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<div><h1 class="title">
<a name="math_toolkit"></a>Math Toolkit</h1></div>
<div><div class="authorgroup">
<div class="author"><h3 class="author">
<span class="firstname">Paul A.</span> <span class="surname">Bristow</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Hubert</span> <span class="surname">Holin</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Christopher</span> <span class="surname">Kormanyos</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Bruno</span> <span class="surname">Lalande</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">John</span> <span class="surname">Maddock</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Johan</span> <span class="surname">R&#229;de</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Benjamin</span> <span class="surname">Sobotta</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Gautam</span> <span class="surname">Sewani</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Thijs</span> <span class="surname">van den Berg</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Daryle</span> <span class="surname">Walker</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Xiaogang</span> <span class="surname">Zhang</span>
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<div><p class="releaseinfo">
This manual is also available in <a href="http://sourceforge.net/projects/boost/files/boost-docs/" target="_top">printer
friendly PDF format</a>, and as a CD ISBN 0-9504833-2-X 978-0-9504833-2-0,
Classification 519.2-dc22. </p></div>
<div><p class="copyright">Copyright &#169; 2006-2010, 2012, 2013 Paul A. Bristow, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin
Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang</p></div>
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<a name="math_toolkit.legal"></a><p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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<div class="toc">
<p><b>Table of Contents</b></p>
<dl>
<dt><span class="chapter"><a href="overview.html">1. Overview</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/main_intro.html">About the Math Toolkit</a></span></dt>
<dt><span class="section"><a href="math_toolkit/navigation.html">Navigation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/conventions.html">Document Conventions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/hints.html">Other Hints and tips</a></span></dt>
<dt><span class="section"><a href="math_toolkit/directories.html">Directory and File Structure</a></span></dt>
<dt><span class="section"><a href="math_toolkit/namespaces.html">Namespaces</a></span></dt>
<dt><span class="section"><a href="math_toolkit/result_type.html">Calculation of the Type of the
Result</a></span></dt>
<dt><span class="section"><a href="math_toolkit/error_handling.html">Error Handling</a></span></dt>
<dt><span class="section"><a href="math_toolkit/compilers_overview.html">Compilers</a></span></dt>
<dt><span class="section"><a href="math_toolkit/config_macros.html">Configuration Macros</a></span></dt>
<dt><span class="section"><a href="math_toolkit/intro_pol_overview.html">Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/threads.html">Thread Safety</a></span></dt>
<dt><span class="section"><a href="math_toolkit/perf_over1.html">Performance</a></span></dt>
<dt><span class="section"><a href="math_toolkit/building.html">If and How to Build a Boost.Math
Library, and its Examples and Tests</a></span></dt>
<dt><span class="section"><a href="math_toolkit/history1.html">History and What's New</a></span></dt>
<dt><span class="section"><a href="math_toolkit/overview_tr1.html">C99 and C++ TR1 C-style Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/main_faq.html">Frequently Asked Questions FAQ</a></span></dt>
<dt><span class="section"><a href="math_toolkit/contact.html">Contact Info and Support</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="dist.html">2. Statistical Distributions and Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut.html">Statistical Distributions Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview.html">Overview of Distributions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/headers.html">Headers and
Namespaces</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/objects.html">Distributions
are Objects</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/generic.html">Generic operations
common to all distributions are non-member functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/complements.html">Complements
are supported too - and when to use them</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/parameters.html">Parameters
can be calculated</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/overview/summary.html">Summary</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg.html">Worked Examples</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/dist_construct_eg.html">Distribution
Construction Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/st_eg.html">Student's t Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/cs_eg.html">Chi Squared Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/f_eg.html">F Distribution Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/binom_eg.html">Binomial Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/geometric_eg.html">Geometric Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/neg_binom_eg.html">Negative Binomial
Distribution Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/normal_example.html">Normal Distribution
Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/inverse_chi_squared_eg.html">Inverse
Chi-Squared Distribution Bayes Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/nccs_eg.html">Non Central Chi
