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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.history1"></a><a class="link" href="history1.html" title="History and What's New">History and What's New</a>
</h2></div></div></div>
<p>
      Currently open bug reports can be viewed <a href="https://github.com/boostorg/math/issues" target="_top">here</a>
      on GitHub.
    </p>
<p>
      All old bug reports including closed ones can be viewed on Trac <a href="https://svn.boost.org/trac/boost/query?status=assigned&amp;status=closed&amp;status=new&amp;status=reopened&amp;component=math&amp;col=id&amp;col=summary&amp;col=status&amp;col=type&amp;col=milestone&amp;col=component&amp;order=priority" target="_top">here</a>.
    </p>
<p>
      Recent issues on GitHub <a href="https://github.com/boostorg/math/issues?utf8=%E2%9C%93&amp;q=is%3Aissue" target="_top">here</a>.
    </p>
<h5>
<a name="math_toolkit.history1.h0"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_11_0_boost_1_72"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_11_0_boost_1_72">Math-2.11.0
      (Boost-1.72)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added Hypergeometric functions <a class="link" href="hypergeometric/hypergeometric_1f0.html" title="Hypergeometric 1F0">1F0</a>,
          <a class="link" href="hypergeometric/hypergeometric_0f1.html" title="Hypergeometric 0F1">0F1</a>,
          <a class="link" href="hypergeometric/hypergeometric_2f0.html" title="Hypergeometric 2F0">2F0</a>,
          <a class="link" href="hypergeometric/hypergeometric_1f1.html" title="Hypergeometric 1F1">1F1</a>
          and <a class="link" href="hypergeometric/hypergeometric_pfq.html" title="Hypergeometric pFq">pFq</a>.
        </li>
<li class="listitem">
          Added <a class="link" href="sf_poly/jacobi.html" title="Jacobi Polynomials">Jacobi polynomial</a>
          (and derivatives) evaluation.
        </li>
<li class="listitem">
          Added <a class="link" href="sf_poly/gegenbauer.html" title="Gegenbauer Polynomials">Gegenbauer polynomial</a>
          (and derivatives) evaluation.
        </li>
<li class="listitem">
          Added <a class="link" href="sf_poly/cardinal_b_splines.html" title="Cardinal B-splines">Cardinal
          B-Splines</a> (and derivatives) as polynomial functions in their own
          right.
        </li>
<li class="listitem">
          Added <a class="link" href="cardinal_trigonometric.html" title="Cardinal Trigonometric interpolation">Cardinal Trigonometric
          Interpolation</a>.
        </li>
<li class="listitem">
          Added new statistics sub-section.
        </li>
<li class="listitem">
          Added <a class="link" href="t_test.html" title="t-tests">One Sample Student's T Test</a>.
        </li>
<li class="listitem">
          Added <a class="link" href="anderson_darling.html" title="The Anderson-Darling Test">Anderson Darling test
          for normality</a>.
        </li>
<li class="listitem">
          Added <a class="link" href="ljung_box.html" title="The Ljung-Box Test">Ljung Box test for auto-correlation</a>.
        </li>
<li class="listitem">
          Added <a class="link" href="runs_test.html" title="Runs tests">Runs test for random sequences</a>.
        </li>
<li class="listitem">
          The headers <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">univariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code> and <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">tools</span><span class="special">/</span><span class="identifier">bivariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>,
          have been deprecated in favor of <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">univariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>
          and <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">bivariate_statistics</span><span class="special">.</span><span class="identifier">hpp</span></code>.
        </li>
<li class="listitem">
          Added <a class="link" href="dist_ref/dists/empirical_cdf.html" title="Empirical Cumulative Distribution Function">The Empirical
          CDF distribution</a>.
        </li>
<li class="listitem">
          Reworked the Sterling approximation used by multiprecision gamma functions
          to be applicable to all the function that use the Lanczos approximation
          at regular precision. Also extended Lanczos approximations up to 100 decimal
          digit precision.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h1"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_10_0_boost_1_71"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_10_0_boost_1_71">Math-2.10.0
      (Boost-1.71)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Catmull-Rom interpolator now works in C++11.
