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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.history2"></a><a class="link" href="history2.html" title="History and What's New">History and What's New</a>
  28 </h2></div></div></div>
  29 <p>
  30       Currently open bug reports can be viewed <a href="https://github.com/boostorg/math/issues" target="_top">here</a>
  31       on GitHub.
  32     </p>
  33 <p>
  34       All old bug reports including closed ones can be viewed on Trac <a href="https://svn.boost.org/trac/boost/query?status=assigned&amp;status=closed&amp;status=new&amp;status=reopened&amp;component=math&amp;col=id&amp;col=summary&amp;col=status&amp;col=type&amp;col=milestone&amp;col=component&amp;order=priority" target="_top">here</a>.
  35     </p>
  36 <p>
  37       Recent issues on GitHub <a href="https://github.com/boostorg/math/issues?utf8=%E2%9C%93&amp;q=is%3Aissue" target="_top">here</a>.
  38     </p>
  39 <h5>
  40 <a name="math_toolkit.history2.h0"></a>
  41       <span class="phrase"><a name="math_toolkit.history2.math_2_11_0_boost_1_72"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_11_0_boost_1_72">Math-2.11.0
  42       (Boost-1.72)</a>
  43     </h5>
  44 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  45 <li class="listitem">
  46           Added Hypergeometric functions <a class="link" href="hypergeometric/hypergeometric_1f0.html" title="Hypergeometric 1F0">1F0</a>,
  47           <a class="link" href="hypergeometric/hypergeometric_0f1.html" title="Hypergeometric 0F1">0F1</a>,
  48           <a class="link" href="hypergeometric/hypergeometric_2f0.html" title="Hypergeometric 2F0">2F0</a>,
  49           <a class="link" href="hypergeometric/hypergeometric_1f1.html" title="Hypergeometric 1F1">1F1</a>
  50           and <a class="link" href="hypergeometric/hypergeometric_pfq.html" title="Hypergeometric pFq">pFq</a>.
  51         </li>
  52 <li class="listitem">
  53           Added <a class="link" href="sf_poly/jacobi.html" title="Jacobi Polynomials">Jacobi polynomial</a>
  54           (and derivatives) evaluation.
  55         </li>
  56 <li class="listitem">
  57           Added <a class="link" href="sf_poly/gegenbauer.html" title="Gegenbauer Polynomials">Gegenbauer polynomial</a>
  58           (and derivatives) evaluation.
  59         </li>
  60 <li class="listitem">
  61           Added <a class="link" href="sf_poly/cardinal_b_splines.html" title="Cardinal B-splines">Cardinal
  62           B-Splines</a> (and derivatives) as polynomial functions in their own
  63           right.
  64         </li>
  65 <li class="listitem">
  66           Added <a class="link" href="cardinal_trigonometric.html" title="Cardinal Trigonometric interpolation">Cardinal Trigonometric
  67           Interpolation</a>.
  68         </li>
  69 <li class="listitem">
  70           Added new statistics sub-section.
  71         </li>
  72 <li class="listitem">
  73           Added <a class="link" href="t_test.html" title="t-tests">One Sample Student's T Test</a>.
  74         </li>
  75 <li class="listitem">
  76           Added <a class="link" href="anderson_darling.html" title="The Anderson-Darling Test">Anderson Darling test
  77           for normality</a>.
  78         </li>
  79 <li class="listitem">
  80           Added <a class="link" href="ljung_box.html" title="The Ljung-Box Test">Ljung Box test for auto-correlation</a>.
  81         </li>
  82 <li class="listitem">
  83           Added <a class="link" href="runs_test.html" title="Runs tests">Runs test for random sequences</a>.
  84         </li>
  85 <li class="listitem">
  86           The headers <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">univariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code> and <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">bivariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>,
  87           have been deprecated in favor of <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">univariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>
  88           and <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">bivariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>.
  89         </li>
  90 <li class="listitem">
  91           Added <a class="link" href="dist_ref/dists/empirical_cdf.html" title="Empirical Cumulative Distribution Function">The Empirical
  92           CDF distribution</a>.
  93         </li>
  94 <li class="listitem">
  95           Reworked the Sterling approximation used by multiprecision gamma functions
  96           to be applicable to all the function that use the Lanczos approximation
  97           at regular precision. Also extended Lanczos approximations up to 100 decimal
  98           digit precision.
  99         </li>
 100 </ul></div>
 101 <h5>
 102 <a name="math_toolkit.history2.h1"></a>
 103       <span class="phrase"><a name="math_toolkit.history2.math_2_10_0_boost_1_71"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_10_0_boost_1_71">Math-2.10.0
 104       (Boost-1.71)</a>
 105     </h5>
 106 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 107 <li class="listitem">
 108           Catmull-Rom interpolator now works in C++11.
 109         </li>
 110 <li class="listitem">
 111           Cardinal quadratic B-spline interpolation.
 112         </li>
 113 <li class="listitem">
 114           Domain of elliptic integrals extended.
 115         </li>
 116 <li class="listitem">
 117           sin_pi and cos_pi performance improvements.
 118         </li>
 119 <li class="listitem">
 120           Forward-mode automatic differentiation.
 121         </li>
 122 <li class="listitem">
 123           Vector valued barycentric rational interpolation.
 124         </li>
 125 <li class="listitem">
 126           Ooura's method for evaluation of Fourier integrals.
 127         </li>
 128 <li class="listitem">
 129           Multiple compatibility issues with Multiprecision fixed.
 130         </li>
 131 <li class="listitem">
 132           Lambert-W fixed on a rare architecture.
 133         </li>
 134 </ul></div>
 135 <h5>
 136 <a name="math_toolkit.history2.h2"></a>
 137       <span class="phrase"><a name="math_toolkit.history2.math_2_9_0_boost_1_70"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_9_0_boost_1_70">Math-2.9.0
 138       (Boost-1.70)</a>
 139     </h5>
 140 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 141 <li class="listitem">
 142           Add Lanczos smoothing derivatives
 143         </li>
 144 <li class="listitem">
 145           Move <code class="computeroutput"><span class="identifier">numerical_differentiation</span><span class="special">.</span><span class="identifier">hpp</span></code>
 146           from <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span></code>
 147           to <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">differentiation</span><span class="special">/</span><span class="identifier">finite_difference</span><span class="special">.</span><span class="identifier">hpp</span></code>.
 148         </li>
 149 <li class="listitem">
 150           Add mean, variance, skewness, kurtosis, median, Gini coefficient, and median
 151           absolute deviation to <code class="computeroutput"><span class="identifier">tools</span><span class="special">/</span><span class="identifier">univariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>.
 152         </li>
 153 <li class="listitem">
 154           Add correlation coefficients and covariance to <code class="computeroutput"><span class="identifier">tools</span><span class="special">/</span><span class="identifier">bivariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>
 155         </li>
 156 <li class="listitem">
 157           Add absolute Gini coefficient, Hoyer sparsity, oracle SNR, and the <span class="emphasis"><em>M</em></span><sub>2</sub><span class="emphasis"><em>M</em></span><sub>4</sub> SNR
 158           estimator to <code class="computeroutput"><span class="identifier">tools</span><span class="special">/</span><span class="identifier">signal_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>.
 159         </li>
 160 <li class="listitem">
 161           Add total variation, l0, l1, l2, and sup norms, as well as corresponding
 162           distance functions to <code class="computeroutput"><span class="identifier">tools</span><span class="special">/</span><span class="identifier">norms</span><span class="special">.</span><span class="identifier">hpp</span></code>.
 163         </li>
 164 <li class="listitem">
 165           Add move constructors for polynomials, support complex coefficients, add
 166           <code class="computeroutput"><span class="special">.</span><span class="identifier">prime</span><span class="special">()</span></code> and <code class="computeroutput"><span class="special">.</span><span class="identifier">integrate</span><span class="special">()</span></code>
 167           methods.
 168         </li>
 169 <li class="listitem">
 170           Add <code class="computeroutput"><span class="identifier">quadratic_roots</span></code> to
 171           <code class="computeroutput"><span class="identifier">tools</span><span class="special">/</span><span class="identifier">roots</span><span class="special">.</span><span class="identifier">hpp</span></code>.
