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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://svn.boost.org/trac/boost/query?status=assigned&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>.
  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     </p>
  35 <h5>
  36 <a name="math_toolkit.history2.h0"></a>
  37       <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
  38       (Boost-1.64)</a>
  39     </h5>
  40 <p>
  41       Patches:
  42     </p>
  43 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  44 <li class="listitem">
  45           Big push to ensure all functions in also in C99 are compatible with Annex
  46           F.
  47         </li>
  48 <li class="listitem">
  49           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>.
  50         </li>
  51 </ul></div>
  52 <h5>
  53 <a name="math_toolkit.history2.h1"></a>
  54       <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
  55       (Boost-1.63)</a>
  56     </h5>
  57 <p>
  58       Patches:
  59     </p>
  60 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  61 <li class="listitem">
  62           Fixed evaluation of zero polynomial in polynomial.hpp, see <a href="https://svn.boost.org/trac/boost/ticket/12532" target="_top">12532</a>.
  63         </li>
  64 <li class="listitem">
  65           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>.
  66         </li>
  67 </ul></div>
  68 <h5>
  69 <a name="math_toolkit.history2.h2"></a>
  70       <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
  71       (Boost-1.62)</a>
  72     </h5>
  73 <p>
  74       New Features:
  75     </p>
  76 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
  77           Enabled all the special function code to work correctly with types whose
  78           precision can change at runtime: for example type <code class="computeroutput"><span class="identifier">mpfr_float</span></code>
  79           from Boost.Multiprecision.
  80         </li></ul></div>
  81 <p>
  82       Patches:
  83     </p>
  84 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  85 <li class="listitem">
  86           Fix tgamma_delta_ratio for cases where the delta is small compared to the
  87           base.
  88         </li>
  89 <li class="listitem">
  90           Fix misc GCC-4.4 test failures.
  91         </li>
  92 </ul></div>
  93 <h5>
  94 <a name="math_toolkit.history2.h3"></a>
  95       <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
  96       (Boost-1.61)</a>
  97     </h5>
  98 <p>
  99       New Features:
 100     </p>
 101 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 102           Polynomial arithmetic added to tools.
 103         </li></ul></div>
 104 <h5>
 105 <a name="math_toolkit.history2.h4"></a>
 106       <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
 107       (Boost-1.60)</a>
 108     </h5>
 109 <p>
 110       New Features:
 111     </p>
 112 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 113 <li class="listitem">
 114           Promote the root finding and function minimization code to first class
 115           citizens - these are now officially supported as part of the library.
 116         </li>
 117 <li class="listitem">
 118           Allow the library to be used and tested with compiler exception handling
 119           support turned off. To better facilitate this the default error handling
 120           policies have been changed to <span class="emphasis"><em>errno_on_error</em></span> but only
 121           when the compiler has no exception handling support.
 122         </li>
 123 </ul></div>
 124 <p>
 125       Patches:
 126     </p>
 127 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 128 <li class="listitem">
 129           Fix behaviour of the non-central chi-squared distribution when the non-centrality
 130           parameter is zero to match the chi-squared, see <a href="https://svn.boost.org/trac/boost/ticket/11557" target="_top">11557</a>.
 131         </li>
 132 <li class="listitem">
 133           Fix comments in code for the hypergeometric to match what it actually does,
 134           also fixes the parameter access functions to return the correct values.
 135           See <a href="https://svn.boost.org/trac/boost/ticket/11556" target="_top">11556</a>.
 136         </li>
 137 <li class="listitem">
 138           Stopped using hidden visiblity library build with the Oracle compiler as
 139           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>.
 140         </li>
 141 <li class="listitem">
 142           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>.
 143         </li>
 144 <li class="listitem">
 145           Fix corner case bug in root bracketing code, see <a href="https://svn.boost.org/trac/boost/ticket/11532" target="_top">11532</a>.
 146         </li>
 147 <li class="listitem">
 148           Add some missing typecasts in arguments to std::max in Bernoulli code.
 149           See <a href="https://svn.boost.org/trac/boost/ticket/11453" target="_top">11453</a>.
 150         </li>
 151 <li class="listitem">
 152           Fix mistaken assumptions about the possible values for FLT_EVAL_METHOD.
 153           See <a href="https://svn.boost.org/trac/boost/ticket/11429" target="_top">11429</a>.
 154         </li>
 155 <li class="listitem">
 156           Completely revamped performance testing and error-rate measuring code so
 157           we can more easily document how well (or not!) we're doing. This information
 158           will hopefully get more frequently updated in future as it's more or less
 159           automatically generated - see the <span class="emphasis"><em>reporting</em></span> sub-directory
 160           for more information.
 161         </li>
 162 <li class="listitem">
 163           Fix some corner cases in the beta, incomplete beta, and incomplete beta
 164           derivative. With thanks to Rocco Romeo.
 165         </li>
 166 <li class="listitem">
 167           Reorganized the Bessel functions internally to improve the performance
 168           of Jn and Yn.
 169         </li>
 170 <li class="listitem">
 171           Fixed skewness formula for triangular distribution, see <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">#11768</a>.
 172         </li>
 173 <li class="listitem">
 174           Fixed some examples so they compile on Unix platforms which have an ::exception
 175           struct declared, see <a href="https://svn.boost.org/trac/boost/ticket/11827" target="_top">#11827</a>.
