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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     </p>
  32 <p>
  33       All bug reports including closed ones can be viewed <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>
  34       and <a href="https://github.com/boostorg/math/issues?utf8=%E2%9C%93&amp;q=is%3Aissue" target="_top">here</a>.
  35     </p>
  36 <h5>
  37 <a name="math_toolkit.history2.h0"></a>
  38       <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
  39       (Boost-1.71)</a>
  40     </h5>
  41 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  42 <li class="listitem">
  43           Catmull-Rom interpolator now works in C++11
  44         </li>
  45 <li class="listitem">
  46           Cardinal quadratic B-spline interpolation
  47         </li>
  48 <li class="listitem">
  49           Domain of elliptic integrals extended
  50         </li>
  51 <li class="listitem">
  52           sin_pi and cos_pi performance improvements
  53         </li>
  54 <li class="listitem">
  55           Forward-mode automatic differentiation
  56         </li>
  57 <li class="listitem">
  58           Vector valued barycentric rational interpolation
  59         </li>
  60 <li class="listitem">
  61           Ooura's method for evaluation of Fourier integrals
  62         </li>
  63 <li class="listitem">
  64           Multiple compatibility issues with Multiprecision fixed
  65         </li>
  66 <li class="listitem">
  67           Lambert-W fixed on a rare architecture
  68         </li>
  69 </ul></div>
  70 <h5>
  71 <a name="math_toolkit.history2.h1"></a>
  72       <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
  73       (Boost-1.70)</a>
  74     </h5>
  75 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  76 <li class="listitem">
  77           Add Lanczos smoothing derivatives
  78         </li>
  79 <li class="listitem">
  80           Move <code class="computeroutput"><span class="identifier">numerical_differentiation</span><span class="special">.</span><span class="identifier">hpp</span></code>
  81           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>
  82           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>.
  83         </li>
  84 <li class="listitem">
  85           Add mean, variance, skewness, kurtosis, median, Gini coefficient, and median
  86           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>.
  87         </li>
  88 <li class="listitem">
  89           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>
  90         </li>
  91 <li class="listitem">
  92           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
  93           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>.
  94         </li>
  95 <li class="listitem">
  96           Add total variation, l0, l1, l2, and sup norms, as well as corresponding
  97           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>.
  98         </li>
  99 <li class="listitem">
 100           Add move constructors for polynomials, support complex coefficients, add
 101           <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>
 102           methods.
 103         </li>
 104 <li class="listitem">
 105           Add <code class="computeroutput"><span class="identifier">quadratic_roots</span></code> to
 106           <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>.
 107         </li>
 108 <li class="listitem">
 109           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>.
 110         </li>
 111 <li class="listitem">
 112           Add Catmull-Rom interpolator.
 113         </li>
 114 <li class="listitem">
 115           Fix bug in <code class="computeroutput"><span class="identifier">newton_raphson_iterate</span></code>
 116           where we could terminate incorrectly under certain exceptional cases.
 117         </li>
 118 <li class="listitem">
 119           Suppressed warnings from use of <code class="computeroutput"><span class="identifier">Q</span></code>
 120           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>
 121           <span class="special">-</span><span class="identifier">pedantic</span></code>.
 122         </li>
 123 </ul></div>
 124 <h5>
 125 <a name="math_toolkit.history2.h2"></a>
 126       <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
 127       (Boost-1.69)</a>
 128     </h5>
 129 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 130 <li class="listitem">
 131           Add LambertW functions.
 132         </li>
 133 <li class="listitem">
 134           Update integration routines to support complex valued integrands and contour
 135           integrals.
 136         </li>
 137 <li class="listitem">
 138           Added the derivative of the Barycentric rational approximation.
 139         </li>
 140 <li class="listitem">
 141           Updated continued fraction and series evaluation code to support complex
 142           types.
 143         </li>
 144 <li class="listitem">
 145           Minor fixes to better support variable precision floating point types.
 146         </li>
 147 <li class="listitem">
 148           Removed use of deprecated Boost.Endian in favour of Predef.
 149         </li>
 150 <li class="listitem">
 151           Prevent logic error leading to infinite loop in toms748_solve. See <a href="https://github.com/boostorg/math/issues/138" target="_top">#138</a>.
 152         </li>
 153 <li class="listitem">
 154           Fix mean and standard_deviation for extreme_value_distribution. See <a href="https://github.com/boostorg/math/issues/139" target="_top">#139</a>.
 155         </li>
 156 <li class="listitem">
 157           Improve heuristics used in newton_raphson_iterate. See <a href="https://github.com/boostorg/math/issues/145" target="_top">#145</a>.
 158         </li>
 159 <li class="listitem">
 160           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>.
 161           See <a href="https://github.com/boostorg/math/issues/141" target="_top">#141</a>.
 162         </li>
 163 <li class="listitem">
 164           Big push to reduce GCC warnings. See <a href="https://github.com/boostorg/math/issues/136" target="_top">#136</a>.
 165         </li>
 166 <li class="listitem">
 167           Refactor polynomial addition. See <a href="https://github.com/boostorg/math/pull/132" target="_top">PR132</a>.
 168         </li>
 169 <li class="listitem">
 170           Fix for vxWorks having a <code class="computeroutput"><span class="identifier">real</span></code>
 171           function in the global namespace. See <a href="https://github.com/boostorg/math/pull/131" target="_top">PR131</a>.
 172         </li>
 173 <li class="listitem">
 174           Improve <code class="computeroutput"><span class="identifier">sinc</span></code> approximations
 175           and add better tests.
 176         </li>
 177 <li class="listitem">
 178           Fix typo in Student's T hypothesis testing documentation, see <a href="https://github.com/boostorg/math/issues/143" target="_top">#143</a>.
 179         </li>
 180 </ul></div>
 181 <h5>
 182 <a name="math_toolkit.history2.h3"></a>
 183       <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
 184       (Boost-1.68)</a>
 185     </h5>
 186 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 187 <li class="listitem">
 188           Continue to improve numerical integration routines, and in particular add
 189           support for contour integrals.