 172         </li>
 173 <li class="listitem">
 174           Add support for complex-valued functions to Newton's method in <code class="computeroutput"><span class="identifier">roots</span><span class="special">.</span><span class="identifier">hpp</span></code>.
 175         </li>
 176 <li class="listitem">
 177           Add Catmull-Rom interpolator.
 178         </li>
 179 <li class="listitem">
 180           Fix bug in <code class="computeroutput"><span class="identifier">newton_raphson_iterate</span></code>
 181           where we could terminate incorrectly under certain exceptional cases.
 182         </li>
 183 <li class="listitem">
 184           Suppressed warnings from use of <code class="computeroutput"><span class="identifier">Q</span></code>
 185           suffix on constants when compiling with <code class="computeroutput"><span class="identifier">g</span><span class="special">++</span> <span class="special">-</span><span class="identifier">Wall</span>
 186           <span class="special">-</span><span class="identifier">pedantic</span></code>.
 187         </li>
 188 </ul></div>
 189 <h5>
 190 <a name="math_toolkit.history2.h3"></a>
 191       <span class="phrase"><a name="math_toolkit.history2.math_2_8_0_boost_1_69"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_8_0_boost_1_69">Math-2.8.0
 192       (Boost-1.69)</a>
 193     </h5>
 194 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 195 <li class="listitem">
 196           Add LambertW functions.
 197         </li>
 198 <li class="listitem">
 199           Update integration routines to support complex valued integrands and contour
 200           integrals.
 201         </li>
 202 <li class="listitem">
 203           Added the derivative of the Barycentric rational approximation.
 204         </li>
 205 <li class="listitem">
 206           Updated continued fraction and series evaluation code to support complex
 207           types.
 208         </li>
 209 <li class="listitem">
 210           Minor fixes to better support variable precision floating point types.
 211         </li>
 212 <li class="listitem">
 213           Removed use of deprecated Boost.Endian in favour of Predef.
 214         </li>
 215 <li class="listitem">
 216           Prevent logic error leading to infinite loop in toms748_solve. See <a href="https://github.com/boostorg/math/issues/138" target="_top">#138</a>.
 217         </li>
 218 <li class="listitem">
 219           Fix mean and standard_deviation for extreme_value_distribution. See <a href="https://github.com/boostorg/math/issues/139" target="_top">#139</a>.
 220         </li>
 221 <li class="listitem">
 222           Improve heuristics used in newton_raphson_iterate. See <a href="https://github.com/boostorg/math/issues/145" target="_top">#145</a>.
 223         </li>
 224 <li class="listitem">
 225           Fix result of <code class="computeroutput"><span class="identifier">erf</span><span class="special">(</span><span class="identifier">NaN</span><span class="special">)</span></code>.
 226           See <a href="https://github.com/boostorg/math/issues/141" target="_top">#141</a>.
 227         </li>
 228 <li class="listitem">
 229           Big push to reduce GCC warnings. See <a href="https://github.com/boostorg/math/issues/136" target="_top">#136</a>.
 230         </li>
 231 <li class="listitem">
 232           Refactor polynomial addition. See <a href="https://github.com/boostorg/math/pull/132" target="_top">PR132</a>.
 233         </li>
 234 <li class="listitem">
 235           Fix for vxWorks having a <code class="computeroutput"><span class="identifier">real</span></code>
 236           function in the global namespace. See <a href="https://github.com/boostorg/math/pull/131" target="_top">PR131</a>.
 237         </li>
 238 <li class="listitem">
 239           Improve <code class="computeroutput"><span class="identifier">sinc</span></code> approximations
 240           and add better tests.
 241         </li>
 242 <li class="listitem">
 243           Fix typo in Student's T hypothesis testing documentation, see <a href="https://github.com/boostorg/math/issues/143" target="_top">#143</a>.
 244         </li>
 245 </ul></div>
 246 <h5>
 247 <a name="math_toolkit.history2.h4"></a>
 248       <span class="phrase"><a name="math_toolkit.history2.math_2_7_1_boost_1_68"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_7_1_boost_1_68">Math-2.7.1
 249       (Boost-1.68)</a>
 250     </h5>
 251 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 252 <li class="listitem">
 253           Continue to improve numerical integration routines, and in particular add
 254           support for contour integrals.
 255         </li>
 256 <li class="listitem">
 257           Improve accuracy of erfc function's rational approximations.
 258         </li>
 259 </ul></div>
 260 <h5>
 261 <a name="math_toolkit.history2.h5"></a>
 262       <span class="phrase"><a name="math_toolkit.history2.math_2_7_0_boost_1_66"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_7_0_boost_1_66">Math-2.7.0
 263       (Boost-1.66)</a>
 264     </h5>
 265 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 266 <li class="listitem">
 267           Add Gauss and Gauss-Kronrod quadrature routines.
 268         </li>
 269 <li class="listitem">
 270           Add double-exponential (tanh-sinh, exp-sinh and sinh-sinh) quadrature routines.
 271         </li>
 272 <li class="listitem">
 273           Add Chebyshev polynomial evaluation, roots, integration, differentiation,
 274           and interpolation routines.
 275         </li>
 276 </ul></div>
 277 <h5>
 278 <a name="math_toolkit.history2.h6"></a>
 279       <span class="phrase"><a name="math_toolkit.history2.math_2_6_0_boost_1_65"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_6_0_boost_1_65">Math-2.6.0
 280       (Boost-1.65)</a>
 281     </h5>
 282 <p>
 283       New Features:
 284     </p>
 285 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 286 <li class="listitem">
 287           Add <a class="link" href="cardinal_cubic_b.html" title="Cardinal Cubic B-spline interpolation">Cardinal cubic B-Spline
 288           interpolation functions</a>, with thanks to Nick Thompson.
 289         </li>
 290 <li class="listitem">
 291           Add <a class="link" href="barycentric.html" title="Barycentric Rational Interpolation">barycentric rational interpolation
 292           functions</a>, with thanks to Nick Thompson.
 293         </li>
 294 <li class="listitem">
 295           Add <a class="link" href="trapezoidal.html" title="Trapezoidal Quadrature">adaptive trapezoidal quadrature</a>,
 296           with thanks to Nick Thompson.
 297         </li>
 298 <li class="listitem">
 299           Add <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">support for the zeros
 300           and derivatives of Legendre polynomials</a>, with thanks to Nick Thompson.
 301         </li>
 302 </ul></div>
 303 <p>
 304       Patches:
 305     </p>
 306 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 307 <li class="listitem">
 308           Improve polynomial GCD algorithms, with thanks to Jeremy Murphy.
 309         </li>
 310 <li class="listitem">
 311           Removed gcd/lcm routines from Boost.Math - these are now in Boost.Integer.
 312         </li>
 313 </ul></div>
 314 <h5>
 315 <a name="math_toolkit.history2.h7"></a>
 316       <span class="phrase"><a name="math_toolkit.history2.math_2_5_2_boost_1_64"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_5_2_boost_1_64">Math-2.5.2
 317       (Boost-1.64)</a>
 318     </h5>
 319 <p>
 320       Patches:
 321     </p>
 322 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 323 <li class="listitem">
 324           Big push to ensure all functions in also in C99 are compatible with Annex
 325           F.
 326         </li>
 327 <li class="listitem">
 328           Improved accuracy of the Bessel functions I0, I1, K0 and K1, see <a href="https://svn.boost.org/trac/boost/ticket/12066" target="_top">12066</a>.
 329         </li>
 330 </ul></div>
 331 <h5>
 332 <a name="math_toolkit.history2.h8"></a>
 333       <span class="phrase"><a name="math_toolkit.history2.math_2_5_1_boost_1_63"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_5_1_boost_1_63">Math-2.5.1
 334       (Boost-1.63)</a>
 335     </h5>
 336 <p>
 337       Patches:
 338     </p>
 339 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 340 <li class="listitem">
 341           Fixed evaluation of zero polynomial in polynomial.hpp, see <a href="https://svn.boost.org/trac/boost/ticket/12532" target="_top">12532</a>.
