diff --git a/doc/sf_and_dist/html/index.html b/doc/sf_and_dist/html/index.html index 7a89f407b..a86cce756 100644 --- a/doc/sf_and_dist/html/index.html +++ b/doc/sf_and_dist/html/index.html @@ -3,7 +3,7 @@ Math Toolkit - + @@ -18,7 +18,7 @@
Next
-
+

@@ -53,7 +53,7 @@ Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg

-

+

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)

@@ -488,7 +488,7 @@

- +

Last revised: July 01, 2010 at 21:46:24 GMT

Last revised: July 15, 2010 at 16:56:47 GMT


diff --git a/doc/sf_and_dist/html/math_toolkit/backgrounders.html b/doc/sf_and_dist/html/math_toolkit/backgrounders.html index d25671c58..bbd4dc469 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders.html @@ -3,7 +3,7 @@ Backgrounders - + @@ -22,7 +22,7 @@
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-
+
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 5ee616462..eff52d314 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/implementation.html @@ -3,7 +3,7 @@ Additional Implementation Notes - + @@ -22,7 +22,7 @@
PrevUpHomeNext
-
+

Additional Implementation Notes @@ -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
@@ -130,18 +130,18 @@ binary value).

- + Tolerance of Tests

The tolerances need to be set to the maximum of:

-
    -
  • +
      +
    • Some epsilon value.
    • -
    • +
    • The accuracy of the data (often only near 64-bit double).
    @@ -156,7 +156,7 @@ first that the suffix L is present, and then that the tolerance is big enough.

    - + Handling Unsuitable Arguments
    @@ -166,7 +166,7 @@ it is proposed that signalling a domain error is mandatory when the argument would give an mathematically undefined result.

    -
    • +
      • Guideline 1

      @@ -183,7 +183,7 @@ a domain error whenever evaluated with argument values for which the mathematical function is undefined.

      -
      - + Median of distributions
      @@ -291,7 +291,7 @@ Basic Statistics. give more detail, in particular for discrete distributions.

      - + Handling of Floating-Point Infinity
      @@ -335,7 +335,7 @@ handling policies.

      - + Scale, Shape and Location
      @@ -362,11 +362,11 @@ functions, they can be added if required.

      - + Notes on Implementation of Specific Functions & Distributions
      -
      • +
        • Default parameters for the Triangular Distribution. We are uncertain about the best default parameters. Some sources suggest that the Standard Triangular Distribution has lower = 0, mode = half and upper = 1. However @@ -374,7 +374,7 @@ lower = -1, mode = 0 and upper = 1 would be more suitable.
        - + Rational Approximations Used
        @@ -417,7 +417,7 @@ to the "true" minimax solution.

        - + Representation of Mathematical Constants
        @@ -478,7 +478,7 @@ double p = boost::math::constants::pi(); // Context does not allow for disambiguation of overloaded function
        - + Thread safety
        @@ -503,7 +503,7 @@ the right thing here at some point.

        - + Sources of Test Data
        @@ -541,7 +541,7 @@ the underlying special function is known to be difficult to implement.

        - + Creating and Managing the Equations
        @@ -713,7 +713,7 @@ done HTML: this needs further investigation.

        - + Producing Graphs
        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 a67ebb501..9517c4bd4 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/lanczos.html @@ -3,7 +3,7 @@ The Lanczos Approximation - + @@ -22,12 +22,12 @@
        PrevUpHomeNext
        -
        +
        - + Motivation

        @@ -45,8 +45,8 @@ Lanczos approximation does have a couple of properties that make it worthy of further consideration:

        -
          -
        • +
            +
          • The approximation has an easy to compute truncation error that holds for all z > 0. In practice that means we can use the same approximation for all z > 0, and @@ -54,7 +54,7 @@ the truncation error will at worst be bounded by some finite value.
          • -
          • +
          • The approximation has a form that is particularly amenable to analytic manipulation, in particular ratios of gamma or gamma-like functions are particularly easy to compute without resorting to logarithms. @@ -99,7 +99,7 @@ functions divided by large powers into single (simpler) expressions.

            - + The Approximation
            @@ -161,7 +161,7 @@

          - + Computing the Coefficients
          @@ -205,7 +205,7 @@ multiplied by F as the last step.

          - + Choosing the Right Parameters
          @@ -229,7 +229,7 @@ computing to float precision with double precision arithmetic.

          -

          Table 53. Optimal choices for N and g when computing with guard digits (source: +

          Table 53. Optimal choices for N and g when computing with guard digits (source: Pugh)

          @@ -372,7 +372,7 @@ exactly matches the machine epsilon for the type in question.

          -

          Table 54. Optimum value for N and g when computing at fixed precision

          +

          Table 54. Optimum value for N and g when computing at fixed precision

          @@ -535,24 +535,24 @@ is exact, and so isn't used for the gamma function.

          - + References
          -
            -
          1. +
              +
            1. Paul Godfrey, "A note on the computation of the convergent Lanczos complex Gamma approximation".
            2. -
            3. +
            4. Glendon Ralph Pugh, "An Analysis of the Lanczos Gamma Approximation", PhD Thesis November 2004.
            5. -
            6. +
            7. Viktor T. Toth, "Calculators and the Gamma Function".
            8. -
            9. +
            10. Mathworld, The Lanczos Approximation.
            11. 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 680bba4a4..abd2486e4 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/refs.html @@ -3,7 +3,7 @@ References - + @@ -22,12 +22,12 @@
              PrevUpHomeNext
              -
              +
              - + General references
              @@ -91,7 +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). @@ -101,7 +101,7 @@ Binomial Probability Distribution Calculator.

              - + Other Libraries

              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 43833e782..7b2ef2a91 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 @@ -3,7 +3,7 @@ Relative Error - + @@ -22,7 +22,7 @@

              PrevUpHomeNext
              -
              +

              Relative Error @@ -81,7 +81,7 @@

              - + The Impossibility of Zero Error
              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 1a6811424..a5e6eba1e 100644 --- a/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html +++ b/doc/sf_and_dist/html/math_toolkit/backgrounders/remez.html @@ -3,7 +3,7 @@ The Remez Method - + @@ -22,7 +22,7 @@
              PrevUpHomeNext
              -
              +
              @@ -65,15 +65,15 @@ yields the smallest maximal value of the error function. Chebyshev showed that there is a unique minimax solution for R(x) that has the following properties:

              -
                -
              • +
                  +
                • If R(x) is a polynomial of degree N, then there are N+2 unknowns: the N+1 coefficients of the polynomial, and maximal value of the error function.
                • -
                • +
                • The error function has N+1 roots, and N+2 extrema (minima and maxima).
                • -
                • +
                • The extrema alternate in sign, and all have the same magnitude.
                @@ -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
          @@ -416,18 +416,18 @@ wrong, it is by no means an exhaustive list, but is provided in the hopes that it will prove useful.

          -
            -
          • +
              +
            • Is the function smooth enough? Can it be better separated into a rapidly changing part, and an asymptotic part?
            • -
            • +
            • Does the function being approximated have any "blips" in it? Check for problems as the function changes computation method, or if a root, or an infinity has been divided out. The telltale sign is if there is a narrow region where the Remez method will not converge.
            • -
            • +
            • Check you have enough accuracy in your calculations: remember that the Remez method works on the difference between the approximation and the function being approximated: so you must have more digits of precision @@ -435,33 +435,33 @@ So for example at double precision, you shouldn't expect to be able to get better than a float precision approximation.
            • -
            • +
            • Try skewing the initial interpolated approximation to minimise the error before you begin the Remez steps.
            • -
            • +
            • If the approximation won't converge or is ill-conditioned from one starting location, try starting from a different location.
            • -
            • +
            • If a rational function won't converge, one can minimise a polynomial (which presents no problems), then rotate one term from the numerator to the denominator and minimise again. In theory one can continue moving terms one at a time from numerator to denominator, and then re-minimising, retaining the last set of control points at each stage.
            • -
            • +
            • Try using a smaller interval. It may also be possible to optimise over one (small) interval, rescale the control points over a larger interval, and then re-minimise.
            • -
            • +
            • Keep absissa values small: use a change of variable to keep the abscissa over, say [0, b], for some smallish value b.
            - + References

            diff --git a/doc/sf_and_dist/html/math_toolkit/dist.html b/doc/sf_and_dist/html/math_toolkit/dist.html index 3b57c4ef2..bad249420 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist.html @@ -3,7 +3,7 @@ Statistical Distributions and Functions - + @@ -22,7 +22,7 @@

            PrevUpHomeNext
            -
            +
            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 d03379368..06b08fd3a 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 @@ -3,7 +3,7 @@ Statistical Distributions Reference - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +

            Statistical Distributions Reference 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 f3da099c6..3702db923 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 @@ -3,7 +3,7 @@ Distribution Algorithms - + @@ -22,13 +22,13 @@
            PrevUpHomeNext
            -
            +
            - + 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
            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 17cee5b58..463802cf3 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 @@ -3,7 +3,7 @@ Distributions - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            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 8243c65f6..a322c6cf4 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 @@ -3,7 +3,7 @@ Bernoulli Distribution - + @@ -22,7 +22,7 @@
            PrevUpHomeNext
            -
            +
            Bernoulli Distribution @@ -87,7 +87,7 @@

            - + 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

            @@ -327,15 +327,15 @@

            - + References
            -
              -
            • +
                +
              • Wikpedia Bernoulli distribution
              • -
              • +
              • Weisstein, Eric W. "Bernoulli Distribution." From MathWorld--A Wolfram Web Resource.
              • 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 c5c48c30a..a913ff917 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 @@ -3,7 +3,7 @@ Beta Distribution - + @@ -22,7 +22,7 @@
                PrevUpHomeNext
                -
                +
                Beta Distribution @@ -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

                @@ -596,7 +596,7 @@ from presumed-known mean and variance.

                - + References

                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 11fa519c0..27674652f 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 @@ -3,7 +3,7 @@ Binomial Distribution - + @@ -22,7 +22,7 @@

                PrevUpHomeNext
                -
                +
                Binomial Distribution @@ -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 11. Meaning of the non-member accessors

                +

                Table 11. Meaning of the non-member accessors

                @@ -628,7 +628,7 @@

                - + Examples

                @@ -636,7 +636,7 @@ examples are available illustrating the use of the binomial distribution.

                - + Accuracy

                @@ -646,7 +646,7 @@ please refer to these functions for information on accuracy.

                - + Implementation

                @@ -890,20 +890,20 @@

                - + References
                -
                  -
                • +
                    +
                  • Weisstein, Eric W. "Binomial Distribution." From MathWorld--A Wolfram Web Resource.
                  • -
                  • +
                  • Wikipedia binomial distribution.
                  • -
                  • +
                  • NIST Explorary Data Analysis.
                  • 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 f66cd5d2b..745b1be59 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 @@ -3,7 +3,7 @@ Cauchy-Lorentz Distribution - + @@ -22,7 +22,7 @@
                    PrevUpHomeNext
                    -
                    +
                    Cauchy-Lorentz Distribution @@ -88,7 +88,7 @@

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

                    - + Non-member Accessors
                    @@ -148,7 +148,7 @@ The domain of the random variable is [-[max_value], +[min_value]].

                    - + Accuracy

                    @@ -157,7 +157,7 @@ have very low error rates.

                    - + Implementation

                    @@ -273,19 +273,19 @@

                    - + References
                    -
                      -
                    • +
                        +
                      • Cauchy-Lorentz distribution
                      • -
                      • +
                      • NIST Exploratory Data Analysis
                      • -
                      • +
                      • Weisstein, Eric W. "Cauchy Distribution." From MathWorld--A Wolfram Web Resource. 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 3628c3b04..b0c125903 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 @@ -3,7 +3,7 @@ Chi Squared Distribution - + @@ -22,7 +22,7 @@
                        PrevUpHomeNext
                        -
                        +
                        Chi Squared Distribution @@ -87,7 +87,7 @@ independent, normally distributed random

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

                        - + Non-member Accessors
                        @@ -196,7 +196,7 @@ independent, normally distributed random The domain of the random variable is [0, +∞].

                        - + Examples

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

                        - + Accuracy

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

                        - + Implementation

                        @@ -379,19 +379,19 @@ independent, normally distributed random

                        - + References
                        -
                          -
                        • +
                            +
                          • NIST Exploratory Data Analysis
                          • -
                          • +
                          • Chi-square distribution
                          • -
                          • +
                          • Weisstein, Eric W. "Chi-Squared Distribution." From MathWorld--A Wolfram Web Resource. 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 18b23c5c3..d1fa74bcf 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 @@ -3,7 +3,7 @@ Exponential Distribution - + @@ -22,7 +22,7 @@
                            PrevUpHomeNext
                            -
                            +
                            Exponential Distribution @@ -71,7 +71,7 @@

                            - + 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

                            @@ -283,24 +283,24 @@

                            - + references
                            -
                              -
                            • +
                                +
                              • Weisstein, Eric W. "Exponential Distribution." From MathWorld--A Wolfram Web Resource
                              • -
                              • +
                              • Wolfram Mathematica calculator
                              • -
                              • +
                              • NIST Exploratory Data Analysis
                              • -
                              • +
                              • Wikipedia Exponential distribution
                              • @@ -309,7 +309,7 @@ (See also the reference documentation for the related Extreme Distributions.)

                                -
                                • +
                                  • Extreme Value Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah discuss the relationship of the types of extreme 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 313d6c77a..7c00560b2 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 @@ -3,7 +3,7 @@ Extreme Value Distribution - + @@ -22,7 +22,7 @@
                                    PrevUpHomeNext
                                    -
                                    +
                                    Extreme Value Distribution @@ -100,7 +100,7 @@

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

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

                                    - + Accuracy

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

                                    - + Implementation

                                    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 272d1f458..a32d2c2f3 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 @@ -3,7 +3,7 @@ F Distribution - + @@ -22,7 +22,7 @@

                                    PrevUpHomeNext
                                    -
                                    +
                                    @@ -80,7 +80,7 @@

                                    - + 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

                                    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 1edca746e..5d4304064 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 @@ -3,7 +3,7 @@ Gamma (and Erlang) Distribution - + @@ -22,7 +22,7 @@

                                    PrevUpHomeNext
                                    -
                                    +
                                    Gamma (and Erlang) Distribution @@ -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

                                    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html index bb60dd1fc..3e5905b73 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.html @@ -3,7 +3,7 @@ Hypergeometric Distribution - + @@ -22,7 +22,7 @@

                                    PrevUpHomeNext
                                    -
                                    +
                                    Hypergeometric Distribution @@ -102,7 +102,7 @@

                                    - + Member Functions
                                    @@ -131,7 +131,7 @@ from the population N.

                                    - + Non-member Accessors
                                    @@ -185,7 +185,7 @@
                                    - + Accuracy

                                    @@ -211,7 +211,7 @@ meaningless for N >= 1015.

                                    - + Testing

                                    @@ -223,7 +223,7 @@ this implementation and NTL::RR.

                                    - + Implementation

                                    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html index 3f7b0de5e..e28e22562 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.html @@ -3,7 +3,7 @@ Laplace Distribution - + @@ -22,7 +22,7 @@

                                    PrevUpHomeNext
                                    -
                                    +
                                    Laplace Distribution @@ -81,7 +81,7 @@

                                    - + Member Functions
                                    @@ -113,7 +113,7 @@ Returns the scale parameter of this distribution.

                                    - + Non-member Accessors
                                    @@ -133,7 +133,7 @@ The domain of the random variable is [-∞,+∞].

                                    - + Accuracy

                                    @@ -141,7 +141,7 @@ log and exp functions and as such should have very small errors.

                                    - + Implementation

                                    @@ -329,20 +329,20 @@

                                    - + References
                                    -
                                      -
                                    • +
                                        +
                                      • Weisstein, Eric W. "Laplace Distribution." From MathWorld--A Wolfram Web Resource.
                                      • -
                                      • +
                                      • Laplace Distribution
                                      • -
                                      • +
                                      • M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972, p. 930.
                                      • diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html index 5867d8a48..d5667a712 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.html @@ -3,7 +3,7 @@ Logistic Distribution - + @@ -22,7 +22,7 @@
                                        PrevUpHomeNext
                                        -
                                        +
                                        Logistic Distribution @@ -72,7 +72,7 @@

                                        - + Member Functions
                                        @@ -98,7 +98,7 @@ Returns the scale of this distribution.

                                        - + Non-member Accessors
                                        @@ -128,7 +128,7 @@ as special cases if RealType and +overflow_error respectively.

                                        - + Accuracy

                                        @@ -140,7 +140,7 @@ as special cases if RealType error can be guarenteed.

                                        - + Implementation
                                        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 3ecbffa13..1d81575bf 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 @@ -3,7 +3,7 @@ Log Normal Distribution - + @@ -22,7 +22,7 @@
                                        PrevUpHomeNext
                                        -
                                        +
                                        Log Normal Distribution @@ -88,7 +88,7 @@

                                        - + 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

                                        diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html index ab86e2ec4..9edc65793 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_beta_dist.html @@ -3,7 +3,7 @@ Noncentral Beta Distribution - + @@ -22,7 +22,7 @@

                                        PrevUpHomeNext
                                        -
                                        +
                                        Noncentral Beta Distribution @@ -96,7 +96,7 @@ is a central χ2 random variable with

                                        - + Member Functions
                                        @@ -128,7 +128,7 @@ is a central χ2 random variable with was constructed.

                                        - + Non-member Accessors
                                        @@ -152,7 +152,7 @@ is a central χ2 random variable with The domain of the random variable is [0, 1].

                                        - + Accuracy

                                        @@ -168,7 +168,7 @@ is a central χ2 random variable with zero error.

                                        -

                                        Table 13. Errors In CDF of the Noncentral Beta

                                        +

                                        Table 13. Errors In CDF of the Noncentral Beta

                                        @@ -295,7 +295,7 @@ is a central χ2 random variable with functions are broadly similar.

                                        - + Tests

                                        @@ -307,7 +307,7 @@ is a central χ2 random variable with tests.

                                        - + Implementation

                                        diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html index 63c6c8ae9..8b4fd2230 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_chi_squared_dist.html @@ -3,7 +3,7 @@ Noncentral Chi-Squared Distribution - + @@ -22,7 +22,7 @@

                                        PrevUpHomeNext
                                        -
                                        +
                                        Noncentral Chi-Squared Distribution @@ -110,7 +110,7 @@

                                        - + Member Functions
                                        @@ -183,7 +183,7 @@ == q.

                                        - + Non-member Accessors
                                        @@ -203,7 +203,7 @@ The domain of the random variable is [0, +∞].