 190         </li>
 191 <li class="listitem">
 192           Improve accuracy of erfc function's rational approximations.
 193         </li>
 194 </ul></div>
 195 <h5>
 196 <a name="math_toolkit.history2.h4"></a>
 197       <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
 198       (Boost-1.66)</a>
 199     </h5>
 200 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 201 <li class="listitem">
 202           Add Gauss and Gauss-Kronrod quadrature routines.
 203         </li>
 204 <li class="listitem">
 205           Add double-exponential (tanh-sinh, exp-sinh and sinh-sinh) quadrature routines.
 206         </li>
 207 <li class="listitem">
 208           Add Chebyshev polynomial evaluation, roots, integration, differentiation,
 209           and interpolation routines.
 210         </li>
 211 </ul></div>
 212 <h5>
 213 <a name="math_toolkit.history2.h5"></a>
 214       <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
 215       (Boost-1.65)</a>
 216     </h5>
 217 <p>
 218       New Features:
 219     </p>
 220 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 221 <li class="listitem">
 222           Add <a class="link" href="cubic_b.html" title="Cubic B-spline interpolation">cubic B-Spline interpolation functions</a>,
 223           with thanks to Nick Thompson.
 224         </li>
 225 <li class="listitem">
 226           Add <a class="link" href="barycentric.html" title="Barycentric Rational Interpolation">barycentric rational interpolation
 227           functions</a>, with thanks to Nick Thompson.
 228         </li>
 229 <li class="listitem">
 230           Add <a class="link" href="trapezoidal.html" title="Trapezoidal Quadrature">adaptive trapezoidal quadrature</a>,
 231           with thanks to Nick Thompson.
 232         </li>
 233 <li class="listitem">
 234           Add <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">support for the zeros
 235           and derivatives of Legendre polynomials</a>, with thanks to Nick Thompson.
 236         </li>
 237 </ul></div>
 238 <p>
 239       Patches:
 240     </p>
 241 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 242 <li class="listitem">
 243           Improve polynomial GCD algorithms, with thanks to Jeremy Murphy.
 244         </li>
 245 <li class="listitem">
 246           Removed gcd/lcm routines from Boost.Math - these are now in Boost.Integer.
 247         </li>
 248 </ul></div>
 249 <h5>
 250 <a name="math_toolkit.history2.h6"></a>
 251       <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
 252       (Boost-1.64)</a>
 253     </h5>
 254 <p>
 255       Patches:
 256     </p>
 257 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 258 <li class="listitem">
 259           Big push to ensure all functions in also in C99 are compatible with Annex
 260           F.
 261         </li>
 262 <li class="listitem">
 263           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>.
 264         </li>
 265 </ul></div>
 266 <h5>
 267 <a name="math_toolkit.history2.h7"></a>
 268       <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
 269       (Boost-1.63)</a>
 270     </h5>
 271 <p>
 272       Patches:
 273     </p>
 274 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 275 <li class="listitem">
 276           Fixed evaluation of zero polynomial in polynomial.hpp, see <a href="https://svn.boost.org/trac/boost/ticket/12532" target="_top">12532</a>.
 277         </li>
 278 <li class="listitem">
 279           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>.
 280         </li>
 281 </ul></div>
 282 <h5>
 283 <a name="math_toolkit.history2.h8"></a>
 284       <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
 285       (Boost-1.62)</a>
 286     </h5>
 287 <p>
 288       New Features:
 289     </p>
 290 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 291           Enabled all the special function code to work correctly with types whose
 292           precision can change at runtime: for example type <code class="computeroutput"><span class="identifier">mpfr_float</span></code>
 293           from Boost.Multiprecision.
 294         </li></ul></div>
 295 <p>
 296       Patches:
 297     </p>
 298 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 299 <li class="listitem">
 300           Fix tgamma_delta_ratio for cases where the delta is small compared to the
 301           base.
 302         </li>
 303 <li class="listitem">
 304           Fix misc GCC-4.4 test failures.
 305         </li>
 306 </ul></div>
 307 <h5>
 308 <a name="math_toolkit.history2.h9"></a>
 309       <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
 310       (Boost-1.61)</a>
 311     </h5>
 312 <p>
 313       New Features:
 314     </p>
 315 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 316           Polynomial arithmetic added to tools.
 317         </li></ul></div>
 318 <h5>
 319 <a name="math_toolkit.history2.h10"></a>
 320       <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
 321       (Boost-1.60)</a>
 322     </h5>
 323 <p>
 324       New Features:
 325     </p>
 326 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 327 <li class="listitem">
 328           Promote the root finding and function minimization code to first class
 329           citizens - these are now officially supported as part of the library.
 330         </li>
 331 <li class="listitem">
 332           Allow the library to be used and tested with compiler exception handling
 333           support turned off. To better facilitate this the default error handling
 334           policies have been changed to <span class="emphasis"><em>errno_on_error</em></span> but only
 335           when the compiler has no exception handling support.
 336         </li>
 337 </ul></div>
 338 <p>
 339       Patches:
 340     </p>
 341 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 342 <li class="listitem">
 343           Fix behaviour of the non-central chi-squared distribution when the non-centrality
 344           parameter is zero to match the chi-squared, see <a href="https://svn.boost.org/trac/boost/ticket/11557" target="_top">11557</a>.
 345         </li>
 346 <li class="listitem">
 347           Fix comments in code for the hypergeometric to match what it actually does,
 348           also fixes the parameter access functions to return the correct values.
 349           See <a href="https://svn.boost.org/trac/boost/ticket/11556" target="_top">11556</a>.
 350         </li>
 351 <li class="listitem">
 352           Stopped using hidden visiblity library build with the Oracle compiler as
 353           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>.
 354         </li>
 355 <li class="listitem">
 356           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>.
 357         </li>
 358 <li class="listitem">
 359           Fix corner case bug in root bracketing code, see <a href="https://svn.boost.org/trac/boost/ticket/11532" target="_top">11532</a>.
 360         </li>
 361 <li class="listitem">
 362           Add some missing typecasts in arguments to std::max in Bernoulli code.
 363           See <a href="https://svn.boost.org/trac/boost/ticket/11453" target="_top">11453</a>.
 364         </li>
 365 <li class="listitem">
 366           Fix mistaken assumptions about the possible values for FLT_EVAL_METHOD.
 367           See <a href="https://svn.boost.org/trac/boost/ticket/11429" target="_top">11429</a>.
 368         </li>
 369 <li class="listitem">
 370           Completely revamped performance testing and error-rate measuring code so
 371           we can more easily document how well (or not!) we're doing. This information
 372           will hopefully get more frequently updated in future as it's more or less
 373           automatically generated - see the <span class="emphasis"><em>reporting</em></span> sub-directory
 374           for more information.