Squared Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/error_eg.html">Error Handling
Example</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/find_eg.html">Find Location and
Scale Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/nag_library.html">Comparison with
C, R, FORTRAN-style Free Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/weg/c_sharp.html">Using the Distributions
from Within C#</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/stat_tut/variates.html">Random Variates and Distribution
Parameters</a></span></dt>
<dt><span class="section"><a href="math_toolkit/stat_tut/dist_params.html">Discrete Probability
Distributions</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/dist_ref.html">Statistical Distributions Reference</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/dist_ref/nmp.html">Non-Member Properties</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists.html">Distributions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/bernoulli_dist.html">Bernoulli
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/beta_dist.html">Beta Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/binomial_dist.html">Binomial
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/cauchy_dist.html">Cauchy-Lorentz
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/chi_squared_dist.html">Chi Squared
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/exp_dist.html">Exponential Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/extreme_dist.html">Extreme Value
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/f_dist.html">F Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/gamma_dist.html">Gamma (and
Erlang) Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/geometric_dist.html">Geometric
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/hypergeometric_dist.html">Hypergeometric
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_chi_squared_dist.html">Inverse
Chi Squared Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gamma_dist.html">Inverse
Gamma Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/inverse_gaussian_dist.html">Inverse
Gaussian (or Inverse Normal) Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/laplace_dist.html">Laplace Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/logistic_dist.html">Logistic
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/lognormal_dist.html">Log Normal
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/negative_binomial_dist.html">Negative
Binomial Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_beta_dist.html">Noncentral
Beta Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_chi_squared_dist.html">Noncentral
Chi-Squared Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_f_dist.html">Noncentral F
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/nc_t_dist.html">Noncentral T
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/normal_dist.html">Normal (Gaussian)
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/pareto.html">Pareto Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/poisson_dist.html">Poisson Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/rayleigh.html">Rayleigh Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/skew_normal_dist.html">Skew
Normal Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/students_t_dist.html">Students
t Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/triangular_dist.html">Triangular
Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/uniform_dist.html">Uniform Distribution</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_ref/dists/weibull_dist.html">Weibull Distribution</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/dist_ref/dist_algorithms.html">Distribution Algorithms</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/future.html">Extras/Future Directions</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="special.html">3. Special Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_gamma.html">Gamma Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_gamma/tgamma.html">Gamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/lgamma.html">Log Gamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/digamma.html">Digamma</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/gamma_ratios.html">Ratios of Gamma Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/igamma.html">Incomplete Gamma Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/igamma_inv.html">Incomplete Gamma Function
Inverses</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_gamma/gamma_derivatives.html">Derivative of
the Incomplete Gamma Function</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/factorials.html">Factorials and Binomial Coefficients</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/factorials/sf_factorial.html">Factorial</a></span></dt>
<dt><span class="section"><a href="math_toolkit/factorials/sf_double_factorial.html">Double Factorial</a></span></dt>
<dt><span class="section"><a href="math_toolkit/factorials/sf_rising_factorial.html">Rising Factorial</a></span></dt>
<dt><span class="section"><a href="math_toolkit/factorials/sf_falling_factorial.html">Falling
Factorial</a></span></dt>
<dt><span class="section"><a href="math_toolkit/factorials/sf_binomial.html">Binomial Coefficients</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/sf_beta.html">Beta Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_beta/beta_function.html">Beta</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_beta/ibeta_function.html">Incomplete Beta
Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_beta/ibeta_inv_function.html">The Incomplete
Beta Function Inverses</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_beta/beta_derivative.html">Derivative of the
