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26<div class="titlepage"><div><div><h2 class="title" style="clear: both">
27<a name="math_toolkit.credits"></a><a class="link" href="credits.html" title="Credits and Acknowledgements">Credits and Acknowledgements</a>
28</h2></div></div></div>
29<p>
30 Hubert Holin started the Boost.Math library. The Quaternions, Octonions, inverse
31 hyperbolic functions, and the sinus cardinal functions are his.
32 </p>
33<p>
34 Daryle Walker wrote the integer gcd and lcm functions.
35 </p>
36<p>
37 John Maddock started the special functions, the beta, gamma, erf, polynomial,
38 and factorial functions are his, as is the "Toolkit" section, and
39 many of the statistical distributions.
40 </p>
41<p>
42 Paul A. Bristow threw down the challenge in <a href="http://www2.open-std.org/JTC1/SC22/WG21/docs/papers/2004/n1668.pdf" target="_top">A
43 Proposal to add Mathematical Functions for Statistics to the C++ Standard Library</a>
44 to add the key math functions, especially those essential for statistics. After
45 JM accepted and solved the difficult problems, not only numerically, but in
46 full C++ template style, PAB implemented a few of the statistical distributions.
47 PAB also tirelessly proof-read everything that JM threw at him (so that all
48 remaining editorial mistakes are his fault).
49 </p>
50<p>
51 Xiaogang Zhang worked on the Bessel functions and elliptic integrals for his
52 Google Summer of Code project 2006.
53 </p>
54<p>
55 Bruno Lalande submitted the "compile time power of a runtime base"
56 code.
57 </p>
58<p>
59 Johan R&#229;de wrote the optimised floating-point classification and manipulation
60 code, and nonfinite facets to permit C99 output of infinities and NaNs. (nonfinite
61 facets were not added until Boost 1.47 but had been in use with Boost.Spirit).
62 This library was based on a suggestion from Robert Ramey, author of Boost.Serialization.
63 Paul A. Bristow expressed the need for better handling of <a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2006/n2022.pdf" target="_top">Input
64 &amp; Output of NaN and infinity for the C++ Standard Library</a> and suggested
65 following the C99 format.
66 </p>
67<p>
68 Antony Polukhin improved lexical cast avoiding stringstream so that it was
69 no longer necessary to use a globale C99 facet to handle nonfinites.
70 </p>
71<p>
72 H&#229;kan Ard&#246;, Boris Gubenko, John Maddock, Markus Sch&#246;pflin and Olivier Verdier
73 tested the floating-point library and Martin Bonner, Peter Dimov and John Maddock
74 provided valuable advice.
75 </p>
76<p>
77 Gautam Sewani coded the logistic distribution as part of a Google Summer of
78 Code project 2008.
79 </p>
80<p>
81 M. A. (Thijs) van den Berg coded the Laplace distribution. (Thijs has also
82 threatened to implement some multivariate distributions).
83 </p>
84<p>
85 Thomas Mang requested the inverse gamma in chi squared distributions for Bayesian
86 applications and helped in their implementation, and provided a nice example
87 of their use.
88 </p>
89<p>
90 Professor Nico Temme for advice on the inverse incomplete beta function.
91 </p>
92<p>
93 <a href="http://www.shoup.net" target="_top">Victor Shoup for NTL</a>, without which
94 it would have much more difficult to produce high accuracy constants, and especially
95 the tables of accurate values for testing.
96 </p>
97<p>
98 We are grateful to Joel Guzman for helping us stress-test his <a href="http://www.boost.org/tools/quickbook/index.htm" target="_top">Boost.Quickbook</a>
99 program used to generate the html and pdf versions of this document, adding
100 several new features en route.
101 </p>
102<p>
103 Plots of the functions and distributions were prepared in <a href="http://www.w3.org/" target="_top">W3C</a>
104 standard <a href="http://www.svg.org/" target="_top">Scalable Vector Graphic (SVG)</a>
105 format using a program created by Jacob Voytko during a <a href="http://code.google.com/soc/2007/" target="_top">Google
106 Summer of Code (2007)</a>. From 2012, the latest versions of all Internet
107 Browsers have support for rendering SVG (with varying quality). Older versions,
108 especially (Microsoft Internet Explorer (before IE 9) lack native SVG support
109 but can be made to work with <a href="http://www.adobe.com/svg/viewer/install/" target="_top">Adobe's
110 free SVG viewer</a> plugin). The SVG files can be converted to JPEG or
111 PNG using <a href="http://www.inkscape.org/" target="_top">Inkscape</a>.
112 </p>
113<p>
114 We are also indebted to Matthias Schabel for managing the formal Boost-review
115 of this library, and to all the reviewers - including Guillaume Melquiond,
116 Arnaldur Gylfason, John Phillips, Stephan Tolksdorf and Jeff Garland - for
117 their many helpful comments.
118 </p>
119<p>
120 Thanks to Mark Coleman and Georgi Boshnakov for spot test values from <a href="http://www.wolfram.com/products/mathematica/index.html" target="_top">Wolfram Mathematica</a>,
121 and of course, to Eric Weisstein for nurturing <a href="http://mathworld.wolfram.com" target="_top">Wolfram
122 MathWorld</a>, an invaluable resource.
123 </p>
124<p>
125 The Skew-normal distribution and Owen's t function were written by Benjamin
126 Sobotta.
127 </p>
128<p>
129 We thank Thomas Mang for persuading us to allow t distributions to have infinite
130 degrees of freedom and contributing to some long discussions about how to improve
131 accuracy for large non-centrality and/or large degrees of freedom.
132 </p>
133<p>
134 Christopher Kormanyos wrote the e_float multiprecision library <a href="http://portal.acm.org/citation.cfm?id=1916469" target="_top">TOMS
135 Algorithm 910: A Portable C++ Multiple-Precision System for Special-Function
136 Calculations</a> which formed the basis for the Boost.Multiprecision library
137 which now can be used to allow most functions and distributions to be computed
138 up to a precision of the users' choice, no longer restricted to built-in floating-point
139 types like double. (And thanks to Topher Cooper for bring Christopher's e_float
140 to our attention).
141 </p>
142<p>
143 Christopher Kormanyos wrote some examples for using <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>,
144 and added methods for finding zeros of Bessel Functions.
145 </p>
146<p>
147 Marco Guazzone provided the hyper-geometric distribution.
148 </p>
149<p>
150 Rocco Romeo has found numerous small bugs and generally stress tested the special
151 functions code to near destruction!
152 </p>
153<p>
154 Jeremy William Murphy added polynomial arithmetic tools.
155 </p>
156<p>
157 Thomas Luu provided improvements to the quantile of the non-central chi squared
158 distribution quantile. and his thesis * <a href="http://discovery.ucl.ac.uk/1482128/" target="_top">Fast
159 and accurate parallel computation of quantile functions for random number generation,
160 2016</a>.
161 </p>
162<p>
163 and his paper
164 </p>
165<p>
166 Luu, Thomas; (2015), Efficient and Accurate Parallel Inversion of the Gamma
167 Distribution, SIAM Journal on Scientific Computing , 37 (1) C122 - C141, <a href="http://dx.doi.org/10.1137/14095875X" target="_top">http://dx.doi.org/10.1137/14095875X</a>.
168 </p>
169<p>
170 These also promise to help improve algorithms for computation of quantile of
171 several disitributions, especially for parallel computation using GPUs.
172 </p>
173</div>
174<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
175<td align="left"></td>
176<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
177 Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
178 Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
179 Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
180 Distributed under the Boost Software License, Version 1.0. (See accompanying
181 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>)
182 </p>
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