 375         </li>
 376 <li class="listitem">
 377           Fix some corner cases in the beta, incomplete beta, and incomplete beta
 378           derivative. With thanks to Rocco Romeo.
 379         </li>
 380 <li class="listitem">
 381           Reorganized the Bessel functions internally to improve the performance
 382           of Jn and Yn.
 383         </li>
 384 <li class="listitem">
 385           Fixed skewness formula for triangular distribution, see <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">#11768</a>.
 386         </li>
 387 <li class="listitem">
 388           Fixed some examples so they compile on Unix platforms which have an ::exception
 389           struct declared, see <a href="https://svn.boost.org/trac/boost/ticket/11827" target="_top">#11827</a>.
 390         </li>
 391 <li class="listitem">
 392           Correct mistake in triangular distribution skewness formula <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">11768</a>,
 393           reported by Juan Leni.
 394         </li>
 395 </ul></div>
 396 <h5>
 397 <a name="math_toolkit.history2.h11"></a>
 398       <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>
 399     </h5>
 400 <p>
 401       Patch release for Boost-1.58:
 402     </p>
 403 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 404 <li class="listitem">
 405           Minor <a href="https://github.com/boostorg/math/pull/13#issuecomment-98905579" target="_top">patch
 406           for Haiku support.</a>
 407         </li>
 408 <li class="listitem">
 409           Fix the decimal digit count for 128-bit floating point types.
 410         </li>
 411 <li class="listitem">
 412           Fix a few documentation typos.
 413         </li>
 414 </ul></div>
 415 <h5>
 416 <a name="math_toolkit.history2.h12"></a>
 417       <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
 418       (boost-1.58.0)</a>
 419     </h5>
 420 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 421 <li class="listitem">
 422           Added two new special functions - <a class="link" href="sf_gamma/trigamma.html" title="Trigamma">trigamma</a>
 423           and <a class="link" href="sf_gamma/polygamma.html" title="Polygamma">polygamma</a>.
 424         </li>
 425 <li class="listitem">
 426           Fixed namespace scope constants so they are constexpr on conforming compilers,
 427           see https://svn.boost.org/trac/boost/ticket/10901.
 428         </li>
 429 <li class="listitem">
 430           Fixed various cases of spurious under/overflow in the incomplete beta and
 431           gamma functions, plus the elliptic integrals, with thanks to Rocco Romeo.
 432         </li>
 433 <li class="listitem">
 434           Fix 3-arg <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
 435           and <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_q</a> functions
 436           to not call the policy based overload if the final argument is not actually
 437           a policy.
 438         </li>
 439 <li class="listitem">
 440           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>.
 441         </li>
 442 <li class="listitem">
 443           Fixed extreme-value pdf for large valued inputs, see <a href="https://svn.boost.org/trac/boost/ticket/10938" target="_top">#10938</a>.
 444         </li>
 445 <li class="listitem">
 446           Large update to the Elliptic integral code to use Carlson's latest algorithms
 447           - these should be more stable, more accurate and slightly faster than before.
 448           Also added support for Carlson's RG integral.
 449         </li>
 450 <li class="listitem">
 451           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
 452           integrals.
 453         </li>
 454 <li class="listitem">
 455           Switched documentation to use SVG rather than PNG graphs and equations
 456           - browsers seem to have finally caught up!
 457         </li>
 458 </ul></div>
 459 <h5>
 460 <a name="math_toolkit.history2.h13"></a>
 461       <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
 462       (boost-1.57.0)</a>
 463     </h5>
 464 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 465 <li class="listitem">
 466           Added <a class="link" href="dist_ref/dists/hyperexponential_dist.html" title="Hyperexponential Distribution">Hyperexponential
 467           Distribution</a>.
 468         </li>
 469 <li class="listitem">
 470           Fix some spurious overflows in the incomplete gamma functions (with thanks
 471           to Rocco Romeo).
 472         </li>
 473 <li class="listitem">
 474           Fix bug in derivative of incomplete beta when a = b = 0.5 - this also effects
 475           several non-central distributions, see <a href="https://svn.boost.org/trac/boost/ticket/10480" target="_top">10480</a>.
 476         </li>
 477 <li class="listitem">
 478           Fixed some corner cases in <a class="link" href="rounding/round.html" title="Rounding Functions">round</a>.
 479         </li>
 480 <li class="listitem">
 481           Don't support 80-bit floats in cstdfloat.hpp if standard library support
 482           is broken.
 483         </li>
 484 </ul></div>
 485 <h5>
 486 <a name="math_toolkit.history2.h14"></a>
 487       <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
 488       (Boost-1.56.0)</a>
 489     </h5>
 490 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 491 <li class="listitem">
 492           <span class="bold"><strong>Breaking change</strong></span>: moved a number of non-core
 493           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
 494           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>,
 495           <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>,
 496           <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
 497           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
 498           path.
 499         </li>
 500 <li class="listitem">
 501           <span class="bold"><strong>Breaking change</strong></span>: A number of distributions
 502           and special functions were returning the maximum finite value rather than
 503           raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>,
 504           this has now been fixed, which means these functions now behave as documented.
 505           However, since the default behavior on raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>
 506           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
 507           which have come to reply rely on these functions not throwing may experience
 508           exceptions where they did not before. The special functions involved are
 509           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>,
 510           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>,
 511           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
 512           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
 513           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>,
 514           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>,
 515           <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
 516           involved are <a class="link" href="dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto
 517           Distribution</a>, <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta
 518           Distribution</a>, <a class="link" href="dist_ref/dists/geometric_dist.html" title="Geometric Distribution">Geometric
 519           Distribution</a>, <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
 520           Binomial Distribution</a>, <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
 521           Distribution</a>, <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
 522           Squared Distribution</a>, <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
 523           Distribution</a>, <a class="link" href="dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">Inverse
 524           chi squared Distribution</a>, <a class="link" href="dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution">Inverse
 525           Gamma Distribution</a>. See <a href="https://svn.boost.org/trac/boost/ticket/10111" target="_top">#10111</a>.