                                        - + Examples

                                        @@ -211,7 +211,7 @@ example for the noncentral chi-squared distribution.

                                        - + Accuracy

                                        @@ -223,7 +223,7 @@ zero error.

                                        -

                                        Table 14. Errors In CDF of the Noncentral Chi-Squared

                                        +

                                        Table 14. Errors In CDF of the Noncentral Chi-Squared

                                        @@ -359,7 +359,7 @@ produce an accuracy greater than the square root of the machine epsilon.

                                        - + Tests

                                        @@ -373,7 +373,7 @@ to at least 50 decimal digits - and is the used for our accuracy tests.

                                        - + Implementation

                                        diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html index e6eac930e..c1e2c089c 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_f_dist.html @@ -3,7 +3,7 @@ Noncentral F Distribution - + @@ -22,7 +22,7 @@

                                        PrevUpHomeNext
                                        -
                                        +
                                        Noncentral F Distribution @@ -95,7 +95,7 @@ random variable with v1

                                        - + Member Functions
                                        @@ -127,7 +127,7 @@ random variable with v1 which this object was constructed.

                                        - + Non-member Accessors
                                        @@ -147,7 +147,7 @@ random variable with v1 The domain of the random variable is [0, +∞].

                                        - + Accuracy

                                        @@ -155,7 +155,7 @@ random variable with v1 Beta Distribution: refer to that distribution for accuracy data.

                                        - + Tests

                                        @@ -164,7 +164,7 @@ random variable with v1 Math library statistical package and its pbeta and dbeta functions.

                                        - + Implementation

                                        diff --git a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html index 62e1565f0..5c65d5a78 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/nc_t_dist.html @@ -3,7 +3,7 @@ Noncentral T Distribution - + @@ -22,7 +22,7 @@

                                        PrevUpHomeNext
                                        -
                                        +
                                        Noncentral T Distribution @@ -85,7 +85,7 @@

                                        - + Member Functions
                                        @@ -111,7 +111,7 @@ which this object was constructed.

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

                                        - + Accuracy

                                        @@ -141,7 +141,7 @@ one shown will have effectively zero error.

                                        -

                                        Table 15. Errors In CDF of the Noncentral T Distribution

                                        +

                                        Table 15. Errors In CDF of the Noncentral T Distribution

                                        @@ -255,7 +255,7 @@ epsilon.

                                        - + Tests

                                        @@ -270,7 +270,7 @@ least 50 decimal places.

                                        - + Implementation

                                        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 195c80aac..a601d6925 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 @@ -3,7 +3,7 @@ Negative Binomial Distribution - + @@ -22,7 +22,7 @@

                                        PrevUpHomeNext
                                        -
                                        +
                                        Negative Binomial Distribution @@ -123,7 +123,7 @@

                                        - + 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 12. Meaning of the non-member accessors.

                                        +

                                        Table 12. Meaning of the non-member accessors.

                                        @@ -606,7 +606,7 @@

                                        - + Accuracy

                                        @@ -616,7 +616,7 @@ please refer to these functions for information on accuracy.

                                        - + Implementation

                                        @@ -885,13 +885,13 @@

                                        Implementation notes:

                                        -
                                          -
                                        • +
                                            +
                                          • The real concept type (that deliberately lacks the Lanczos approximation), was found to take several minutes to evaluate some extreme test values, so the test has been disabled for this type.
                                          • -
                                          • +
                                          • Much greater speed, and perhaps greater accuracy, might be achieved for extreme values by using a normal approximation. This is NOT been tested or implemented. 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 54a973aca..2877b1a27 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 @@ -3,7 +3,7 @@ Normal (Gaussian) Distribution - + @@ -22,7 +22,7 @@
                                            PrevUpHomeNext
                                            -
                                            +
                                            Normal (Gaussian) Distribution @@ -79,7 +79,7 @@

                                            - + 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

                                            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 6a00c4878..d0ed879d1 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 @@ -3,7 +3,7 @@ Pareto Distribution - + @@ -22,7 +22,7 @@

                                            PrevUpHomeNext
                                            -
                                            +
                                            Pareto Distribution @@ -87,12 +87,12 @@

                                            - + Related distributions
                                            - + Member Functions
                                            @@ -118,7 +118,7 @@ Returns the shape parameter of this distribution.

                                            - + Non-member Accessors
                                            @@ -138,7 +138,7 @@ The supported domain of the random variable is [scale, ∞].

                                            - + Accuracy

                                            @@ -151,7 +151,7 @@ zero) see also why complements?.

                                            - + Implementation

                                            @@ -319,20 +319,20 @@

                                            - + References
                                            -
                                              -
                                            • +
                                                +
                                              • Pareto Distribution
                                              • -
                                              • +
                                              • Weisstein, Eric W. "Pareto Distribution." From MathWorld--A Wolfram Web Resource.
                                              • -
                                              • +
                                              • Handbook of Statistical Distributions with Applications, K Krishnamoorthy, ISBN 1-58488-635-8, Chapter 23, pp 257 - 267. (Note the meaning of a and b is reversed in Wolfram and Krishnamoorthy). 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 dbe812dec..79d325c54 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 @@ -3,7 +3,7 @@ Poisson Distribution - + @@ -22,7 +22,7 @@
                                                PrevUpHomeNext
                                                -
                                                +
                                                Poisson Distribution @@ -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

                                                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 f620be36e..537f92db4 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 @@ -3,7 +3,7 @@ Rayleigh Distribution - + @@ -22,7 +22,7 @@

                                                PrevUpHomeNext
                                                -
                                                +
                                                Rayleigh Distribution @@ -86,7 +86,7 @@

                                                - + 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

                                                @@ -320,14 +320,14 @@

                                                - + References
                                                -
                                                  -
                                                • +
                                                    +
                                                  • http://en.wikipedia.org/wiki/Rayleigh_distribution
                                                  • -
                                                  • +
                                                  • Weisstein, Eric W. "Rayleigh Distribution." From MathWorld--A Wolfram Web Resource. 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 12196e275..ef98e9881 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 @@ -3,7 +3,7 @@ Students t Distribution - + @@ -22,7 +22,7 @@
                                                    PrevUpHomeNext
                                                    -
                                                    +
                                                    Students t Distribution @@ -97,7 +97,7 @@

                                                    - + 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

                                                    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 f307e40e2..16f560bbb 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 @@ -3,7 +3,7 @@ Triangular Distribution - + @@ -22,7 +22,7 @@

                                                    PrevUpHomeNext
                                                    -
                                                    +
                                                    Triangular Distribution @@ -81,11 +81,11 @@

                                                    f(x) =

                                                    -
                                                      -
                                                    • +
                                                        +
                                                      • 2(x-a)/(b-a) (c-a) for a <= x <= c
                                                      • -
                                                      • +
                                                      • 2(b-x)/(b-a)(b-c) for c < x <= b
                                                      @@ -128,7 +128,7 @@

                                                      - + 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

                                                      @@ -378,33 +378,33 @@ Calculate and plot probability distributions

                                                      - + References
                                                      -
                                                        -
                                                      • +
                                                          +
                                                        • Wikpedia triangular distribution
                                                        • -
                                                        • +
                                                        • Weisstein, Eric W. "Triangular Distribution." From MathWorld--A Wolfram Web Resource.
                                                        • -
                                                        • +
                                                        • Evans, M.; Hastings, N.; and Peacock, B. "Triangular Distribution." Ch. 40 in Statistical Distributions, 3rd ed. New York: Wiley, pp. 187-188, 2000, ISBN - 0471371246]
                                                        • -
                                                        • +
                                                        • Brighton Webs Ltd. BW D-Calc 1.0 Distribution Calculator
                                                        • -
                                                        • +
                                                        • The Triangular Distribution including its history.
                                                        • -
                                                        • +
                                                        • Gejza Wimmer, Viktor Witkovsky and Tomas Duby, Measurement Science Review, Volume 2, Section 1, 2002, Proper Rounding Of The Measurement Results 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 878021b5c..dd570fa4d 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 @@ -3,7 +3,7 @@ Uniform Distribution - + @@ -22,7 +22,7 @@ -
                                                          +
                                                          Uniform Distribution @@ -67,18 +67,18 @@

                                                          f(x) =

                                                          -
                                                            -
                                                          • +
                                                              +
                                                            • 1 / (upper - lower) for lower < x < upper
                                                            • -
                                                            • +
                                                            • zero for x < lower or x > upper

                                                            and in this implementation:

                                                            -
                                                            • +
                                                              • 1 / (upper - lower) for x = lower or x = upper

                                                              @@ -117,7 +117,7 @@

                                                              - + 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

                                                              @@ -337,20 +337,20 @@

                                                            - + References
                                                            -
                                                              -
                                                            • + 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 239f5258d..c9e5ffba3 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 @@ -3,7 +3,7 @@ Weibull Distribution - + @@ -22,7 +22,7 @@
                                                              PrevUpHomeNext
                                                              -
                                                              +
                                                              Weibull Distribution @@ -72,15 +72,15 @@ in particular it can mimic distributions where the failure rate varies over time. If the failure rate is:

                                                              -
                                                                -
                                                              • +
                                                                  +
                                                                • constant over time, then α = 1, suggests that items are failing from random events.
                                                                • -
                                                                • +
                                                                • decreases over time, then α < 1, suggesting "infant mortality".
                                                                • -
                                                                • +
                                                                • increases over time, then α > 1, suggesting "wear out" - more likely to fail as time goes by.
                                                                • @@ -100,7 +100,7 @@

                                                                  - + Related distributions
                                                                  @@ -114,7 +114,7 @@ Distributions, Theory and Applications Samuel Kotz & Saralees Nadarajah.

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

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

                                                                  - + Accuracy

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

                                                                  - + Implementation

                                                                  @@ -337,19 +337,19 @@

                                                                - + References
                                                                -
                                                                  -
                                                                • +
                                                                    +
                                                                  • http://en.wikipedia.org/wiki/Weibull_distribution
                                                                  • -
                                                                  • +
                                                                  • Weisstein, Eric W. "Weibull Distribution." From MathWorld--A Wolfram Web Resource.
                                                                  • -
                                                                  • +
                                                                  • Weibull in NIST Exploratory Data Analysis
                                                                  • 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 ed71a2753..461610b03 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 @@ -3,7 +3,7 @@ Non-Member Properties - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    @@ -37,152 +37,152 @@ the function you want if you already know its name.

                                                                    - + Function Index
                                                                    -
                                                                    - + mean
                                                                    template<class RealType, class Policy>
                                                                    @@ -318,7 +318,7 @@
                                                                               distribution).
                                                                             

                                                                    - + median
                                                                    template<class RealType, class Policy>
                                                                    @@ -328,7 +328,7 @@
                                                                               Returns the median of the distribution dist.
                                                                             

                                                                    - + mode
                                                                    template<class RealType, Policy>
                                                                    @@ -342,7 +342,7 @@
                                                                               if the distribution does not have a defined mode.
                                                                             

                                                                    - + Probability Density Function
                                                                    @@ -371,7 +371,7 @@ pdf

                                                                    - + range
                                                                    template<class RealType, class Policy>
                                                                    @@ -381,7 +381,7 @@
                                                                               Returns the valid range of the random variable over distribution dist.
                                                                             

                                                                    - + Quantile
                                                                    template <class RealType, class Policy>
                                                                    @@ -410,7 +410,7 @@
                                                                               quantile
                                                                             

                                                                    - + Quantile from the complement of the probability.
                                                                    @@ -456,7 +456,7 @@ survival_inv

                                                                    - + Standard Deviation
                                                                    @@ -471,7 +471,7 @@ if the distribution does not have a defined standard deviation.

                                                                    - + support
                                                                    template<class RealType, class Policy>
                                                                    @@ -488,7 +488,7 @@
                                                                               where the pdf is zero, and the cdf zero or unity.
                                                                             

                                                                    - + Variance
                                                                    template <class RealType, class Policy>
                                                                    @@ -502,7 +502,7 @@
                                                                               if the distribution does not have a defined variance.
                                                                             

                                                                    - + Skewness
                                                                    template <class RealType, class Policy>
                                                                    @@ -516,7 +516,7 @@
                                                                               if the distribution does not have a defined skewness.
                                                                             

                                                                    - + Kurtosis
                                                                    template <class RealType, class Policy>
                                                                    @@ -558,7 +558,7 @@
                                                                               'Proper' kurtosis can have a value from zero to + infinity.
                                                                             

                                                                    - + Kurtosis excess
                                                                    @@ -593,7 +593,7 @@ The kurtosis excess of a normal distribution is zero.

                                                                    - + P and Q

                                                                    @@ -603,7 +603,7 @@ returned by these functions.

                                                                    - + Percent Point Function
                                                                    @@ -612,7 +612,7 @@ the Quantile.

                                                                    - + Inverse CDF Function.
                                                                    @@ -621,7 +621,7 @@ Quantile.

                                                                    - + Inverse Survival Function.
                                                                    @@ -629,7 +629,7 @@ The inverse of the survival function, is the same as computing the quantile from the complement of the probability.

                                                                    - + Probability Mass Function
                                                                    @@ -643,7 +643,7 @@ applies to continuous distributions.

                                                                    - + Lower Critical Value.
                                                                    @@ -653,7 +653,7 @@ the Quantile.

                                                                    - + Upper Critical Value.
                                                                    @@ -664,7 +664,7 @@ complement of the probability.

                                                                    - + Survival Function
                                                                    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 8555d364a..998316c8b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/future.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/future.html @@ -3,7 +3,7 @@ Extras/Future Directions - + @@ -22,12 +22,12 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    - + 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
                                                                    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 2c140669b..030c1f7bf 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 @@ -3,7 +3,7 @@ Statistical Distributions Tutorial - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +

                                                                    Statistical Distributions Tutorial 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 c713fb021..810e6031c 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 @@ -3,7 +3,7 @@ Discrete Probability Distributions - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +

                                                                    Discrete Probability Distributions 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 0ea7a6b66..397b8f8f6 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 @@ -3,7 +3,7 @@ Overview of Distributions - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html index c1348aded..54b6be714 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.html @@ -3,7 +3,7 @@ Complements are supported too - and when to use them - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    Complements are supported too - and when to use them diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html index 5a8ae0d22..44e01246b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.html @@ -3,7 +3,7 @@ Generic operations common to all distributions are non-member functions - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    Generic operations common to all distributions are non-member functions diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html index 5dad9e82e..a6aff87e4 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.html @@ -3,7 +3,7 @@ Headers and Namespaces - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    Headers and Namespaces diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html index 21b9415b3..38bb2ab76 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.html @@ -3,7 +3,7 @@ Distributions are Objects - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    Distributions are Objects @@ -50,13 +50,13 @@

                                                                    Making distributions class types does two things:

                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • It encapsulates the kind of distribution in the C++ type system; so, for example, Students-t distributions are always a different C++ type from Chi-Squared distributions.
                                                                      • -
                                                                      • +
                                                                      • The distribution objects store any parameters associated with the distribution: for example, the Students-t distribution has a degrees of freedom parameter that controls the shape of the distribution. diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html index 035983464..2d56de96b 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.html @@ -3,7 +3,7 @@ Parameters can be calculated - + @@ -22,7 +22,7 @@
                                                                        PrevUpHomeNext
                                                                        -
                                                                        +
                                                                        Parameters can be calculated diff --git a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html index c098e42c1..b370f0837 100644 --- a/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html +++ b/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.html @@ -3,7 +3,7 @@ Summary - + @@ -22,32 +22,32 @@
                                                                        PrevUpHomeNext
                                                                        -
                                                                        +
                                                                        -

                                                                    - + Quick Reference

                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html index f03df8a60..29e21958a 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1.html @@ -3,7 +3,7 @@ C99 and TR1 C Functions Overview - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    @@ -48,15 +48,15 @@

                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • The header to include is lightweight (i.e. fast to compile).
                                                                      • -
                                                                      • +
                                                                      • The functions have extern "C" linkage, and so are usable from other languages (not just C and C++).
                                                                      • -
                                                                      • +
                                                                      • C99 and C++ TR1 Standard compatibility.
                                                                      @@ -67,15 +67,15 @@

                                                                      -
                                                                        -
                                                                      • +
                                                                          +
                                                                        • You will need to compile and link to the external Boost.Math libraries.
                                                                        • -
                                                                        • +
                                                                        • Limited to support for the types, float, double and long double.
                                                                        • -
                                                                        • +
                                                                        • Error handling is handled via setting ::errno and returning NaN's and infinities: this may be less flexible than an C++ exception based approach.
                                                                        • @@ -285,7 +285,7 @@

                                                                          - + Usage Recomendations

                                                                          @@ -295,12 +295,12 @@

                                                                          -
                                                                            -
                                                                          • +
                                                                              +
                                                                            • To include the header only versions of the functions and have an easier time linking, but a longer compile time.
                                                                            • -
                                                                            • +
                                                                            • To include the TR1 headers and link against an external library.
                                                                            @@ -336,7 +336,7 @@

                                                                            - + Supported C99 Functions
                                                                            @@ -440,7 +440,7 @@

                                                                            - + Supported TR1 Functions
                                                                            @@ -579,7 +579,7 @@

                                                                            - + Currently Unsupported C99 Functions
                                                                            @@ -650,7 +650,7 @@

                                                                            - + Currently Unsupported TR1 Functions
                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html index 43d362c01..d9a5ceab1 100644 --- a/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html +++ b/doc/sf_and_dist/html/math_toolkit/extern_c/tr1_ref.html @@ -3,7 +3,7 @@ TR1 C Functions Quick Reference - + @@ -22,13 +22,13 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + Supported TR1 Functions
                                                                            @@ -163,7 +163,7 @@ expint(2); // integer argument is treated as a double, returns double.
                                                                    - + Quick Reference
                                                                    // [5.2.1.1] associated Laguerre polynomials:
                                                                    @@ -494,7 +494,7 @@
                                                                             for the full template (header only) version of this function.
                                                                           

                                                                    - + Currently Unsupported TR1 Functions
                                                                    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 d9c24dc1b..823f38dc2 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview.html @@ -3,7 +3,7 @@ Overview - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html index c933c6bf4..3835195af 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/building.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/building.html @@ -3,7 +3,7 @@ If and How to Build the Library and its Examples and Tests - + @@ -22,13 +22,13 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    - + Building the Library
                                                                    @@ -93,7 +93,7 @@ building the sources. Boost.Build will do this automatically when appropriate.

                                                                    - + Building the Examples
                                                                    @@ -104,7 +104,7 @@ the Boost headers are in your compilers #include search path.