 342         </li>
 343 <li class="listitem">
 344           Fixed missing header include in boost/math/tools/tuple.hpp, see <a href="https://svn.boost.org/trac/boost/ticket/12537" target="_top">12537</a>.
 345         </li>
 346 </ul></div>
 347 <h5>
 348 <a name="math_toolkit.history2.h9"></a>
 349       <span class="phrase"><a name="math_toolkit.history2.math_2_5_0_boost_1_62"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_5_0_boost_1_62">Math-2.5.0
 350       (Boost-1.62)</a>
 351     </h5>
 352 <p>
 353       New Features:
 354     </p>
 355 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 356           Enabled all the special function code to work correctly with types whose
 357           precision can change at runtime: for example type <code class="computeroutput"><span class="identifier">mpfr_float</span></code>
 358           from Boost.Multiprecision.
 359         </li></ul></div>
 360 <p>
 361       Patches:
 362     </p>
 363 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 364 <li class="listitem">
 365           Fix tgamma_delta_ratio for cases where the delta is small compared to the
 366           base.
 367         </li>
 368 <li class="listitem">
 369           Fix misc GCC-4.4 test failures.
 370         </li>
 371 </ul></div>
 372 <h5>
 373 <a name="math_toolkit.history2.h10"></a>
 374       <span class="phrase"><a name="math_toolkit.history2.math_2_4_0_boost_1_61"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_4_0_boost_1_61">Math-2.4.0
 375       (Boost-1.61)</a>
 376     </h5>
 377 <p>
 378       New Features:
 379     </p>
 380 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 381           Polynomial arithmetic added to tools.
 382         </li></ul></div>
 383 <h5>
 384 <a name="math_toolkit.history2.h11"></a>
 385       <span class="phrase"><a name="math_toolkit.history2.math_2_3_0_boost_1_60"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_3_0_boost_1_60">Math-2.3.0
 386       (Boost-1.60)</a>
 387     </h5>
 388 <p>
 389       New Features:
 390     </p>
 391 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 392 <li class="listitem">
 393           Promote the root finding and function minimization code to first class
 394           citizens - these are now officially supported as part of the library.
 395         </li>
 396 <li class="listitem">
 397           Allow the library to be used and tested with compiler exception handling
 398           support turned off. To better facilitate this the default error handling
 399           policies have been changed to <span class="emphasis"><em>errno_on_error</em></span> but only
 400           when the compiler has no exception handling support.
 401         </li>
 402 </ul></div>
 403 <p>
 404       Patches:
 405     </p>
 406 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 407 <li class="listitem">
 408           Fix behaviour of the non-central chi-squared distribution when the non-centrality
 409           parameter is zero to match the chi-squared, see <a href="https://svn.boost.org/trac/boost/ticket/11557" target="_top">11557</a>.
 410         </li>
 411 <li class="listitem">
 412           Fix comments in code for the hypergeometric to match what it actually does,
 413           also fixes the parameter access functions to return the correct values.
 414           See <a href="https://svn.boost.org/trac/boost/ticket/11556" target="_top">11556</a>.
 415         </li>
 416 <li class="listitem">
 417           Stopped using hidden visiblity library build with the Oracle compiler as
 418           it leads to unresolved externals from the C++ standard library. See <a href="https://svn.boost.org/trac/boost/ticket/11547" target="_top">11547</a>.
 419         </li>
 420 <li class="listitem">
 421           Fix unintended use of __declspec when building with Oracle C++. See <a href="https://svn.boost.org/trac/boost/ticket/11546" target="_top">11546</a>.
 422         </li>
 423 <li class="listitem">
 424           Fix corner case bug in root bracketing code, see <a href="https://svn.boost.org/trac/boost/ticket/11532" target="_top">11532</a>.
 425         </li>
 426 <li class="listitem">
 427           Add some missing typecasts in arguments to std::max in Bernoulli code.
 428           See <a href="https://svn.boost.org/trac/boost/ticket/11453" target="_top">11453</a>.
 429         </li>
 430 <li class="listitem">
 431           Fix mistaken assumptions about the possible values for FLT_EVAL_METHOD.
 432           See <a href="https://svn.boost.org/trac/boost/ticket/11429" target="_top">11429</a>.
 433         </li>
 434 <li class="listitem">
 435           Completely revamped performance testing and error-rate measuring code so
 436           we can more easily document how well (or not!) we're doing. This information
 437           will hopefully get more frequently updated in future as it's more or less
 438           automatically generated - see the <span class="emphasis"><em>reporting</em></span> sub-directory
 439           for more information.
 440         </li>
 441 <li class="listitem">
 442           Fix some corner cases in the beta, incomplete beta, and incomplete beta
 443           derivative. With thanks to Rocco Romeo.
 444         </li>
 445 <li class="listitem">
 446           Reorganized the Bessel functions internally to improve the performance
 447           of Jn and Yn.
 448         </li>
 449 <li class="listitem">
 450           Fixed skewness formula for triangular distribution, see <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">#11768</a>.
 451         </li>
 452 <li class="listitem">
 453           Fixed some examples so they compile on Unix platforms which have an ::exception
 454           struct declared, see <a href="https://svn.boost.org/trac/boost/ticket/11827" target="_top">#11827</a>.
 455         </li>
 456 <li class="listitem">
 457           Correct mistake in triangular distribution skewness formula <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">11768</a>,
 458           reported by Juan Leni.
 459         </li>
 460 </ul></div>
 461 <h5>
 462 <a name="math_toolkit.history2.h12"></a>
 463       <span class="phrase"><a name="math_toolkit.history2.math_2_2_1"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_2_1">Math-2.2.1</a>
 464     </h5>
 465 <p>
 466       Patch release for Boost-1.58:
 467     </p>
 468 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 469 <li class="listitem">
 470           Minor <a href="https://github.com/boostorg/math/pull/13#issuecomment-98905579" target="_top">patch
 471           for Haiku support.</a>
 472         </li>
 473 <li class="listitem">
 474           Fix the decimal digit count for 128-bit floating point types.
 475         </li>
 476 <li class="listitem">
 477           Fix a few documentation typos.
 478         </li>
 479 </ul></div>
 480 <h5>
 481 <a name="math_toolkit.history2.h13"></a>
 482       <span class="phrase"><a name="math_toolkit.history2.math_2_2_0_boost_1_58_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_2_0_boost_1_58_0">Math-2.2.0
 483       (boost-1.58.0)</a>
 484     </h5>
 485 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 486 <li class="listitem">
 487           Added two new special functions - <a class="link" href="sf_gamma/trigamma.html" title="Trigamma">trigamma</a>
 488           and <a class="link" href="sf_gamma/polygamma.html" title="Polygamma">polygamma</a>.
 489         </li>
 490 <li class="listitem">
 491           Fixed namespace scope constants so they are constexpr on conforming compilers,
 492           see https://svn.boost.org/trac/boost/ticket/10901.
 493         </li>
 494 <li class="listitem">
 495           Fixed various cases of spurious under/overflow in the incomplete beta and
 496           gamma functions, plus the elliptic integrals, with thanks to Rocco Romeo.
 497         </li>
 498 <li class="listitem">
 499           Fix 3-arg <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
 500           and <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_q</a> functions
 501           to not call the policy based overload if the final argument is not actually
 502           a policy.
 503         </li>
 504 <li class="listitem">
 505           Cleaned up some dead code in the incomplete beta function, see <a href="https://svn.boost.org/trac/boost/ticket/10985" target="_top">#10985</a>.
 506         </li>
 507 <li class="listitem">
 508           Fixed extreme-value pdf for large valued inputs, see <a href="https://svn.boost.org/trac/boost/ticket/10938" target="_top">#10938</a>.
 509         </li>
 510 <li class="listitem">
 511           Large update to the Elliptic integral code to use Carlson's latest algorithms
 512           - these should be more stable, more accurate and slightly faster than before.