        </li>
<li class="listitem">
          Cardinal quadratic B-spline interpolation.
        </li>
<li class="listitem">
          Domain of elliptic integrals extended.
        </li>
<li class="listitem">
          sin_pi and cos_pi performance improvements.
        </li>
<li class="listitem">
          Forward-mode automatic differentiation.
        </li>
<li class="listitem">
          Vector valued barycentric rational interpolation.
        </li>
<li class="listitem">
          Ooura's method for evaluation of Fourier integrals.
        </li>
<li class="listitem">
          Multiple compatibility issues with Multiprecision fixed.
        </li>
<li class="listitem">
          Lambert-W fixed on a rare architecture.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h2"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_9_0_boost_1_70"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_9_0_boost_1_70">Math-2.9.0
      (Boost-1.70)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Add Lanczos smoothing derivatives
        </li>
<li class="listitem">
          Move <code class="computeroutput"><span class="identifier">numerical_differentiation</span><span class="special">.</span><span class="identifier">hpp</span></code>
          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>
          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>.
        </li>
<li class="listitem">
          Add mean, variance, skewness, kurtosis, median, Gini coefficient, and median
          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>.
        </li>
<li class="listitem">
          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>
        </li>
<li class="listitem">
          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
          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>.
        </li>
<li class="listitem">
          Add total variation, l0, l1, l2, and sup norms, as well as corresponding
          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>.
        </li>
<li class="listitem">
          Add move constructors for polynomials, support complex coefficients, add
          <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>
          methods.
        </li>
<li class="listitem">
          Add <code class="computeroutput"><span class="identifier">quadratic_roots</span></code> to
          <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>.
        </li>
<li class="listitem">
          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>.
        </li>
<li class="listitem">
          Add Catmull-Rom interpolator.
        </li>
<li class="listitem">
          Fix bug in <code class="computeroutput"><span class="identifier">newton_raphson_iterate</span></code>
          where we could terminate incorrectly under certain exceptional cases.
        </li>
<li class="listitem">
          Suppressed warnings from use of <code class="computeroutput"><span class="identifier">Q</span></code>
          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>
          <span class="special">-</span><span class="identifier">pedantic</span></code>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h3"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_8_0_boost_1_69"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_8_0_boost_1_69">Math-2.8.0
      (Boost-1.69)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Add LambertW functions.
        </li>
<li class="listitem">
          Update integration routines to support complex valued integrands and contour
          integrals.
        </li>
<li class="listitem">
          Added the derivative of the Barycentric rational approximation.
        </li>
<li class="listitem">
          Updated continued fraction and series evaluation code to support complex
          types.
        </li>
<li class="listitem">
          Minor fixes to better support variable precision floating point types.
        </li>
<li class="listitem">
          Removed use of deprecated Boost.Endian in favour of Predef.
        </li>
<li class="listitem">
          Prevent logic error leading to infinite loop in toms748_solve. See <a href="https://github.com/boostorg/math/issues/138" target="_top">#138</a>.
        </li>
<li class="listitem">
          Fix mean and standard_deviation for extreme_value_distribution. See <a href="https://github.com/boostorg/math/issues/139" target="_top">#139</a>.
        </li>
<li class="listitem">
          Improve heuristics used in newton_raphson_iterate. See <a href="https://github.com/boostorg/math/issues/145" target="_top">#145</a>.
        </li>
<li class="listitem">
          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>.
          See <a href="https://github.com/boostorg/math/issues/141" target="_top">#141</a>.
        </li>
<li class="listitem">
          Big push to reduce GCC warnings. See <a href="https://github.com/boostorg/math/issues/136" target="_top">#136</a>.
        </li>
<li class="listitem">
          Refactor polynomial addition. See <a href="https://github.com/boostorg/math/pull/132" target="_top">PR132</a>.
        </li>
<li class="listitem">
          Fix for vxWorks having a <code class="computeroutput"><span class="identifier">real</span></code>
          function in the global namespace. See <a href="https://github.com/boostorg/math/pull/131" target="_top">PR131</a>.
        </li>
<li class="listitem">
          Improve <code class="computeroutput"><span class="identifier">sinc</span></code> approximations
          and add better tests.
