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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>About the Math Toolkit</title>
<link rel="stylesheet" href="../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../index.html" title="Math Toolkit 2.6.0">
<link rel="up" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="prev" href="../overview.html" title="Chapter&#160;1.&#160;Overview">
<link rel="home" href="../index.html" title="Math Toolkit 3.0.0">
<link rel="up" href="../overview.html" title="Chapter 1. Overview">
<link rel="prev" href="../overview.html" title="Chapter 1. Overview">
<link rel="next" href="navigation.html" title="Navigation">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
@@ -27,15 +27,49 @@
<a name="math_toolkit.main_intro"></a><a class="link" href="main_intro.html" title="About the Math Toolkit">About the Math Toolkit</a>
</h2></div></div></div>
<p>
This library is divided into three interconnected parts:
This library is divided into several interconnected parts:
</p>
<h5>
<a name="math_toolkit.main_intro.h0"></a>
<span class="phrase"><a name="math_toolkit.main_intro.floating_point_utilities"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.floating_point_utilities">Floating
Point Utilities</a>
</h5>
<p>
Utility functions for dealing with floating-point arithmetic, includes functions
for floating point classification (<code class="computeroutput"><span class="identifier">fpclassify</span></code>,
<code class="computeroutput"><span class="identifier">isnan</span></code>, <code class="computeroutput"><span class="identifier">isinf</span></code>
etc), sign manipulation, rounding, comparison, and computing the distance between
floating point numbers.
</p>
<h5>
<a name="math_toolkit.main_intro.h1"></a>
<span class="phrase"><a name="math_toolkit.main_intro.specific_width_floating_point_ty"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.specific_width_floating_point_ty">Specific
Width Floating-Point Types</a>
</h5>
<p>
A set of <code class="computeroutput"><span class="keyword">typedef</span></code>s similar to those
provided by <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">cstdint</span><span class="special">&gt;</span></code> but for floating-point types.
</p>
<h5>
<a name="math_toolkit.main_intro.h2"></a>
<span class="phrase"><a name="math_toolkit.main_intro.mathematical_constants"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.mathematical_constants">Mathematical
Constants</a>
</h5>
<p>
A wide range of high-precision constants ranging from various multiples of
π, fractions, through to Euler's constant etc.
</p>
<p>
These are of course usable from template code, or as non-templates with a simplified
interface if that is more appropriate.
</p>
<h5>
<a name="math_toolkit.main_intro.h3"></a>
<span class="phrase"><a name="math_toolkit.main_intro.statistical_distributions"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.statistical_distributions">Statistical
Distributions</a>
</h5>
<p>
Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="Chapter&#160;5.&#160;Statistical Distributions and Functions">statistical
Provides a reasonably comprehensive set of <a class="link" href="../dist.html" title="Chapter 5. Statistical Distributions and Functions">statistical
distributions</a>, upon which higher level statistical tests can be built.
</p>
<p>
@@ -55,12 +89,12 @@
illustrating how the library is used to conduct statistical tests.
</p>
<h5>
<a name="math_toolkit.main_intro.h1"></a>
<a name="math_toolkit.main_intro.h4"></a>
<span class="phrase"><a name="math_toolkit.main_intro.mathematical_special_functions"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.mathematical_special_functions">Mathematical
Special Functions</a>
</h5>
<p>
Provides a small number of high quality <a class="link" href="../special.html" title="Chapter&#160;6.&#160;Special Functions">special functions</a>,
Provides a small number of high quality <a class="link" href="../special.html" title="Chapter 8. Special Functions">special functions</a>,
initially these were concentrated on functions used in statistical applications
along with those in the <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1836.pdf" target="_top">Technical
Report on C++ Library Extensions</a>.
@@ -70,7 +104,7 @@
along with the incomplete gamma and beta functions (four variants of each)
and all the possible inverses of these, plus digamma, various factorial functions,
Bessel functions, elliptic integrals, sinus cardinals (along with their hyperbolic
variants), inverse hyperbolic functions, Legrendre/Laguerre/Hermite polynomials
variants), inverse hyperbolic functions, Legendre/Laguerre/Hermite polynomials
and various special power and logarithmic functions.
</p>
<p>
@@ -81,54 +115,76 @@
<code class="computeroutput"><span class="keyword">double</span></code> or <code class="computeroutput"><span class="keyword">long</span>
<span class="keyword">double</span></code>.
</p>
<p>
These functions also provide the basis of support for the TR1 special functions.