 513           Also added support for Carlson's RG integral.
 514         </li>
 515 <li class="listitem">
 516           Added <a class="link" href="ellint/ellint_d.html" title="Elliptic Integral D - Legendre Form">ellint_d</a>, <a class="link" href="ellint/jacobi_zeta.html" title="Jacobi Zeta Function">jacobi_zeta</a> and <a class="link" href="ellint/heuman_lambda.html" title="Heuman Lambda Function">heuman_lambda</a> elliptic
 517           integrals.
 518         </li>
 519 <li class="listitem">
 520           Switched documentation to use SVG rather than PNG graphs and equations
 521           - browsers seem to have finally caught up!
 522         </li>
 523 </ul></div>
 524 <h5>
 525 <a name="math_toolkit.history2.h14"></a>
 526       <span class="phrase"><a name="math_toolkit.history2.math_2_1_0_boost_1_57_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_1_0_boost_1_57_0">Math-2.1.0
 527       (boost-1.57.0)</a>
 528     </h5>
 529 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 530 <li class="listitem">
 531           Added <a class="link" href="dist_ref/dists/hyperexponential_dist.html" title="Hyperexponential Distribution">Hyperexponential
 532           Distribution</a>.
 533         </li>
 534 <li class="listitem">
 535           Fix some spurious overflows in the incomplete gamma functions (with thanks
 536           to Rocco Romeo).
 537         </li>
 538 <li class="listitem">
 539           Fix bug in derivative of incomplete beta when a = b = 0.5 - this also effects
 540           several non-central distributions, see <a href="https://svn.boost.org/trac/boost/ticket/10480" target="_top">10480</a>.
 541         </li>
 542 <li class="listitem">
 543           Fixed some corner cases in <a class="link" href="rounding/round.html" title="Rounding Functions">round</a>.
 544         </li>
 545 <li class="listitem">
 546           Don't support 80-bit floats in cstdfloat.hpp if standard library support
 547           is broken.
 548         </li>
 549 </ul></div>
 550 <h5>
 551 <a name="math_toolkit.history2.h15"></a>
 552       <span class="phrase"><a name="math_toolkit.history2.math_2_0_0_boost_1_56_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_0_0_boost_1_56_0">Math-2.0.0
 553       (Boost-1.56.0)</a>
 554     </h5>
 555 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 556 <li class="listitem">
 557           <span class="bold"><strong>Breaking change</strong></span>: moved a number of non-core
 558           headers that are predominantly used for internal maintenance into <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">include_private</span></code>. The headers effected
 559           are <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test_data</span><span class="special">.</span><span class="identifier">hpp</span></code>, <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">remez</span><span class="special">.</span><span class="identifier">hpp</span></code>,
 560           <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">generate</span><span class="special">.</span><span class="identifier">hpp</span></code>, <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">solve</span><span class="special">.</span><span class="identifier">hpp</span></code>,
 561           <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">test</span><span class="special">.</span><span class="identifier">hpp</span></code>. You can continue to use these headers
 562           by adding <code class="computeroutput"><span class="identifier">libs</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">include_private</span></code> to your compiler's include
 563           path.
 564         </li>
 565 <li class="listitem">
 566           <span class="bold"><strong>Breaking change</strong></span>: A number of distributions
 567           and special functions were returning the maximum finite value rather than
 568           raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>,
 569           this has now been fixed, which means these functions now behave as documented.
 570           However, since the default behavior on raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>
 571           is to throw a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> exception, applications
 572           which have come to reply rely on these functions not throwing may experience
 573           exceptions where they did not before. The special functions involved are
 574           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>,
 575           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>,
 576           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
 577           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
 578           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>,
 579           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>,
 580           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>, <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>. The distributions
 581           involved are <a class="link" href="dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto
 582           Distribution</a>, <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta
 583           Distribution</a>, <a class="link" href="dist_ref/dists/geometric_dist.html" title="Geometric Distribution">Geometric
 584           Distribution</a>, <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
 585           Binomial Distribution</a>, <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
 586           Distribution</a>, <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
 587           Squared Distribution</a>, <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
 588           Distribution</a>, <a class="link" href="dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">Inverse
 589           chi squared Distribution</a>, <a class="link" href="dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution">Inverse
 590           Gamma Distribution</a>. See <a href="https://svn.boost.org/trac/boost/ticket/10111" target="_top">#10111</a>.
 591         </li>
 592 <li class="listitem">
 593           Fix <a class="link" href="rounding/round.html" title="Rounding Functions">round</a> and <a class="link" href="rounding/trunc.html" title="Truncation Functions">trunc</a> functions so they can
 594           be used with integer arguments, see <a href="https://svn.boost.org/trac/boost/ticket/10066" target="_top">#10066</a>.
 595         </li>
 596 <li class="listitem">
 597           Fix Halley iteration to handle zero derivative (with non-zero second derivative),
 598           see <a href="https://svn.boost.org/trac/boost/ticket/10046" target="_top">#10046</a>.
 599         </li>
 600 </ul></div>
 601 <h5>
 602 <a name="math_toolkit.history2.h16"></a>
 603       <span class="phrase"><a name="math_toolkit.history2.math_1_9_1"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_1_9_1">Math-1.9.1</a>
 604     </h5>
 605 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 606 <li class="listitem">
 607           Fix Geometric distribution use of Policies, see <a href="https://svn.boost.org/trac/boost/ticket/9833" target="_top">#9833</a>.
 608         </li>
 609 <li class="listitem">
 610           Fix corner cases in the negative binomial distribution, see <a href="https://svn.boost.org/trac/boost/ticket/9834" target="_top">#9834</a>.
 611         </li>
 612 <li class="listitem">
 613           Fix compilation failures on Mac OS.
 614         </li>
 615 </ul></div>
 616 <h5>
 617 <a name="math_toolkit.history2.h17"></a>
 618       <span class="phrase"><a name="math_toolkit.history2.math_1_9_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_1_9_0">Math-1.9.0</a>
 619     </h5>
 620 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 621 <li class="listitem">
 622           Changed version number to new Boost.Math specific version now that we're
 623           in the modular Boost world.
 624         </li>
 625 <li class="listitem">
 626           Added <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
 627           numbers</a>, changed arbitrary precision <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>/<a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> to use Sterling's
 628           approximation (from Nikhar Agrawal).
 629         </li>
 630 <li class="listitem">
 631           Added first derivatives of the Bessel functions: <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_j_prime</a>,
 632           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_neumann_prime</a>,
 633           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_i_prime</a>,
 634           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_k_prime</a>,
 635           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_bessel_prime</a>
 636           and <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_neumann_prime</a>
 637           (from Anton Bikineev).
 638         </li>
 639 <li class="listitem">
 640           Fixed buggy Student's t example code, along with docs for testing sample
 641           means for equivalence.
 642         </li>
 643 <li class="listitem">
 644           Documented <code class="computeroutput"><span class="identifier">max_iter</span></code> parameter
 645           in root finding code better, see <a href="https://svn.boost.org/trac/boost/ticket/9225" target="_top">#9225</a>.
 646         </li>
 647 <li class="listitem">
 648           Add option to explicitly enable/disable use of __float128 in constants
 649           code, see <a href="https://svn.boost.org/trac/boost/ticket/9240" target="_top">#9240</a>.
 650         </li>
 651 <li class="listitem">
 652           Cleaned up handling of negative values in Bessel I0 and I1 code (removed
 653           dead code), see <a href="https://svn.boost.org/trac/boost/ticket/9512" target="_top">#9512</a>.
 654         </li>
 655 <li class="listitem">
 656           Fixed handling of very small values passed to <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
 657           and <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> so they
 658           don't generate spurious overflows (thanks to Rocco Romeo).
 659         </li>
 660 <li class="listitem">
 661           <a href="https://svn.boost.org/trac/boost/ticket/9672" target="_top">#9672 PDF and
 662           CDF of a Laplace distribution throwing domain_error</a> Random variate
 663           can now be infinite.
 664         </li>
 665 <li class="listitem">
 666           Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
 667           <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
 668           and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
 669           with thanks to Rocco Romeo.
 670         </li>
 671 <li class="listitem">
 672           Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
 673           <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
 674           and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
 675           (thanks to Rocco Romeo).