                                                                    - + Building the Tests
                                                                    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 58413ad45..2e20dc758 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 @@ -3,7 +3,7 @@ Compilers - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    @@ -37,7 +37,7 @@

                                                                    -

                                                                    Table 9. Supported/Tested Compilers

                                                                    +

                                                                    Table 9. Supported/Tested Compilers

                                                                    @@ -549,7 +549,7 @@


                                                                    -

                                                                    Table 10. Unsupported Compilers

                                                                    +

                                                                    Table 10. Unsupported Compilers

                                                                    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 3c2b46b79..0c0e6102f 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 @@ -3,7 +3,7 @@ Contact Info and Support - + @@ -22,7 +22,7 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +

                                                                    Contact Info and Support @@ -30,12 +30,12 @@

                                                                    The main support for this library is via the Boost mailing lists:

                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • Use the boost-user list for general support questions.
                                                                      • -
                                                                      • +
                                                                      • Use the boost-developer list for discussion about implementation and or submission of extensions. 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 828f5dca1..bc3541854 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 @@ -3,7 +3,7 @@ Directory and File Structure - + @@ -22,13 +22,13 @@
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                                                                        -
                                                                        +
                                                                        - + boost/math
                                                                        @@ -73,7 +73,7 @@
                                                                        - + boost/libs
                                                                        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 a1b5bffab..f1979ac52 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 @@ -3,7 +3,7 @@ Error Handling - + @@ -22,23 +22,23 @@
                                                                        PrevUpHomeNext
                                                                        -
                                                                        +
                                                                        - + Quick Reference

                                                                        Handling of errors by this library is split into two orthogonal parts:

                                                                        -
                                                                          -
                                                                        • +
                                                                            +
                                                                          • What kind of error has been raised?
                                                                          • -
                                                                          • +
                                                                          • What should be done when the error is raised?
                                                                          @@ -134,7 +134,7 @@ the default action for each error shown in bold:

                                                                          -

                                                                          Table 1. Possible Actions for Domain Errors

                                                                          +

                                                                          Table 1. Possible Actions for Domain Errors

                                                                    @@ -209,7 +209,7 @@

                                                                    -

                                                                    Table 2. Possible Actions for Pole Errors

                                                                    +

                                                                    Table 2. Possible Actions for Pole Errors

                                                                    @@ -284,7 +284,7 @@

                                                                    -

                                                                    Table 3. Possible Actions for Overflow Errors

                                                                    +

                                                                    Table 3. Possible Actions for Overflow Errors

                                                                    @@ -359,7 +359,7 @@

                                                                    -

                                                                    Table 4. Possible Actions for Underflow Errors

                                                                    +

                                                                    Table 4. Possible Actions for Underflow Errors

                                                                    @@ -434,7 +434,7 @@

                                                                    -

                                                                    Table 5. Possible Actions for Denorm Errors

                                                                    +

                                                                    Table 5. Possible Actions for Denorm Errors

                                                                    @@ -509,7 +509,7 @@

                                                                    -

                                                                    Table 6. Possible Actions for Rounding Errors

                                                                    +

                                                                    Table 6. Possible Actions for Rounding Errors

                                                                    @@ -584,7 +584,7 @@

                                                                    -

                                                                    Table 7. Possible Actions for Internal Evaluation Errors

                                                                    +

                                                                    Table 7. Possible Actions for Internal Evaluation Errors

                                                                    @@ -659,7 +659,7 @@

                                                                    -

                                                                    Table 8. Possible Actions for Indeterminate Result Errors

                                                                    +

                                                                    Table 8. Possible Actions for Indeterminate Result Errors

                                                                    @@ -735,7 +735,7 @@

                                                                    - + Rationale

                                                                    @@ -743,18 +743,18 @@ the default behaviours were chosen based on feedback during the formal review of this library. It was felt that:

                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • Genuine errors should be flagged with exceptions rather than following C-compatible behaviour and setting ::errno.
                                                                      • -
                                                                      • +
                                                                      • Numeric underflow and denormalised results were not considered to be fatal errors in most cases, so it was felt that these should be ignored.
                                                                      - + Finding More Information
                                                                      @@ -776,7 +776,7 @@ The various kind of errors are described in more detail below.

                                                                      - + Domain Errors
                                                                      @@ -848,7 +848,7 @@ for more details.

                                                                      - + Evaluation at a pole
                                                                      @@ -887,7 +887,7 @@ for more details.

                                                                      - + Numeric Overflow
                                                                      @@ -912,7 +912,7 @@ doesn't support infinities, the maximum value for the type is returned.

                                                                      - + Numeric Underflow
                                                                      @@ -935,7 +935,7 @@ an std::underflow_error C++ exception.

                                                                      - + Denormalisation Errors
                                                                      @@ -958,7 +958,7 @@ throws an std::underflow_error C++ exception.

                                                                      - + Evaluation Errors
                                                                      @@ -995,7 +995,7 @@ for more details.

                                                                      - + Indeterminate Result Errors
                                                                      @@ -1022,7 +1022,7 @@ the result of 00 is 1, even though the result is actually mathematically indeterminate.

                                                                      - + Rounding Errors
                                                                      @@ -1062,7 +1062,7 @@ for more details.

                                                                      - + Errors from typecasts
                                                                      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 be338ed3b..1fc7034c8 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 @@ -3,7 +3,7 @@ History and What's New - + @@ -22,21 +22,33 @@
                                                                      PrevUpHomeNext
                                                                      -
                                                                      +
                                                                      +

                                                                      + +

                                                                      +
                                                                      + + Boost-1.44.0 +
                                                                      +

                                                                      +

                                                                      +
                                                                      • + Fixed incorrect range and support for Rayleigh distribution. +

                                                                      - + Boost-1.41.0

                                                                      -
                                                                      • +
                                                                        • Significantly improved performance for the incomplete gamma function and it's inverse.
                                                                        @@ -44,41 +56,41 @@

                                                                        - + Boost-1.40.0

                                                                        -
                                                                          -
                                                                        • +
                                                                            +
                                                                          • Added support for MPFR as a bignum type.
                                                                          • -
                                                                          • +
                                                                          • Added some full specializations of the policy classes to reduce compile times.
                                                                          • -
                                                                          • +
                                                                          • Added logistic and hypergeometric distributions, from Gautam Sewani's Google Summer of Code project.
                                                                          • -
                                                                          • +
                                                                          • Added Laplace distribution submitted by Thijs van den Berg.
                                                                          • -
                                                                          • +
                                                                          • Updated performance test code to include new distributions, and improved the performance of the non-central distributions.
                                                                          • -
                                                                          • +
                                                                          • Added SSE2 optimised Lanczos approximation code, from Gautam Sewani's Google Summer of Code project.
                                                                          • -
                                                                          • +
                                                                          • Fixed bug in cyl_bessel_i that used an incorrect approximation for ν = 0.5, also effects the non-central Chi Square Distribution when ν = 3, see bug report #2877.
                                                                          • -
                                                                          • +
                                                                          • Fixed minor bugs #2873.
                                                                          @@ -86,16 +98,16 @@

                                                                          - + Boost-1.38.0

                                                                          -
                                                                            -
                                                                          • +
                                                                              +
                                                                            • Added Johan Råde's optimised floating point classification routines.
                                                                            • -
                                                                            • +
                                                                            • Fixed code so that it compiles in GCC's -pedantic mode (bug report #1451).
                                                                            • @@ -104,49 +116,49 @@

                                                                              - + Boost-1.37.0

                                                                              -
                                                                              • +
                                                                                • Improved accuracy and testing of the inverse hypergeometric functions.

                                                                                - + Boost-1.36.0

                                                                                -
                                                                                  -
                                                                                • +
                                                                                    +
                                                                                  • Added Noncentral Chi Squared Distribution.
                                                                                  • -
                                                                                  • +
                                                                                  • Added Noncentral Beta Distribution.
                                                                                  • -
                                                                                  • +
                                                                                  • Added Noncentral F Distribution.
                                                                                  • -
                                                                                  • +
                                                                                  • Added Noncentral T Distribution.
                                                                                  • -
                                                                                  • +
                                                                                  • Added Exponential Integral Functions.
                                                                                  • -
                                                                                  • +
                                                                                  • Added Zeta Function.
                                                                                  • -
                                                                                  • +
                                                                                  • Added Rounding and Truncation functions.
                                                                                  • -
                                                                                  • +
                                                                                  • Added Compile time powers of runtime bases.
                                                                                  • -
                                                                                  • +
                                                                                  • Added SSE2 optimizations for Lanczos evaluation.
                                                                                  @@ -154,37 +166,37 @@

                                                                                  - + Boost-1.35.0: Post Review First Official Release

                                                                                  -
                                                                                    -
                                                                                  • +
                                                                                      +
                                                                                    • Added Policy based framework that allows fine grained control over function behaviour.
                                                                                    • -
                                                                                    • +
                                                                                    • Breaking change: Changed default behaviour for domain, pole and overflow errors to throw an exception (based on review feedback), this behaviour can be customised using Policy's.
                                                                                    • -
                                                                                    • +
                                                                                    • Breaking change: Changed exception thrown when an internal evaluation error occurs to boost::math::evaluation_error.
                                                                                    • -
                                                                                    • +
                                                                                    • Breaking change: Changed discrete quantiles to return an integer result: this is anything up to 20 times faster than finding the true root, this behaviour can be customised using Policy's.
                                                                                    • -
                                                                                    • +
                                                                                    • Polynomial/rational function evaluation is now customisable and hopefully faster than before.
                                                                                    • -
                                                                                    • +
                                                                                    • Added performance test program.
                                                                                    @@ -192,18 +204,18 @@

                                                                                    - + Milestone 4: Second Review Candidate (1st March 2007)

                                                                                    -
                                                                                      -
                                                                                    • +
                                                                                        +
                                                                                      • Moved Xiaogang Zhang's Bessel Functions code into the library, and brought them into line with the rest of the code.
                                                                                      • -
                                                                                      • +
                                                                                      • Added C# "Distribution Explorer" demo application.
                                                                                      @@ -211,31 +223,31 @@

                                                                                      - + Milestone 3: First Review Candidate (31st Dec 2006)

                                                                                      -
                                                                                        -
                                                                                      • +
                                                                                          +
                                                                                        • Implemented the main probability distribution and density functions.
                                                                                        • -
                                                                                        • +
                                                                                        • Implemented digamma.
                                                                                        • -
                                                                                        • +
                                                                                        • Added more factorial functions.
                                                                                        • -
                                                                                        • +
                                                                                        • Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical harmonic functions from TR1.
                                                                                        • -
                                                                                        • +
                                                                                        • Moved Xiaogang Zhang's elliptic integral code into the library, and brought them into line with the rest of the code.
                                                                                        • -
                                                                                        • +
                                                                                        • Moved Hubert Holin's existing Boost.Math special functions into this library and brought them into line with the rest of the code.
                                                                                        • @@ -244,40 +256,40 @@

                                                                                          - + Milestone 2: Released September 10th 2006

                                                                                          -
                                                                                            -
                                                                                          • +
                                                                                              +
                                                                                            • Implement preview release of the statistical distributions.
                                                                                            • -
                                                                                            • +
                                                                                            • Added statistical distributions tutorial.
                                                                                            • -
                                                                                            • +
                                                                                            • Implemented root finding algorithms.
                                                                                            • -
                                                                                            • +
                                                                                            • Implemented the inverses of the incomplete gamma and beta functions.
                                                                                            • -
                                                                                            • +
                                                                                            • Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
                                                                                            • -
                                                                                            • +
                                                                                            • Integrated the statistical results generated from the test data with Boost.Test: uses a database of expected results, indexed by test, floating point type, platform, and compiler.
                                                                                            • -
                                                                                            • +
                                                                                            • Improved lgamma near 1 and 2 (rational approximations).
                                                                                            • -
                                                                                            • +
                                                                                            • Improved erf/erfc inverses (rational approximations).
                                                                                            • -
                                                                                            • +
                                                                                            • Implemented Rational function generation (the Remez method).
                                                                                            @@ -285,29 +297,29 @@

                                                                                            - + Milestone 1: Released March 31st 2006

                                                                                            -
                                                                                              -
                                                                                            • +
                                                                                                +
                                                                                              • Implement gamma/beta/erf functions along with their incomplete counterparts.
                                                                                              • -
                                                                                              • +
                                                                                              • Generate high quality test data, against which future improvements can be judged.
                                                                                              • -
                                                                                              • +
                                                                                              • Provide tools for the evaluation of infinite series, continued fractions, and rational functions.
                                                                                              • -
                                                                                              • +
                                                                                              • Provide tools for testing against tabulated test data, and collecting statistics on error rates.
                                                                                              • -
                                                                                              • +
                                                                                              • Provide sufficient docs for people to be able to find their way around the library.
                                                                                              • 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 cfd68d5bb..41189fb92 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 @@ -3,7 +3,7 @@ About the Math Toolkit - + @@ -22,7 +22,7 @@
                                                                                                PrevUpHomeNext
                                                                                                -
                                                                                                +
                                                                                                @@ -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
                                                                                                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 76f8d84d1..84d4df680 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 @@ -3,7 +3,7 @@ Namespaces - + @@ -22,7 +22,7 @@
                                                                                                PrevUpHomeNext
                                                                                                -
                                                                                                +
                                                                                                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 1a7681952..447c76ac3 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 @@ -3,7 +3,7 @@ Navigation - + @@ -22,7 +22,7 @@
                                                                                                PrevUpHomeNext
                                                                                                -
                                                                                                +
                                                                                                @@ -31,7 +31,7 @@ as handy shortcuts for common navigation tasks.

                                                                                                - + Shortcuts
                                                                                                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 b60b759d4..44b09195b 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 @@ -3,7 +3,7 @@ Performance - + @@ -22,7 +22,7 @@
                                                                                                PrevUpHomeNext
                                                                                                -
                                                                                                +
                                                                                                @@ -54,13 +54,13 @@

                                                                                                -
                                                                                                  -
                                                                                                1. +
                                                                                                    +
                                                                                                  1. Turn on your compilers optimisations: the difference between "release" and "debug" builds can easily be a factor of 20.
                                                                                                  2. -
                                                                                                  3. +
                                                                                                  4. Pick your compiler carefully: performance differences of up to 8 fold have been found between some windows compilers for example. 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 3c7d812a2..3e0cd8917 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 @@ -3,7 +3,7 @@ Configuration and Policies - + @@ -22,7 +22,7 @@
                                                                                                    PrevUpHomeNext
                                                                                                    -
                                                                                                    +

                                                                                                    Configuration and Policies @@ -62,31 +62,31 @@

                                                                                                    -
                                                                                                      -
                                                                                                    • +
                                                                                                        +
                                                                                                      • How results from 'bad' arguments are handled, including those that cannot be fully evaluated.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • How accuracy is controlled by internal promotion to use more precise types.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • What working precision should be used to calculate results.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • What to do when a mathematically undefined function is used: Should this raise a run-time or compile-time error?
                                                                                                      • -
                                                                                                      • +
                                                                                                      • Whether discrete functions, like the binomial, should return real or only integral values, and how they are rounded.
                                                                                                      • -
                                                                                                      • +
                                                                                                      • How many iterations a special function is permitted to perform in a series evaluation or root finding algorithm before it gives up and raises an evaluation_error. @@ -99,18 +99,18 @@

                                                                                                        -
                                                                                                          -
                                                                                                        • +
                                                                                                            +
                                                                                                          • Using macros to change any default policy: the is the prefered method for installation wide policies.
                                                                                                          • -
                                                                                                          • +
                                                                                                          • At your chosen namespace scope for distributions and/or functions: this is the prefered method for project, namespace, or translation unit scope policies.
                                                                                                          • -
                                                                                                          • +
                                                                                                          • In an ad-hoc manner by passing a specific policy to a special function, or to a statistical distribution. 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 4b65e99e3..645f9dd54 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 @@ -3,7 +3,7 @@ Calculation of the Type of the Result - + @@ -22,7 +22,7 @@
                                                                                                            PrevUpHomeNext
                                                                                                            -
                                                                                                            +

                                                                                                            Calculation of the Type of the Result @@ -53,31 +53,31 @@

                                                                                                            Otherwise, the type of the result is computed using the following logic:

                                                                                                            -
                                                                                                              -
                                                                                                            1. +
                                                                                                                +
                                                                                                              1. Any arguments that are not template arguments are disregarded from further analysis.
                                                                                                              2. -
                                                                                                              3. +
                                                                                                              4. For each type in the argument list, if that type is an integer type then it is treated as if it were of type double for the purposes of further analysis.
                                                                                                              5. -
                                                                                                              6. +
                                                                                                              7. If any of the arguments is a user-defined class type, then the result type is the first such class type that is constructible from all of the other argument types.
                                                                                                              8. -
                                                                                                              9. +
                                                                                                              10. If any of the arguments is of type long double, then the result is of type long double.
                                                                                                              11. -
                                                                                                              12. +
                                                                                                              13. If any of the arguments is of type double, then the result is of type double.
                                                                                                              14. -
                                                                                                              15. +
                                                                                                              16. Otherwise the result is of type float.
                                                                                                              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 1de79ab97..8dffb45a0 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 @@ -3,7 +3,7 @@ Thread Safety - + @@ -22,7 +22,7 @@
                                                                                                              PrevUpHomeNext
                                                                                                              -
                                                                                                              +
                                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html b/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html index 3146dd773..4544ce504 100644 --- a/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html +++ b/doc/sf_and_dist/html/math_toolkit/main_overview/tr1.html @@ -3,7 +3,7 @@ C99 and C++ TR1 C-style Functions - + @@ -22,7 +22,7 @@
                                                                                                              PrevUpHomeNext
                                                                                                              -
                                                                                                              +

                                                                                                              C99 and C++ TR1 C-style Functions @@ -49,15 +49,15 @@

                                                                                                              -
                                                                                                                -
                                                                                                              • +
                                                                                                                  +
                                                                                                                • The header to include is lightweight (i.e. fast to compile).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • The functions have extern "C" linkage, and so are usable from other languages (not just C and C++).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • C99 and C++ TR1 Standard compatibility.
                                                                                                                @@ -68,15 +68,15 @@

                                                                                                                -
                                                                                                                  -
                                                                                                                • +
                                                                                                                    +
                                                                                                                  • You will need to compile and link to the external Boost.Math libraries.
                                                                                                                  • -
                                                                                                                  • +
                                                                                                                  • Limited to support for the types, float, double and long double.
                                                                                                                  • -
                                                                                                                  • +
                                                                                                                  • Error handling is handled via setting ::errno and returning NaN's and infinities: this may be less flexible than an C++ exception based approach.
                                                                                                                  • @@ -286,7 +286,7 @@

                                                                                                                    - + Usage Recomendations
                                                                                                                    @@ -297,12 +297,12 @@

                                                                                                                    -
                                                                                                                      -
                                                                                                                    • +
                                                                                                                        +
                                                                                                                      • To include the header only versions of the functions and have an easier time linking, but a longer compile time.
                                                                                                                      • -
                                                                                                                      • +
                                                                                                                      • To include the TR1 headers and link against an external library.
                                                                                                                      @@ -338,7 +338,7 @@

                                                                                                                      - + Supported C99 Functions
                                                                                                                      @@ -442,7 +442,7 @@

                                                                                                                      - + Supported TR1 Functions
                                                                                                                      @@ -581,7 +581,7 @@

                                                                                                                      - + Currently Unsupported C99 Functions
                                                                                                                      @@ -652,7 +652,7 @@

                                                                                                                      - + Currently Unsupported TR1 Functions
                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/perf.html b/doc/sf_and_dist/html/math_toolkit/perf.html index ef08dd71b..f7edb9156 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf.html +++ b/doc/sf_and_dist/html/math_toolkit/perf.html @@ -3,7 +3,7 @@ Performance - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      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 7aacd6f82..0d6b53c06 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 @@ -3,7 +3,7 @@ Comparing Compilers - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      @@ -35,7 +35,7 @@ in this respect).