        </li>
<li class="listitem">
          Fix typo in Student's T hypothesis testing documentation, see <a href="https://github.com/boostorg/math/issues/143" target="_top">#143</a>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h4"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_7_1_boost_1_68"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_7_1_boost_1_68">Math-2.7.1
      (Boost-1.68)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Continue to improve numerical integration routines, and in particular add
          support for contour integrals.
        </li>
<li class="listitem">
          Improve accuracy of erfc function's rational approximations.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h5"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_7_0_boost_1_66"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_7_0_boost_1_66">Math-2.7.0
      (Boost-1.66)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Add Gauss and Gauss-Kronrod quadrature routines.
        </li>
<li class="listitem">
          Add double-exponential (tanh-sinh, exp-sinh and sinh-sinh) quadrature routines.
        </li>
<li class="listitem">
          Add Chebyshev polynomial evaluation, roots, integration, differentiation,
          and interpolation routines.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h6"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_6_0_boost_1_65"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_6_0_boost_1_65">Math-2.6.0
      (Boost-1.65)</a>
    </h5>
<p>
      New Features:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Add <a class="link" href="cardinal_cubic_b.html" title="Cardinal Cubic B-spline interpolation">Cardinal cubic B-Spline
          interpolation functions</a>, with thanks to Nick Thompson.
        </li>
<li class="listitem">
          Add <a class="link" href="barycentric.html" title="Barycentric Rational Interpolation">barycentric rational interpolation
          functions</a>, with thanks to Nick Thompson.
        </li>
<li class="listitem">
          Add <a class="link" href="trapezoidal.html" title="Trapezoidal Quadrature">adaptive trapezoidal quadrature</a>,
          with thanks to Nick Thompson.
        </li>
<li class="listitem">
          Add <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">support for the zeros
          and derivatives of Legendre polynomials</a>, with thanks to Nick Thompson.
        </li>
</ul></div>
<p>
      Patches:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Improve polynomial GCD algorithms, with thanks to Jeremy Murphy.
        </li>
<li class="listitem">
          Removed gcd/lcm routines from Boost.Math - these are now in Boost.Integer.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h7"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_5_2_boost_1_64"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_5_2_boost_1_64">Math-2.5.2
      (Boost-1.64)</a>
    </h5>
<p>
      Patches:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Big push to ensure all functions in also in C99 are compatible with Annex
          F.
        </li>
<li class="listitem">
          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>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h8"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_5_1_boost_1_63"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_5_1_boost_1_63">Math-2.5.1
      (Boost-1.63)</a>
    </h5>
<p>
      Patches:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Fixed evaluation of zero polynomial in polynomial.hpp, see <a href="https://svn.boost.org/trac/boost/ticket/12532" target="_top">12532</a>.
        </li>
<li class="listitem">
          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>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h9"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_5_0_boost_1_62"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_5_0_boost_1_62">Math-2.5.0
      (Boost-1.62)</a>
    </h5>
<p>
      New Features:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
          Enabled all the special function code to work correctly with types whose
          precision can change at runtime: for example type <code class="computeroutput"><span class="identifier">mpfr_float</span></code>
          from Boost.Multiprecision.
        </li></ul></div>
<p>
      Patches:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Fix tgamma_delta_ratio for cases where the delta is small compared to the
          base.
        </li>
<li class="listitem">
          Fix misc GCC-4.4 test failures.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h10"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_4_0_boost_1_61"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_4_0_boost_1_61">Math-2.4.0
      (Boost-1.61)</a>
    </h5>
<p>
      New Features:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
          Polynomial arithmetic added to tools.
        </li></ul></div>
<h5>
<a name="math_toolkit.history1.h11"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_3_0_boost_1_60"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_3_0_boost_1_60">Math-2.3.0
      (Boost-1.60)</a>
    </h5>
<p>
      New Features:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Promote the root finding and function minimization code to first class
          citizens - these are now officially supported as part of the library.
        </li>
<li class="listitem">
          Allow the library to be used and tested with compiler exception handling
          support turned off. To better facilitate this the default error handling
          policies have been changed to <span class="emphasis"><em>errno_on_error</em></span> but only
          when the compiler has no exception handling support.