 676         </li>
 677 <li class="listitem">
 678           Removed constant <code class="computeroutput"><span class="identifier">pow23_four_minus_pi</span>
 679           </code> whose value did not match the name (and was unused by Boost.Math),
 680           see <a href="https://svn.boost.org/trac/boost/ticket/9712" target="_top">#9712</a>.
 681         </li>
 682 </ul></div>
 683 <h5>
 684 <a name="math_toolkit.history2.h18"></a>
 685       <span class="phrase"><a name="math_toolkit.history2.boost_1_55"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_55">Boost-1.55</a>
 686     </h5>
 687 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 688 <li class="listitem">
 689           Suppress numerous warnings (mostly from GCC-4.8 and MSVC) <a href="https://svn.boost.org/trac/boost/ticket/8384" target="_top">#8384</a>,
 690           <a href="https://svn.boost.org/trac/boost/ticket/8855" target="_top">#8855</a>,
 691           <a href="https://svn.boost.org/trac/boost/ticket/9107" target="_top">#9107</a>,
 692           <a href="https://svn.boost.org/trac/boost/ticket/9109" target="_top">#9109</a>..
 693         </li>
 694 <li class="listitem">
 695           Fixed PGI compilation issue <a href="https://svn.boost.org/trac/boost/ticket/8333" target="_top">#8333</a>.
 696         </li>
 697 <li class="listitem">
 698           Fixed PGI constant value initialization issue that caused erf to generate
 699           incorrect results <a href="https://svn.boost.org/trac/boost/ticket/8621" target="_top">#8621</a>.
 700         </li>
 701 <li class="listitem">
 702           Prevent macro expansion of some C99 macros that are also C++ functions
 703           <a href="https://svn.boost.org/trac/boost/ticket/8732" target="_top">#8732</a>
 704           and <a href="https://svn.boost.org/trac/boost/ticket/8733" target="_top">#8733</a>..
 705         </li>
 706 <li class="listitem">
 707           Fixed Student's T distribution to behave correctly with huge degrees of
 708           freedom (larger than the largest representable integer) <a href="https://svn.boost.org/trac/boost/ticket/8837" target="_top">#8837</a>.
 709         </li>
 710 <li class="listitem">
 711           Make some core functions usable with <code class="computeroutput"><span class="keyword">long</span>
 712           <span class="keyword">double</span></code> even when the platform has
 713           no standard library <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code> support <a href="https://svn.boost.org/trac/boost/ticket/8940" target="_top">#8940</a>.
 714         </li>
 715 <li class="listitem">
 716           Fix error handling of distributions to catch invalid scale and location
 717           parameters when the random variable is infinite <a href="https://svn.boost.org/trac/boost/ticket/9042" target="_top">#9042</a>
 718           and <a href="https://svn.boost.org/trac/boost/ticket/9126" target="_top">#9126</a>.
 719         </li>
 720 <li class="listitem">
 721           Add workaround for broken &lt;tuple&gt; in Intel C++ 14 <a href="https://svn.boost.org/trac/boost/ticket/9087" target="_top">#9087</a>.
 722         </li>
 723 <li class="listitem">
 724           Improve consistency of argument reduction in the elliptic integrals <a href="https://svn.boost.org/trac/boost/ticket/9104" target="_top">#9104</a>.
 725         </li>
 726 <li class="listitem">
 727           Fix bug in inverse incomplete beta that results in cancellation errors
 728           when the beta function is really an arcsine or Student's T distribution.
 729         </li>
 730 <li class="listitem">
 731           Fix issue in Bessel I and K function continued fractions that causes spurious
 732           over/underflow.
 733         </li>
 734 <li class="listitem">
 735 <p class="simpara">
 736           Add improvement to non-central chi squared distribution quantile due to
 737           Thomas Luu, <a href="http://discovery.ucl.ac.uk/1482128/" target="_top">Fast and accurate
 738           parallel computation of quantile functions for random number generation,
 739           Doctorial Thesis 2016</a>. <a href="http://discovery.ucl.ac.uk/1463470/" target="_top">Efficient
 740           and Accurate Parallel Inversion of the Gamma Distribution, Thomas Luu</a>
 741         </p>
 742 <h5>
 743 <a name="math_toolkit.history2.h19"></a>
 744           <span class="phrase"><a name="math_toolkit.history2.boost_1_54"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_54">Boost-1.54</a>
 745         </h5>
 746 </li>
 747 <li class="listitem">
 748           Major reorganization to incorporate other Boost.Math like Integer Utilities
 749           Integer Utilities (Greatest Common Divisor and Least Common Multiple),
 750           quaternions and octonions. Making new chapter headings.
 751         </li>
 752 <li class="listitem">
 753           Added many references to Boost.Multiprecision and <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>
 754           as an example of a User-defined Type (UDT).
 755         </li>
 756 <li class="listitem">
 757           Added Clang to list of supported compilers.
 758         </li>
 759 <li class="listitem">
 760           Fixed constants to use a thread-safe cache of computed values when used
 761           at arbitrary precision.
 762         </li>
 763 <li class="listitem">
 764           Added finding zeros of Bessel functions <code class="computeroutput"><span class="identifier">cyl_bessel_j_zero</span></code>,
 765           <code class="computeroutput"><span class="identifier">cyl_neumann_zero</span></code>, <code class="computeroutput"><span class="identifier">airy_ai_zero</span></code> and <code class="computeroutput"><span class="identifier">airy_bi_zero</span></code>(by
 766           Christopher Kormanyos).
 767         </li>
 768 <li class="listitem">
 769           More accuracy improvements to the Bessel J and Y functions from Rocco Romeo.
 770         </li>
 771 <li class="listitem">
 772           Fixed nasty cyclic dependency bug that caused some headers to not compile
 773           <a href="https://svn.boost.org/trac/boost/ticket/7999" target="_top">#7999</a>.
 774         </li>
 775 <li class="listitem">
 776           Fixed bug in <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
 777           that caused spurious overflow for arguments between 142.5 and 143.
 778         </li>
 779 <li class="listitem">
 780           Fixed bug in raise_rounding_error that caused it to return an incorrect
 781           result when throwing an exception is turned off <a href="https://svn.boost.org/trac/boost/ticket/7905" target="_top">#7905</a>.
 782         </li>
 783 <li class="listitem">
 784           Added minimal __float128 support.
 785         </li>
 786 <li class="listitem">
 787           Fixed bug in edge-cases of poisson quantile <a href="https://svn.boost.org/trac/boost/ticket/8308" target="_top">#8308</a>.
 788         </li>
 789 <li class="listitem">
 790           Adjusted heuristics used in Halley iteration to cope with inverting the
 791           incomplete beta in tricky regions where the derivative is flatlining. Example
 792           is computing the quantile of the Fisher F distribution for probabilities
 793           smaller than machine epsilon. See ticket <a href="https://svn.boost.org/trac/boost/ticket/8314" target="_top">#8314</a>.
 794         </li>
 795 </ul></div>
 796 <h5>
 797 <a name="math_toolkit.history2.h20"></a>
 798       <span class="phrase"><a name="math_toolkit.history2.boost_1_53"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_53">Boost-1.53</a>
 799     </h5>
 800 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 801 <li class="listitem">
 802           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/7325" target="_top">#7325</a>,
 803           <a href="https://svn.boost.org/trac/boost/ticket/7415" target="_top">#7415</a>
 804           and <a href="https://svn.boost.org/trac/boost/ticket/7416" target="_top">#7416</a>,
 805           <a href="https://svn.boost.org/trac/boost/ticket/7183" target="_top">#7183</a>,
 806           <a href="https://svn.boost.org/trac/boost/ticket/7649" target="_top">#7649</a>,
 807           <a href="https://svn.boost.org/trac/boost/ticket/7694" target="_top">#7694</a>,
 808           <a href="https://svn.boost.org/trac/boost/ticket/4445" target="_top">#4445</a>,
 809           <a href="https://svn.boost.org/trac/boost/ticket/7492" target="_top">#7492</a>,
 810           <a href="https://svn.boost.org/trac/boost/ticket/7891" target="_top">#7891</a>,
 811           <a href="https://svn.boost.org/trac/boost/ticket/7429" target="_top">#7429</a>.