 526         </li>
 527 <li class="listitem">
 528           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
 529           be used with integer arguments, see <a href="https://svn.boost.org/trac/boost/ticket/10066" target="_top">#10066</a>.
 530         </li>
 531 <li class="listitem">
 532           Fix Halley iteration to handle zero derivative (with non-zero second derivative),
 533           see <a href="https://svn.boost.org/trac/boost/ticket/10046" target="_top">#10046</a>.
 534         </li>
 535 </ul></div>
 536 <h5>
 537 <a name="math_toolkit.history2.h15"></a>
 538       <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>
 539     </h5>
 540 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 541 <li class="listitem">
 542           Fix Geometric distribution use of Policies, see <a href="https://svn.boost.org/trac/boost/ticket/9833" target="_top">#9833</a>.
 543         </li>
 544 <li class="listitem">
 545           Fix corner cases in the negative binomial distribution, see <a href="https://svn.boost.org/trac/boost/ticket/9834" target="_top">#9834</a>.
 546         </li>
 547 <li class="listitem">
 548           Fix compilation failures on Mac OS.
 549         </li>
 550 </ul></div>
 551 <h5>
 552 <a name="math_toolkit.history2.h16"></a>
 553       <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>
 554     </h5>
 555 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 556 <li class="listitem">
 557           Changed version number to new Boost.Math specific version now that we're
 558           in the modular Boost world.
 559         </li>
 560 <li class="listitem">
 561           Added <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
 562           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
 563           approximation (from Nikhar Agrawal).
 564         </li>
 565 <li class="listitem">
 566           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>,
 567           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_neumann_prime</a>,
 568           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_i_prime</a>,
 569           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_k_prime</a>,
 570           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_bessel_prime</a>
 571           and <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_neumann_prime</a>
 572           (from Anton Bikineev).
 573         </li>
 574 <li class="listitem">
 575           Fixed buggy Student's t example code, along with docs for testing sample
 576           means for equivalence.
 577         </li>
 578 <li class="listitem">
 579           Documented <code class="computeroutput"><span class="identifier">max_iter</span></code> parameter
 580           in root finding code better, see <a href="https://svn.boost.org/trac/boost/ticket/9225" target="_top">#9225</a>.
 581         </li>
 582 <li class="listitem">
 583           Add option to explicitly enable/disable use of __float128 in constants
 584           code, see <a href="https://svn.boost.org/trac/boost/ticket/9240" target="_top">#9240</a>.
 585         </li>
 586 <li class="listitem">
 587           Cleaned up handling of negative values in Bessel I0 and I1 code (removed
 588           dead code), see <a href="https://svn.boost.org/trac/boost/ticket/9512" target="_top">#9512</a>.
 589         </li>
 590 <li class="listitem">
 591           Fixed handling of very small values passed to <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
 592           and <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> so they
 593           don't generate spurious overflows (thanks to Rocco Romeo).
 594         </li>
 595 <li class="listitem">
 596           <a href="https://svn.boost.org/trac/boost/ticket/9672" target="_top">#9672 PDF and
 597           CDF of a Laplace distribution throwing domain_error</a> Random variate
 598           can now be infinite.
 599         </li>
 600 <li class="listitem">
 601           Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
 602           <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
 603           and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
 604           with thanks to Rocco Romeo.
 605         </li>
 606 <li class="listitem">
 607           Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
 608           <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
 609           and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
 610           (thanks to Rocco Romeo).
 611         </li>
 612 <li class="listitem">
 613           Removed constant <code class="computeroutput"><span class="identifier">pow23_four_minus_pi</span>
 614           </code> whose value did not match the name (and was unused by Boost.Math),
 615           see <a href="https://svn.boost.org/trac/boost/ticket/9712" target="_top">#9712</a>.
 616         </li>
 617 </ul></div>
 618 <h5>
 619 <a name="math_toolkit.history2.h17"></a>
 620       <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>
 621     </h5>
 622 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 623 <li class="listitem">
 624           Suppress numerous warnings (mostly from GCC-4.8 and MSVC) <a href="https://svn.boost.org/trac/boost/ticket/8384" target="_top">#8384</a>,
 625           <a href="https://svn.boost.org/trac/boost/ticket/8855" target="_top">#8855</a>,
 626           <a href="https://svn.boost.org/trac/boost/ticket/9107" target="_top">#9107</a>,
 627           <a href="https://svn.boost.org/trac/boost/ticket/9109" target="_top">#9109</a>..
 628         </li>
 629 <li class="listitem">
 630           Fixed PGI compilation issue <a href="https://svn.boost.org/trac/boost/ticket/8333" target="_top">#8333</a>.
 631         </li>
 632 <li class="listitem">
 633           Fixed PGI constant value initialization issue that caused erf to generate
 634           incorrect results <a href="https://svn.boost.org/trac/boost/ticket/8621" target="_top">#8621</a>.
 635         </li>
 636 <li class="listitem">
 637           Prevent macro expansion of some C99 macros that are also C++ functions
 638           <a href="https://svn.boost.org/trac/boost/ticket/8732" target="_top">#8732</a>
 639           and <a href="https://svn.boost.org/trac/boost/ticket/8733" target="_top">#8733</a>..
 640         </li>
 641 <li class="listitem">
 642           Fixed Student's T distribution to behave correctly with huge degrees of
 643           freedom (larger than the largest representable integer) <a href="https://svn.boost.org/trac/boost/ticket/8837" target="_top">#8837</a>.
 644         </li>
 645 <li class="listitem">
 646           Make some core functions usable with <code class="computeroutput"><span class="keyword">long</span>
 647           <span class="keyword">double</span></code> even when the platform has
 648           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>.
 649         </li>
 650 <li class="listitem">
 651           Fix error handling of distributions to catch invalid scale and location
 652           parameters when the random variable is infinite <a href="https://svn.boost.org/trac/boost/ticket/9042" target="_top">#9042</a>
 653           and <a href="https://svn.boost.org/trac/boost/ticket/9126" target="_top">#9126</a>.
 654         </li>
 655 <li class="listitem">
 656           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>.