 176         </li>
 177 <li class="listitem">
 178           Correct mistake in triangular distribution skewness formula <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">11768</a>,
 179           reported by Juan Leni.
 180         </li>
 181 </ul></div>
 182 <h5>
 183 <a name="math_toolkit.history2.h5"></a>
 184       <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>
 185     </h5>
 186 <p>
 187       Patch release for Boost-1.58:
 188     </p>
 189 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 190 <li class="listitem">
 191           Minor <a href="https://github.com/boostorg/math/pull/13#issuecomment-98905579" target="_top">patch
 192           for Haiku support.</a>
 193         </li>
 194 <li class="listitem">
 195           Fix the decimal digit count for 128-bit floating point types.
 196         </li>
 197 <li class="listitem">
 198           Fix a few documentation typos.
 199         </li>
 200 </ul></div>
 201 <h5>
 202 <a name="math_toolkit.history2.h6"></a>
 203       <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
 204       (boost-1.58.0)</a>
 205     </h5>
 206 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 207 <li class="listitem">
 208           Added two new special functions - <a class="link" href="sf_gamma/trigamma.html" title="Trigamma">trigamma</a>
 209           and <a class="link" href="sf_gamma/polygamma.html" title="Polygamma">polygamma</a>.
 210         </li>
 211 <li class="listitem">
 212           Fixed namespace scope constants so they are constexpr on conforming compilers,
 213           see https://svn.boost.org/trac/boost/ticket/10901.
 214         </li>
 215 <li class="listitem">
 216           Fixed various cases of spurious under/overflow in the incomplete beta and
 217           gamma functions, plus the elliptic integrals, with thanks to Rocco Romeo.
 218         </li>
 219 <li class="listitem">
 220           Fix 3-arg <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
 221           and <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_q</a> functions
 222           to not call the policy based overload if the final argument is not actually
 223           a policy.
 224         </li>
 225 <li class="listitem">
 226           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>.
 227         </li>
 228 <li class="listitem">
 229           Fixed extreme-value pdf for large valued inputs, see <a href="https://svn.boost.org/trac/boost/ticket/10938" target="_top">#10938</a>.
 230         </li>
 231 <li class="listitem">
 232           Large update to the Elliptic integral code to use Carlson's latest algorithms
 233           - these should be more stable, more accurate and slightly faster than before.
 234           Also added support for Carlson's RG integral.
 235         </li>
 236 <li class="listitem">
 237           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
 238           integrals.
 239         </li>
 240 <li class="listitem">
 241           Switched documentation to use SVG rather than PNG graphs and equations
 242           - browsers seem to have finally caught up!
 243         </li>
 244 </ul></div>
 245 <h5>
 246 <a name="math_toolkit.history2.h7"></a>
 247       <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
 248       (boost-1.57.0)</a>
 249     </h5>
 250 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 251 <li class="listitem">
 252           Added <a class="link" href="dist_ref/dists/hyperexponential_dist.html" title="Hyperexponential Distribution">Hyperexponential
 253           Distribution</a>.
 254         </li>
 255 <li class="listitem">
 256           Fix some spurious overflows in the incomplete gamma functions (with thanks
 257           to Rocco Romeo).
 258         </li>
 259 <li class="listitem">
 260           Fix bug in derivative of incomplete beta when a = b = 0.5 - this also effects
 261           several non-central distributions, see <a href="https://svn.boost.org/trac/boost/ticket/10480" target="_top">10480</a>.
 262         </li>
 263 <li class="listitem">
 264           Fixed some corner cases in <a class="link" href="rounding/round.html" title="Rounding Functions">round</a>.
 265         </li>
 266 <li class="listitem">
 267           Don't support 80-bit floats in cstdfloat.hpp if standard library support
 268           is broken.
 269         </li>
 270 </ul></div>
 271 <h5>
 272 <a name="math_toolkit.history2.h8"></a>
 273       <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
 274       (Boost-1.56.0)</a>
 275     </h5>
 276 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 277 <li class="listitem">
 278           <span class="bold"><strong>Breaking change</strong></span>: moved a number of non-core
 279           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
 280           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>,
 281           <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>,
 282           <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
 283           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
 284           path.
 285         </li>
 286 <li class="listitem">
 287           <span class="bold"><strong>Breaking change</strong></span>: A number of distributions
 288           and special functions were returning the maximum finite value rather than
 289           raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>,
 290           this has now been fixed, which means these functions now behave as documented.
 291           However, since the default behavior on raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>
 292           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
 293           which have come to reply rely on these functions not throwing may experience
 294           exceptions where they did not before. The special functions involved are
 295           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>,
 296           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>,
 297           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
 298           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
 299           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>,
 300           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>,
 301           <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
 302           involved are <a class="link" href="dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto
 303           Distribution</a>, <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta
 304           Distribution</a>, <a class="link" href="dist_ref/dists/geometric_dist.html" title="Geometric Distribution">Geometric
 305           Distribution</a>, <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
 306           Binomial Distribution</a>, <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
 307           Distribution</a>, <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
 308           Squared Distribution</a>, <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
 309           Distribution</a>, <a class="link" href="dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">Inverse
 310           chi squared Distribution</a>, <a class="link" href="dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution">Inverse
 311           Gamma Distribution</a>. See <a href="https://svn.boost.org/trac/boost/ticket/10111" target="_top">#10111</a>.