                                                                                                                      -

                                                                                                                      Table 48. Performance Comparison of Various Windows Compilers

                                                                                                                      +

                                                                                                                      Table 48. Performance Comparison of Various Windows Compilers

                                                                                                                      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 577f22a0e..daa179d71 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/comparisons.html @@ -3,7 +3,7 @@ Comparisons to Other Open Source Libraries - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      - + Comparison to GSL-1.13 and Cephes
                                                                                                                      @@ -344,7 +344,7 @@

                                                                                                                      - +INF [1] + +INF [1]

                                                                                                                      @@ -423,7 +423,7 @@

                                                                                                                      -

                                                                                                                      17.89[2]

                                                                                                                      +

                                                                                                                      17.89[2]

                                                                                                                      (4.248e-005s)

                                                                                                                      @@ -548,11 +548,11 @@ -

                                                                                                                      [1] +

                                                                                                                      [1] Cephes gets stuck in an infinite loop while trying to execute our test cases.

                                                                                                                      -

                                                                                                                      [2] +

                                                                                                                      [2] The performance here is dominated by a few cases where the parameters grow very large: faster asymptotic expansions are available, but are of limited (or even frankly terrible) precision. The @@ -563,7 +563,7 @@

                                                                                                                      - + Comparison to the R and DCDFLIB Statistical Libraries on Windows
                                                                                                                      @@ -574,7 +574,7 @@ (R-2.9.2 appears not to be buildable with Visual C++).

                                                                                                                      -

                                                                                                                      Table 51. A Comparison to the R Statistical Library on Windows XP

                                                                                                                      +

                                                                                                                      Table 51. A Comparison to the R Statistical Library on Windows XP

                                                                                                                      @@ -659,7 +659,7 @@

                                                                                                                      -

                                                                                                                      67.66[1]

                                                                                                                      +

                                                                                                                      67.66[1]

                                                                                                                      (3.366e-004s)

                                                                                                                      @@ -1089,7 +1089,7 @@

                                                                                                                      -

                                                                                                                      3.60[2]

                                                                                                                      +

                                                                                                                      3.60[2]

                                                                                                                      (5.987e-007s)

                                                                                                                      @@ -1319,7 +1319,7 @@

                                                                                                                      -

                                                                                                                      43.43[3]

                                                                                                                      +

                                                                                                                      43.43[3]

                                                                                                                      (3.732e-004s)

                                                                                                                      @@ -1389,7 +1389,7 @@

                                                                                                                      -

                                                                                                                      393.90[4]

                                                                                                                      +

                                                                                                                      393.90[4]

                                                                                                                      (2.673e-002s)

                                                                                                                      @@ -1525,7 +1525,7 @@

                                                                                                                      -

                                                                                                                      1.00[5]

                                                                                                                      +

                                                                                                                      1.00[5]

                                                                                                                      (4.411e-004s)

                                                                                                                      @@ -1811,28 +1811,28 @@

                                                                                                                      -

                                                                                                                      [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] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.

                                                                                                                      -

                                                                                                                      [3] +

                                                                                                                      [3] 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

                                                                                                                      -

                                                                                                                      [4] +

                                                                                                                      [4] 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.

                                                                                                                      -

                                                                                                                      [5] +

                                                                                                                      [5] 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. @@ -1841,7 +1841,7 @@


                                                                                                                      - + Comparison to the R Statistical Library on Linux
                                                                                                                      @@ -1851,7 +1851,7 @@ G++ 4.3.3 using -O3 -DNDEBUG=1.

                                                                                                                      -

                                                                                                                      Table 52. A Comparison to the R Statistical Library on Linux

                                                                                                                      +

                                                                                                                      Table 52. A Comparison to the R Statistical Library on Linux

                                                                                                                      @@ -1936,7 +1936,7 @@

                                                                                                                      -

                                                                                                                      30.51[1]

                                                                                                                      +

                                                                                                                      30.51[1]

                                                                                                                      (3.616e-004s)

                                                                                                                      @@ -2366,7 +2366,7 @@

                                                                                                                      -

                                                                                                                      2.20[2]

                                                                                                                      +

                                                                                                                      2.20[2]

                                                                                                                      (3.522e-007s)

                                                                                                                      @@ -2596,7 +2596,7 @@

                                                                                                                      -

                                                                                                                      25.92[3]

                                                                                                                      +

                                                                                                                      25.92[3]

                                                                                                                      (4.407e-004s)

                                                                                                                      @@ -2666,7 +2666,7 @@

                                                                                                                      -

                                                                                                                      144.91[4]

                                                                                                                      +

                                                                                                                      144.91[4]

                                                                                                                      (3.214e-002s)

                                                                                                                      @@ -2802,7 +2802,7 @@

                                                                                                                      -

                                                                                                                      1.00[5]

                                                                                                                      +

                                                                                                                      1.00[5]

                                                                                                                      (5.916e-004s)

                                                                                                                      @@ -3088,28 +3088,28 @@

                                                                                                                      -

                                                                                                                      [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] This result is somewhat misleading: for small values of the parameters there is virtually no difference between the two libraries, but for large values the Boost implementation is much slower, albeit with much improved precision.

                                                                                                                      -

                                                                                                                      [3] +

                                                                                                                      [3] 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

                                                                                                                      -

                                                                                                                      [4] +

                                                                                                                      [4] 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.

                                                                                                                      -

                                                                                                                      [5] +

                                                                                                                      [5] 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. 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 c22829a74..48d7d8bfe 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 @@ -3,7 +3,7 @@ Getting the Best Performance from this Library - + @@ -22,7 +22,7 @@

                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +

                                                                                                                      Getting the Best Performance from this Library @@ -33,7 +33,7 @@ penalty for using the library in debug mode can be quite large.

                                                                                                                      -

                                                                                                                      Table 47. Performance Comparison of Release and Debug Settings

                                                                                                                      +

                                                                                                                      Table 47. Performance Comparison of Release and Debug Settings

                                                                                                                      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 ec3e36b5f..036989a19 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/interp.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/interp.html @@ -3,7 +3,7 @@ Interpreting these Results - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      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 5f511566e..c1d53a135 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 @@ -3,7 +3,7 @@ Performance Overview - + @@ -22,7 +22,7 @@
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                                                                                                                      -
                                                                                                                      +
                                                                                                                      @@ -54,13 +54,13 @@

                                                                                                                      -
                                                                                                                        -
                                                                                                                      1. +
                                                                                                                          +
                                                                                                                        1. Turn on your compilers optimisations: the difference between "release" and "debug" builds can easily be a factor of 20.
                                                                                                                        2. -
                                                                                                                        3. +
                                                                                                                        4. Pick your compiler carefully: performance differences of up to 8 fold have been found between some windows compilers for example. 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 e633d5104..e9ec1d08f 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 @@ -3,7 +3,7 @@ The Performance Test Application - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +

                                                                                                                          The Performance Test Application 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 5bb67d69c..5fcdae49e 100644 --- a/doc/sf_and_dist/html/math_toolkit/perf/tuning.html +++ b/doc/sf_and_dist/html/math_toolkit/perf/tuning.html @@ -3,7 +3,7 @@ Performance Tuning Macros - + @@ -22,7 +22,7 @@
                                                                                                                          PrevUpHomeNext
                                                                                                                          -
                                                                                                                          +
                                                                                                                          @@ -238,7 +238,7 @@ highly vectorisable processors in the future.

                                                                                                                          -

                                                                                                                          Table 49. A Comparison of Polynomial Evaluation Methods

                                                                                                                          +

                                                                                                                          Table 49. A Comparison of Polynomial Evaluation Methods

                                                                                                                      @@ -638,7 +638,7 @@ tutorial.

                                                                                                                      -

                                                                                                                      Table 50. Performance Comparison with and Without Internal Promotion to long +

                                                                                                                      Table 50. Performance Comparison with and Without Internal Promotion to long double

                                                                                                                      diff --git a/doc/sf_and_dist/html/math_toolkit/policy.html b/doc/sf_and_dist/html/math_toolkit/policy.html index 435f9584e..a6a5e9c76 100644 --- a/doc/sf_and_dist/html/math_toolkit/policy.html +++ b/doc/sf_and_dist/html/math_toolkit/policy.html @@ -3,7 +3,7 @@ Policies - + @@ -22,7 +22,7 @@
                                                                                                                      PrevUpHomeNext
                                                                                                                      -
                                                                                                                      +
                                                                                                                      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 41e0ff840..2b6ed135a 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 @@ -3,7 +3,7 @@ Policy Overview - + @@ -22,7 +22,7 @@
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                                                                                                                      @@ -61,31 +61,31 @@

                                                                                                                      -
                                                                                                                        -
                                                                                                                      • +
                                                                                                                          +
                                                                                                                        • How results from 'bad' arguments are handled, including those that cannot be fully evaluated.
                                                                                                                        • -
                                                                                                                        • +
                                                                                                                        • How accuracy is controlled by internal promotion to use more precise types.
                                                                                                                        • -
                                                                                                                        • +
                                                                                                                        • What working precision should be used to calculate results.
                                                                                                                        • -
                                                                                                                        • +
                                                                                                                        • What to do when a mathematically undefined function is used: Should this raise a run-time or compile-time error?
                                                                                                                        • -
                                                                                                                        • +
                                                                                                                        • Whether discrete functions, like the binomial, should return real or only integral values, and how they are rounded.
                                                                                                                        • -
                                                                                                                        • +
                                                                                                                        • How many iterations a special function is permitted to perform in a series evaluation or root finding algorithm before it gives up and raises an evaluation_error. @@ -98,18 +98,18 @@

                                                                                                                          -
                                                                                                                            -
                                                                                                                          • +
                                                                                                                              +
                                                                                                                            • Using macros to change any default policy: the is the prefered method for installation wide policies.
                                                                                                                            • -
                                                                                                                            • +
                                                                                                                            • At your chosen namespace scope for distributions and/or functions: this is the prefered method for project, namespace, or translation unit scope policies.
                                                                                                                            • -
                                                                                                                            • +
                                                                                                                            • In an ad-hoc manner by passing a specific policy to a special function, or to a statistical distribution. 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 3e6a0b7f3..0ca5e3d56 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 @@ -3,7 +3,7 @@ Policy Reference - + @@ -22,7 +22,7 @@
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                                                                                                                              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 9901dcf0f..c99c59444 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 @@ -3,7 +3,7 @@ Mathematically Undefined Function Policies - + @@ -22,7 +22,7 @@
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                                                                                                                              Mathematically Undefined Function Policies 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 a1b3811a9..19f162422 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 @@ -3,7 +3,7 @@ Discrete Quantile Policies - + @@ -22,7 +22,7 @@
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                                                                                                                              Discrete Quantile Policies @@ -55,7 +55,7 @@ can take have the following meanings:

                                                                                                                              - + real

                                                                                                                              @@ -93,18 +93,18 @@ = 68.1584.

                                                                                                                              - + integer_round_outwards

                                                                                                                              This is the default policy: an integer value is returned so that:

                                                                                                                              -
                                                                                                                                -
                                                                                                                              • +
                                                                                                                                  +
                                                                                                                                • Lower quantiles (where the probability is less than 0.5) are rounded down.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Upper quantiles (where the probability is greater than 0.5) are rounded up.
                                                                                                                                • @@ -151,19 +151,19 @@ in each tail.

                                                                                                                                  - + integer_round_inwards

                                                                                                                                  This is the opposite of integer_round_outwards: an integer value is returned so that:

                                                                                                                                  -
                                                                                                                                    -
                                                                                                                                  • +
                                                                                                                                      +
                                                                                                                                    • Lower quantiles (where the probability is less than 0.5) are rounded up.
                                                                                                                                    • -
                                                                                                                                    • +
                                                                                                                                    • Upper quantiles (where the probability is greater than 0.5) are rounded down.
                                                                                                                                    • @@ -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

                                                                                                                                      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 f04745dd3..b7d459145 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 @@ -3,7 +3,7 @@ Error Handling Policies - + @@ -22,7 +22,7 @@

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                                                                                                                                      Error Handling Policies @@ -30,16 +30,16 @@

                                                                                                                                      There are two orthogonal aspects to error handling:

                                                                                                                                      -

                                                                                                                      - + errno_on_error

                                                                                                                      @@ -287,7 +287,7 @@

                                                                                                                      - + ignore_error

                                                                                                                      @@ -400,7 +400,7 @@

                                                                                                                      - + user_error

                                                                                                                      @@ -449,7 +449,7 @@ here.

                                                                                                                      - + Kinds of Error Raised
                                                                                                                      @@ -689,7 +689,7 @@
                                                                                                                      - + Examples

                                                                                                                      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 10b80cedf..30af99787 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 @@ -3,7 +3,7 @@ Internal Promotion Policies - + @@ -22,7 +22,7 @@

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                                                                                                                      Internal Promotion Policies @@ -84,7 +84,7 @@

                                                                                                                      - + Examples

                                                                                                                      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 009cc08b2..ca97978a6 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 @@ -3,7 +3,7 @@ Iteration Limits Policies - + @@ -22,7 +22,7 @@

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                                                                                                                      Iteration Limits Policies 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 2b0e692fc..05e2e6b66 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 @@ -3,7 +3,7 @@ Setting Polices at Namespace Scope - + @@ -22,7 +22,7 @@
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                                                                                                                      Setting Polices at Namespace Scope 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 100d572de..fc4a76ae7 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 @@ -3,7 +3,7 @@ Policy Class Reference - + @@ -22,7 +22,7 @@
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                                                                                                                      Policy Class Reference 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 58a004a30..5c491b51d 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 @@ -3,7 +3,7 @@ Using macros to Change the Policy Defaults - + @@ -22,7 +22,7 @@
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                                                                                                                      Using macros to Change the Policy Defaults @@ -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

                                                                                                                      @@ -91,7 +91,7 @@ ignore_error or user_error.

                                                                                                                      - + BOOST_MATH_ROUNDING_ERROR_POLICY

                                                                                                                      @@ -101,7 +101,7 @@ ignore_error or user_error.

                                                                                                                      - + BOOST_MATH_EVALUATION_ERROR_POLICY

                                                                                                                      @@ -111,7 +111,7 @@ ignore_error or user_error.

                                                                                                                      - + BOOST_MATH_UNDERFLOW_ERROR_POLICY

                                                                                                                      @@ -121,7 +121,7 @@ ignore_error or user_error.

                                                                                                                      - + BOOST_MATH_DENORM_ERROR_POLICY

                                                                                                                      @@ -131,7 +131,7 @@ ignore_error or user_error.

                                                                                                                      - + BOOST_MATH_INDETERMINATE_RESULT_ERROR_POLICY

                                                                                                                      @@ -142,7 +142,7 @@ ignore_error or user_error.

                                                                                                                      - + BOOST_MATH_DIGITS10_POLICY

                                                                                                                      @@ -153,7 +153,7 @@ recommended that you change this from the default.

                                                                                                                      - + BOOST_MATH_PROMOTE_FLOAT_POLICY

                                                                                                                      @@ -165,7 +165,7 @@ off.

                                                                                                                      - + BOOST_MATH_PROMOTE_DOUBLE_POLICY

                                                                                                                      @@ -177,7 +177,7 @@ off.

                                                                                                                      - + BOOST_MATH_DISCRETE_QUANTILE_POLICY

                                                                                                                      @@ -188,7 +188,7 @@ Defaults to integer_round_outwards.

                                                                                                                      - + BOOST_MATH_ASSERT_UNDEFINED_POLICY

                                                                                                                      @@ -201,7 +201,7 @@ whether or not a particular property is well defined.

                                                                                                                      - + BOOST_MATH_MAX_SERIES_ITERATION_POLICY

                                                                                                                      @@ -210,7 +210,7 @@ Defaults to 1000000.

                                                                                                                      - + BOOST_MATH_MAX_ROOT_ITERATION_POLICY

                                                                                                                      @@ -219,7 +219,7 @@ Defaults to 200.