 657         </li>
 658 <li class="listitem">
 659           Improve consistency of argument reduction in the elliptic integrals <a href="https://svn.boost.org/trac/boost/ticket/9104" target="_top">#9104</a>.
 660         </li>
 661 <li class="listitem">
 662           Fix bug in inverse incomplete beta that results in cancellation errors
 663           when the beta function is really an arcsine or Student's T distribution.
 664         </li>
 665 <li class="listitem">
 666           Fix issue in Bessel I and K function continued fractions that causes spurious
 667           over/underflow.
 668         </li>
 669 <li class="listitem">
 670 <p class="simpara">
 671           Add improvement to non-central chi squared distribution quantile due to
 672           Thomas Luu, <a href="http://discovery.ucl.ac.uk/1482128/" target="_top">Fast and accurate
 673           parallel computation of quantile functions for random number generation,
 674           Doctorial Thesis 2016</a>. <a href="http://discovery.ucl.ac.uk/1463470/" target="_top">Efficient
 675           and Accurate Parallel Inversion of the Gamma Distribution, Thomas Luu</a>
 676         </p>
 677 <h5>
 678 <a name="math_toolkit.history2.h18"></a>
 679           <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>
 680         </h5>
 681 </li>
 682 <li class="listitem">
 683           Major reorganization to incorporate other Boost.Math like Integer Utilities
 684           Integer Utilities (Greatest Common Divisor and Least Common Multiple),
 685           quaternions and octonions. Making new chapter headings.
 686         </li>
 687 <li class="listitem">
 688           Added many references to Boost.Multiprecision and <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>
 689           as an example of a User-defined Type (UDT).
 690         </li>
 691 <li class="listitem">
 692           Added Clang to list of supported compilers.
 693         </li>
 694 <li class="listitem">
 695           Fixed constants to use a thread-safe cache of computed values when used
 696           at arbitrary precision.
 697         </li>
 698 <li class="listitem">
 699           Added finding zeros of Bessel functions <code class="computeroutput"><span class="identifier">cyl_bessel_j_zero</span></code>,
 700           <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
 701           Christopher Kormanyos).
 702         </li>
 703 <li class="listitem">
 704           More accuracy improvements to the Bessel J and Y functions from Rocco Romeo.
 705         </li>
 706 <li class="listitem">
 707           Fixed nasty cyclic dependency bug that caused some headers to not compile
 708           <a href="https://svn.boost.org/trac/boost/ticket/7999" target="_top">#7999</a>.
 709         </li>
 710 <li class="listitem">
 711           Fixed bug in <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
 712           that caused spurious overflow for arguments between 142.5 and 143.
 713         </li>
 714 <li class="listitem">
 715           Fixed bug in raise_rounding_error that caused it to return an incorrect
 716           result when throwing an exception is turned off <a href="https://svn.boost.org/trac/boost/ticket/7905" target="_top">#7905</a>.
 717         </li>
 718 <li class="listitem">
 719           Added minimal __float128 support.
 720         </li>
 721 <li class="listitem">
 722           Fixed bug in edge-cases of poisson quantile <a href="https://svn.boost.org/trac/boost/ticket/8308" target="_top">#8308</a>.
 723         </li>
 724 <li class="listitem">
 725           Adjusted heuristics used in Halley iteration to cope with inverting the
 726           incomplete beta in tricky regions where the derivative is flatlining. Example
 727           is computing the quantile of the Fisher F distribution for probabilities
 728           smaller than machine epsilon. See ticket <a href="https://svn.boost.org/trac/boost/ticket/8314" target="_top">#8314</a>.
 729         </li>
 730 </ul></div>
 731 <h5>
 732 <a name="math_toolkit.history2.h19"></a>
 733       <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>
 734     </h5>
 735 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 736 <li class="listitem">
 737           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/7325" target="_top">#7325</a>,
 738           <a href="https://svn.boost.org/trac/boost/ticket/7415" target="_top">#7415</a>
 739           and <a href="https://svn.boost.org/trac/boost/ticket/7416" target="_top">#7416</a>,
 740           <a href="https://svn.boost.org/trac/boost/ticket/7183" target="_top">#7183</a>,
 741           <a href="https://svn.boost.org/trac/boost/ticket/7649" target="_top">#7649</a>,
 742           <a href="https://svn.boost.org/trac/boost/ticket/7694" target="_top">#7694</a>,
 743           <a href="https://svn.boost.org/trac/boost/ticket/4445" target="_top">#4445</a>,
 744           <a href="https://svn.boost.org/trac/boost/ticket/7492" target="_top">#7492</a>,
 745           <a href="https://svn.boost.org/trac/boost/ticket/7891" target="_top">#7891</a>,
 746           <a href="https://svn.boost.org/trac/boost/ticket/7429" target="_top">#7429</a>.
 747         </li>
 748 <li class="listitem">
 749           Fixed mistake in calculating pooled standard deviation in two-sample students
 750           t example <a href="https://svn.boost.org/trac/boost/ticket/7402" target="_top">#7402</a>.
 751         </li>
 752 <li class="listitem">
 753           Improve complex acos/asin/atan, see <a href="https://svn.boost.org/trac/boost/ticket/7290" target="_top">#7290</a>,
 754           <a href="https://svn.boost.org/trac/boost/ticket/7291" target="_top">#7291</a>.
 755         </li>
 756 <li class="listitem">
 757           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>
 758           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>
 759           thanks to suggestions from Rocco Romeo.
 760         </li>
 761 <li class="listitem">
 762           Improve accuracy of Bessel J and Y for integer orders thanks to suggestions
 763           from Rocco Romeo.
 764         </li>
 765 </ul></div>
 766 <h5>
 767 <a name="math_toolkit.history2.h20"></a>
 768       <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>
 769     </h5>
 770 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 771 <li class="listitem">
 772           Corrected moments for small degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7177" target="_top">#7177</a>
 773           (reported by Thomas Mang).
 774         </li>
 775 <li class="listitem">
 776           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>.
 777         </li>
 778 <li class="listitem">
 779           Corrected failure to detect bad parameters in many distributions <a href="https://svn.boost.org/trac/boost/ticket/6934" target="_top">#6934</a> (reported
 780           by Florian Schoppmann) by adding a function check_out_of_range to test
 781           many possible bad parameters. This test revealed several distributions
 782           where the checks for bad parameters were ineffective, and these have been
 783           rectified.