 312         </li>
 313 <li class="listitem">
 314           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
 315           be used with integer arguments, see <a href="https://svn.boost.org/trac/boost/ticket/10066" target="_top">#10066</a>.
 316         </li>
 317 <li class="listitem">
 318           Fix Halley iteration to handle zero derivative (with non-zero second derivative),
 319           see <a href="https://svn.boost.org/trac/boost/ticket/10046" target="_top">#10046</a>.
 320         </li>
 321 </ul></div>
 322 <h5>
 323 <a name="math_toolkit.history2.h9"></a>
 324       <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>
 325     </h5>
 326 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 327 <li class="listitem">
 328           Fix Geometric distribution use of Policies, see <a href="https://svn.boost.org/trac/boost/ticket/9833" target="_top">#9833</a>.
 329         </li>
 330 <li class="listitem">
 331           Fix corner cases in the negative binomial distribution, see <a href="https://svn.boost.org/trac/boost/ticket/9834" target="_top">#9834</a>.
 332         </li>
 333 <li class="listitem">
 334           Fix compilation failures on Mac OS.
 335         </li>
 336 </ul></div>
 337 <h5>
 338 <a name="math_toolkit.history2.h10"></a>
 339       <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>
 340     </h5>
 341 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 342 <li class="listitem">
 343           Changed version number to new Boost.Math specific version now that we're
 344           in the modular Boost world.
 345         </li>
 346 <li class="listitem">
 347           Added <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
 348           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
 349           approximation (from Nikhar Agrawal).
 350         </li>
 351 <li class="listitem">
 352           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>,
 353           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_neumann_prime</a>,
 354           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_i_prime</a>,
 355           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_k_prime</a>,
 356           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_bessel_prime</a>
 357           and <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_neumann_prime</a>
 358           (from Anton Bikineev).
 359         </li>
 360 <li class="listitem">
 361           Fixed buggy Student's t example code, along with docs for testing sample
 362           means for equivalence.
 363         </li>
 364 <li class="listitem">
 365           Documented <code class="computeroutput"><span class="identifier">max_iter</span></code> parameter
 366           in root finding code better, see <a href="https://svn.boost.org/trac/boost/ticket/9225" target="_top">#9225</a>.
 367         </li>
 368 <li class="listitem">
 369           Add option to explicitly enable/disable use of __float128 in constants
 370           code, see <a href="https://svn.boost.org/trac/boost/ticket/9240" target="_top">#9240</a>.
 371         </li>
 372 <li class="listitem">
 373           Cleaned up handling of negative values in Bessel I0 and I1 code (removed
 374           dead code), see <a href="https://svn.boost.org/trac/boost/ticket/9512" target="_top">#9512</a>.
 375         </li>
 376 <li class="listitem">
 377           Fixed handling of very small values passed to <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
 378           and <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> so they
 379           don't generate spurious overflows (thanks to Rocco Romeo).
 380         </li>
 381 <li class="listitem">
 382           <a href="https://svn.boost.org/trac/boost/ticket/9672" target="_top">#9672 PDF and
 383           CDF of a Laplace distribution throwing domain_error</a> Random variate
 384           can now be infinite.
 385         </li>
 386 <li class="listitem">
 387           Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
 388           <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
 389           and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
 390           with thanks to Rocco Romeo.
 391         </li>
 392 <li class="listitem">
 393           Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
 394           <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
 395           and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
 396           (thanks to Rocco Romeo).
 397         </li>
 398 <li class="listitem">
 399           Removed constant <code class="computeroutput"><span class="identifier">pow23_four_minus_pi</span>
 400           </code> whose value did not match the name (and was unused by Boost.Math),
 401           see <a href="https://svn.boost.org/trac/boost/ticket/9712" target="_top">#9712</a>.
 402         </li>
 403 </ul></div>
 404 <h5>
 405 <a name="math_toolkit.history2.h11"></a>
 406       <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>
 407     </h5>
 408 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 409 <li class="listitem">
 410           Suppress numerous warnings (mostly from GCC-4.8 and MSVC) <a href="https://svn.boost.org/trac/boost/ticket/8384" target="_top">#8384</a>,
 411           <a href="https://svn.boost.org/trac/boost/ticket/8855" target="_top">#8855</a>,
 412           <a href="https://svn.boost.org/trac/boost/ticket/9107" target="_top">#9107</a>,
 413           <a href="https://svn.boost.org/trac/boost/ticket/9109" target="_top">#9109</a>..
 414         </li>
 415 <li class="listitem">
 416           Fixed PGI compilation issue <a href="https://svn.boost.org/trac/boost/ticket/8333" target="_top">#8333</a>.
 417         </li>
 418 <li class="listitem">
 419           Fixed PGI constant value initialization issue that caused erf to generate
 420           incorrect results <a href="https://svn.boost.org/trac/boost/ticket/8621" target="_top">#8621</a>.
 421         </li>
 422 <li class="listitem">
 423           Prevent macro expansion of some C99 macros that are also C++ functions
 424           <a href="https://svn.boost.org/trac/boost/ticket/8732" target="_top">#8732</a>
 425           and <a href="https://svn.boost.org/trac/boost/ticket/8733" target="_top">#8733</a>..
