2495443485845467778254047395388879044791) }, 
+      { SC_(-0.327823936939239501953125), SC_(-0.2799982799519977440228461605076452171571) }, 
+      { SC_(-0.317288100719451904296875), SC_(-0.2851488655947230334542341313298974452691) }, 
+      { SC_(-0.261966645717620849609375), SC_(-0.3138527949668934661932558041917113174462) }, 
+      { SC_(-0.2557342052459716796875), SC_(-0.317271262348402548403653041282308443369) }, 
+      { SC_(-0.247936725616455078125), SC_(-0.3216037424750364211708767678886883998309) }, 
+      { SC_(-0.088456094264984130859375), SC_(-0.4259272083317181924380711619296285238665) }, 
+      { SC_(-0.086042940616607666015625), SC_(-0.4277716953524606366478858744722936332152) }, 
+      { SC_(-0.001456916332244873046875), SC_(-0.4986633097035792982997269904612808871223) }, 
+      { SC_(0.034901142120361328125), SC_(-0.533338048759179364792881398709205491114) }, 
+      { SC_(0.088376700878143310546875), SC_(-0.5898057330494933987159364633901975183229) }, 
+      { SC_(0.414400041103363037109375), SC_(-1.174656654636669840597116356984374413125) }, 
+      { SC_(0.611247599124908447265625), SC_(-2.024132913638389303467555729734394339536) }, 
+      { SC_(0.644168853759765625), SC_(-2.259612667973966645670455260002849054666) }, 
+      { SC_(0.779320240020751953125), SC_(-3.970538544084429654769915000159638319936) }, 
+      { SC_(0.81612360477447509765625), SC_(-4.874770988252068737319828926058330714155) }, 
+      { SC_(0.890301287174224853515625), SC_(-8.54670722409884960433372346851249404364) }
+   }};
+#undef SC_
+
diff --git a/tools/expint_data.cpp b/tools/expint_data.cpp
new file mode 100644
index 000000000..a0e4a1045
--- /dev/null
+++ b/tools/expint_data.cpp
@@ -0,0 +1,68 @@
+//  (C) Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+#include "ntl_rr_digamma.hpp"
+#include 
+#include 
+#include 
+
+#include 
+
+using namespace boost::math::tools;
+
+struct expint_data_generator
+{
+   boost::math::ntl::RR operator()(boost::math::ntl::RR a, boost::math::ntl::RR b)
+   {
+      unsigned n = boost::math::tools::real_cast(a);
+      std::cout << n << "  " << b << "  ";
+      boost::math::ntl::RR result = boost::math::expint(n, b);
+      std::cout << result << std::endl;
+      return result;
+   }
+};
+
+
+int main()
+{
+   boost::math::ntl::RR::SetPrecision(1000);
+   boost::math::ntl::RR::SetOutputPrecision(40);
+
+   boost::math::expint(1, 0.06227754056453704833984375);
+   std::cout << boost::math::expint(1, boost::math::ntl::RR(0.5)) << std::endl;
+
+   parameter_info arg1, arg2;
+   test_data data;
+
+   std::cout << "Welcome.\n"
+      "This program will generate spot tests for the expint function:\n"
+      "  expint(a, b)\n\n";
+
+   bool cont;
+   std::string line;
+
+   do{
+      get_user_parameter_info(arg1, "a");
+      get_user_parameter_info(arg2, "b");
+      data.insert(expint_data_generator(), arg1, arg2);
+
+      std::cout << "Any more data [y/n]?";
+      std::getline(std::cin, line);
+      boost::algorithm::trim(line);
+      cont = (line == "y");
+   }while(cont);
+
+   std::cout << "Enter name of test data file [default=expint_data.ipp]";
+   std::getline(std::cin, line);
+   boost::algorithm::trim(line);
+   if(line == "")
+      line = "expint_data.ipp";
+   std::ofstream ofs(line.c_str());
+   write_code(ofs, data, "expint_data");