 784         </li>
 785 <li class="listitem">
 786           Fixed issue in Hankel functions that causes incorrect values to be returned
 787           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>.
 788         </li>
 789 <li class="listitem">
 790           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/6517" target="_top">#6517</a>,
 791           <a href="https://svn.boost.org/trac/boost/ticket/6362" target="_top">#6362</a>,
 792           <a href="https://svn.boost.org/trac/boost/ticket/7053" target="_top">#7053</a>,
 793           <a href="https://svn.boost.org/trac/boost/ticket/2693" target="_top">#2693</a>,
 794           <a href="https://svn.boost.org/trac/boost/ticket/6937" target="_top">#6937</a>,
 795           <a href="https://svn.boost.org/trac/boost/ticket/7099" target="_top">#7099</a>.
 796         </li>
 797 <li class="listitem">
 798           Permitted infinite degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>
 799           implemented using the normal distribution (requested by Thomas Mang).
 800         </li>
 801 <li class="listitem">
 802           Much enhanced accuracy for large degrees of freedom &#957; and/or large non-centrality
 803           &#948;
 804 by switching to use the Students t distribution (or Normal distribution
 805           for infinite degrees of freedom) centered at delta, when &#948; / (4 * &#957;) &lt;
 806           epsilon for the floating-point type in use. <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>.
 807           It was found that the incomplete beta was suffering from serious cancellation
 808           errors when degrees of freedom was very large. (That has now been fixed
 809           in our code, but any code based on Didonato and Morris's original papers
 810           (probably every implementation out there actually) will have the same issue).
 811         </li>
 812 </ul></div>
 813 <h5>
 814 <a name="math_toolkit.history2.h21"></a>
 815       <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>
 816     </h5>
 817 <p>
 818       See Boost-1.52 - some items were added but not listed in time for the release.
 819     </p>
 820 <h5>
 821 <a name="math_toolkit.history2.h22"></a>
 822       <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>
 823     </h5>
 824 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 825 <li class="listitem">
 826           Promoted math constants to be 1st class citizens, including convenient
 827           access to the most widely used built-in float, double, long double via
 828           three namespaces.
 829         </li>
 830 <li class="listitem">
 831           Added the Owen's T function and Skew Normal distribution written by Benjamin
 832           Sobotta: see <a class="link" href="owens_t.html" title="Owen's T function">Owens T</a> and skew_normal_distrib.
 833         </li>
 834 <li class="listitem">
 835           Added Hankel functions <a class="link" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a>,
 836           <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>.
 837         </li>
 838 <li class="listitem">
 839           Corrected issue <a href="https://svn.boost.org/trac/boost/ticket/6627" target="_top">#6627
 840           nonfinite_num_put formatting of 0.0 is incorrect</a> based on a patch
 841           submitted by K R Walker.
 842         </li>
 843 <li class="listitem">
 844           Changed constant initialization mechanism so that it is thread safe even
 845           for user-defined types, also so that user defined types get the full precision
 846           of the constant, even when <code class="computeroutput"><span class="keyword">long</span>
 847           <span class="keyword">double</span></code> does not. So for example
 848           128-bit rational approximations will work with UDT's and do the right thing,
 849           even though <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
 850           may be only 64 or 80 bits.
 851         </li>
 852 <li class="listitem">
 853           Fixed issue in <code class="computeroutput"><span class="identifier">bessel_jy</span></code>
 854           which causes Y<sub>8.5</sub>(4&#960;) to yield a NaN.
 855         </li>
 856 </ul></div>
 857 <h5>
 858 <a name="math_toolkit.history2.h23"></a>
 859       <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>
 860     </h5>
 861 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 862 <li class="listitem">
 863           Deprecated wrongly named <code class="computeroutput"><span class="identifier">twothirds</span></code>
 864           math constant in favour of <code class="computeroutput"><span class="identifier">two_thirds</span></code>
 865           (with underscore separator). (issue <a href="https://svn.boost.org/trac/boost/ticket/6199" target="_top">#6199</a>).
 866         </li>
 867 <li class="listitem">
 868           Refactored test data and some special function code to improve support
 869           for arbitary precision and/or expression-template-enabled types.
 870         </li>
 871 <li class="listitem">
 872           Added new faster zeta function evaluation method.
 873         </li>
 874 </ul></div>
 875 <p>
 876       Fixed issues:
 877     </p>
 878 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 879 <li class="listitem">
 880           Corrected CDF complement for Laplace distribution (issue <a href="https://svn.boost.org/trac/boost/ticket/6151" target="_top">#6151</a>).
 881         </li>
 882 <li class="listitem">
 883           Corrected branch cuts on the complex inverse trig functions, to handle
 884           signed zeros (issue <a href="https://svn.boost.org/trac/boost/ticket/6171" target="_top">#6171</a>).
 885         </li>
 886 <li class="listitem">
 887           Fixed bug in <code class="computeroutput"><span class="identifier">bessel_yn</span></code>
 888           which caused incorrect overflow errors to be raised for negative <span class="emphasis"><em>n</em></span>
 889           (issue <a href="https://svn.boost.org/trac/boost/ticket/6367" target="_top">#6367</a>).
 890         </li>
 891 <li class="listitem">
 892           Also fixed minor/cosmetic/configuration issues <a href="https://svn.boost.org/trac/boost/ticket/6120" target="_top">#6120</a>,
 893           <a href="https://svn.boost.org/trac/boost/ticket/6191" target="_top">#6191</a>,
 894           <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>,
 895           <a href="https://svn.boost.org/trac/boost/ticket/6130" target="_top">#6130</a>,
 896           <a href="https://svn.boost.org/trac/boost/ticket/6234" target="_top">#6234</a>,
 897           <a href="https://svn.boost.org/trac/boost/ticket/6307" target="_top">#6307</a>,
 898           <a href="https://svn.boost.org/trac/boost/ticket/6192" target="_top">#6192</a>.