 426         </li>
 427 <li class="listitem">
 428           Fixed Student's T distribution to behave correctly with huge degrees of
 429           freedom (larger than the largest representable integer) <a href="https://svn.boost.org/trac/boost/ticket/8837" target="_top">#8837</a>.
 430         </li>
 431 <li class="listitem">
 432           Make some core functions usable with <code class="computeroutput"><span class="keyword">long</span>
 433           <span class="keyword">double</span></code> even when the platform has
 434           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>.
 435         </li>
 436 <li class="listitem">
 437           Fix error handling of distributions to catch invalid scale and location
 438           parameters when the random variable is infinite <a href="https://svn.boost.org/trac/boost/ticket/9042" target="_top">#9042</a>
 439           and <a href="https://svn.boost.org/trac/boost/ticket/9126" target="_top">#9126</a>.
 440         </li>
 441 <li class="listitem">
 442           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>.
 443         </li>
 444 <li class="listitem">
 445           Improve consistency of argument reduction in the elliptic integrals <a href="https://svn.boost.org/trac/boost/ticket/9104" target="_top">#9104</a>.
 446         </li>
 447 <li class="listitem">
 448           Fix bug in inverse incomplete beta that results in cancellation errors
 449           when the beta function is really an arcsine or Student's T distribution.
 450         </li>
 451 <li class="listitem">
 452           Fix issue in Bessel I and K function continued fractions that causes spurious
 453           over/underflow.
 454         </li>
 455 <li class="listitem">
 456 <p class="simpara">
 457           Add improvement to non-central chi squared distribution quantile due to
 458           Thomas Luu, <a href="http://discovery.ucl.ac.uk/1482128/" target="_top">Fast and accurate
 459           parallel computation of quantile functions for random number generation,
 460           Doctorial Thesis 2016</a>. <a href="http://discovery.ucl.ac.uk/1463470/" target="_top">Efficient
 461           and Accurate Parallel Inversion of the Gamma Distribution, Thomas Luu</a>
 462         </p>
 463 <h5>
 464 <a name="math_toolkit.history2.h12"></a>
 465           <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>
 466         </h5>
 467 </li>
 468 <li class="listitem">
 469           Major reorganization to incorporate other Boost.Math like Integer Utilities
 470           Integer Utilities (Greatest Common Divisor and Least Common Multiple),
 471           quaternions and octonions. Making new chapter headings.
 472         </li>
 473 <li class="listitem">
 474           Added many references to Boost.Multiprecision and <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>
 475           as an example of a User-defined Type (UDT).
 476         </li>
 477 <li class="listitem">
 478           Added Clang to list of supported compilers.
 479         </li>
 480 <li class="listitem">
 481           Fixed constants to use a thread-safe cache of computed values when used
 482           at arbitrary precision.
 483         </li>
 484 <li class="listitem">
 485           Added finding zeros of Bessel functions <code class="computeroutput"><span class="identifier">cyl_bessel_j_zero</span></code>,
 486           <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
 487           Christopher Kormanyos).
 488         </li>
 489 <li class="listitem">
 490           More accuracy improvements to the Bessel J and Y functions from Rocco Romeo.
 491         </li>
 492 <li class="listitem">
 493           Fixed nasty cyclic dependency bug that caused some headers to not compile
 494           <a href="https://svn.boost.org/trac/boost/ticket/7999" target="_top">#7999</a>.
 495         </li>
 496 <li class="listitem">
 497           Fixed bug in <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
 498           that caused spurious overflow for arguments between 142.5 and 143.
 499         </li>
 500 <li class="listitem">
 501           Fixed bug in raise_rounding_error that caused it to return an incorrect
 502           result when throwing an exception is turned off <a href="https://svn.boost.org/trac/boost/ticket/7905" target="_top">#7905</a>.
 503         </li>
 504 <li class="listitem">
 505           Added minimal __float128 support.
 506         </li>
 507 <li class="listitem">
 508           Fixed bug in edge-cases of poisson quantile <a href="https://svn.boost.org/trac/boost/ticket/8308" target="_top">#8308</a>.
 509         </li>
 510 <li class="listitem">
 511           Adjusted heuristics used in Halley iteration to cope with inverting the
 512           incomplete beta in tricky regions where the derivative is flatlining. Example
 513           is computing the quantile of the Fisher F distribution for probabilities
 514           smaller than machine epsilon. See ticket <a href="https://svn.boost.org/trac/boost/ticket/8314" target="_top">#8314</a>.
 515         </li>
 516 </ul></div>
 517 <h5>
 518 <a name="math_toolkit.history2.h13"></a>
 519       <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>
 520     </h5>
 521 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 522 <li class="listitem">
 523           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/7325" target="_top">#7325</a>,
 524           <a href="https://svn.boost.org/trac/boost/ticket/7415" target="_top">#7415</a>
 525           and <a href="https://svn.boost.org/trac/boost/ticket/7416" target="_top">#7416</a>,
 526           <a href="https://svn.boost.org/trac/boost/ticket/7183" target="_top">#7183</a>,
 527           <a href="https://svn.boost.org/trac/boost/ticket/7649" target="_top">#7649</a>,
 528           <a href="https://svn.boost.org/trac/boost/ticket/7694" target="_top">#7694</a>,
 529           <a href="https://svn.boost.org/trac/boost/ticket/4445" target="_top">#4445</a>,
 530           <a href="https://svn.boost.org/trac/boost/ticket/7492" target="_top">#7492</a>,
 531           <a href="https://svn.boost.org/trac/boost/ticket/7891" target="_top">#7891</a>,
 532           <a href="https://svn.boost.org/trac/boost/ticket/7429" target="_top">#7429</a>.