 812         </li>
 813 <li class="listitem">
 814           Fixed mistake in calculating pooled standard deviation in two-sample students
 815           t example <a href="https://svn.boost.org/trac/boost/ticket/7402" target="_top">#7402</a>.
 816         </li>
 817 <li class="listitem">
 818           Improve complex acos/asin/atan, see <a href="https://svn.boost.org/trac/boost/ticket/7290" target="_top">#7290</a>,
 819           <a href="https://svn.boost.org/trac/boost/ticket/7291" target="_top">#7291</a>.
 820         </li>
 821 <li class="listitem">
 822           Improve accuracy in some corner cases of <a class="link" href="bessel/bessel_first.html" title="Bessel Functions of the First and Second Kinds">cyl_bessel_j</a>
 823           and <a class="link" href="sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>/<a class="link" href="sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>
 824           thanks to suggestions from Rocco Romeo.
 825         </li>
 826 <li class="listitem">
 827           Improve accuracy of Bessel J and Y for integer orders thanks to suggestions
 828           from Rocco Romeo.
 829         </li>
 830 </ul></div>
 831 <h5>
 832 <a name="math_toolkit.history2.h21"></a>
 833       <span class="phrase"><a name="math_toolkit.history2.boost_1_52"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_52">Boost-1.52</a>
 834     </h5>
 835 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 836 <li class="listitem">
 837           Corrected moments for small degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7177" target="_top">#7177</a>
 838           (reported by Thomas Mang).
 839         </li>
 840 <li class="listitem">
 841           Added <a class="link" href="airy.html" title="Airy Functions">Airy functions</a> and <a class="link" href="jacobi.html" title="Jacobi Elliptic Functions">Jacobi Elliptic functions</a>.
 842         </li>
 843 <li class="listitem">
 844           Corrected failure to detect bad parameters in many distributions <a href="https://svn.boost.org/trac/boost/ticket/6934" target="_top">#6934</a> (reported
 845           by Florian Schoppmann) by adding a function check_out_of_range to test
 846           many possible bad parameters. This test revealed several distributions
 847           where the checks for bad parameters were ineffective, and these have been
 848           rectified.
 849         </li>
 850 <li class="listitem">
 851           Fixed issue in Hankel functions that causes incorrect values to be returned
 852           for <span class="emphasis"><em>x &lt; 0</em></span> and &#957; odd, see <a href="https://svn.boost.org/trac/boost/ticket/7135" target="_top">#7135</a>.
 853         </li>
 854 <li class="listitem">
 855           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/6517" target="_top">#6517</a>,
 856           <a href="https://svn.boost.org/trac/boost/ticket/6362" target="_top">#6362</a>,
 857           <a href="https://svn.boost.org/trac/boost/ticket/7053" target="_top">#7053</a>,
 858           <a href="https://svn.boost.org/trac/boost/ticket/2693" target="_top">#2693</a>,
 859           <a href="https://svn.boost.org/trac/boost/ticket/6937" target="_top">#6937</a>,
 860           <a href="https://svn.boost.org/trac/boost/ticket/7099" target="_top">#7099</a>.
 861         </li>
 862 <li class="listitem">
 863           Permitted infinite degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>
 864           implemented using the normal distribution (requested by Thomas Mang).
 865         </li>
 866 <li class="listitem">
 867           Much enhanced accuracy for large degrees of freedom &#957; and/or large non-centrality
 868           &#948;
 869 by switching to use the Students t distribution (or Normal distribution
 870           for infinite degrees of freedom) centered at delta, when &#948; / (4 * &#957;) &lt;
 871           epsilon for the floating-point type in use. <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>.
 872           It was found that the incomplete beta was suffering from serious cancellation
 873           errors when degrees of freedom was very large. (That has now been fixed
 874           in our code, but any code based on Didonato and Morris's original papers
 875           (probably every implementation out there actually) will have the same issue).
 876         </li>
 877 </ul></div>
 878 <h5>
 879 <a name="math_toolkit.history2.h22"></a>
 880       <span class="phrase"><a name="math_toolkit.history2.boost_1_51"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_51">Boost-1.51</a>
 881     </h5>
 882 <p>
 883       See Boost-1.52 - some items were added but not listed in time for the release.
 884     </p>
 885 <h5>
 886 <a name="math_toolkit.history2.h23"></a>
 887       <span class="phrase"><a name="math_toolkit.history2.boost_1_50"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_50">Boost-1.50</a>
 888     </h5>
 889 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 890 <li class="listitem">
 891           Promoted math constants to be 1st class citizens, including convenient
 892           access to the most widely used built-in float, double, long double via
 893           three namespaces.
 894         </li>
 895 <li class="listitem">
 896           Added the Owen's T function and Skew Normal distribution written by Benjamin
 897           Sobotta: see <a class="link" href="owens_t.html" title="Owen's T function">Owens T</a> and skew_normal_distrib.
 898         </li>
 899 <li class="listitem">
 900           Added Hankel functions <a class="link" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a>,
 901           <a class="link" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_2</a>, <a class="link" href="hankel/sph_hankel.html" title="Spherical Hankel Functions">sph_hankel_1</a> and <a class="link" href="hankel/sph_hankel.html" title="Spherical Hankel Functions">sph_hankel_2</a>.
 902         </li>
 903 <li class="listitem">
 904           Corrected issue <a href="https://svn.boost.org/trac/boost/ticket/6627" target="_top">#6627
 905           nonfinite_num_put formatting of 0.0 is incorrect</a> based on a patch
 906           submitted by K R Walker.
 907         </li>
 908 <li class="listitem">
 909           Changed constant initialization mechanism so that it is thread safe even
 910           for user-defined types, also so that user defined types get the full precision
 911           of the constant, even when <code class="computeroutput"><span class="keyword">long</span>
 912           <span class="keyword">double</span></code> does not. So for example
 913           128-bit rational approximations will work with UDT's and do the right thing,
 914           even though <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
 915           may be only 64 or 80 bits.
 916         </li>
 917 <li class="listitem">
 918           Fixed issue in <code class="computeroutput"><span class="identifier">bessel_jy</span></code>
 919           which causes Y<sub>8.5</sub>(4&#960;) to yield a NaN.
 920         </li>
 921 </ul></div>
 922 <h5>
 923 <a name="math_toolkit.history2.h24"></a>
 924       <span class="phrase"><a name="math_toolkit.history2.boost_1_49"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_49">Boost-1.49</a>
 925     </h5>
 926 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 927 <li class="listitem">
 928           Deprecated wrongly named <code class="computeroutput"><span class="identifier">twothirds</span></code>
 929           math constant in favour of <code class="computeroutput"><span class="identifier">two_thirds</span></code>
 930           (with underscore separator). (issue <a href="https://svn.boost.org/trac/boost/ticket/6199" target="_top">#6199</a>).
 931         </li>
 932 <li class="listitem">
 933           Refactored test data and some special function code to improve support
 934           for arbitary precision and/or expression-template-enabled types.
 935         </li>
 936 <li class="listitem">
 937           Added new faster zeta function evaluation method.
 938         </li>
 939 </ul></div>
 940 <p>
 941       Fixed issues:
 942     </p>
 943 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 944 <li class="listitem">
 945           Corrected CDF complement for Laplace distribution (issue <a href="https://svn.boost.org/trac/boost/ticket/6151" target="_top">#6151</a>).
 946         </li>
 947 <li class="listitem">
 948           Corrected branch cuts on the complex inverse trig functions, to handle
 949           signed zeros (issue <a href="https://svn.boost.org/trac/boost/ticket/6171" target="_top">#6171</a>).
 950         </li>
 951 <li class="listitem">
 952           Fixed bug in <code class="computeroutput"><span class="identifier">bessel_yn</span></code>
 953           which caused incorrect overflow errors to be raised for negative <span class="emphasis"><em>n</em></span>
 954           (issue <a href="https://svn.boost.org/trac/boost/ticket/6367" target="_top">#6367</a>).