 899         </li>
 900 </ul></div>
 901 <h5>
 902 <a name="math_toolkit.history2.h24"></a>
 903       <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>
 904     </h5>
 905 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 906 <li class="listitem">
 907           Added new series evaluation methods to the cyclic Bessel I, J, K and Y
 908           functions. Also taken great care to avoid spurious over and underflow of
 909           these functions. Fixes issue <a href="https://svn.boost.org/trac/boost/ticket/5560" target="_top">#5560</a>
 910         </li>
 911 <li class="listitem">
 912           Added an example of using Inverse Chi-Squared distribution for Bayesian
 913           statistics, provided by Thomas Mang.
 914         </li>
 915 <li class="listitem">
 916           Added tests to use improved version of lexical_cast which handles C99 nonfinites
 917           without using globale facets.
 918         </li>
 919 <li class="listitem">
 920           Corrected wrong out-of-bound uniform distribution CDF complement values
 921           <a href="https://svn.boost.org/trac/boost/ticket/5733" target="_top">#5733</a>.
 922         </li>
 923 <li class="listitem">
 924           Enabled long double support on OpenBSD (issue <a href="https://svn.boost.org/trac/boost/ticket/6014" target="_top">#6014</a>).
 925         </li>
 926 <li class="listitem">
 927           Changed nextafter and related functions to behave in the same way as other
 928           implementations - so that nextafter(+INF, 0) is a finite value (issue
 929           <a href="https://svn.boost.org/trac/boost/ticket/5823" target="_top">#5832</a>).
 930         </li>
 931 <li class="listitem">
 932           Changed tuple include configuration to fix issue when using in conjunction
 933           with Boost.Tr1 (issue <a href="https://svn.boost.org/trac/boost/ticket/5934" target="_top">#5934</a>).
 934         </li>
 935 <li class="listitem">
 936           Changed class eps_tolerance to behave correctly when both ends of the range
 937           are zero (issue <a href="https://svn.boost.org/trac/boost/ticket/6001" target="_top">#6001</a>).
 938         </li>
 939 <li class="listitem">
 940           Fixed missing include guards on prime.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5927" target="_top">#5927</a>).
 941         </li>
 942 <li class="listitem">
 943           Removed unused/undocumented constants from constants.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>).
 944         </li>
 945 <li class="listitem">
 946           Fixed missing std:: prefix in nonfinite_num_facets.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5914" target="_top">#5914</a>).
 947         </li>
 948 <li class="listitem">
 949           Minor patches for Cray compiler compatibility.
 950         </li>
 951 </ul></div>
 952 <h5>
 953 <a name="math_toolkit.history2.h25"></a>
 954       <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>
 955     </h5>
 956 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 957 <li class="listitem">
 958           Added changesign function to sign.hpp to facilitate addition of nonfinite
 959           facets.
 960         </li>
 961 <li class="listitem">
 962           Addition of nonfinite facets from Johan Rade, with tests, examples of use
 963           for C99 format infinity and NaN, and documentation.
 964         </li>
 965 <li class="listitem">
 966           Added tests and documentation of changesign from Johan Rade.
 967         </li>
 968 </ul></div>
 969 <h5>
 970 <a name="math_toolkit.history2.h26"></a>
 971       <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>
 972     </h5>
 973 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 974           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5095</a>,
 975           <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
 976         </li></ul></div>
 977 <h5>
 978 <a name="math_toolkit.history2.h27"></a>
 979       <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>
 980     </h5>
 981 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 982 <li class="listitem">
 983           Added Wald, Inverse Gaussian and geometric distributions.
 984         </li>
 985 <li class="listitem">
 986           Added information about configuration macros.
 987         </li>
 988 <li class="listitem">
 989           Added support for mpreal as a real-numbered type.
 990         </li>
 991 </ul></div>
 992 <h5>
 993 <a name="math_toolkit.history2.h28"></a>
 994       <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>
 995     </h5>
 996 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 997 <li class="listitem">
 998           Added warnings about potential ambiguity with std random library in distribution
 999           and function names.
1000         </li>
1001 <li class="listitem">
1002           Added inverse gamma distribution and inverse chi_square and scaled inverse
1003           chi_square.
1004         </li>
1005 <li class="listitem">
1006           Editorial revision of documentation, and added FAQ.
1007         </li>
1008 </ul></div>
1009 <h5>
1010 <a name="math_toolkit.history2.h29"></a>
1011       <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>
1012     </h5>
1013 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1014 <li class="listitem">
1015           Fixed incorrect range and support for Rayleigh distribution.
1016         </li>
1017 <li class="listitem">
1018           Fixed numerical error in the quantile of the Student's T distribution:
1019           the function was returning garbage values for non-integer degrees of freedom
1020           between 2 and 3.
1021         </li>
1022 </ul></div>
1023 <h5>
1024 <a name="math_toolkit.history2.h30"></a>
1025       <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>
1026     </h5>
1027 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
1028           Significantly improved performance for the incomplete gamma function and
1029           its inverse.
1030         </li></ul></div>
1031 <h5>
1032 <a name="math_toolkit.history2.h31"></a>
1033       <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>
1034     </h5>
1035 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1036 <li class="listitem">
1037           Added support for MPFR as a bignum type.
1038         </li>
1039 <li class="listitem">
1040           Added some full specializations of the policy classes to reduce compile
1041           times.
1042         </li>
1043 <li class="listitem">
1044           Added logistic and hypergeometric distributions, from Gautam Sewani's Google
1045           Summer of Code project.
1046         </li>
1047 <li class="listitem">
1048           Added Laplace distribution submitted by Thijs van den Berg.
1049         </li>
1050 <li class="listitem">
1051           Updated performance test code to include new distributions, and improved
1052           the performance of the non-central distributions.
1053         </li>
1054 <li class="listitem">
1055           Added SSE2 optimised <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
1056           code, from Gautam Sewani's Google Summer of Code project.
1057         </li>
1058 <li class="listitem">
1059           Fixed bug in cyl_bessel_i that used an incorrect approximation for &#957; = 0.5,
1060           also effects the non-central Chi Square Distribution when &#957; = 3, see bug
1061           report <a href="https://svn.boost.org/trac/boost/ticket/2877" target="_top">#2877</a>.