        </li>
</ul></div>
<p>
      Patches:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Fix behaviour of the non-central chi-squared distribution when the non-centrality
          parameter is zero to match the chi-squared, see <a href="https://svn.boost.org/trac/boost/ticket/11557" target="_top">11557</a>.
        </li>
<li class="listitem">
          Fix comments in code for the hypergeometric to match what it actually does,
          also fixes the parameter access functions to return the correct values.
          See <a href="https://svn.boost.org/trac/boost/ticket/11556" target="_top">11556</a>.
        </li>
<li class="listitem">
          Stopped using hidden visiblity library build with the Oracle compiler as
          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>.
        </li>
<li class="listitem">
          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>.
        </li>
<li class="listitem">
          Fix corner case bug in root bracketing code, see <a href="https://svn.boost.org/trac/boost/ticket/11532" target="_top">11532</a>.
        </li>
<li class="listitem">
          Add some missing typecasts in arguments to std::max in Bernoulli code.
          See <a href="https://svn.boost.org/trac/boost/ticket/11453" target="_top">11453</a>.
        </li>
<li class="listitem">
          Fix mistaken assumptions about the possible values for FLT_EVAL_METHOD.
          See <a href="https://svn.boost.org/trac/boost/ticket/11429" target="_top">11429</a>.
        </li>
<li class="listitem">
          Completely revamped performance testing and error-rate measuring code so
          we can more easily document how well (or not!) we're doing. This information
          will hopefully get more frequently updated in future as it's more or less
          automatically generated - see the <span class="emphasis"><em>reporting</em></span> sub-directory
          for more information.
        </li>
<li class="listitem">
          Fix some corner cases in the beta, incomplete beta, and incomplete beta
          derivative. With thanks to Rocco Romeo.
        </li>
<li class="listitem">
          Reorganized the Bessel functions internally to improve the performance
          of Jn and Yn.
        </li>
<li class="listitem">
          Fixed skewness formula for triangular distribution, see <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">#11768</a>.
        </li>
<li class="listitem">
          Fixed some examples so they compile on Unix platforms which have an ::exception
          struct declared, see <a href="https://svn.boost.org/trac/boost/ticket/11827" target="_top">#11827</a>.
        </li>
<li class="listitem">
          Correct mistake in triangular distribution skewness formula <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">11768</a>,
          reported by Juan Leni.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h12"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_2_1"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_2_1">Math-2.2.1</a>
    </h5>
<p>
      Patch release for Boost-1.58:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Minor <a href="https://github.com/boostorg/math/pull/13#issuecomment-98905579" target="_top">patch
          for Haiku support.</a>
        </li>
<li class="listitem">
          Fix the decimal digit count for 128-bit floating point types.
        </li>
<li class="listitem">
          Fix a few documentation typos.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h13"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_2_0_boost_1_58_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_2_0_boost_1_58_0">Math-2.2.0
      (boost-1.58.0)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added two new special functions - <a class="link" href="sf_gamma/trigamma.html" title="Trigamma">trigamma</a>
          and <a class="link" href="sf_gamma/polygamma.html" title="Polygamma">polygamma</a>.
        </li>
<li class="listitem">
          Fixed namespace scope constants so they are constexpr on conforming compilers,
          see https://svn.boost.org/trac/boost/ticket/10901.
        </li>
<li class="listitem">
          Fixed various cases of spurious under/overflow in the incomplete beta and
          gamma functions, plus the elliptic integrals, with thanks to Rocco Romeo.
        </li>
<li class="listitem">
          Fix 3-arg <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
          and <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_q</a> functions
          to not call the policy based overload if the final argument is not actually
          a policy.
        </li>
<li class="listitem">
          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>.
        </li>
<li class="listitem">
          Fixed extreme-value pdf for large valued inputs, see <a href="https://svn.boost.org/trac/boost/ticket/10938" target="_top">#10938</a>.
        </li>
<li class="listitem">
          Large update to the Elliptic integral code to use Carlson's latest algorithms
          - these should be more stable, more accurate and slightly faster than before.