 955         </li>
 956 <li class="listitem">
 957           Also fixed minor/cosmetic/configuration issues <a href="https://svn.boost.org/trac/boost/ticket/6120" target="_top">#6120</a>,
 958           <a href="https://svn.boost.org/trac/boost/ticket/6191" target="_top">#6191</a>,
 959           <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>,
 960           <a href="https://svn.boost.org/trac/boost/ticket/6130" target="_top">#6130</a>,
 961           <a href="https://svn.boost.org/trac/boost/ticket/6234" target="_top">#6234</a>,
 962           <a href="https://svn.boost.org/trac/boost/ticket/6307" target="_top">#6307</a>,
 963           <a href="https://svn.boost.org/trac/boost/ticket/6192" target="_top">#6192</a>.
 964         </li>
 965 </ul></div>
 966 <h5>
 967 <a name="math_toolkit.history2.h25"></a>
 968       <span class="phrase"><a name="math_toolkit.history2.boost_1_48"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_48">Boost-1.48</a>
 969     </h5>
 970 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 971 <li class="listitem">
 972           Added new series evaluation methods to the cyclic Bessel I, J, K and Y
 973           functions. Also taken great care to avoid spurious over and underflow of
 974           these functions. Fixes issue <a href="https://svn.boost.org/trac/boost/ticket/5560" target="_top">#5560</a>
 975         </li>
 976 <li class="listitem">
 977           Added an example of using Inverse Chi-Squared distribution for Bayesian
 978           statistics, provided by Thomas Mang.
 979         </li>
 980 <li class="listitem">
 981           Added tests to use improved version of lexical_cast which handles C99 nonfinites
 982           without using globale facets.
 983         </li>
 984 <li class="listitem">
 985           Corrected wrong out-of-bound uniform distribution CDF complement values
 986           <a href="https://svn.boost.org/trac/boost/ticket/5733" target="_top">#5733</a>.
 987         </li>
 988 <li class="listitem">
 989           Enabled long double support on OpenBSD (issue <a href="https://svn.boost.org/trac/boost/ticket/6014" target="_top">#6014</a>).
 990         </li>
 991 <li class="listitem">
 992           Changed nextafter and related functions to behave in the same way as other
 993           implementations - so that nextafter(+INF, 0) is a finite value (issue
 994           <a href="https://svn.boost.org/trac/boost/ticket/5823" target="_top">#5832</a>).
 995         </li>
 996 <li class="listitem">
 997           Changed tuple include configuration to fix issue when using in conjunction
 998           with Boost.Tr1 (issue <a href="https://svn.boost.org/trac/boost/ticket/5934" target="_top">#5934</a>).
 999         </li>
1000 <li class="listitem">
1001           Changed class eps_tolerance to behave correctly when both ends of the range
1002           are zero (issue <a href="https://svn.boost.org/trac/boost/ticket/6001" target="_top">#6001</a>).
1003         </li>
1004 <li class="listitem">
1005           Fixed missing include guards on prime.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5927" target="_top">#5927</a>).
1006         </li>
1007 <li class="listitem">
1008           Removed unused/undocumented constants from constants.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>).
1009         </li>
1010 <li class="listitem">
1011           Fixed missing std:: prefix in nonfinite_num_facets.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5914" target="_top">#5914</a>).
1012         </li>
1013 <li class="listitem">
1014           Minor patches for Cray compiler compatibility.
1015         </li>
1016 </ul></div>
1017 <h5>
1018 <a name="math_toolkit.history2.h26"></a>
1019       <span class="phrase"><a name="math_toolkit.history2.boost_1_47"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_47">Boost-1.47</a>
1020     </h5>
1021 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1022 <li class="listitem">
1023           Added changesign function to sign.hpp to facilitate addition of nonfinite
1024           facets.
1025         </li>
1026 <li class="listitem">
1027           Addition of nonfinite facets from Johan Rade, with tests, examples of use
1028           for C99 format infinity and NaN, and documentation.
1029         </li>
1030 <li class="listitem">
1031           Added tests and documentation of changesign from Johan Rade.
1032         </li>
1033 </ul></div>
1034 <h5>
1035 <a name="math_toolkit.history2.h27"></a>
1036       <span class="phrase"><a name="math_toolkit.history2.boost_1_46_1"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_46_1">Boost-1.46.1</a>
1037     </h5>
1038 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
1039           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5095</a>,
1040           <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
1041         </li></ul></div>
1042 <h5>
1043 <a name="math_toolkit.history2.h28"></a>
1044       <span class="phrase"><a name="math_toolkit.history2.boost_1_46_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_46_0">Boost-1.46.0</a>
1045     </h5>
1046 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1047 <li class="listitem">
1048           Added Wald, Inverse Gaussian and geometric distributions.
1049         </li>
1050 <li class="listitem">
1051           Added information about configuration macros.
1052         </li>
1053 <li class="listitem">
1054           Added support for mpreal as a real-numbered type.
1055         </li>
1056 </ul></div>
1057 <h5>
1058 <a name="math_toolkit.history2.h29"></a>
1059       <span class="phrase"><a name="math_toolkit.history2.boost_1_45_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_45_0">Boost-1.45.0</a>
1060     </h5>
1061 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1062 <li class="listitem">
1063           Added warnings about potential ambiguity with std random library in distribution
1064           and function names.
1065         </li>
1066 <li class="listitem">
1067           Added inverse gamma distribution and inverse chi_square and scaled inverse
1068           chi_square.
1069         </li>
1070 <li class="listitem">
1071           Editorial revision of documentation, and added FAQ.
1072         </li>
1073 </ul></div>
1074 <h5>
1075 <a name="math_toolkit.history2.h30"></a>
1076       <span class="phrase"><a name="math_toolkit.history2.boost_1_44_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_44_0">Boost-1.44.0</a>
1077     </h5>
1078 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1079 <li class="listitem">
1080           Fixed incorrect range and support for Rayleigh distribution.
1081         </li>
1082 <li class="listitem">
1083           Fixed numerical error in the quantile of the Student's T distribution:
1084           the function was returning garbage values for non-integer degrees of freedom
1085           between 2 and 3.
1086         </li>
1087 </ul></div>
1088 <h5>
1089 <a name="math_toolkit.history2.h31"></a>
1090       <span class="phrase"><a name="math_toolkit.history2.boost_1_41_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_41_0">Boost-1.41.0</a>
1091     </h5>
1092 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
1093           Significantly improved performance for the incomplete gamma function and
1094           its inverse.
1095         </li></ul></div>
1096 <h5>
1097 <a name="math_toolkit.history2.h32"></a>
1098       <span class="phrase"><a name="math_toolkit.history2.boost_1_40_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_40_0">Boost-1.40.0</a>
1099     </h5>
1100 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1101 <li class="listitem">
1102           Added support for MPFR as a bignum type.
1103         </li>
1104 <li class="listitem">
1105           Added some full specializations of the policy classes to reduce compile
1106           times.
1107         </li>
1108 <li class="listitem">
1109           Added logistic and hypergeometric distributions, from Gautam Sewani's Google
1110           Summer of Code project.
1111         </li>
1112 <li class="listitem">
1113           Added Laplace distribution submitted by Thijs van den Berg.
1114         </li>
1115 <li class="listitem">
1116           Updated performance test code to include new distributions, and improved
1117           the performance of the non-central distributions.
1118         </li>
1119 <li class="listitem">
1120           Added SSE2 optimised <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
1121           code, from Gautam Sewani's Google Summer of Code project.
1122         </li>
1123 <li class="listitem">
1124           Fixed bug in cyl_bessel_i that used an incorrect approximation for &#957; = 0.5,
1125           also effects the non-central Chi Square Distribution when &#957; = 3, see bug
1126           report <a href="https://svn.boost.org/trac/boost/ticket/2877" target="_top">#2877</a>.