                                                                                                                      - + Example

                                                                                                                      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 1798f7b43..06e9ec1ed 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 @@ -3,7 +3,7 @@ Precision Policies - + @@ -22,7 +22,7 @@

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                                                                                                                      Precision Policies 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 489648d66..7770d8c39 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 @@ -3,7 +3,7 @@ Policy Tutorial - + @@ -22,7 +22,7 @@
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                                                                                                                      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 2f181f215..2ae0b28d0 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 @@ -3,7 +3,7 @@ Setting Policies for Distributions on an Ad Hoc Basis - + @@ -22,7 +22,7 @@
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                                                                                                                      Setting Policies for Distributions on an Ad Hoc Basis 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 3279036e4..3032ca5c7 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 @@ -3,7 +3,7 @@ Changing the Policy on an Ad Hoc Basis for the Special Functions - + @@ -22,7 +22,7 @@
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                                                                                                                      Changing the Policy on an Ad Hoc Basis for the Special Functions 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 851052179..09dfa3529 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 @@ -3,7 +3,7 @@ Changing the Policy Defaults - + @@ -22,7 +22,7 @@
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                                                                                                                      Changing the Policy Defaults @@ -102,14 +102,14 @@

                                                                                                                      That means there are only two safe ways to use these macros:

                                                                                                                      -
                                                                                                                        -
                                                                                                                      • +
                                                                                                                          +
                                                                                                                        • Edit them in boost/math/tools/user.hpp, so that the defaults are set on an installation-wide basis. Unfortunately this may not be convenient if you are using a pre-installed Boost distribution (on Linux for example).
                                                                                                                        • -
                                                                                                                        • +
                                                                                                                        • Set the defines in your project's Makefile or build environment, so that they are set uniformly across all translation units.
                                                                                                                        • @@ -117,7 +117,7 @@

                                                                                                                          What you should not do is:

                                                                                                                          -
                                                                                                                          • +
                                                                                                                            • Set the defines in the source file using #define as doing so almost certainly will break your program, unless you're absolutely certain that the program is restricted to a single translation 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 04ef76f5d..820b6d1b9 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 @@ -3,7 +3,7 @@ Setting Policies at Namespace or Translation Unit Scope - + @@ -22,7 +22,7 @@
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                                                                                                                              Setting Policies at Namespace or Translation Unit Scope @@ -232,14 +232,14 @@ errno = 33

                                                                                                                              -
                                                                                                                                -
                                                                                                                              • +
                                                                                                                                  +
                                                                                                                                • Return infinity on overflow, rather than throwing an exception.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Don't perform any promotion from double to long double internally.
                                                                                                                                • -
                                                                                                                                • +
                                                                                                                                • Return the closest integer result from the quantiles of discrete distributions.
                                                                                                                                • 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 0058e12f6..d7fdb3c21 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 @@ -3,7 +3,7 @@ Policies Have Sensible Defaults - + @@ -22,7 +22,7 @@
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                                                                                                                                  Policies Have Sensible Defaults 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 bac49f33d..796ffb8c6 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 @@ -3,7 +3,7 @@ So How are Policies Used Anyway? - + @@ -22,7 +22,7 @@
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                                                                                                                                  So How are Policies Used Anyway? @@ -30,20 +30,20 @@

                                                                                                                                  The details follow later, but basically policies can be set by either:

                                                                                                                                  -
                                                                                                                                    -
                                                                                                                                  • +
                                                                                                                                      +
                                                                                                                                    • Defining some macros that change the default behaviour: this is the recommended method for setting installation-wide policies.
                                                                                                                                    • -
                                                                                                                                    • +
                                                                                                                                    • By instantiating a distribution object with an explicit policy: this is mainly reserved for ad hoc policy changes.
                                                                                                                                    • -
                                                                                                                                    • +
                                                                                                                                    • By passing a policy to a special function as an optional final argument: this is mainly reserved for ad hoc policy changes.
                                                                                                                                    • -
                                                                                                                                    • +
                                                                                                                                    • By using some helper macros to define a set of functions or distributions in the current namespace that use a specific policy: this is the recommended method for setting policies on a project- or translation-unit-wide 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 6cddc0b0f..f87a1c174 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 @@ -3,7 +3,7 @@ Understanding Quantiles of Discrete Distributions - + @@ -22,7 +22,7 @@
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                                                                                                                                      Understanding Quantiles of Discrete Distributions @@ -53,11 +53,11 @@ As can be seen there is no random variable that corresponds to a probability of exactly 0.05, so we're left with two choices as shown in the figure:

                                                                                                                                      -
                                                                                                                                        -
                                                                                                                                      • +
                                                                                                                                          +
                                                                                                                                        • We could round the result down to 18.
                                                                                                                                        • -
                                                                                                                                        • +
                                                                                                                                        • We could round the result up to 19.
                                                                                                                                        @@ -77,12 +77,12 @@

                                                                                                                                        In coming to an answer we should realise that:

                                                                                                                                        -
                                                                                                                                          -
                                                                                                                                        • +
                                                                                                                                            +
                                                                                                                                          • Calculating an integer result is often much faster than calculating a real-valued result: in fact in our tests it was up to 20 times faster.
                                                                                                                                          • -
                                                                                                                                          • +
                                                                                                                                          • Normally people calculate quantiles so that they can perform a test of some kind: "If the random variable is less than N then we can reject our null-hypothesis with 90% confidence." @@ -177,7 +177,7 @@ base your comparisons on CDF's instead.

                                                                                                                                            - + Other Rounding Policies are Available
                                                                                                                                            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 5ad6474eb..183662c8c 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 @@ -3,7 +3,7 @@ Calling User Defined Error Handlers - + @@ -22,7 +22,7 @@
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                                                                                                                                            Calling User Defined Error Handlers 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 b0031c1c6..8dce32674 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 @@ -3,7 +3,7 @@ So Just What is a Policy Anyway? - + @@ -22,7 +22,7 @@
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                                                                                                                                            So Just What is a Policy Anyway? @@ -32,23 +32,23 @@ special function, or a statistical distribution. With Policies you can control:

                                                                                                                                            -
                                                                                                                                              -
                                                                                                                                            • +
                                                                                                                                                +
                                                                                                                                              • What action to take when an error occurs.
                                                                                                                                              • -
                                                                                                                                              • +
                                                                                                                                              • What happens when you call a function that is mathematically undefined (for example if you ask for the mean of a Cauchy distribution).
                                                                                                                                              • -
                                                                                                                                              • +
                                                                                                                                              • What happens when you ask for a quantile of a discrete distribution.
                                                                                                                                              • -
                                                                                                                                              • +
                                                                                                                                              • Whether the library is allowed to internally promote float to double and double to long double in order to improve precision.
                                                                                                                                              • -
                                                                                                                                              • +
                                                                                                                                              • What precision to use when calculating the result.
                                                                                                                                              diff --git a/doc/sf_and_dist/html/math_toolkit/special.html b/doc/sf_and_dist/html/math_toolkit/special.html index 78caf5ade..b5eda48e0 100644 --- a/doc/sf_and_dist/html/math_toolkit/special.html +++ b/doc/sf_and_dist/html/math_toolkit/special.html @@ -3,7 +3,7 @@ Special Functions - + @@ -22,7 +22,7 @@
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                                                                                                                                              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 eaa41f1fa..f13a5c2a9 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/bessel.html +++ b/doc/sf_and_dist/html/math_toolkit/special/bessel.html @@ -3,7 +3,7 @@ Bessel Functions - + @@ -22,7 +22,7 @@
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                                                                                                                                              -
                                                                                                                                              +
                                                                                                                                              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 6e2eb06f7..71f629e22 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 @@ -3,7 +3,7 @@ Bessel Functions of the First and Second Kinds - + @@ -22,13 +22,13 @@
                                                                                                                                              PrevUpHomeNext
                                                                                                                                              -
                                                                                                                                              +
                                                                                                                                              - + Synopsis
                                                                                                                                              template <class T1, class T2>
                                                                                                                                              @@ -44,7 +44,7 @@
                                                                                                                                               calculated-result-type cyl_neumann(T1 v, T2 x, const Policy&);
                                                                                                                                               
                                                                                                                                              - + Description

                                                                                                                                              @@ -110,7 +110,7 @@

                                                                                                                                              - + 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 36. Errors Rates in cyl_bessel_j

                                                                                                                                              +

                                                                                                                                              Table 36. Errors Rates in cyl_bessel_j

                                                                                                                                              @@ -304,7 +304,7 @@

                                                                                                                                              -

                                                                                                                                              Table 37. Errors Rates in cyl_neumann

                                                                                                                                              +

                                                                                                                                              Table 37. Errors Rates in cyl_neumann

                                                                                                                                              @@ -494,7 +494,7 @@ were found.

                                                                                                                                              - + Implementation

                                                                                                                                              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 464a34a1c..dd0404342 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 @@ -3,7 +3,7 @@ Bessel Function Overview - + @@ -22,13 +22,13 @@

                                                                                                                                              PrevUpHomeNext
                                                                                                                                              -
                                                                                                                                              +
                                                                                                                                              - + 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
                                                                                                                                              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 1dfb3be90..88caa4e70 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 @@ -3,7 +3,7 @@ Modified Bessel Functions of the First and Second Kinds - + @@ -22,13 +22,13 @@
                                                                                                                                              PrevUpHomeNext
                                                                                                                                              -
                                                                                                                                              +
                                                                                                                                              - + Synopsis
                                                                                                                                              template <class T1, class T2>
                                                                                                                                              @@ -44,7 +44,7 @@
                                                                                                                                               calculated-result-type cyl_bessel_k(T1 v, T2 x, const Policy&);
                                                                                                                                               
                                                                                                                                              - + Description

                                                                                                                                              @@ -109,7 +109,7 @@

                                                                                                                                              - + 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 38. Errors Rates in cyl_bessel_i

                                                                                                                                              +

                                                                                                                                              Table 38. Errors Rates in cyl_bessel_i

                                                                                                                                              @@ -226,7 +226,7 @@

                                                                                                                                              -

                                                                                                                                              Table 39. Errors Rates in cyl_bessel_k

                                                                                                                                              +

                                                                                                                                              Table 39. Errors Rates in cyl_bessel_k

                                                                                                                                              @@ -326,7 +326,7 @@

                                                                                                                                              - + Implementation

                                                                                                                                              @@ -344,13 +344,13 @@ The 0 and 1 cases use minimax rational approximations on finite and infinite intervals. The coefficients are from:

                                                                                                                                              -
                                                                                                                                                -
                                                                                                                                              • +
                                                                                                                                                  +
                                                                                                                                                • J.M. Blair and C.A. Edwards, Stable rational minimax approximations to the modified Bessel functions I_0(x) and I_1(x), Atomic Energy of Canada Limited Report 4928, Chalk River, 1974.
                                                                                                                                                • -
                                                                                                                                                • +
                                                                                                                                                • S. Moshier, Methods and Programs for Mathematical Functions, Ellis Horwood Ltd, Chichester, 1989.
                                                                                                                                                • 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 01b150f94..7d8ded2f4 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 @@ -3,7 +3,7 @@ Spherical Bessel Functions of the First and Second Kinds - + @@ -22,13 +22,13 @@
                                                                                                                                                  PrevUpHomeNext
                                                                                                                                                  -
                                                                                                                                                  +
                                                                                                                                                  - + Synopsis
                                                                                                                                                  template <class T1, class T2>
                                                                                                                                                  @@ -44,7 +44,7 @@
                                                                                                                                                   calculated-result-type sph_neumann(unsigned v, T2 x, const Policy&);
                                                                                                                                                   
                                                                                                                                                  - + Description

                                                                                                                                                  @@ -97,7 +97,7 @@ for small x:

                                                                                                                                                  - + 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

                                                                                                                                                  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 cc6d4bf62..05d7a60bc 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/ellint.html +++ b/doc/sf_and_dist/html/math_toolkit/special/ellint.html @@ -3,7 +3,7 @@ Elliptic Integrals - + @@ -22,7 +22,7 @@

                                                                                                                                                  PrevUpHomeNext
                                                                                                                                                  -
                                                                                                                                                  +
                                                                                                                                                  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 e81a8c654..d4198c5c9 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 @@ -3,7 +3,7 @@ Elliptic Integrals of the First Kind - Legendre Form - + @@ -22,13 +22,13 @@
                                                                                                                                                  PrevUpHomeNext
                                                                                                                                                  -
                                                                                                                                                  +
                                                                                                                                                  - + Synopsis

                                                                                                                                                  @@ -55,7 +55,7 @@ }} // namespaces

                                                                    - + Description

                                                                    @@ -123,7 +123,7 @@

                                                                    - + Accuracy

                                                                    @@ -134,7 +134,7 @@ All values are relative errors in units of epsilon.

                                                                    -

                                                                    Table 41. Errors Rates in the Elliptic Integrals of the First Kind

                                                                    +

                                                                    Table 41. Errors Rates in the Elliptic Integrals of the First Kind

                                                                    @@ -235,7 +235,7 @@

                                                                    - + Testing

                                                                    @@ -245,7 +245,7 @@ this implementation.

                                                                    - + Implementation

                                                                    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 1aa7c0932..a0b4f0631 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 @@ -3,7 +3,7 @@ Elliptic Integrals of the Second Kind - Legendre Form - + @@ -22,13 +22,13 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    - + Description

                                                                    @@ -123,7 +123,7 @@

                                                                    - + Accuracy

                                                                    @@ -134,7 +134,7 @@ All values are relative errors in units of epsilon.

                                                                    -

                                                                    Table 42. Errors Rates in the Elliptic Integrals of the Second Kind

                                                                    +

                                                                    Table 42. Errors Rates in the Elliptic Integrals of the Second Kind

                                                                    @@ -235,7 +235,7 @@

                                                                    - + Testing

                                                                    @@ -245,7 +245,7 @@ this implementation.

                                                                    - + Implementation

                                                                    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 0f577cd85..67a9e6d0d 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 @@ -3,7 +3,7 @@ Elliptic Integrals of the Third Kind - Legendre Form - + @@ -22,13 +22,13 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    - + Synopsis

                                                                    @@ -55,7 +55,7 @@ }} // namespaces

                                                                    - + Description

                                                                    @@ -129,7 +129,7 @@

                                                                    - + Accuracy

                                                                    @@ -140,7 +140,7 @@ All values are relative errors in units of epsilon.

                                                                    -

                                                                    Table 43. Errors Rates in the Elliptic Integrals of the Third Kind

                                                                    +

                                                                    Table 43. Errors Rates in the Elliptic Integrals of the Third Kind

                                                                    @@ -241,7 +241,7 @@

                                                                    - + Testing

                                                                    @@ -251,7 +251,7 @@ this implementation.

                                                                    - + Implementation

                                                                    @@ -288,7 +288,7 @@ Π(n, φ+mπ, k) = Π(n, φ, k) + 2mΠ(n, k) ; n <= 1

                                                                    - Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1 [1] + Π(n, φ+mπ, k) = Π(n, φ, k) ; n > 1 [1]

                                                                    are used to move φ to the range [0, π/2]. @@ -308,7 +308,7 @@



                                                                    -

                                                                    [1] +

                                                                    [1] I haven't been able to find a literature reference for this relation, but it appears to be the convention used by Mathematica. Intuitively the first 2 * m * Π(n, k) terms cancel out as the 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 9442b2c1d..9f0c1c449 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 @@ -3,7 +3,7 @@ Elliptic Integrals - Carlson Form - + @@ -22,13 +22,13 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    - + Synopsis

                                                                    @@ -100,7 +100,7 @@ }} // namespaces

                                                                    - + Description

                                                                    @@ -236,7 +236,7 @@

                                                                    - + Testing

                                                                    @@ -259,7 +259,7 @@ to verify their correctness: see the above Carlson paper for details.

                                                                    - + Accuracy

                                                                    @@ -270,7 +270,7 @@ All values are relative errors in units of epsilon.

                                                                    -

                                                                    Table 40. Errors Rates in the Carlson Elliptic Integrals

                                                                    +

                                                                    Table 40. Errors Rates in the Carlson Elliptic Integrals

                                                                    @@ -413,7 +413,7 @@

                                                                    - + Implementation

                                                                    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 2fd03ae66..8a439bcee 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 @@ -3,7 +3,7 @@ Elliptic Integral Overview - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +

                                                                    Elliptic Integral Overview @@ -49,14 +49,14 @@ Elliptic integral.

                                                                    - + Notation

                                                                    All variables are real numbers unless otherwise noted.

                                                                    - + Definition

                                                                    @@ -245,7 +245,7 @@

                                                                    - + Duplication Theorem
                                                                    @@ -257,7 +257,7 @@

                                                                    - + Carlson's Formulas
                                                                    @@ -275,7 +275,7 @@

                                                                    - + Numerical Algorithms
                                                                    @@ -289,7 +289,7 @@ integrals with satisfactory precisions.

                                                                    - + References

                                                                    @@ -302,63 +302,63 @@

                                                                    However the main references are:

                                                                    -
                                                                      -
                                                                    1. +
                                                                        +
                                                                      1. M. Abramowitz and I. A. Stegun (Eds.) (1964) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, U.S. Government Printing Office, Washington, D.C.
                                                                      2. -
                                                                      3. +
                                                                      4. B.C. Carlson, Computing elliptic integrals by duplication, Numerische Mathematik, vol 33, 1 (1979).
                                                                      5. -
                                                                      6. +
                                                                      7. B.C. Carlson, Elliptic Integrals of the First Kind, SIAM Journal on Mathematical Analysis, vol 8, 231 (1977).
                                                                      8. -
                                                                      9. +
                                                                      10. B.C. Carlson, Short Proofs of Three Theorems on Elliptic Integrals, SIAM Journal on Mathematical Analysis, vol 9, 524 (1978).
                                                                      11. -
                                                                      12. +
                                                                      13. B.C. Carlson and E.M. Notis, ALGORITHM 577: Algorithms for Incomplete Elliptic Integrals, ACM Transactions on Mathematmal Software, vol 7, 398 (1981).
                                                                      14. -
                                                                      15. +
                                                                      16. B. C. Carlson, On computing elliptic integrals and functions. J. Math. and Phys., 44 (1965), pp. 36-51.
                                                                      17. -
                                                                      18. +
                                                                      19. B. C. Carlson, A table of elliptic integrals of the second kind. Math. Comp., 49 (1987), pp. 595-606. (Supplement, ibid., pp. S13-S17.)
                                                                      20. -
                                                                      21. +
                                                                      22. B. C. Carlson, A table of elliptic integrals of the third kind. Math. Comp., 51 (1988), pp. 267-280. (Supplement, ibid., pp. S1-S5.)
                                                                      23. -
                                                                      24. +
                                                                      25. B. C. Carlson, A table of elliptic integrals: cubic cases. Math. Comp., 53 (1989), pp. 327-333.
                                                                      26. -
                                                                      27. +
                                                                      28. B. C. Carlson, A table of elliptic integrals: one quadratic factor. Math. Comp., 56 (1991), pp. 267-280.
                                                                      29. -
                                                                      30. +
                                                                      31. B. C. Carlson, A table of elliptic integrals: two quadratic factors. Math. Comp., 59 (1992), pp. 165-180.
                                                                      32. -
                                                                      33. +
                                                                      34. B. C. Carlson, Numerical computation of real or complex elliptic integrals. Numerical Algorithms, Volume 10, Number 1 / March, 1995, p13-26.
                                                                      35. -
                                                                      36. +
                                                                      37. B. C. Carlson and John L. Gustafson, Asymptotic Approximations for Symmetric Elliptic Integrals, SIAM Journal on Mathematical Analysis, Volume 25, Issue 2 (March 1994), @@ -369,21 +369,21 @@ The following references, while not directly relevent to our implementation, may also be of interest:

                                                                        -
                                                                          -
                                                                        1. +
                                                                            +
                                                                          1. R. Burlisch, Numerical Compuation of Elliptic Integrals and Elliptic Functions. Numerical Mathematik 7, 78-90.
                                                                          2. -
                                                                          3. +
                                                                          4. R. Burlisch, An extension of the Bartky Transformation to Incomplete Elliptic Integrals of the Third Kind. Numerical Mathematik 13, 266-284.
                                                                          5. -
                                                                          6. +
                                                                          7. R. Burlisch, Numerical Compuation of Elliptic Integrals and Elliptic Functions. III. Numerical Mathematik 13, 305-315.
                                                                          8. -
                                                                          9. +
                                                                          10. T. Fukushima and H. Ishizaki, Numerical Computation of Incomplete Elliptic Integrals of a General Form. Celestial Mechanics and Dynamical Astronomy, Volume 59, Number 3 / diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint.html b/doc/sf_and_dist/html/math_toolkit/special/expint.html index a94a454ce..bb8255cf8 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint.html @@ -3,7 +3,7 @@ Exponential Integrals - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html index 1c9a62e78..92fbf5181 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_i.html @@ -3,7 +3,7 @@ Exponential Integral Ei - + @@ -22,13 +22,13 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + Synopsis

                                                                            @@ -63,7 +63,7 @@

                                                                            - + Description
                                                                            template <class T>
                                                                            @@ -83,7 +83,7 @@
                                                                                       
                                                                                     

                                                                            - + Accuracy

                                                                            @@ -95,7 +95,7 @@ error.