          Also added support for Carlson's RG integral.
        </li>
<li class="listitem">
          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
          integrals.
        </li>
<li class="listitem">
          Switched documentation to use SVG rather than PNG graphs and equations
          - browsers seem to have finally caught up!
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h14"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_1_0_boost_1_57_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_1_0_boost_1_57_0">Math-2.1.0
      (boost-1.57.0)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added <a class="link" href="dist_ref/dists/hyperexponential_dist.html" title="Hyperexponential Distribution">Hyperexponential
          Distribution</a>.
        </li>
<li class="listitem">
          Fix some spurious overflows in the incomplete gamma functions (with thanks
          to Rocco Romeo).
        </li>
<li class="listitem">
          Fix bug in derivative of incomplete beta when a = b = 0.5 - this also effects
          several non-central distributions, see <a href="https://svn.boost.org/trac/boost/ticket/10480" target="_top">10480</a>.
        </li>
<li class="listitem">
          Fixed some corner cases in <a class="link" href="rounding/round.html" title="Rounding Functions">round</a>.
        </li>
<li class="listitem">
          Don't support 80-bit floats in cstdfloat.hpp if standard library support
          is broken.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h15"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_2_0_0_boost_1_56_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_2_0_0_boost_1_56_0">Math-2.0.0
      (Boost-1.56.0)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          <span class="bold"><strong>Breaking change</strong></span>: moved a number of non-core
          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
          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>,
          <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>,
          <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
          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
          path.
        </li>
<li class="listitem">
          <span class="bold"><strong>Breaking change</strong></span>: A number of distributions
          and special functions were returning the maximum finite value rather than
          raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>,
          this has now been fixed, which means these functions now behave as documented.
          However, since the default behavior on raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>
          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
          which have come to reply rely on these functions not throwing may experience
          exceptions where they did not before. The special functions involved are
          <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>,
          <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>,
          <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
          <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
          <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>,
          <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>,
          <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
          involved are <a class="link" href="dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto
          Distribution</a>, <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta
          Distribution</a>, <a class="link" href="dist_ref/dists/geometric_dist.html" title="Geometric Distribution">Geometric
          Distribution</a>, <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
          Binomial Distribution</a>, <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
          Distribution</a>, <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
          Squared Distribution</a>, <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
          Distribution</a>, <a class="link" href="dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">Inverse
          chi squared Distribution</a>, <a class="link" href="dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution">Inverse
          Gamma Distribution</a>. See <a href="https://svn.boost.org/trac/boost/ticket/10111" target="_top">#10111</a>.
        </li>
<li class="listitem">
          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
          be used with integer arguments, see <a href="https://svn.boost.org/trac/boost/ticket/10066" target="_top">#10066</a>.
        </li>
<li class="listitem">
          Fix Halley iteration to handle zero derivative (with non-zero second derivative),
          see <a href="https://svn.boost.org/trac/boost/ticket/10046" target="_top">#10046</a>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h16"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_1_9_1"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_1_9_1">Math-1.9.1</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Fix Geometric distribution use of Policies, see <a href="https://svn.boost.org/trac/boost/ticket/9833" target="_top">#9833</a>.
        </li>
<li class="listitem">
          Fix corner cases in the negative binomial distribution, see <a href="https://svn.boost.org/trac/boost/ticket/9834" target="_top">#9834</a>.
        </li>
<li class="listitem">
          Fix compilation failures on Mac OS.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h17"></a>
      <span class="phrase"><a name="math_toolkit.history1.math_1_9_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.math_1_9_0">Math-1.9.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Changed version number to new Boost.Math specific version now that we're
          in the modular Boost world.
        </li>
<li class="listitem">
          Added <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
          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
          approximation (from Nikhar Agrawal).
        </li>
<li class="listitem">
          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>,
          <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_neumann_prime</a>,
          <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_i_prime</a>,
          <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_k_prime</a>,
          <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_bessel_prime</a>
          and <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_neumann_prime</a>
          (from Anton Bikineev).
        </li>
<li class="listitem">
          Fixed buggy Student's t example code, along with docs for testing sample
          means for equivalence.