1127         </li>
1128 <li class="listitem">
1129           Fixed minor bugs <a href="https://svn.boost.org/trac/boost/ticket/2873" target="_top">#2873</a>.
1130         </li>
1131 </ul></div>
1132 <h5>
1133 <a name="math_toolkit.history2.h33"></a>
1134       <span class="phrase"><a name="math_toolkit.history2.boost_1_38_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_38_0">Boost-1.38.0</a>
1135     </h5>
1136 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1137 <li class="listitem">
1138           Added Johan R&#229;de's optimised floating point classification routines.
1139         </li>
1140 <li class="listitem">
1141           Fixed code so that it compiles in GCC's -pedantic mode (bug report <a href="https://svn.boost.org/trac/boost/ticket/1451" target="_top">#1451</a>).
1142         </li>
1143 </ul></div>
1144 <h5>
1145 <a name="math_toolkit.history2.h34"></a>
1146       <span class="phrase"><a name="math_toolkit.history2.boost_1_37_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_37_0">Boost-1.37.0</a>
1147     </h5>
1148 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
1149           Improved accuracy and testing of the inverse hypergeometric functions.
1150         </li></ul></div>
1151 <h5>
1152 <a name="math_toolkit.history2.h35"></a>
1153       <span class="phrase"><a name="math_toolkit.history2.boost_1_36_0"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_36_0">Boost-1.36.0</a>
1154     </h5>
1155 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1156 <li class="listitem">
1157           Added Noncentral Chi Squared Distribution.
1158         </li>
1159 <li class="listitem">
1160           Added Noncentral Beta Distribution.
1161         </li>
1162 <li class="listitem">
1163           Added Noncentral F Distribution.
1164         </li>
1165 <li class="listitem">
1166           Added Noncentral T Distribution.
1167         </li>
1168 <li class="listitem">
1169           Added Exponential Integral Functions.
1170         </li>
1171 <li class="listitem">
1172           Added Zeta Function.
1173         </li>
1174 <li class="listitem">
1175           Added Rounding and Truncation functions.
1176         </li>
1177 <li class="listitem">
1178           Added Compile time powers of runtime bases.
1179         </li>
1180 <li class="listitem">
1181           Added SSE2 optimizations for Lanczos evaluation.
1182         </li>
1183 </ul></div>
1184 <h5>
1185 <a name="math_toolkit.history2.h36"></a>
1186       <span class="phrase"><a name="math_toolkit.history2.boost_1_35_0_post_review_first_o"></a></span><a class="link" href="history2.html#math_toolkit.history2.boost_1_35_0_post_review_first_o">Boost-1.35.0:
1187       Post Review First Official Release</a>
1188     </h5>
1189 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1190 <li class="listitem">
1191           Added Policy based framework that allows fine grained control over function
1192           behaviour.
1193         </li>
1194 <li class="listitem">
1195           <span class="bold"><strong>Breaking change:</strong></span> Changed default behaviour
1196           for domain, pole and overflow errors to throw an exception (based on review
1197           feedback), this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
1198         </li>
1199 <li class="listitem">
1200           <span class="bold"><strong>Breaking change:</strong></span> Changed exception thrown
1201           when an internal evaluation error occurs to boost::math::evaluation_error.
1202         </li>
1203 <li class="listitem">
1204           <span class="bold"><strong>Breaking change:</strong></span> Changed discrete quantiles
1205           to return an integer result: this is anything up to 20 times faster than
1206           finding the true root, this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
1207         </li>
1208 <li class="listitem">
1209           Polynomial/rational function evaluation is now customisable and hopefully
1210           faster than before.
1211         </li>
1212 <li class="listitem">
1213           Added performance test program.
1214         </li>
1215 </ul></div>
1216 <h5>
1217 <a name="math_toolkit.history2.h37"></a>
1218       <span class="phrase"><a name="math_toolkit.history2.milestone_4_second_review_candid"></a></span><a class="link" href="history2.html#math_toolkit.history2.milestone_4_second_review_candid">Milestone
1219       4: Second Review Candidate (1st March 2007)</a>
1220     </h5>
1221 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1222 <li class="listitem">
1223           Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
1224           them into line with the rest of the code.
1225         </li>
1226 <li class="listitem">
1227           Added C# "Distribution Explorer" demo application.
1228         </li>
1229 </ul></div>
1230 <h5>
1231 <a name="math_toolkit.history2.h38"></a>
1232       <span class="phrase"><a name="math_toolkit.history2.milestone_3_first_review_candida"></a></span><a class="link" href="history2.html#math_toolkit.history2.milestone_3_first_review_candida">Milestone
1233       3: First Review Candidate (31st Dec 2006)</a>
1234     </h5>
1235 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1236 <li class="listitem">
1237           Implemented the main probability distribution and density functions.
1238         </li>
1239 <li class="listitem">
1240           Implemented digamma.
1241         </li>
1242 <li class="listitem">
1243           Added more factorial functions.
1244         </li>
1245 <li class="listitem">
1246           Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
1247           harmonic functions from TR1.
1248         </li>
1249 <li class="listitem">
1250           Moved Xiaogang Zhang's elliptic integral code into the library, and brought
1251           them into line with the rest of the code.
1252         </li>
1253 <li class="listitem">
1254           Moved Hubert Holin's existing Boost.Math special functions into this library
1255           and brought them into line with the rest of the code.
1256         </li>
1257 </ul></div>
1258 <h5>
1259 <a name="math_toolkit.history2.h39"></a>
1260       <span class="phrase"><a name="math_toolkit.history2.milestone_2_released_september_1"></a></span><a class="link" href="history2.html#math_toolkit.history2.milestone_2_released_september_1">Milestone
1261       2: Released September 10th 2006</a>
1262     </h5>
1263 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1264 <li class="listitem">
1265           Implement preview release of the statistical distributions.
1266         </li>
1267 <li class="listitem">
1268           Added statistical distributions tutorial.
1269         </li>
1270 <li class="listitem">
1271           Implemented root finding algorithms.
1272         </li>
1273 <li class="listitem">
1274           Implemented the inverses of the incomplete gamma and beta functions.
1275         </li>
1276 <li class="listitem">
1277           Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
1278         </li>
1279 <li class="listitem">
1280           Integrated the statistical results generated from the test data with Boost.Test:
1281           uses a database of expected results, indexed by test, floating point type,
1282           platform, and compiler.
1283         </li>
1284 <li class="listitem">
1285           Improved lgamma near 1 and 2 (rational approximations).
1286         </li>
1287 <li class="listitem">
1288           Improved erf/erfc inverses (rational approximations).
1289         </li>
1290 <li class="listitem">
1291           Implemented Rational function generation (the Remez method).
1292         </li>
1293 </ul></div>
1294 <h5>
1295 <a name="math_toolkit.history2.h40"></a>
1296       <span class="phrase"><a name="math_toolkit.history2.milestone_1_released_march_31st_"></a></span><a class="link" href="history2.html#math_toolkit.history2.milestone_1_released_march_31st_">Milestone
1297       1: Released March 31st 2006</a>
1298     </h5>
1299 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1300 <li class="listitem">
1301           Implement gamma/beta/erf functions along with their incomplete counterparts.
1302         </li>
1303 <li class="listitem">
1304           Generate high quality test data, against which future improvements can
1305           be judged.
1306         </li>
1307 <li class="listitem">
1308           Provide tools for the evaluation of infinite series, continued fractions,
1309           and rational functions.
1310         </li>
1311 <li class="listitem">
1312           Provide tools for testing against tabulated test data, and collecting statistics
1313           on error rates.
1314         </li>
1315 <li class="listitem">
1316           Provide sufficient docs for people to be able to find their way around
1317           the library.
1318         </li>
1319 </ul></div>
1320 <p>
1321       SVN Revisions:
1322     </p>
1323 <p>
1324       Sandbox and trunk last synchonised at revision: .
1325     </p>
1326 </div>
1327 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
1328 <td align="left"></td>
1329 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
1330       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
1331       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
1332       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
1333       Daryle Walker and Xiaogang Zhang<p>
1334         Distributed under the Boost Software License, Version 1.0. (See accompanying
1335         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>)
1336       </p>
1337 </div></td>
1338 </tr></table>
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