 533         </li>
 534 <li class="listitem">
 535           Fixed mistake in calculating pooled standard deviation in two-sample students
 536           t example <a href="https://svn.boost.org/trac/boost/ticket/7402" target="_top">#7402</a>.
 537         </li>
 538 <li class="listitem">
 539           Improve complex acos/asin/atan, see <a href="https://svn.boost.org/trac/boost/ticket/7290" target="_top">#7290</a>,
 540           <a href="https://svn.boost.org/trac/boost/ticket/7291" target="_top">#7291</a>.
 541         </li>
 542 <li class="listitem">
 543           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>
 544           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>
 545           thanks to suggestions from Rocco Romeo.
 546         </li>
 547 <li class="listitem">
 548           Improve accuracy of Bessel J and Y for integer orders thanks to suggestions
 549           from Rocco Romeo.
 550         </li>
 551 </ul></div>
 552 <h5>
 553 <a name="math_toolkit.history2.h14"></a>
 554       <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>
 555     </h5>
 556 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 557 <li class="listitem">
 558           Corrected moments for small degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7177" target="_top">#7177</a>
 559           (reported by Thomas Mang).
 560         </li>
 561 <li class="listitem">
 562           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>.
 563         </li>
 564 <li class="listitem">
 565           Corrected failure to detect bad parameters in many distributions <a href="https://svn.boost.org/trac/boost/ticket/6934" target="_top">#6934</a> (reported
 566           by Florian Schoppmann) by adding a function check_out_of_range to test
 567           many possible bad parameters. This test revealed several distributions
 568           where the checks for bad parameters were ineffective, and these have been
 569           rectified.
 570         </li>
 571 <li class="listitem">
 572           Fixed issue in Hankel functions that causes incorrect values to be returned
 573           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>.
 574         </li>
 575 <li class="listitem">
 576           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/6517" target="_top">#6517</a>,
 577           <a href="https://svn.boost.org/trac/boost/ticket/6362" target="_top">#6362</a>,
 578           <a href="https://svn.boost.org/trac/boost/ticket/7053" target="_top">#7053</a>,
 579           <a href="https://svn.boost.org/trac/boost/ticket/2693" target="_top">#2693</a>,
 580           <a href="https://svn.boost.org/trac/boost/ticket/6937" target="_top">#6937</a>,
 581           <a href="https://svn.boost.org/trac/boost/ticket/7099" target="_top">#7099</a>.
 582         </li>
 583 <li class="listitem">
 584           Permitted infinite degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>
 585           implemented using the normal distribution (requested by Thomas Mang).
 586         </li>
 587 <li class="listitem">
 588           Much enhanced accuracy for large degrees of freedom &#957; and/or large non-centrality
 589           &#948;
 590 by switching to use the Students t distribution (or Normal distribution
 591           for infinite degrees of freedom) centered at delta, when &#948; / (4 * &#957;) &lt;
 592           epsilon for the floating-point type in use. <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>.
 593           It was found that the incomplete beta was suffering from serious cancellation
 594           errors when degrees of freedom was very large. (That has now been fixed
 595           in our code, but any code based on Didonato and Morris's original papers
 596           (probably every implementation out there actually) will have the same issue).
 597         </li>
 598 </ul></div>
 599 <h5>
 600 <a name="math_toolkit.history2.h15"></a>
 601       <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>
 602     </h5>
 603 <p>
 604       See Boost-1.52 - some items were added but not listed in time for the release.
 605     </p>
 606 <h5>
 607 <a name="math_toolkit.history2.h16"></a>
 608       <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>
 609     </h5>
 610 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 611 <li class="listitem">
 612           Promoted math constants to be 1st class citizens, including convenient
 613           access to the most widely used built-in float, double, long double via
 614           three namespaces.
 615         </li>
 616 <li class="listitem">
 617           Added the Owen's T function and Skew Normal distribution written by Benjamin
 618           Sobotta: see <a class="link" href="owens_t.html" title="Owen's T function">Owens T</a> and skew_normal_distrib.
 619         </li>
 620 <li class="listitem">
 621           Added Hankel functions <a class="link" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a>,
 622           <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>.
 623         </li>
 624 <li class="listitem">
 625           Corrected issue <a href="https://svn.boost.org/trac/boost/ticket/6627" target="_top">#6627
 626           nonfinite_num_put formatting of 0.0 is incorrect</a> based on a patch
 627           submitted by K R Walker.
 628         </li>
 629 <li class="listitem">
 630           Changed constant initialization mechanism so that it is thread safe even
 631           for user-defined types, also so that user defined types get the full precision
 632           of the constant, even when <code class="computeroutput"><span class="keyword">long</span>
 633           <span class="keyword">double</span></code> does not. So for example
 634           128-bit rational approximations will work with UDT's and do the right thing,
 635           even though <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
 636           may be only 64 or 80 bits.