Incomplete Beta Function</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/sf_erf.html">Error Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_erf/error_function.html">Error Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_erf/error_inv.html">Error Function Inverses</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/sf_poly.html">Polynomials</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_poly/legendre.html">Legendre (and Associated)
Polynomials</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_poly/laguerre.html">Laguerre (and Associated)
Polynomials</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_poly/hermite.html">Hermite Polynomials</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sf_poly/sph_harm.html">Spherical Harmonics</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/bessel.html">Bessel Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/bessel/bessel_over.html">Bessel Function Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bessel/bessel_first.html">Bessel Functions of
the First and Second Kinds</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bessel/bessel_root.html">Finding Zeros of Bessel
Functions of the First and Second Kinds</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bessel/mbessel.html">Modified Bessel Functions
of the First and Second Kinds</a></span></dt>
<dt><span class="section"><a href="math_toolkit/bessel/sph_bessel.html">Spherical Bessel Functions
of the First and Second Kinds</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/hankel.html">Hankel Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/hankel/cyl_hankel.html">Cyclic Hankel Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/hankel/sph_hankel.html">Spherical Hankel Functions</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/airy.html">Airy Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/airy/ai.html">Airy Ai Function</a></span></dt>
<dt><span class="section"><a href="math_toolkit/airy/bi.html">Airy Bi Function</a></span></dt>
<dt><span class="section"><a href="math_toolkit/airy/aip.html">Airy Ai' Function</a></span></dt>
<dt><span class="section"><a href="math_toolkit/airy/bip.html">Airy Bi' Function</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/ellint.html">Elliptic Integrals</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_intro.html">Elliptic Integral Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_carlson.html">Elliptic Integrals
- Carlson Form</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_1.html">Elliptic Integrals of the
First Kind - Legendre Form</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_2.html">Elliptic Integrals of the
Second Kind - Legendre Form</a></span></dt>
<dt><span class="section"><a href="math_toolkit/ellint/ellint_3.html">Elliptic Integrals of the
Third Kind - Legendre Form</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/jacobi.html">Jacobi Elliptic Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/jacobi/jac_over.html">Overvew of the Jacobi Elliptic
Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_elliptic.html">Jacobi Elliptic
SN, CN and DN</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cd.html">Jacobi Elliptic Function
cd</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cn.html">Jacobi Elliptic Function
cn</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_cs.html">Jacobi Elliptic Function
cs</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_dc.html">Jacobi Elliptic Function
dc</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_dn.html">Jacobi Elliptic Function
dn</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_ds.html">Jacobi Elliptic Function
ds</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_nc.html">Jacobi Elliptic Function
nc</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_nd.html">Jacobi Elliptic Function
nd</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_ns.html">Jacobi Elliptic Function
ns</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sc.html">Jacobi Elliptic Function
sc</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sd.html">Jacobi Elliptic Function
sd</a></span></dt>
<dt><span class="section"><a href="math_toolkit/jacobi/jacobi_sn.html">Jacobi Elliptic Function
sn</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/zetas.html">Zeta Functions</a></span></dt>
<dd><dl><dt><span class="section"><a href="math_toolkit/zetas/zeta.html">Riemann Zeta Function</a></span></dt></dl></dd>
<dt><span class="section"><a href="math_toolkit/expint.html">Exponential Integrals</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/expint/expint_n.html">Exponential Integral En</a></span></dt>
<dt><span class="section"><a href="math_toolkit/expint/expint_i.html">Exponential Integral Ei</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/powers.html">Basic Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/powers/sin_pi.html">sin_pi</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/cos_pi.html">cos_pi</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/log1p.html">log1p</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/expm1.html">expm1</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/cbrt.html">cbrt</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/sqrt1pm1.html">sqrt1pm1</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/powm1.html">powm1</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/hypot.html">hypot</a></span></dt>
<dt><span class="section"><a href="math_toolkit/powers/ct_pow.html">Compile Time Power of a Runtime
Base</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/sinc.html">Sinus Cardinal and Hyperbolic Sinus
Cardinal Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sinc/sinc_overview.html">Sinus Cardinal and Hyperbolic