+   
+   return 0;
+}
+
diff --git a/tools/expint_i_data.cpp b/tools/expint_i_data.cpp
new file mode 100644
index 000000000..1c443f137
--- /dev/null
+++ b/tools/expint_i_data.cpp
@@ -0,0 +1,54 @@
+//  (C) Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+#include "ntl_rr_digamma.hpp"
+#include 
+#include 
+#include 
+
+#include 
+
+using namespace boost::math::tools;
+
+
+int main()
+{
+   boost::math::ntl::RR::SetPrecision(1000);
+   boost::math::ntl::RR::SetOutputPrecision(40);
+
+   parameter_info arg1;
+   test_data data;
+
+   boost::math::ntl::RR (*f)(boost::math::ntl::RR) = boost::math::expint;
+
+   std::cout << "Welcome.\n"
+      "This program will generate spot tests for the expint Ei function:\n"
+      "  expint(a)\n\n";
+
+   bool cont;
+   std::string line;
+
+   do{
+      get_user_parameter_info(arg1, "a");
+      data.insert(f, arg1);
+
+      std::cout << "Any more data [y/n]?";
+      std::getline(std::cin, line);
+      boost::algorithm::trim(line);
+      cont = (line == "y");
+   }while(cont);
+
+   std::cout << "Enter name of test data file [default=expinti_data.ipp]";
+   std::getline(std::cin, line);
+   boost::algorithm::trim(line);
+   if(line == "")
+      line = "expinti_data.ipp";
+   std::ofstream ofs(line.c_str());
+   write_code(ofs, data, "expinti_data");
+   
+   return 0;
+}
+
diff --git a/tools/zeta_data.cpp b/tools/zeta_data.cpp
new file mode 100644
index 000000000..f3fbec7ca
--- /dev/null
+++ b/tools/zeta_data.cpp
@@ -0,0 +1,77 @@
+//  Copyright John Maddock 2007.
+//  Use, modification and distribution are subject to the
+//  Boost Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include 
+#include 
+#include 
+#include 
+#include 
+#include 
+
+#include 
+
+using namespace boost::math::tools;
+using namespace std;
+
+struct zeta_data_generator
+{
+   boost::math::ntl::RR operator()(boost::math::ntl::RR z)
+   {
+      std::cout << z << " ";
+      boost::math::ntl::RR result = boost::math::zeta(z);
+      std::cout << result << std::endl;
+      return result;
+   }
+};
+
+struct zeta_data_generator2
+{
+   std::tr1::tuple operator()(boost::math::ntl::RR z)
+   {
+      std::cout << -z << " ";
+      boost::math::ntl::RR result = boost::math::zeta(-z);
+      std::cout << result << std::endl;
+      return std::tr1::make_tuple(-z, result);
+   }
+};
+
+
+int test_main(int argc, char*argv [])
+{
+   boost::math::ntl::RR::SetPrecision(500);
+   boost::math::ntl::RR::SetOutputPrecision(40);
+
+   parameter_info arg1;
+   test_data data;
+
+   bool cont;
+   std::string line;
+
+   std::cout << "Welcome.\n"
+      "This program will generate spot tests for the zeta function:\n";
+
+   do{
+      if(0 == get_user_parameter_info(arg1, "z"))
+         return 1;
+      arg1.type |= dummy_param;
+      data.insert(zeta_data_generator2(), arg1);
+
+      std::cout << "Any more data [y/n]?";
+      std::getline(std::cin, line);
+      boost::algorithm::trim(line);
+      cont = (line == "y");
+   }while(cont);
+
+   std::cout << "Enter name of test data file [default=zeta_data.ipp]";
+   std::getline(std::cin, line);
+   boost::algorithm::trim(line);
+   if(line == "")
+      line = "zeta_data.ipp";
+   std::ofstream ofs(line.c_str());
+   write_code(ofs, data, "zeta_data");
+   
+   return 0;
+}
+

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