</p>
<h5>
<a name="math_toolkit.main_intro.h2"></a>
<span class="phrase"><a name="math_toolkit.main_intro.implementation_toolkit"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.implementation_toolkit">Implementation
Toolkit</a>
<a name="math_toolkit.main_intro.h5"></a>
<span class="phrase"><a name="math_toolkit.main_intro.root_finding_and_function_minimi"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.root_finding_and_function_minimi">Root Finding
and Function Minimisation</a>
</h5>
<p>
The section <a class="link" href="internals_overview.html" title="Overview">Internal tools</a>
provides many of the tools required to implement mathematical special functions:
hopefully the presence of these will encourage other authors to contribute
more special function implementations in the future.
A comprehensive set of root finding algorithms over the real-line, both with
and without derivative support.
</p>
<p>
Some tools are now considered well-tried and their signatures stable and unlikely
to change.
Also function minimisation via Brent's Method.
</p>
<h5>
<a name="math_toolkit.main_intro.h6"></a>
<span class="phrase"><a name="math_toolkit.main_intro.polynomials_and_rational_functio"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.polynomials_and_rational_functio">Polynomials
and Rational Functions</a>
</h5>
<p>
Tools for manipulating polynomials and for efficient evaluation of rationals
or polynomials.
</p>
<h5>
<a name="math_toolkit.main_intro.h7"></a>
<span class="phrase"><a name="math_toolkit.main_intro.interpolation"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.interpolation">Interpolation</a>
</h5>
<p>
Function interpolation via Barycentric or cubic B_spline approximations. Smoothing.
</p>
<h5>
<a name="math_toolkit.main_intro.h8"></a>
<span class="phrase"><a name="math_toolkit.main_intro.numerical_integration_quadrature"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.numerical_integration_quadrature">Numerical
Integration (Quadrature) and Differentiation</a>
</h5>
<p>
A reasonably comprehensive set of routines for integration (trapezoidal, Gauss-Legendre,
Gauss-Kronrod and double-exponential) and differentiation. (See also automatic
differentiation).
</p>
<p>
There is a fairly comprehensive set of root finding both <a class="link" href="roots_noderiv.html" title="Root Finding Without Derivatives">root-finding
without derivatives</a> and <a class="link" href="roots_deriv.html" title="Root Finding With Derivatives: Newton-Raphson, Halley &amp; Schr&#246;der">root-finding
with derivatives</a> with derivative support, and function minimization
using <a class="link" href="brent_minima.html" title="Locating Function Minima using Brent's algorithm">Brent's method</a>.
The integration routines are all usable for functions returning complex results
- and as a result for contour integrals as well.
</p>
<h5>
<a name="math_toolkit.main_intro.h9"></a>
<span class="phrase"><a name="math_toolkit.main_intro.quaternions_and_octonions"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.quaternions_and_octonions">Quaternions
and Octonions</a>
</h5>
<p>
Other <a class="link" href="internals_overview.html" title="Overview">Internal tools</a>
are currently still considered experimental: they are "exposed implementation
details" whose interfaces and/or implementations may change without notice.
Quaternions and Octonians as class templates similar to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span></code>.
</p>
<h5>
<a name="math_toolkit.main_intro.h10"></a>
<span class="phrase"><a name="math_toolkit.main_intro.automatic_differentiation"></a></span><a class="link" href="main_intro.html#math_toolkit.main_intro.automatic_differentiation">Automatic
Differentiation</a>
</h5>
<p>
There are helpers for the <a class="link" href="internals/series_evaluation.html" title="Series Evaluation">evaluation
of infinite series</a>, <a class="link" href="internals/cf.html" title="Continued Fraction Evaluation">continued
fractions</a> and <a class="link" href="rational.html" title="Polynomial and Rational Function Evaluation">rational approximations</a>.
A <a class="link" href="internals/minimax.html" title="Minimax Approximations and the Remez Algorithm">Remez algorithm implementation</a>
allows for the locating of minimax rational approximations.
</p>
<p>
There are also (experimental) classes for the <a class="link" href="polynomials.html" title="Polynomials">manipulation
of polynomials</a>, for <a class="link" href="internals/error_test.html" title="Relative Error and Testing">testing
a special function against tabulated test data</a>, and for the <a class="link" href="internals/test_data.html" title="Graphing, Profiling, and Generating Test Data for Special Functions">rapid
generation of test data</a> and/or data for output to an external graphing
application.
Autodiff is a header-only C++ library that facilitates the automaticdifferentiation
(forward mode) of mathematical functions of single and multiple variables.
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014, 2017 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam
Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle Walker
and Xiaogang Zhang<p>
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>