Sinus Cardinal Functions Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sinc/sinc_pi.html">sinc_pi</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sinc/sinhc_pi.html">sinhc_pi</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/inv_hyper.html">Inverse Hyperbolic Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/inv_hyper/inv_hyper_over.html">Inverse Hyperbolic
Functions Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/inv_hyper/acosh.html">acosh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/inv_hyper/asinh.html">asinh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/inv_hyper/atanh.html">atanh</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/owens_t.html">Owen's T function</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="utils.html">4. Floating Point Utilities</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/rounding.html">Rounding Truncation and Integer
Conversion</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/rounding/round.html">Rounding Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/rounding/trunc.html">Truncation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/rounding/modf.html">Integer and Fractional Part
Splitting (modf)</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/fpclass.html">Floating-Point Classification: Infinities
and NaNs</a></span></dt>
<dt><span class="section"><a href="math_toolkit/sign_functions.html">Sign Manipulation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets.html">Facets for Floating-Point Infinities
and NaNs</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/fp_facets/facets_intro.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets/reference.html">Reference</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets/examples.html">Examples</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets/portability.html">Portability</a></span></dt>
<dt><span class="section"><a href="math_toolkit/fp_facets/rationale.html">Design Rationale</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/next_float.html">Floating-Point Representation
Distance (ULP), and Finding Adjacent Floating-Point Values</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/next_float/nextafter.html">Finding the Next Representable
Value in a Specific Direction (nextafter)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/next_float/float_next.html">Finding the Next
Greater Representable Value (float_next)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/next_float/float_prior.html">Finding the Next
Smaller Representable Value (float_prior)</a></span></dt>
<dt><span class="section"><a href="math_toolkit/next_float/float_distance.html">Calculating the
Representation Distance Between Two Floating Point Values (ULP) float_distance</a></span></dt>
<dt><span class="section"><a href="math_toolkit/next_float/float_advance.html">Advancing a Floating
Point Value by a Specific Representation Distance (ULP) float_advance</a></span></dt>
</dl></dd>
</dl></dd>
<dt><span class="chapter"><a href="extern_c.html">5. TR1 and C99 external "C" Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/main_tr1.html">C99 and TR1 C Functions Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/c99.html">C99 C Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tr1_ref.html">TR1 C Functions Quick Reference</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="constants.html">6. Mathematical Constants</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/constants_intro.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tutorial.html">Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/tutorial/non_templ.html">Use in non-template
code</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tutorial/templ.html">Use in template code</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tutorial/user_def.html">Use With User-Defined
Types</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/constants.html">The Mathematical Constants</a></span></dt>
<dt><span class="section"><a href="math_toolkit/new_const.html">Defining New Constants</a></span></dt>
<dt><span class="section"><a href="math_toolkit/constants_faq.html">FAQs</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="inverse_complex.html">7. Complex Number Functions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/complex_implementation.html">Implementation and
Accuracy</a></span></dt>
<dt><span class="section"><a href="math_toolkit/asin.html">asin</a></span></dt>
<dt><span class="section"><a href="math_toolkit/acos.html">acos</a></span></dt>
<dt><span class="section"><a href="math_toolkit/atan.html">atan</a></span></dt>
<dt><span class="section"><a href="math_toolkit/asinh.html">asinh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/acosh.html">acosh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/atanh.html">atanh</a></span></dt>
<dt><span class="section"><a href="math_toolkit/complex_history.html">History</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="quaternions.html">8. Quaternions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/quat_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_header.html">Header File</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_synopsis.html">Synopsis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat.html">Template Class quaternion</a></span></dt>
<dt><span class="section"><a href="math_toolkit/spec.html">Quaternion Specializations</a></span></dt>
<dt><span class="section"><a href="math_toolkit/mem_typedef.html">Quaternion Member Typedefs</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_mem_fun.html">Quaternion Member Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_non_mem.html">Quaternion Non-Member Operators</a></span></dt>