                                                                            -

                                                                            Table 46. Errors In the Function expint(z)

                                                                            +

                                                                            Table 46. Errors In the Function expint(z)

                                                                            @@ -207,7 +207,7 @@ slightly over the range [4,6].

                                                                            - + Testing

                                                                            @@ -222,7 +222,7 @@ check.

                                                                            - + Implementation

                                                                            @@ -252,7 +252,7 @@ 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 [2] experienced the same issue and converted the polynomials into + Cody and Thacher [2] 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]. @@ -282,7 +282,7 @@



                                                                            -

                                                                            [2] +

                                                                            [2] W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for the exponential integral E1(x), Math. Comp. 22 (1968), 641-649, and W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for the exponential diff --git a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html index 2ae7040d7..c9fcd1d28 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html +++ b/doc/sf_and_dist/html/math_toolkit/special/expint/expint_n.html @@ -3,7 +3,7 @@ Exponential Integral En - + @@ -22,13 +22,13 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + Synopsis

                                                                            @@ -63,7 +63,7 @@

                                                                            - + Description
                                                                            template <class T>
                                                                            @@ -83,7 +83,7 @@
                                                                                       
                                                                                     

                                                                            - + Accuracy

                                                                            @@ -94,7 +94,7 @@ the one shown will have effectively zero error.

                                                                            -

                                                                            Table 45. Errors In the Function expint(n, z)

                                                                            +

                                                                            Table 45. Errors In the Function expint(n, z)

                                                                            @@ -225,7 +225,7 @@

                                                                            - + Testing

                                                                            @@ -240,7 +240,7 @@ check.

                                                                            - + Implementation

                                                                            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 173e570bf..6fcb189ab 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/factorials.html +++ b/doc/sf_and_dist/html/math_toolkit/special/factorials.html @@ -3,7 +3,7 @@ Factorials and Binomial Coefficients - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Factorials and Binomial Coefficients 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 3ba95d0ba..da48cf4a7 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 @@ -3,7 +3,7 @@ Binomial Coefficients - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Binomial Coefficients @@ -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

                                                                            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 abfed9d7e..e91c09ed1 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 @@ -3,7 +3,7 @@ Double Factorial - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Double Factorial @@ -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

                                                                            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 0fa2c8dfe..7334fb9c5 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 @@ -3,7 +3,7 @@ Factorial - + @@ -22,12 +22,12 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + 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

                                                                            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 d5e5d2162..5af3fe5bf 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 @@ -3,7 +3,7 @@ Falling Factorial - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Falling Factorial @@ -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

                                                                            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 f032542ff..cd61ad3d5 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 @@ -3,7 +3,7 @@ Rising Factorial - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Rising Factorial @@ -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

                                                                            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 26e7c5a77..0f0408d82 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 @@ -3,7 +3,7 @@ Inverse Hyperbolic Functions - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            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 ffdadde4f..a774cc4fb 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 @@ -3,7 +3,7 @@ acosh - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            @@ -67,14 +67,14 @@

                                                                            - + Accuracy

                                                                            Generally accuracy is to within 1 or 2 epsilon across all supported platforms.

                                                                            - + Testing

                                                                            @@ -90,7 +90,7 @@ to at least 50 decimal digits.

                                                                            - + Implementation

                                                                            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 be431886a..b60db5d3f 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 @@ -3,7 +3,7 @@ asinh - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            @@ -62,14 +62,14 @@

                                                                            - + Accuracy

                                                                            Generally accuracy is to within 1 or 2 epsilon across all supported platforms.

                                                                            - + Testing

                                                                            @@ -85,7 +85,7 @@ to at least 50 decimal digits.

                                                                            - + Implementation

                                                                            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 276163722..b14767590 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 @@ -3,7 +3,7 @@ atanh - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            @@ -76,14 +76,14 @@ denoting

                                                                            - + Accuracy

                                                                            Generally accuracy is to within 1 or 2 epsilon across all supported platforms.

                                                                            - + Testing

                                                                            @@ -99,7 +99,7 @@ denoting to at least 50 decimal digits.

                                                                            - + Implementation

                                                                            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 8fc49f4d8..53a2a5049 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 @@ -3,7 +3,7 @@ Inverse Hyperbolic Functions Overview - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Inverse Hyperbolic Functions Overview 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 036ce8d3b..b89ac43e1 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers.html @@ -3,7 +3,7 @@ Logs, Powers, Roots and Exponentials - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Logs, Powers, Roots and Exponentials 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 a662d031f..a13215279 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 @@ -3,7 +3,7 @@ cbrt - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            @@ -71,7 +71,7 @@

                                                                            - + Accuracy

                                                                            @@ -79,7 +79,7 @@ should have approximately 2 epsilon accuracy.

                                                                            - + Testing

                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html index be57dff51..7e2f3404a 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html +++ b/doc/sf_and_dist/html/math_toolkit/special/powers/ct_pow.html @@ -3,7 +3,7 @@ Compile Time Power of a Runtime Base - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Compile Time Power of a Runtime Base @@ -32,7 +32,7 @@ computes the compile-time integral power of a run-time base.

                                                                            - + Synopsis

                                                                            @@ -49,7 +49,7 @@ }}

                                                                            - + Rationale and Usage
                                                                            @@ -91,28 +91,28 @@ Only 3 different products were actually computed.

                                                                            - + Return Type

                                                                            The return type of these functions is computed using the result type calculation rules. For example:

                                                                            -
                                                                    - + Acknowledgements

                                                                    @@ -243,7 +243,7 @@ improving the implementation.

                                                                    - + References

                                                                    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 67317187e..d0681b470 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 @@ -3,7 +3,7 @@ expm1 - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    @@ -80,7 +80,7 @@

                                                                    - + Accuracy

                                                                    @@ -88,7 +88,7 @@ should have approximately 1 epsilon accuracy.

                                                                    - + Testing

                                                                    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 ae9f1e2aa..2fe8780fc 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 @@ -3,7 +3,7 @@ hypot - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    @@ -58,7 +58,7 @@ in such a representable.

                                                                    - + Implementation

                                                                    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 7e07556f0..4b1c0e163 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 @@ -3,7 +3,7 @@ log1p - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    @@ -93,7 +93,7 @@

                                                                    - + Accuracy

                                                                    @@ -101,7 +101,7 @@ should have approximately 1 epsilon accuracy.

                                                                    - + Testing

                                                                    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 0051989d3..fbee54eda 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 @@ -3,7 +3,7 @@ powm1 - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    @@ -74,14 +74,14 @@

                                                                    - + Accuracy

                                                                    Should have approximately 2-3 epsilon accuracy.

                                                                    - + Testing

                                                                    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 483ddb66e..01e60e712 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 @@ -3,7 +3,7 @@ sqrt1pm1 - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    @@ -76,7 +76,7 @@

                                                                    - + Accuracy

                                                                    @@ -84,7 +84,7 @@ should have approximately 3 epsilon accuracy.

                                                                    - + Testing

                                                                    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 a961debca..4b2371946 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 @@ -3,7 +3,7 @@ Beta Functions - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    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 02ea8c784..8cfb12771 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 @@ -3,7 +3,7 @@ Derivative of the Incomplete Beta Function - + @@ -22,13 +22,13 @@
                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    - + Synopsis

                                                                    @@ -49,7 +49,7 @@ }} // namespaces

                                                                    - + Description

                                                                    @@ -76,14 +76,14 @@

                                                                    - + Accuracy

                                                                    Almost identical to the incomplete beta function ibeta.

                                                                    - + Implementation

                                                                    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 c3d014317..9f1e5e0be 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 @@ -3,7 +3,7 @@ Beta - + @@ -22,12 +22,12 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    - + Synopsis

                                                                    @@ -48,7 +48,7 @@ }} // namespaces

                                                                    - + Description

                                                                    @@ -86,7 +86,7 @@ type calculation rules when T1 and T2 are different types.

                                                                    - + Accuracy

                                                                    @@ -98,7 +98,7 @@ zero error.

                                                                    -

                                                                    Table 22. Peak Errors In the Beta Function

                                                                    +

                                                                    Table 22. Peak Errors In the Beta Function

                                                                    @@ -244,7 +244,7 @@ very small.

                                                                    - + Testing

                                                                    @@ -253,7 +253,7 @@ at 1000-bit precision.

                                                                    - + Implementation

                                                                    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 2d47db16e..282dafc9c 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 @@ -3,7 +3,7 @@ Incomplete Beta Functions - + @@ -22,13 +22,13 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +
                                                                    - + Synopsis

                                                                    @@ -67,7 +67,7 @@ }} // namespaces

                                                                    - + Description

                                                                    @@ -163,7 +163,7 @@

                                                                    - + Accuracy

                                                                    @@ -182,7 +182,7 @@ with the wider exponent range of the long double types.

                                                                    -

                                                                    Table 23. Errors In the Function ibeta(a,b,x)

                                                                    +

                                                                    Table 23. Errors In the Function ibeta(a,b,x)

                                                                    @@ -369,7 +369,7 @@

                                                                    -

                                                                    Table 24. Errors In the Function ibetac(a,b,x)

                                                                    +

                                                                    Table 24. Errors In the Function ibetac(a,b,x)

                                                                    @@ -536,7 +536,7 @@

                                                                    -

                                                                    Table 25. Errors In the Function beta(a, b, x)

                                                                    +

                                                                    Table 25. Errors In the Function beta(a, b, x)

                                                                    @@ -703,7 +703,7 @@

                                                                    -

                                                                    Table 26. Errors In the Function betac(a,b,x)

                                                                    +

                                                                    Table 26. Errors In the Function betac(a,b,x)

                                                                    @@ -870,7 +870,7 @@

                                                                    - + Testing

                                                                    @@ -888,7 +888,7 @@ have test data that is fully independent of the code.

                                                                    - + Implementation

                                                                    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 ed78dcc8a..d04d0bea3 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 @@ -3,7 +3,7 @@ The Incomplete Beta Function Inverses - + @@ -22,7 +22,7 @@

                                                                    PrevUpHomeNext
                                                                    -
                                                                    +

                                                                    The Incomplete Beta Function Inverses @@ -87,7 +87,7 @@ }} // namespaces

                                                                    - + Description

                                                                    @@ -323,7 +323,7 @@

                                                                    - + Accuracy

                                                                    @@ -335,14 +335,14 @@ or 1.

                                                                    - + Testing

                                                                    There are two sets of tests:

                                                                    -
                                                                      -
                                                                    • +
                                                                        +
                                                                      • Basic sanity checks attempt to "round-trip" from a, b and x to p or q and back again. These tests have quite generous @@ -353,13 +353,13 @@ enough "information content" in the input to the inverse function to get back where you started.
                                                                      • -
                                                                      • +
                                                                      • Accuracy checks using high precision test values. These measure the accuracy of the result, given exact input values.
                                                                      - + 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
                                                                      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 277ce3b66..e0fba27a1 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 @@ -3,7 +3,7 @@ Error Functions - + @@ -22,7 +22,7 @@
                                                                      PrevUpHomeNext
                                                                      -
                                                                      +
                                                                      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 c9072bcdd..188d1ac3c 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 @@ -3,7 +3,7 @@ Error Functions - + @@ -22,13 +22,13 @@
                                                                      PrevUpHomeNext
                                                                      -
                                                                      +
                                                                      - + Synopsis

                                                                      @@ -69,7 +69,7 @@

                                                                      - + Description
                                                                      template <class T>
                                                                      @@ -106,7 +106,7 @@
                                                                                 
                                                                               

                                                                      - + Accuracy

                                                                      @@ -119,7 +119,7 @@ the one shown will have effectively zero error.

                                                                      -

                                                                      Table 27. Errors In the Function erf(z)

                                                                      +

                                                                      Table 27. Errors In the Function erf(z)

                                                                      @@ -325,7 +325,7 @@

                                                                      -

                                                                      Table 28. Errors In the Function erfc(z)

                                                                      +

                                                                      Table 28. Errors In the Function erfc(z)

                                                                      @@ -531,7 +531,7 @@

                                                                      - + Testing

                                                                      @@ -546,7 +546,7 @@ check.

                                                                      - + Implementation

                                                                      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 450d830d7..d28dc1a4d 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 @@ -3,7 +3,7 @@ Error Function Inverses - + @@ -22,13 +22,13 @@

                                                                      PrevUpHomeNext
                                                                      -
                                                                      +
                                                                      - + Synopsis

                                                                      @@ -69,7 +69,7 @@

                                                                      - + Description
                                                                      template <class T>
                                                                      @@ -103,7 +103,7 @@
                                                                                 
                                                                               

                                                                      - + Accuracy

                                                                      @@ -113,14 +113,14 @@ error functions.

                                                                      - + Testing

                                                                      There are two sets of tests:

                                                                      -
                                                                        -
                                                                      • +
                                                                          +
                                                                        • Basic sanity checks attempt to "round-trip" from x to p and back again. These tests have quite generous tolerances: in general both the error functions and their inverses @@ -130,13 +130,13 @@ enough "information content" in the input to the inverse function to get back where you started.
                                                                        • -
                                                                        • +
                                                                        • Accuracy checks using high-precision test values. These measure the accuracy of the result, given exact input values.
                                                                        - + Implementation

                                                                        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 f93a7ec36..e3daa616a 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 @@ -3,7 +3,7 @@ Gamma Functions - + @@ -22,7 +22,7 @@

                                                                        PrevUpHomeNext
                                                                        -
                                                                        +
                                                                        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 e65a5b862..e48fa47b7 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 @@ -3,7 +3,7 @@ Digamma - + @@ -22,12 +22,12 @@
                                                                        PrevUpHomeNext
                                                                        -
                                                                        +
                                                                        - + Synopsis

                                                                        @@ -48,7 +48,7 @@ }} // namespaces

                                                                      - + Description

                                                                      @@ -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

                                                                      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 689a87584..ec31e5fea 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 @@ -3,7 +3,7 @@ Derivative of the Incomplete Gamma Function - + @@ -22,13 +22,13 @@

                                                                      PrevUpHomeNext
                                                                      -
                                                                      +
                                                                      - + 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

                                                                      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 267ce4bc4..b975ef675 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 @@ -3,7 +3,7 @@ Ratios of Gamma Functions - + @@ -22,7 +22,7 @@

                                                                      PrevUpHomeNext
                                                                      -
                                                                      +

                                                                      Ratios of Gamma Functions @@ -51,7 +51,7 @@ }} // namespaces

                                                                      - + Description
                                                                      template <class T1, class T2> 
                                                                      @@ -117,7 +117,7 @@
                                                                                 
                                                                               

                                                                      - + Accuracy

                                                                      @@ -127,7 +127,7 @@ effectively zero error.

                                                                      -

                                                                      Table 16. Errors In the Function tgamma_delta_ratio(a, delta)

                                                                      +

                                                                      Table 16. Errors In the Function tgamma_delta_ratio(a, delta)

                                                                      @@ -230,7 +230,7 @@

                                                                      -

                                                                      Table 17. Errors In the Function tgamma_ratio(a, b)

                                                                      +

                                                                      Table 17. Errors In the Function tgamma_ratio(a, b)

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

                                                                      - + Testing

                                                                      @@ -336,7 +336,7 @@ a deliberately naive calculation of Γ(x)/Γ(y).

                                                                      - + Implementation

                                                                      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 3effd02a3..240fc1f2f 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 @@ -3,7 +3,7 @@ Incomplete Gamma Functions - + @@ -22,13 +22,13 @@

                                                                      PrevUpHomeNext
                                                                      -
                                                                      +
                                                                      - + Synopsis

                                                                      @@ -67,7 +67,7 @@ }} // namespaces

                                                                      - + Description

                                                                      @@ -160,7 +160,7 @@

                                                                      - + Accuracy

                                                                      @@ -185,7 +185,7 @@ All values are in units of epsilon.

                                                                      -

                                                                      Table 18. Errors In the Function gamma_p(a,z)

                                                                      +

                                                                      Table 18. Errors In the Function gamma_p(a,z)

                                                                      @@ -372,7 +372,7 @@

                                                                      -

                                                                      Table 19. Errors In the Function gamma_q(a,z)

                                                                      +

                                                                      Table 19. Errors In the Function gamma_q(a,z)

                                                                      @@ -558,7 +558,7 @@

                                                                      -

                                                                      Table 20. Errors In the Function tgamma_lower(a,z)

                                                                      +

                                                                      Table 20. Errors In the Function tgamma_lower(a,z)

                                                                      @@ -693,7 +693,7 @@

                                                                      -

                                                                      Table 21. Errors In the Function tgamma(a,z)

                                                                      +

                                                                      Table 21. 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

                                                                      @@ -1013,24 +1013,24 @@ by Temme (see references below).

                                                                      - + References
                                                                      -
                                                                        -
                                                                      • +
                                                                          +
                                                                        • N. M. Temme, A Set of Algorithms for the Incomplete Gamma Functions, Probability in the Engineering and Informational Sciences, 8, 1994.
                                                                        • -
                                                                        • +
                                                                        • N. M. Temme, The Asymptotic Expansion of the Incomplete Gamma Functions, Siam J. Math Anal. Vol 10 No 4, July 1979, p757.
                                                                        • -
                                                                        • +
                                                                        • A. R. Didonato and A. H. Morris, Computation of the Incomplete Gamma Function Ratios and their Inverse. ACM TOMS, Vol 12, No 4, Dec 1986, p377.
                                                                        • -
                                                                        • +
                                                                        • W. Gautschi, The Incomplete Gamma Functions Since Tricomi, In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei, Roma, 1998, pp. 203--237. 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 23950b9e2..b7236c316 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 @@ -3,7 +3,7 @@ Incomplete Gamma Function Inverses - + @@ -22,13 +22,13 @@
                                                                          PrevUpHomeNext
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                                                                          - + Synopsis

                                                                          @@ -67,7 +67,7 @@ }} // namespaces

                                                                          - + Description

                                                                          @@ -173,7 +173,7 @@ 0.