 637         </li>
 638 <li class="listitem">
 639           Fixed issue in <code class="computeroutput"><span class="identifier">bessel_jy</span></code>
 640           which causes Y<sub>8.5</sub>(4&#960;) to yield a NaN.
 641         </li>
 642 </ul></div>
 643 <h5>
 644 <a name="math_toolkit.history2.h17"></a>
 645       <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>
 646     </h5>
 647 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 648 <li class="listitem">
 649           Deprecated wrongly named <code class="computeroutput"><span class="identifier">twothirds</span></code>
 650           math constant in favour of <code class="computeroutput"><span class="identifier">two_thirds</span></code>
 651           (with underscore separator). (issue <a href="https://svn.boost.org/trac/boost/ticket/6199" target="_top">#6199</a>).
 652         </li>
 653 <li class="listitem">
 654           Refactored test data and some special function code to improve support
 655           for arbitary precision and/or expression-template-enabled types.
 656         </li>
 657 <li class="listitem">
 658           Added new faster zeta function evaluation method.
 659         </li>
 660 </ul></div>
 661 <p>
 662       Fixed issues:
 663     </p>
 664 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 665 <li class="listitem">
 666           Corrected CDF complement for Laplace distribution (issue <a href="https://svn.boost.org/trac/boost/ticket/6151" target="_top">#6151</a>).
 667         </li>
 668 <li class="listitem">
 669           Corrected branch cuts on the complex inverse trig functions, to handle
 670           signed zeros (issue <a href="https://svn.boost.org/trac/boost/ticket/6171" target="_top">#6171</a>).
 671         </li>
 672 <li class="listitem">
 673           Fixed bug in <code class="computeroutput"><span class="identifier">bessel_yn</span></code>
 674           which caused incorrect overflow errors to be raised for negative <span class="emphasis"><em>n</em></span>
 675           (issue <a href="https://svn.boost.org/trac/boost/ticket/6367" target="_top">#6367</a>).
 676         </li>
 677 <li class="listitem">
 678           Also fixed minor/cosmetic/configuration issues <a href="https://svn.boost.org/trac/boost/ticket/6120" target="_top">#6120</a>,
 679           <a href="https://svn.boost.org/trac/boost/ticket/6191" target="_top">#6191</a>,
 680           <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>,
 681           <a href="https://svn.boost.org/trac/boost/ticket/6130" target="_top">#6130</a>,
 682           <a href="https://svn.boost.org/trac/boost/ticket/6234" target="_top">#6234</a>,
 683           <a href="https://svn.boost.org/trac/boost/ticket/6307" target="_top">#6307</a>,
 684           <a href="https://svn.boost.org/trac/boost/ticket/6192" target="_top">#6192</a>.
 685         </li>
 686 </ul></div>
 687 <h5>
 688 <a name="math_toolkit.history2.h18"></a>
 689       <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>
 690     </h5>
 691 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 692 <li class="listitem">
 693           Added new series evaluation methods to the cyclic Bessel I, J, K and Y
 694           functions. Also taken great care to avoid spurious over and underflow of
 695           these functions. Fixes issue <a href="https://svn.boost.org/trac/boost/ticket/5560" target="_top">#5560</a>
 696         </li>
 697 <li class="listitem">
 698           Added an example of using Inverse Chi-Squared distribution for Bayesian
 699           statistics, provided by Thomas Mang.
 700         </li>
 701 <li class="listitem">
 702           Added tests to use improved version of lexical_cast which handles C99 nonfinites
 703           without using globale facets.
 704         </li>
 705 <li class="listitem">
 706           Corrected wrong out-of-bound uniform distribution CDF complement values
 707           <a href="https://svn.boost.org/trac/boost/ticket/5733" target="_top">#5733</a>.
 708         </li>
 709 <li class="listitem">
 710           Enabled long double support on OpenBSD (issue <a href="https://svn.boost.org/trac/boost/ticket/6014" target="_top">#6014</a>).
 711         </li>
 712 <li class="listitem">
 713           Changed nextafter and related functions to behave in the same way as other
 714           implementations - so that nextafter(+INF, 0) is a finite value (issue
 715           <a href="https://svn.boost.org/trac/boost/ticket/5823" target="_top">#5832</a>).
 716         </li>
 717 <li class="listitem">
 718           Changed tuple include configuration to fix issue when using in conjunction
 719           with Boost.Tr1 (issue <a href="https://svn.boost.org/trac/boost/ticket/5934" target="_top">#5934</a>).
 720         </li>
 721 <li class="listitem">
 722           Changed class eps_tolerance to behave correctly when both ends of the range
 723           are zero (issue <a href="https://svn.boost.org/trac/boost/ticket/6001" target="_top">#6001</a>).
 724         </li>
 725 <li class="listitem">
 726           Fixed missing include guards on prime.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5927" target="_top">#5927</a>).
 727         </li>
 728 <li class="listitem">
 729           Removed unused/undocumented constants from constants.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>).
 730         </li>
 731 <li class="listitem">
 732           Fixed missing std:: prefix in nonfinite_num_facets.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5914" target="_top">#5914</a>).