<dt><span class="section"><a href="math_toolkit/value_op.html">Quaternion Value Operations</a></span></dt>
<dt><span class="section"><a href="math_toolkit/create.html">Quaternion Creation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/trans.html">Quaternion Transcendentals</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_tests.html">Test Program</a></span></dt>
<dt><span class="section"><a href="math_toolkit/exp.html">The Quaternionic Exponential</a></span></dt>
<dt><span class="section"><a href="math_toolkit/acknowledgement.html">Acknowledgements</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_history.html">History</a></span></dt>
<dt><span class="section"><a href="math_toolkit/quat_todo.html">To Do</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="octonions.html">9. Octonions</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/oct_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_header.html">Header File</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_synopsis.html">Synopsis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/octonion.html">Template Class octonion</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_specialization.html">Octonion Specializations</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_typedefs.html">Octonion Member Typedefs</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_mem_fun.html">Octonion Member Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_non_mem.html">Octonion Non-Member Operators</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_value_ops.html">Octonion Value Operations</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_create.html">Octonion Creation Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_trans.html">Octonions Transcendentals</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_tests.html">Test Program</a></span></dt>
<dt><span class="section"><a href="math_toolkit/acknowledgements.html">Acknowledgements</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_history.html">History</a></span></dt>
<dt><span class="section"><a href="math_toolkit/oct_todo.html">To Do</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="gcd_lcm.html">10. Integer Utilities (Greatest Common Divisor and Least Common Multiple)</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/introduction.html">Introduction</a></span></dt>
<dt><span class="section"><a href="math_toolkit/synopsis.html">Synopsis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_function_object.html">GCD Function Object</a></span></dt>
<dt><span class="section"><a href="math_toolkit/lcm_function_object.html">LCM Function Object</a></span></dt>
<dt><span class="section"><a href="math_toolkit/run_time.html">Run-time GCD &amp; LCM Determination</a></span></dt>
<dt><span class="section"><a href="math_toolkit/compile_time.html">Compile time GCD and LCM determination</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_header.html">Header &lt;boost/math/common_factor.hpp&gt;</a></span></dt>
<dt><span class="section"><a href="math_toolkit/demo.html">Demonstration Program</a></span></dt>
<dt><span class="section"><a href="math_toolkit/rationale.html">Rationale</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_history.html">History</a></span></dt>
<dt><span class="section"><a href="math_toolkit/gcd_credits.html">Credits</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="toolkit.html">11. Internals (Series, Rationals and Continued Fractions, Root Finding, Function
Minimization, Testing and Development Tools)</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/internals_overview.html">Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1.html">Utilities &amp; internals</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/internals1/series_evaluation.html">Series Evaluation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/cf.html">Continued Fraction Evaluation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/rational.html">Polynomial and Rational
Function Evaluation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/roots.html">Root Finding With Derivatives:
Newton-Raphson, Halley &amp; Schroeder</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/roots2.html">Root Finding Without
Derivatives: Bisection, Bracket and TOMS748</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/minima.html">Locating Function Minima:
Brent's algorithm</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals1/tuples.html">Tuples</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/internals2.html">Testing and Development</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/internals2/polynomials.html">Polynomials</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals2/minimax.html">Minimax Approximations
and the Remez Algorithm</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals2/error_test.html">Relative Error and
Testing</a></span></dt>
<dt><span class="section"><a href="math_toolkit/internals2/test_data.html">Graphing, Profiling,
and Generating Test Data for Special Functions</a></span></dt>
</dl></dd>
</dl></dd>
<dt><span class="chapter"><a href="using_udt.html">12. Use with User-Defined Floating-Point Types - Boost.Multiprecision and
others</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/high_precision.html">Using Boost.Math with High-Precision
Floating-Point Libraries</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/high_precision/why_high_precision.html">Why use
a high-precision library rather than built-in floating-point types?</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/use_multiprecision.html">Using
Boost.Multiprecision</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/float128.html">Using with GCC's