                                                                          - + Accuracy

                                                                          @@ -187,14 +187,14 @@ functions.

                                                                          - + Testing

                                                                          There are two sets of tests:

                                                                          -
                                                                            -
                                                                          • +
                                                                              +
                                                                            • Basic sanity checks attempt to "round-trip" from a and x to p or q and back again. These tests have quite generous tolerances: in general @@ -205,13 +205,13 @@ content" in the input to the inverse function to get back where you started.
                                                                            • -
                                                                            • +
                                                                            • Accuracy checks using high precision test values. These measure the accuracy of the result, given exact input values.
                                                                            - + Implementation

                                                                            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 a7a6d5b84..bb319aa4d 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 @@ -3,7 +3,7 @@ Log Gamma - + @@ -22,12 +22,12 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + Synopsis

                                                                            @@ -54,7 +54,7 @@ }} // namespaces

                                                                            - + Description

                                                                            @@ -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

                                                                            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 8cca0df30..6daf27ff3 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 @@ -3,7 +3,7 @@ Gamma - + @@ -22,12 +22,12 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + Synopsis

                                                                            @@ -54,7 +54,7 @@ }} // namespaces

                                                                            - + Description
                                                                            template <class T>
                                                                            @@ -129,7 +129,7 @@
                                                                             

                                                                            - + Accuracy

                                                                            @@ -384,7 +384,7 @@

                                                                            - + Testing

                                                                            @@ -399,7 +399,7 @@ a lanczos approximation accurate to around 100 decimal digits.

                                                                            - + Implementation

                                                                            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 c44ed8098..25ba62ac9 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 @@ -3,7 +3,7 @@ Polynomials - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            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 d19e0e26b..69e78664a 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 @@ -3,7 +3,7 @@ Hermite Polynomials - + @@ -22,12 +22,12 @@
                                                                            PrevUpHomeNext
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                                                                            - + Synopsis

                                                                            @@ -51,7 +51,7 @@ }} // namespaces

                                                                            - + Description

                                                                            @@ -136,7 +136,7 @@

                                                                            - + Accuracy

                                                                            @@ -146,7 +146,7 @@ zero error.

                                                                            -

                                                                            Table 34. Peak Errors In the Hermite Polynomial

                                                                            +

                                                                            Table 34. Peak Errors In the Hermite Polynomial

                                                                            @@ -253,7 +253,7 @@ is very close to a root.

                                                                            - + Testing

                                                                            @@ -263,7 +263,7 @@ precision.

                                                                            - + Implementation

                                                                            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 1e0b06ec6..413512ac7 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 @@ -3,7 +3,7 @@ Laguerre (and Associated) Polynomials - + @@ -22,13 +22,13 @@

                                                                            PrevUpHomeNext
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                                                                            +
                                                                            - + Synopsis

                                                                            @@ -62,7 +62,7 @@ }} // namespaces

                                                                            - + Description

                                                                            @@ -210,7 +210,7 @@

                                                                            - + Accuracy

                                                                            @@ -220,7 +220,7 @@ zero error.

                                                                            -

                                                                            Table 32. Peak Errors In the Laguerre Polynomial

                                                                            +

                                                                            Table 32. Peak Errors In the Laguerre Polynomial

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

                                                                            -

                                                                            Table 33. Peak Errors In the Associated Laguerre Polynomial

                                                                            +

                                                                            Table 33. Peak Errors In the Associated Laguerre Polynomial

                                                                            @@ -427,7 +427,7 @@ is very close to a root.

                                                                            - + Testing

                                                                            @@ -437,7 +437,7 @@ precision.

                                                                            - + Implementation

                                                                            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 2094ebae3..27c280c4c 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 @@ -3,7 +3,7 @@ Legendre (and Associated) Polynomials - + @@ -22,13 +22,13 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + Synopsis

                                                                            @@ -84,7 +84,7 @@

                                                                            - + Description
                                                                            template <class T>
                                                                            @@ -292,7 +292,7 @@
                                                                             
                                                                             
                                                                            - + Accuracy

                                                                            @@ -302,7 +302,7 @@ zero error.

                                                                            -

                                                                            Table 29. Peak Errors In the Legendre P Function

                                                                            +

                                                                            Table 29. Peak Errors In the Legendre P Function

                                                                            @@ -431,7 +431,7 @@

                                                                            -

                                                                            Table 30. Peak Errors In the Associated Legendre P Function

                                                                            +

                                                                            Table 30. Peak Errors In the Associated Legendre P Function

                                                                            @@ -531,7 +531,7 @@

                                                                            -

                                                                            Table 31. Peak Errors In the Legendre Q Function

                                                                            +

                                                                            Table 31. Peak Errors In the Legendre Q Function

                                                                            @@ -673,7 +673,7 @@ given here.

                                                                            - + Testing

                                                                            @@ -683,7 +683,7 @@ precision.

                                                                            - + Implementation

                                                                            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 fb168def3..446ce9edf 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 @@ -3,7 +3,7 @@ Spherical Harmonics - + @@ -22,12 +22,12 @@

                                                                            PrevUpHomeNext
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                                                                            +
                                                                            - + Synopsis

                                                                            @@ -60,7 +60,7 @@ }} // namespaces

                                                                            - + Description

                                                                            @@ -155,7 +155,7 @@

                                                                            - + Accuracy

                                                                            @@ -170,7 +170,7 @@ All values are in units of epsilon.

                                                                            -

                                                                            Table 35. Peak Errors In the Sperical Harmonic Functions

                                                                            +

                                                                            Table 35. 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

                                                                            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 a766086bc..3bb9b8771 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/sinc.html +++ b/doc/sf_and_dist/html/math_toolkit/special/sinc.html @@ -3,7 +3,7 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Sinus Cardinal and Hyperbolic Sinus Cardinal Functions 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 c807c044d..89ab4eeca 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 @@ -3,7 +3,7 @@ Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview 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 0728ea740..5cde6093f 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 @@ -3,7 +3,7 @@ sinc_pi - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            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 9071aca70..12e757ae1 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 @@ -3,7 +3,7 @@ sinhc_pi - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas.html b/doc/sf_and_dist/html/math_toolkit/special/zetas.html index cd5cab3d5..06f5af539 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas.html @@ -3,7 +3,7 @@ Zeta Functions - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html index cb3a6c75c..abaaa0264 100644 --- a/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html +++ b/doc/sf_and_dist/html/math_toolkit/special/zetas/zeta.html @@ -3,7 +3,7 @@ Riemann Zeta Function - + @@ -22,12 +22,12 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + Synopsis

                                                                            @@ -62,7 +62,7 @@

                                                                            - + Description
                                                                            template <class T>
                                                                            @@ -85,7 +85,7 @@
                                                                                       
                                                                                     

                                                                            - + Accuracy

                                                                            @@ -97,7 +97,7 @@ shown will have effectively zero error.

                                                                            -

                                                                            Table 44. Errors In the Function zeta(z)

                                                                            +

                                                                            Table 44. Errors In the Function zeta(z)

                                                                            @@ -234,7 +234,7 @@

                                                                            - + Testing

                                                                            @@ -249,7 +249,7 @@ check.

                                                                            - + Implementation

                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/status.html b/doc/sf_and_dist/html/math_toolkit/status.html index 8a8d1e608..7c2349ade 100644 --- a/doc/sf_and_dist/html/math_toolkit/status.html +++ b/doc/sf_and_dist/html/math_toolkit/status.html @@ -3,7 +3,7 @@ Library Status - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            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 83c518c38..2d24d4a38 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/compilers.html +++ b/doc/sf_and_dist/html/math_toolkit/status/compilers.html @@ -3,7 +3,7 @@ Compilers - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
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                                                                            @@ -37,7 +37,7 @@

                                                                            -

                                                                            Table 55. Supported/Tested Compilers

                                                                            +

                                                                            Table 55. Supported/Tested Compilers

                                                                            @@ -549,7 +549,7 @@


                                                                            -

                                                                            Table 56. Unsupported Compilers

                                                                            +

                                                                            Table 56. Unsupported Compilers

                                                                            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 cf9c57680..218689e5a 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/credits.html +++ b/doc/sf_and_dist/html/math_toolkit/status/credits.html @@ -3,7 +3,7 @@ Credits and Acknowledgements - + @@ -21,7 +21,7 @@
                                                                            PrevUpHome
                                                                            -
                                                                            +
                                                                            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 b4e352915..b7f74f816 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/history1.html +++ b/doc/sf_and_dist/html/math_toolkit/status/history1.html @@ -3,7 +3,7 @@ History and What's New - + @@ -22,20 +22,32 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            +

                                                                            + +

                                                                            +
                                                                            + + Boost-1.44.0 +
                                                                            +

                                                                            +

                                                                            +
                                                                            • + Fixed incorrect range and support for Rayleigh distribution. +

                                                                            - + Boost-1.41.0

                                                                            -
                                                                            • +
                                                                              • Significantly improved performance for the incomplete gamma function and it's inverse.
                                                                              @@ -43,41 +55,41 @@

                                                                              - + Boost-1.40.0

                                                                              -
                                                                                -
                                                                              • +
                                                                                  +
                                                                                • Added support for MPFR as a bignum type.
                                                                                • -
                                                                                • +
                                                                                • Added some full specializations of the policy classes to reduce compile times.
                                                                                • -
                                                                                • +
                                                                                • Added logistic and hypergeometric distributions, from Gautam Sewani's Google Summer of Code project.
                                                                                • -
                                                                                • +
                                                                                • Added Laplace distribution submitted by Thijs van den Berg.
                                                                                • -
                                                                                • +
                                                                                • Updated performance test code to include new distributions, and improved the performance of the non-central distributions.
                                                                                • -
                                                                                • +
                                                                                • Added SSE2 optimised Lanczos approximation code, from Gautam Sewani's Google Summer of Code project.
                                                                                • -
                                                                                • +
                                                                                • Fixed bug in cyl_bessel_i that used an incorrect approximation for ν = 0.5, also effects the non-central Chi Square Distribution when ν = 3, see bug report #2877.
                                                                                • -
                                                                                • +
                                                                                • Fixed minor bugs #2873.
                                                                                @@ -85,16 +97,16 @@

                                                                                - + Boost-1.38.0

                                                                                -
                                                                                  -
                                                                                • +
                                                                                    +
                                                                                  • Added Johan Råde's optimised floating point classification routines.
                                                                                  • -
                                                                                  • +
                                                                                  • Fixed code so that it compiles in GCC's -pedantic mode (bug report #1451).
                                                                                  • @@ -103,49 +115,49 @@

                                                                                    - + Boost-1.37.0

                                                                                    -
                                                                                    • +
                                                                                      • Improved accuracy and testing of the inverse hypergeometric functions.

                                                                                      - + Boost-1.36.0

                                                                                      -
                                                                                        -
                                                                                      • +
                                                                                          +
                                                                                        • Added Noncentral Chi Squared Distribution.
                                                                                        • -
                                                                                        • +
                                                                                        • Added Noncentral Beta Distribution.
                                                                                        • -
                                                                                        • +
                                                                                        • Added Noncentral F Distribution.
                                                                                        • -
                                                                                        • +
                                                                                        • Added Noncentral T Distribution.
                                                                                        • -
                                                                                        • +
                                                                                        • Added Exponential Integral Functions.
                                                                                        • -
                                                                                        • +
                                                                                        • Added Zeta Function.
                                                                                        • -
                                                                                        • +
                                                                                        • Added Rounding and Truncation functions.
                                                                                        • -
                                                                                        • +
                                                                                        • Added Compile time powers of runtime bases.
                                                                                        • -
                                                                                        • +
                                                                                        • Added SSE2 optimizations for Lanczos evaluation.
                                                                                        @@ -153,37 +165,37 @@

                                                                                        - + Boost-1.35.0: Post Review First Official Release

                                                                                        -
                                                                                          -
                                                                                        • +
                                                                                            +
                                                                                          • Added Policy based framework that allows fine grained control over function behaviour.
                                                                                          • -
                                                                                          • +
                                                                                          • Breaking change: Changed default behaviour for domain, pole and overflow errors to throw an exception (based on review feedback), this behaviour can be customised using Policy's.
                                                                                          • -
                                                                                          • +
                                                                                          • Breaking change: Changed exception thrown when an internal evaluation error occurs to boost::math::evaluation_error.
                                                                                          • -
                                                                                          • +
                                                                                          • Breaking change: Changed discrete quantiles to return an integer result: this is anything up to 20 times faster than finding the true root, this behaviour can be customised using Policy's.
                                                                                          • -
                                                                                          • +
                                                                                          • Polynomial/rational function evaluation is now customisable and hopefully faster than before.
                                                                                          • -
                                                                                          • +
                                                                                          • Added performance test program.
                                                                                          @@ -191,18 +203,18 @@

                                                                                          - + Milestone 4: Second Review Candidate (1st March 2007)

                                                                                          -
                                                                                            -
                                                                                          • +
                                                                                              +
                                                                                            • Moved Xiaogang Zhang's Bessel Functions code into the library, and brought them into line with the rest of the code.
                                                                                            • -
                                                                                            • +
                                                                                            • Added C# "Distribution Explorer" demo application.
                                                                                            @@ -210,31 +222,31 @@

                                                                                            - + Milestone 3: First Review Candidate (31st Dec 2006)

                                                                                            -
                                                                                              -
                                                                                            • +
                                                                                                +
                                                                                              • Implemented the main probability distribution and density functions.
                                                                                              • -
                                                                                              • +
                                                                                              • Implemented digamma.
                                                                                              • -
                                                                                              • +
                                                                                              • Added more factorial functions.
                                                                                              • -
                                                                                              • +
                                                                                              • Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical harmonic functions from TR1.
                                                                                              • -
                                                                                              • +
                                                                                              • Moved Xiaogang Zhang's elliptic integral code into the library, and brought them into line with the rest of the code.
                                                                                              • -
                                                                                              • +
                                                                                              • Moved Hubert Holin's existing Boost.Math special functions into this library and brought them into line with the rest of the code.
                                                                                              • @@ -243,40 +255,40 @@

                                                                                                - + Milestone 2: Released September 10th 2006

                                                                                                -
                                                                                                  -
                                                                                                • +
                                                                                                    +
                                                                                                  • Implement preview release of the statistical distributions.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Added statistical distributions tutorial.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Implemented root finding algorithms.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Implemented the inverses of the incomplete gamma and beta functions.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Integrated the statistical results generated from the test data with Boost.Test: uses a database of expected results, indexed by test, floating point type, platform, and compiler.
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Improved lgamma near 1 and 2 (rational approximations).
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Improved erf/erfc inverses (rational approximations).
                                                                                                  • -
                                                                                                  • +
                                                                                                  • Implemented Rational function generation (the Remez method).
                                                                                                  @@ -284,29 +296,29 @@

                                                                                                  - + Milestone 1: Released March 31st 2006

                                                                                                  -
                                                                                                    -
                                                                                                  • +
                                                                                                      +
                                                                                                    • Implement gamma/beta/erf functions along with their incomplete counterparts.
                                                                                                    • -
                                                                                                    • +
                                                                                                    • Generate high quality test data, against which future improvements can be judged.
                                                                                                    • -
                                                                                                    • +
                                                                                                    • Provide tools for the evaluation of infinite series, continued fractions, and rational functions.
                                                                                                    • -
                                                                                                    • +
                                                                                                    • Provide tools for testing against tabulated test data, and collecting statistics on error rates.
                                                                                                    • -
                                                                                                    • +
                                                                                                    • Provide sufficient docs for people to be able to find their way around the library.
                                                                                                    • 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 e2dcdb29d..96da98b1f 100644 --- a/doc/sf_and_dist/html/math_toolkit/status/issues.html +++ b/doc/sf_and_dist/html/math_toolkit/status/issues.html @@ -3,7 +3,7 @@ Known Issues, and Todo List - + @@ -22,7 +22,7 @@
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                                                                                                      @@ -43,45 +43,45 @@ with it.

                                                                                                      - + tgamma
                                                                                                      -
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                                                                                                        - + Incomplete Beta
                                                                                                        -
                                                                                                        • +
                                                                                                          • Investigate Didonato and Morris' asymptotic expansion for large a and b (medium priority).
                                                                                                          - + Inverse Gamma
                                                                                                          -
                                                                                                          • +
                                                                                                            • Investigate whether we can skip iteration altogether if the first approximation is good enough (Medium Priority).
                                                                                                            - + Polynomials
                                                                                                            -
                                                                                                            • +
                                                                                                              • The Legendre and Laguerre Polynomials have surprisingly different error rates on different platforms, considering they are evaluated with only basic arithmetic operations. Maybe this is telling us something, or maybe not (Low Priority).
                                                                                                              - + Elliptic Integrals
                                                                                                              -
                                                                                                                -
                                                                                                              • +
                                                                                                                  +
                                                                                                                • Carlson's algorithms are essentially unchanged from Xiaogang Zhang's Google Summer of Code student project, and are based on Carlson's original papers. However, Carlson has revised his algorithms since then (refer @@ -89,7 +89,7 @@ performance and accuracy, we may be able to take advantage of these improvements too (Low Priority).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • Carlson's algorithms (mainly RJ) are somewhat prone to internal overflow/underflow when the arguments are very large or small. The homogeneity relations:

                                                                                                                  RF(ka, @@ -101,27 +101,27 @@ accurately identified. (Medium Priority).