 733         </li>
 734 <li class="listitem">
 735           Minor patches for Cray compiler compatibility.
 736         </li>
 737 </ul></div>
 738 <h5>
 739 <a name="math_toolkit.history2.h19"></a>
 740       <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>
 741     </h5>
 742 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 743 <li class="listitem">
 744           Added changesign function to sign.hpp to facilitate addition of nonfinite
 745           facets.
 746         </li>
 747 <li class="listitem">
 748           Addition of nonfinite facets from Johan Rade, with tests, examples of use
 749           for C99 format infinity and NaN, and documentation.
 750         </li>
 751 <li class="listitem">
 752           Added tests and documentation of changesign from Johan Rade.
 753         </li>
 754 </ul></div>
 755 <h5>
 756 <a name="math_toolkit.history2.h20"></a>
 757       <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>
 758     </h5>
 759 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 760           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5095</a>,
 761           <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
 762         </li></ul></div>
 763 <h5>
 764 <a name="math_toolkit.history2.h21"></a>
 765       <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>
 766     </h5>
 767 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 768 <li class="listitem">
 769           Added Wald, Inverse Gaussian and geometric distributions.
 770         </li>
 771 <li class="listitem">
 772           Added information about configuration macros.
 773         </li>
 774 <li class="listitem">
 775           Added support for mpreal as a real-numbered type.
 776         </li>
 777 </ul></div>
 778 <h5>
 779 <a name="math_toolkit.history2.h22"></a>
 780       <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>
 781     </h5>
 782 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 783 <li class="listitem">
 784           Added warnings about potential ambiguity with std random library in distribution
 785           and function names.
 786         </li>
 787 <li class="listitem">
 788           Added inverse gamma distribution and inverse chi_square and scaled inverse
 789           chi_square.
 790         </li>
 791 <li class="listitem">
 792           Editorial revision of documentation, and added FAQ.
 793         </li>
 794 </ul></div>
 795 <h5>
 796 <a name="math_toolkit.history2.h23"></a>
 797       <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>
 798     </h5>
 799 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 800 <li class="listitem">
 801           Fixed incorrect range and support for Rayleigh distribution.
 802         </li>
 803 <li class="listitem">
 804           Fixed numerical error in the quantile of the Student's T distribution:
 805           the function was returning garbage values for non-integer degrees of freedom
 806           between 2 and 3.
 807         </li>
 808 </ul></div>
 809 <h5>
 810 <a name="math_toolkit.history2.h24"></a>
 811       <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>
 812     </h5>
 813 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 814           Significantly improved performance for the incomplete gamma function and
 815           its inverse.
 816         </li></ul></div>
 817 <h5>
 818 <a name="math_toolkit.history2.h25"></a>
 819       <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>
 820     </h5>
 821 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 822 <li class="listitem">
 823           Added support for MPFR as a bignum type.
 824         </li>
 825 <li class="listitem">
 826           Added some full specializations of the policy classes to reduce compile
 827           times.
 828         </li>
 829 <li class="listitem">
 830           Added logistic and hypergeometric distributions, from Gautam Sewani's Google
 831           Summer of Code project.
 832         </li>
 833 <li class="listitem">
 834           Added Laplace distribution submitted by Thijs van den Berg.
 835         </li>
 836 <li class="listitem">
 837           Updated performance test code to include new distributions, and improved
 838           the performance of the non-central distributions.
 839         </li>
 840 <li class="listitem">
 841           Added SSE2 optimised <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
 842           code, from Gautam Sewani's Google Summer of Code project.
 843         </li>
 844 <li class="listitem">
 845           Fixed bug in cyl_bessel_i that used an incorrect approximation for &#957; = 0.5,
 846           also effects the non-central Chi Square Distribution when &#957; = 3, see bug
 847           report <a href="https://svn.boost.org/trac/boost/ticket/2877" target="_top">#2877</a>.
 848         </li>
 849 <li class="listitem">
 850           Fixed minor bugs <a href="https://svn.boost.org/trac/boost/ticket/2873" target="_top">#2873</a>.
 851         </li>
 852 </ul></div>
 853 <h5>
 854 <a name="math_toolkit.history2.h26"></a>
 855       <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>
 856     </h5>
 857 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 858 <li class="listitem">
 859           Added Johan R&#229;de's optimised floating point classification routines.
 860         </li>
 861 <li class="listitem">
 862           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>).
 863         </li>
 864 </ul></div>
 865 <h5>
 866 <a name="math_toolkit.history2.h27"></a>
 867       <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>
 868     </h5>
 869 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 870           Improved accuracy and testing of the inverse hypergeometric functions.
 871         </li></ul></div>
 872 <h5>
 873 <a name="math_toolkit.history2.h28"></a>
 874       <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>
 875     </h5>
 876 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 877 <li class="listitem">
 878           Added Noncentral Chi Squared Distribution.
 879         </li>
 880 <li class="listitem">
 881           Added Noncentral Beta Distribution.
 882         </li>
 883 <li class="listitem">
 884           Added Noncentral F Distribution.
 885         </li>
 886 <li class="listitem">
 887           Added Noncentral T Distribution.
 888         </li>
 889 <li class="listitem">
 890           Added Exponential Integral Functions.
 891         </li>
 892 <li class="listitem">
 893           Added Zeta Function.
 894         </li>
 895 <li class="listitem">
 896           Added Rounding and Truncation functions.
 897         </li>
 898 <li class="listitem">
 899           Added Compile time powers of runtime bases.
 900         </li>
 901 <li class="listitem">
 902           Added SSE2 optimizations for Lanczos evaluation.
 903         </li>
 904 </ul></div>
 905 <h5>
 906 <a name="math_toolkit.history2.h29"></a>
 907       <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:
 908       Post Review First Official Release</a>
 909     </h5>
 910 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 911 <li class="listitem">
 912           Added Policy based framework that allows fine grained control over function
 913           behaviour.