__float128 datatype</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/use_mpfr.html">Using With MPFR
or GMP - High-Precision Floating-Point Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/e_float.html">Using e_float Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/use_ntl.html">Using NTL Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/high_precision/using_test.html">Using without
expression templates for Boost.Test and others</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/concepts.html">Conceptual Requirements for Real
Number Types</a></span></dt>
<dt><span class="section"><a href="math_toolkit/dist_concept.html">Conceptual Requirements for
Distribution Types</a></span></dt>
<dt><span class="section"><a href="math_toolkit/archetypes.html">Conceptual Archetypes for Reals
and Distributions</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="policy.html">13. Policies: Controlling Precision, Error Handling etc</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/pol_overview.html">Policy Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial.html">Policy Tutorial</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/what_is_a_policy.html">So Just What
is a Policy Anyway?</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/policy_tut_defaults.html">Policies
Have Sensible Defaults</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/policy_usage.html">So How are Policies
Used Anyway?</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/changing_policy_defaults.html">Changing
the Policy Defaults</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/ad_hoc_dist_policies.html">Setting
Policies for Distributions on an Ad Hoc Basis</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/ad_hoc_sf_policies.html">Changing
the Policy on an Ad Hoc Basis for the Special Functions</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/namespace_policies.html">Setting
Policies at Namespace or Translation Unit Scope</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/user_def_err_pol.html">Calling User
Defined Error Handlers</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_tutorial/understand_dis_quant.html">Understanding
Quantiles of Discrete Distributions</a></span></dt>
</dl></dd>
<dt><span class="section"><a href="math_toolkit/pol_ref.html">Policy Reference</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/pol_ref/error_handling_policies.html">Error Handling
Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/internal_promotion.html">Internal Floating-point
Promotion Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/assert_undefined.html">Mathematically
Undefined Function Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/discrete_quant_ref.html">Discrete Quantile
Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/precision_pol.html">Precision Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/iteration_pol.html">Iteration Limits
Policies</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/policy_defaults.html">Using Macros to
Change the Policy Defaults</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/namespace_pol.html">Setting Polices at
Namespace Scope</a></span></dt>
<dt><span class="section"><a href="math_toolkit/pol_ref/pol_ref_ref.html">Policy Class Reference</a></span></dt>
</dl></dd>
</dl></dd>
<dt><span class="chapter"><a href="perf.html">14. Performance</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/perf_over2.html">Performance Overview</a></span></dt>
<dt><span class="section"><a href="math_toolkit/interp.html">Interpreting these Results</a></span></dt>
<dt><span class="section"><a href="math_toolkit/getting_best.html">Getting the Best Performance
from this Library</a></span></dt>
<dt><span class="section"><a href="math_toolkit/comp_compilers.html">Comparing Compilers</a></span></dt>
<dt><span class="section"><a href="math_toolkit/tuning.html">Performance Tuning Macros</a></span></dt>
<dt><span class="section"><a href="math_toolkit/comparisons.html">Comparisons to Other Open Source
Libraries</a></span></dt>
<dt><span class="section"><a href="math_toolkit/perf_test_app.html">The Performance Test Application</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="backgrounders.html">15. Backgrounders</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/sf_implementation.html">Additional Implementation
Notes</a></span></dt>
<dt><span class="section"><a href="math_toolkit/relative_error.html">Relative Error</a></span></dt>
<dt><span class="section"><a href="math_toolkit/lanczos.html">The Lanczos Approximation</a></span></dt>
<dt><span class="section"><a href="math_toolkit/remez.html">The Remez Method</a></span></dt>
<dt><span class="section"><a href="math_toolkit/refs.html">References</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="status.html">16. Library Status</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="math_toolkit/history2.html">History and What's New</a></span></dt>
<dt><span class="section"><a href="math_toolkit/issues.html">Known Issues, and TODO List</a></span></dt>
<dt><span class="section"><a href="math_toolkit/credits.html">Credits and Acknowledgements</a></span></dt>
</dl></dd>
<dt><span class="chapter"><a href="indexes.html">17. Indexes</a></span></dt>
<dd><dl>
<dt><span class="section"><a href="indexes/s01.html">Function Index</a></span></dt>
<dt><span class="section"><a href="indexes/s02.html">Class Index</a></span></dt>
<dt><span class="section"><a href="indexes/s03.html">Typedef Index</a></span></dt>
<dt><span class="section"><a href="indexes/s04.html">Macro Index</a></span></dt>
<dt><span class="section"><a href="indexes/s05.html">Index</a></span></dt>
</dl></dd>
</dl>
</div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: May 17, 2013 at 11:02:56 GMT</small></p></td>
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