1062         </li>
1063 <li class="listitem">
1064           Fixed minor bugs <a href="https://svn.boost.org/trac/boost/ticket/2873" target="_top">#2873</a>.
1065         </li>
1066 </ul></div>
1067 <h5>
1068 <a name="math_toolkit.history2.h32"></a>
1069       <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>
1070     </h5>
1071 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1072 <li class="listitem">
1073           Added Johan R&#229;de's optimised floating point classification routines.
1074         </li>
1075 <li class="listitem">
1076           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>).
1077         </li>
1078 </ul></div>
1079 <h5>
1080 <a name="math_toolkit.history2.h33"></a>
1081       <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>
1082     </h5>
1083 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
1084           Improved accuracy and testing of the inverse hypergeometric functions.
1085         </li></ul></div>
1086 <h5>
1087 <a name="math_toolkit.history2.h34"></a>
1088       <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>
1089     </h5>
1090 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1091 <li class="listitem">
1092           Added Noncentral Chi Squared Distribution.
1093         </li>
1094 <li class="listitem">
1095           Added Noncentral Beta Distribution.
1096         </li>
1097 <li class="listitem">
1098           Added Noncentral F Distribution.
1099         </li>
1100 <li class="listitem">
1101           Added Noncentral T Distribution.
1102         </li>
1103 <li class="listitem">
1104           Added Exponential Integral Functions.
1105         </li>
1106 <li class="listitem">
1107           Added Zeta Function.
1108         </li>
1109 <li class="listitem">
1110           Added Rounding and Truncation functions.
1111         </li>
1112 <li class="listitem">
1113           Added Compile time powers of runtime bases.
1114         </li>
1115 <li class="listitem">
1116           Added SSE2 optimizations for Lanczos evaluation.
1117         </li>
1118 </ul></div>
1119 <h5>
1120 <a name="math_toolkit.history2.h35"></a>
1121       <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:
1122       Post Review First Official Release</a>
1123     </h5>
1124 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1125 <li class="listitem">
1126           Added Policy based framework that allows fine grained control over function
1127           behaviour.
1128         </li>
1129 <li class="listitem">
1130           <span class="bold"><strong>Breaking change:</strong></span> Changed default behaviour
1131           for domain, pole and overflow errors to throw an exception (based on review
1132           feedback), this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
1133         </li>
1134 <li class="listitem">
1135           <span class="bold"><strong>Breaking change:</strong></span> Changed exception thrown
1136           when an internal evaluation error occurs to boost::math::evaluation_error.
1137         </li>
1138 <li class="listitem">
1139           <span class="bold"><strong>Breaking change:</strong></span> Changed discrete quantiles
1140           to return an integer result: this is anything up to 20 times faster than
1141           finding the true root, this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;19.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
1142         </li>
1143 <li class="listitem">
1144           Polynomial/rational function evaluation is now customisable and hopefully
1145           faster than before.
1146         </li>
1147 <li class="listitem">
1148           Added performance test program.
1149         </li>
1150 </ul></div>
1151 <h5>
1152 <a name="math_toolkit.history2.h36"></a>
1153       <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
1154       4: Second Review Candidate (1st March 2007)</a>
1155     </h5>
1156 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1157 <li class="listitem">
1158           Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
1159           them into line with the rest of the code.
1160         </li>
1161 <li class="listitem">
1162           Added C# "Distribution Explorer" demo application.
1163         </li>
1164 </ul></div>
1165 <h5>
1166 <a name="math_toolkit.history2.h37"></a>
1167       <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
1168       3: First Review Candidate (31st Dec 2006)</a>
1169     </h5>
1170 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1171 <li class="listitem">
1172           Implemented the main probability distribution and density functions.
1173         </li>
1174 <li class="listitem">
1175           Implemented digamma.
1176         </li>
1177 <li class="listitem">
1178           Added more factorial functions.
1179         </li>
1180 <li class="listitem">
1181           Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
1182           harmonic functions from TR1.
1183         </li>
1184 <li class="listitem">
1185           Moved Xiaogang Zhang's elliptic integral code into the library, and brought
1186           them into line with the rest of the code.
1187         </li>
1188 <li class="listitem">
1189           Moved Hubert Holin's existing Boost.Math special functions into this library
1190           and brought them into line with the rest of the code.
1191         </li>
1192 </ul></div>
1193 <h5>
1194 <a name="math_toolkit.history2.h38"></a>
1195       <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
1196       2: Released September 10th 2006</a>
1197     </h5>
1198 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1199 <li class="listitem">
1200           Implement preview release of the statistical distributions.
1201         </li>
1202 <li class="listitem">
1203           Added statistical distributions tutorial.
1204         </li>
1205 <li class="listitem">
1206           Implemented root finding algorithms.
1207         </li>
1208 <li class="listitem">
1209           Implemented the inverses of the incomplete gamma and beta functions.
1210         </li>
1211 <li class="listitem">
1212           Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
1213         </li>
1214 <li class="listitem">
1215           Integrated the statistical results generated from the test data with Boost.Test:
1216           uses a database of expected results, indexed by test, floating point type,
1217           platform, and compiler.
1218         </li>
1219 <li class="listitem">
1220           Improved lgamma near 1 and 2 (rational approximations).
1221         </li>
1222 <li class="listitem">
1223           Improved erf/erfc inverses (rational approximations).
1224         </li>
1225 <li class="listitem">
1226           Implemented Rational function generation (the Remez method).
1227         </li>
1228 </ul></div>
1229 <h5>
1230 <a name="math_toolkit.history2.h39"></a>
1231       <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
1232       1: Released March 31st 2006</a>
1233     </h5>
1234 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1235 <li class="listitem">
1236           Implement gamma/beta/erf functions along with their incomplete counterparts.
1237         </li>
1238 <li class="listitem">
1239           Generate high quality test data, against which future improvements can
1240           be judged.
1241         </li>
1242 <li class="listitem">
1243           Provide tools for the evaluation of infinite series, continued fractions,
1244           and rational functions.
1245         </li>
1246 <li class="listitem">
1247           Provide tools for testing against tabulated test data, and collecting statistics
1248           on error rates.
1249         </li>
1250 <li class="listitem">
1251           Provide sufficient docs for people to be able to find their way around
1252           the library.
1253         </li>
1254 </ul></div>
1255 <p>
1256       SVN Revisions:
1257     </p>
1258 <p>
1259       Sandbox and trunk last synchonised at revision: .
1260     </p>
1261 </div>
1262 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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