 914         </li>
 915 <li class="listitem">
 916           <span class="bold"><strong>Breaking change:</strong></span> Changed default behaviour
 917           for domain, pole and overflow errors to throw an exception (based on review
 918           feedback), this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
 919         </li>
 920 <li class="listitem">
 921           <span class="bold"><strong>Breaking change:</strong></span> Changed exception thrown
 922           when an internal evaluation error occurs to boost::math::evaluation_error.
 923         </li>
 924 <li class="listitem">
 925           <span class="bold"><strong>Breaking change:</strong></span> Changed discrete quantiles
 926           to return an integer result: this is anything up to 20 times faster than
 927           finding the true root, this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;15.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
 928         </li>
 929 <li class="listitem">
 930           Polynomial/rational function evaluation is now customisable and hopefully
 931           faster than before.
 932         </li>
 933 <li class="listitem">
 934           Added performance test program.
 935         </li>
 936 </ul></div>
 937 <h5>
 938 <a name="math_toolkit.history2.h30"></a>
 939       <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
 940       4: Second Review Candidate (1st March 2007)</a>
 941     </h5>
 942 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 943 <li class="listitem">
 944           Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
 945           them into line with the rest of the code.
 946         </li>
 947 <li class="listitem">
 948           Added C# "Distribution Explorer" demo application.
 949         </li>
 950 </ul></div>
 951 <h5>
 952 <a name="math_toolkit.history2.h31"></a>
 953       <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
 954       3: First Review Candidate (31st Dec 2006)</a>
 955     </h5>
 956 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 957 <li class="listitem">
 958           Implemented the main probability distribution and density functions.
 959         </li>
 960 <li class="listitem">
 961           Implemented digamma.
 962         </li>
 963 <li class="listitem">
 964           Added more factorial functions.
 965         </li>
 966 <li class="listitem">
 967           Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
 968           harmonic functions from TR1.
 969         </li>
 970 <li class="listitem">
 971           Moved Xiaogang Zhang's elliptic integral code into the library, and brought
 972           them into line with the rest of the code.
 973         </li>
 974 <li class="listitem">
 975           Moved Hubert Holin's existing Boost.Math special functions into this library
 976           and brought them into line with the rest of the code.
 977         </li>
 978 </ul></div>
 979 <h5>
 980 <a name="math_toolkit.history2.h32"></a>
 981       <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
 982       2: Released September 10th 2006</a>
 983     </h5>
 984 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 985 <li class="listitem">
 986           Implement preview release of the statistical distributions.
 987         </li>
 988 <li class="listitem">
 989           Added statistical distributions tutorial.
 990         </li>
 991 <li class="listitem">
 992           Implemented root finding algorithms.
 993         </li>
 994 <li class="listitem">
 995           Implemented the inverses of the incomplete gamma and beta functions.
 996         </li>
 997 <li class="listitem">
 998           Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
 999         </li>
1000 <li class="listitem">
1001           Integrated the statistical results generated from the test data with Boost.Test:
1002           uses a database of expected results, indexed by test, floating point type,
1003           platform, and compiler.
1004         </li>
1005 <li class="listitem">
1006           Improved lgamma near 1 and 2 (rational approximations).
1007         </li>
1008 <li class="listitem">
1009           Improved erf/erfc inverses (rational approximations).
1010         </li>
1011 <li class="listitem">
1012           Implemented Rational function generation (the Remez method).
1013         </li>
1014 </ul></div>
1015 <h5>
1016 <a name="math_toolkit.history2.h33"></a>
1017       <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
1018       1: Released March 31st 2006</a>
1019     </h5>
1020 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1021 <li class="listitem">
1022           Implement gamma/beta/erf functions along with their incomplete counterparts.
1023         </li>
1024 <li class="listitem">
1025           Generate high quality test data, against which future improvements can
1026           be judged.
1027         </li>
1028 <li class="listitem">
1029           Provide tools for the evaluation of infinite series, continued fractions,
1030           and rational functions.
1031         </li>
1032 <li class="listitem">
1033           Provide tools for testing against tabulated test data, and collecting statistics
1034           on error rates.
1035         </li>
1036 <li class="listitem">
1037           Provide sufficient docs for people to be able to find their way around
1038           the library.
1039         </li>
1040 </ul></div>
1041 <p>
1042       SVN Revisions:
1043     </p>
1044 <p>
1045       Sandbox and trunk last synchonised at revision: .
1046     </p>
1047 </div>
1048 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
1049 <td align="left"></td>
1050 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
1051       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
1052       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
1053       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
1054         Distributed under the Boost Software License, Version 1.0. (See accompanying
1055         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>)
1056       </p>
1057 </div></td>
1058 </tr></table>
1059 <hr>
1060 <div class="spirit-nav">
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