                                                                                                                • -
                                                                                                                • +
                                                                                                                • Carlson's RC can be reduced to elementary funtions (asin and log), would it be more efficient evaluated this way, rather than by Carlson's algorithms? (Low Priority).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • Should we add an implementation of Carlson's RG? It's not required for the Legendre form integrals, but some people may find it useful (Low Priority).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • There are a several other integrals: D(φ, k), Z(β, k), Λ0(β, k) and Bulirsch's el functions that could be implemented using Carlson's integrals (Low Priority).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • The integrals K(k) and E(k) could be implemented using rational approximations (both for efficiency and accuracy), assuming we can find them. (Medium Priority).
                                                                                                                • -
                                                                                                                • +
                                                                                                                • There is a sub-domain of ellint_3 that is unimplemented (see the docs for details), currently it's not clear how to solve this issue, or if it's ever likely to be an real problem @@ -130,26 +130,26 @@
                                                                                                                - + Inverse Hyperbolic Functions
                                                                                                                -
                                                                                                                • +
                                                                                                                  • These functions are inherited from previous Boost versions, before log1p became widely available. Would they be better expressed in terms of this function? This is probably only an issue for very high precision types (Low Priority).
                                                                                                                  - + Statistical distributions
                                                                                                                  -
                                                                                                                  • +
                                                                                                                    • Student's t Perhaps switch to normal distribution as a better approximation for very large degrees of freedom?
                                                                                                                    - + Feature Requests

                                                                                                                    @@ -1260,16 +1260,16 @@

                                                                                                                    Also asked for more than once:

                                                                                                                    -
                                                                                                                      -
                                                                                                                    • +
                                                                                                                        +
                                                                                                                      • Add support for interpolated distributions, possibly combine with numeric integration and differentiation.
                                                                                                                      • -
                                                                                                                      • +
                                                                                                                      • Add support for bivariate and multivariate distributions: most especially the normal.
                                                                                                                      • -
                                                                                                                      • +
                                                                                                                      • Add support for the log of the cdf and pdf: this is mainly a performance optimisation since we can avoid some special function calls for some distributions by returning the log of the result. diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit.html b/doc/sf_and_dist/html/math_toolkit/toolkit.html index 7bd85bbbf..6ab9ae4fa 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit.html @@ -3,7 +3,7 @@ Internal Details and Tools (Experimental) - + @@ -22,7 +22,7 @@
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                                                                                                                        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 683d6dedc..939b944ef 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 @@ -3,7 +3,7 @@ Continued Fraction Evaluation - + @@ -22,13 +22,13 @@
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                                                                                                                        @@ -78,7 +78,7 @@ }}} // namespaces

                                                                                                                        - + Description

                                                                                                                        @@ -178,7 +178,7 @@ a continued fraction for convergence.

                                                                                                                        - + Implementation

                                                                                                                        @@ -188,7 +188,7 @@ Lentz, W.J. 1976, Applied Optics, vol. 15, pp. 668-671.

                                                                                                                        - + Examples

                                                                                                                        diff --git a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html index 1f4691291..98a1913c8 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals1/constants.html @@ -3,7 +3,7 @@ Numeric Constants - + @@ -22,13 +22,13 @@

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                                                                                                                        - + Description

                                                                                                                        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 f712386e5..dcc10c9e2 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 @@ -3,7 +3,7 @@ Locating Function Minima - + @@ -22,13 +22,13 @@

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                                                                                                                        @@ -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

                                                                                                                        @@ -89,7 +89,7 @@ the abscissa at the minima and the value of f(x) at the minima.

                                                                                                                        - + Implementation

                                                                                                                        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 912511a2c..302e971b3 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 @@ -3,7 +3,7 @@ Polynomial and Rational Function Evaluation - + @@ -22,13 +22,13 @@

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                                                                                                                        @@ -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

                                                                                                                        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 c4b22e3ee..06cf71192 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 @@ -3,7 +3,7 @@ Root Finding With Derivatives - + @@ -22,13 +22,13 @@

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                                                                                                                        - + Description

                                                                                                                        @@ -122,35 +122,35 @@

                                                                                                                        When using these functions you should note that:

                                                                                                                        -
                                                                                                                          -
                                                                                                                        • +
                                                                                                                            +
                                                                                                                          • They may be very sensitive to the initial guess, typically they converge very rapidly if the initial guess has two or three decimal digits correct. However convergence can be no better than bisection, or in some rare cases even worse than bisection if the initial guess is a long way from the correct value and the derivatives are close to zero.
                                                                                                                          • -
                                                                                                                          • +
                                                                                                                          • These functions include special cases to handle zero first (and second where appropriate) derivatives, and fall back to bisection in this case. However, it is helpful if F is defined to return an arbitrarily small value of the correct sign rather than zero.
                                                                                                                          • -
                                                                                                                          • +
                                                                                                                          • If the derivative at the current best guess for the result is infinite (or very close to being infinite) then these functions may terminate prematurely. A large first derivative leads to a very small next step, triggering the termination condition. Derivative based iteration may not be appropriate in such cases.
                                                                                                                          • -
                                                                                                                          • +
                                                                                                                          • These functions fall back to bisection if the next computed step would take the next value out of bounds. The bounds are updated after each step to ensure this leads to convergence. However, a good initial guess backed up by asymptotically-tight bounds will improve performance no end rather than relying on bisection.
                                                                                                                          • -
                                                                                                                          • +
                                                                                                                          • The value of digits is crucial to good performance of these functions, if it is set too high then at best you will get one extra (unnecessary) iteration, and at worst the last few steps @@ -165,7 +165,7 @@ final iteration just takes the next value into the zone where f(x) becomes inaccurate.
                                                                                                                          • -
                                                                                                                          • +
                                                                                                                          • Finally: you may well be able to do better than these functions by hand-coding the heuristics used so that they are tailored to a specific function. You may also be able to compute the ratio of derivatives @@ -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

                                                                                                                            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 775169aab..8082c4e5c 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 @@ -3,7 +3,7 @@ Root Finding Without Derivatives - + @@ -22,13 +22,13 @@

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                                                                                                                            @@ -141,7 +141,7 @@ }}} // namespaces

                                                                                                                            - + Description

                                                                                                                            @@ -561,7 +561,7 @@ as soon as both ends of the interval round to the same nearest integer.

                                                                                                                            - + Implementation

                                                                                                                            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 e839040b6..636b77aa1 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 @@ -3,7 +3,7 @@ Series Evaluation - + @@ -22,13 +22,13 @@

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                                                                                                                            @@ -100,14 +100,14 @@ value of the sum to which the terms of the series should be added. This is useful in two situations:

                                                                                                                            -
                                                                                                                              -
                                                                                                                            • +
                                                                                                                                +
                                                                                                                              • Where the first value of the series has a different formula to successive terms. In this case the first value in the series can be passed as the last argument and the logic of the function object can then be simplified to return subsequent terms.
                                                                                                                              • -
                                                                                                                              • +
                                                                                                                              • Where the series is being added (or subtracted) from some other value: termination of the series will likely occur much more rapidly if that other value is passed as the last argument. For example, there are @@ -127,7 +127,7 @@ summation in this way.

                                                                                                                                - + Example

                                                                                                                                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 eca80a60e..b593cbca0 100644 --- a/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html +++ b/doc/sf_and_dist/html/math_toolkit/toolkit/internals2.html @@ -3,7 +3,7 @@ Testing and Development - + @@ -22,7 +22,7 @@

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                                                                                                                                @@ -45,7 +45,7 @@ test_result<see-below> test(const A& a, F1 test_func, F2 expect_func);

                                                                                                                                - + Description
                                                                                                                                template <class T>
                                                                                                                                @@ -61,11 +61,11 @@
                                                                                                                                 

                                                                                                                                In addition the value returned is zero if:

                                                                                                                                -
                                                                                                                                  -
                                                                                                                                • +
                                                                                                                                    +
                                                                                                                                  • Both a and v are infinite.
                                                                                                                                  • -
                                                                                                                                  • +
                                                                                                                                  • Both a and v are denormalised numbers or zero.
                                                                                                                                  • @@ -157,7 +157,7 @@ is mainly a debugging/development aid (and a good place for a breakpoint).

                                                                                                                                    - + Example

                                                                                                                                    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 f8722ad42..1e98c13a6 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 @@ -3,7 +3,7 @@ Minimax Approximations and the Remez Algorithm - + @@ -22,7 +22,7 @@

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                                                                                                                                    Minimax Approximations and the Remez Algorithm 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 c6cf94033..735d952d3 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 @@ -3,7 +3,7 @@ Polynomials - + @@ -22,12 +22,12 @@
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                                                                                                                                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 3ee48ec52..37b7b7dff 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 @@ -3,7 +3,7 @@ Graphing, Profiling, and Generating Test Data for Special Functions - + @@ -22,7 +22,7 @@

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                                                                                                                                Graphing, Profiling, and Generating Test Data for Special Functions @@ -32,21 +32,21 @@ associated helper functions are designed so that in just a few lines of code you should be able to:

                                                                                                                                -
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                                                                                                                                  • Profile a continued fraction, or infinite series for convergence and accuracy.
                                                                                                                                  • -
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                                                                                                                                  • Generate csv data from a special function that can be imported into your favorite graphing program (or spreadsheet) for further analysis.
                                                                                                                                  • -
                                                                                                                                  • +
                                                                                                                                  • Generate high precision test data.
                                                                                                                                  - + Synopsis
                                                                                                                                  namespace boost{ namespace math{ namespace tools{
                                                                                                                                  @@ -147,7 +147,7 @@
                                                                                                                                   }}} // namespaces
                                                                                                                                   
                                                                                                                                  - + Description

                                                                                                                                  @@ -156,28 +156,28 @@

                                                                                                                                  The functionality of test_data is split into the following parts:

                                                                                                                                  -
                                                                                                                                    -
                                                                                                                                  • +
                                                                                                                                      +
                                                                                                                                    • A functor that implements the function for which data is being generated: this is the bit you have to write.
                                                                                                                                    • -
                                                                                                                                    • +
                                                                                                                                    • One of more parameters that are to be passed to the functor, these are described in fairly abstract terms: give me N points distributed like this etc.
                                                                                                                                    • -
                                                                                                                                    • +
                                                                                                                                    • The class test_data, that takes the functor and descriptions of the parameters and computes how ever many output points have been requested, these are stored in a sorted container.
                                                                                                                                    • -
                                                                                                                                    • +
                                                                                                                                    • Routines to iterate over the test_data container and output the data in either csv format, or as C++ source code (as a table using Boost.Array).
                                                                                                                                    - + Example 1: Output Data for Graph Plotting
                                                                                                                                    @@ -211,7 +211,7 @@

                                                                                                                                    - + Example 2: Creating Test Data
                                                                                                                                    @@ -353,14 +353,14 @@

                                                                                                                                    The first #define serves two purposes:

                                                                                                                                    -
                                                                                                                                      -
                                                                                                                                    • +
                                                                                                                                        +
                                                                                                                                      • It reduces the file sizes considerably: all those static_cast's add up to a lot of bytes otherwise (they are needed to suppress compiler warnings when T is narrower than a long double).
                                                                                                                                      • -
                                                                                                                                      • +
                                                                                                                                      • It provides a useful customisation point: for example if we were testing a user-defined type that has more precision than a long double we could change it to: @@ -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

                                                                                                                                        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 ad629930e..a93cbb14a 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 @@ -3,7 +3,7 @@ Overview - + @@ -22,7 +22,7 @@

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                                                                                                                                        Use with User-Defined Floating-Point Types 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 e5613040b..31336600f 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 @@ -3,7 +3,7 @@ Conceptual Archetypes and Testing - + @@ -22,7 +22,7 @@
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                                                                                                                                        Conceptual Archetypes and Testing 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 62c3bc245..a7321061e 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 @@ -3,7 +3,7 @@ Conceptual Requirements for Real Number Types - + @@ -22,7 +22,7 @@
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                                                                                                                                        Conceptual Requirements for Real Number Types @@ -42,7 +42,7 @@ behaves just like a built in floating point type.

                                                                                                                                        - + Basic Arithmetic Requirements
                                                                                                                                        @@ -977,21 +977,21 @@

                                                                                                                                        Note that:

                                                                                                                                        -
                                                                                                                                          -
                                                                                                                                        1. +
                                                                                                                                            +
                                                                                                                                          1. The functions log_max_value and log_min_value can be synthesised from the others, and so no explicit specialisation is required.
                                                                                                                                          2. -
                                                                                                                                          3. +
                                                                                                                                          4. The function epsilon can be synthesised from the others, so no explicit specialisation is required provided the precision of RealType does not vary at runtime (see the header boost/math/bindings/rr.hpp for an example where the precision does vary at runtime).
                                                                                                                                          5. -
                                                                                                                                          6. +
                                                                                                                                          7. The functions digits, max_value and min_value, all get synthesised automatically from std::numeric_limits. However, if numeric_limits is not specialised for @@ -1035,7 +1035,7 @@

                                                                            - + Standard Library Support Requirements
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                                                                            +

                                                                            Conceptual Requirements for Distribution Types diff --git a/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html b/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html index 5c8c4c094..7f98b563d 100644 --- a/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html +++ b/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.html @@ -3,7 +3,7 @@ Using With MPFR / GMP - a High-Precision Floating-Point Library - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Using With MPFR / GMP - a High-Precision Floating-Point Library 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 d7925e1cc..933ff9b28 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 @@ -3,7 +3,7 @@ Using With NTL - a High-Precision Floating-Point Library - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Using With NTL - a High-Precision Floating-Point Library diff --git a/doc/sf_and_dist/html/math_toolkit/utils.html b/doc/sf_and_dist/html/math_toolkit/utils.html index 190afb71e..f80508596 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils.html +++ b/doc/sf_and_dist/html/math_toolkit/utils.html @@ -3,7 +3,7 @@ Floating Point Utilities - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html b/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html index 963948c70..73c9951d8 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/fpclass.html @@ -3,7 +3,7 @@ Floating-Point Classification: Infinities and NaN's - + @@ -22,13 +22,13 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +
                                                                            - + Synopsis
                                                                            #define FP_ZERO        /* implementation specific value */
                                                                            @@ -58,7 +58,7 @@
                                                                                     to use these functions.
                                                                                   

                                                                            - + Description

                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float.html index 3590c5050..103ada6e2 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float.html @@ -3,7 +3,7 @@ Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values - + @@ -22,7 +22,7 @@

                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Floating-Point Representation Distance (ULP), and Finding Adjacent Floating-Point Values diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html index 8de887f39..659cdf9ac 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_advance.html @@ -3,7 +3,7 @@ Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Advancing a Floating Point Value by a Specific Representation Distance (ULP) float_advance @@ -32,7 +32,7 @@ number of ULP.

                                                                            - + Synopsis

                                                                            @@ -50,7 +50,7 @@ }} // namespaces

                                                                            - + Description - float_advance
                                                                            diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html index b921556af..a3f63878b 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_distance.html @@ -3,7 +3,7 @@ Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance - + @@ -22,7 +22,7 @@
                                                                            PrevUpHomeNext
                                                                            -
                                                                            +

                                                                            Calculating the Representation Distance Between Two Floating Point Values (ULP) float_distance @@ -34,7 +34,7 @@ different.

                                                                            - + Synopsis

                                                                            @@ -52,7 +52,7 @@ }} // namespaces

                                                                            - + Description - float_distance
                                                                            @@ -65,16 +65,16 @@

                                                                            Note that

                                                                            -
                                                                              -
                                                                            • +
                                                                                +
                                                                              • float_distance(a, a) always returns 0.
                                                                              • -
                                                                              • +
                                                                              • float_distance(float_next(a), a) always returns 1.
                                                                              • -
                                                                              • +
                                                                              • float_distance(float_prior(a), a) always returns -1.
                                                                              • diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html index 8478acede..16484a681 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_next.html @@ -3,7 +3,7 @@ Finding the Next Greater Representable Value (float_next) - + @@ -22,13 +22,13 @@
                                                                                PrevUpHomeNext
                                                                                -
                                                                                +
                                                                                - + Synopsis

                                                                                @@ -46,7 +46,7 @@ }} // namespaces

                                                                                - + Description - float_next
                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html index f9a3b2446..2a9d88655 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/float_prior.html @@ -3,7 +3,7 @@ Finding the Next Smaller Representable Value (float_prior) - + @@ -22,13 +22,13 @@
                                                                                PrevUpHomeNext
                                                                                -
                                                                                +
                                                                                - + Synopsis

                                                                                @@ -46,7 +46,7 @@ }} // namespaces

                                                                                - + Description - float_prior
                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html b/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html index 59cbf93ba..a95c000ce 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/next_float/nextafter.html @@ -3,7 +3,7 @@ Finding the Next Representable Value in a Specific Direction (nextafter) - + @@ -22,13 +22,13 @@
                                                                                PrevUpHomeNext
                                                                                -
                                                                                +
                                                                                - + Synopsis

                                                                                @@ -46,7 +46,7 @@ }} // namespaces

                                                                                - + Description - nextafter
                                                                                @@ -76,7 +76,7 @@ returns an overflow_error.

                                                                                - + Examples - nextafter
                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding.html index f957d1cce..6cd277810 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding.html @@ -3,7 +3,7 @@ Rounding Truncation and Integer Conversion - + @@ -22,7 +22,7 @@
                                                                                PrevUpHomeNext
                                                                                -
                                                                                +

                                                                                Rounding Truncation and Integer Conversion diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html index a6db616ba..de4780422 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/modf.html @@ -3,7 +3,7 @@ Integer and Fractional Part Splitting (modf) - + @@ -22,7 +22,7 @@
                                                                                PrevUpHomeNext
                                                                                -
                                                                                +

                                                                                Integer and Fractional Part Splitting (modf) diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html index d9738476b..c73fe5b88 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/round.html @@ -3,7 +3,7 @@ Rounding Functions - + @@ -22,7 +22,7 @@
                                                                                PrevUpHomeNext
                                                                                -
                                                                                +
                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html b/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html index 05bd8eb0e..5b754920d 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/rounding/trunc.html @@ -3,7 +3,7 @@ Truncation Functions - + @@ -22,7 +22,7 @@
                                                                                PrevUpHomeNext
                                                                                -
                                                                                +
                                                                                diff --git a/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html b/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html index b7c19226c..31a3099fa 100644 --- a/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html +++ b/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.html @@ -3,7 +3,7 @@ Sign Manipulation Functions - + @@ -22,13 +22,13 @@
                                                                                PrevUpHomeNext
                                                                                -
                                                                                +
                                                                                - + Synopsis

                                                                                @@ -52,7 +52,7 @@ }} // namespaces

                                                                                - + Description
                                                                                template<class T> 
                                                                                diff --git a/doc/sf_and_dist/roadmap.qbk b/doc/sf_and_dist/roadmap.qbk
                                                                                index a595bd983..defae090b 100644
                                                                                --- a/doc/sf_and_dist/roadmap.qbk
                                                                                +++ b/doc/sf_and_dist/roadmap.qbk
                                                                                @@ -1,5 +1,9 @@
                                                                                 [template history[]
                                                                                 
                                                                                +[h4 Boost-1.44.0]
                                                                                +
                                                                                +* Fixed incorrect range and support for Rayleigh distribution.
                                                                                +
                                                                                 [h4 Boost-1.41.0]
                                                                                 
                                                                                 * Significantly improved performance for the incomplete gamma function and it's inverse.