        </li>
<li class="listitem">
          Documented <code class="computeroutput"><span class="identifier">max_iter</span></code> parameter
          in root finding code better, see <a href="https://svn.boost.org/trac/boost/ticket/9225" target="_top">#9225</a>.
        </li>
<li class="listitem">
          Add option to explicitly enable/disable use of __float128 in constants
          code, see <a href="https://svn.boost.org/trac/boost/ticket/9240" target="_top">#9240</a>.
        </li>
<li class="listitem">
          Cleaned up handling of negative values in Bessel I0 and I1 code (removed
          dead code), see <a href="https://svn.boost.org/trac/boost/ticket/9512" target="_top">#9512</a>.
        </li>
<li class="listitem">
          Fixed handling of very small values passed to <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
          and <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> so they
          don't generate spurious overflows (thanks to Rocco Romeo).
        </li>
<li class="listitem">
          <a href="https://svn.boost.org/trac/boost/ticket/9672" target="_top">#9672 PDF and
          CDF of a Laplace distribution throwing domain_error</a> Random variate
          can now be infinite.
        </li>
<li class="listitem">
          Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
          <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
          and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
          with thanks to Rocco Romeo.
        </li>
<li class="listitem">
          Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
          <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
          and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
          (thanks to Rocco Romeo).
        </li>
<li class="listitem">
          Removed constant <code class="computeroutput"><span class="identifier">pow23_four_minus_pi</span>
          </code> whose value did not match the name (and was unused by Boost.Math),
          see <a href="https://svn.boost.org/trac/boost/ticket/9712" target="_top">#9712</a>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h18"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_55"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_55">Boost-1.55</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Suppress numerous warnings (mostly from GCC-4.8 and MSVC) <a href="https://svn.boost.org/trac/boost/ticket/8384" target="_top">#8384</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/8855" target="_top">#8855</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/9107" target="_top">#9107</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/9109" target="_top">#9109</a>..
        </li>
<li class="listitem">
          Fixed PGI compilation issue <a href="https://svn.boost.org/trac/boost/ticket/8333" target="_top">#8333</a>.
        </li>
<li class="listitem">
          Fixed PGI constant value initialization issue that caused erf to generate
          incorrect results <a href="https://svn.boost.org/trac/boost/ticket/8621" target="_top">#8621</a>.
        </li>
<li class="listitem">
          Prevent macro expansion of some C99 macros that are also C++ functions
          <a href="https://svn.boost.org/trac/boost/ticket/8732" target="_top">#8732</a>
          and <a href="https://svn.boost.org/trac/boost/ticket/8733" target="_top">#8733</a>..
        </li>
<li class="listitem">
          Fixed Student's T distribution to behave correctly with huge degrees of
          freedom (larger than the largest representable integer) <a href="https://svn.boost.org/trac/boost/ticket/8837" target="_top">#8837</a>.
        </li>
<li class="listitem">
          Make some core functions usable with <code class="computeroutput"><span class="keyword">long</span>
          <span class="keyword">double</span></code> even when the platform has
          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>.
        </li>
<li class="listitem">
          Fix error handling of distributions to catch invalid scale and location
          parameters when the random variable is infinite <a href="https://svn.boost.org/trac/boost/ticket/9042" target="_top">#9042</a>
          and <a href="https://svn.boost.org/trac/boost/ticket/9126" target="_top">#9126</a>.
        </li>
<li class="listitem">
          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>.
        </li>
<li class="listitem">
          Improve consistency of argument reduction in the elliptic integrals <a href="https://svn.boost.org/trac/boost/ticket/9104" target="_top">#9104</a>.
        </li>
<li class="listitem">
          Fix bug in inverse incomplete beta that results in cancellation errors
          when the beta function is really an arcsine or Student's T distribution.
        </li>
<li class="listitem">
          Fix issue in Bessel I and K function continued fractions that causes spurious
          over/underflow.
        </li>
<li class="listitem">
<p class="simpara">
          Add improvement to non-central chi squared distribution quantile due to
          Thomas Luu, <a href="http://discovery.ucl.ac.uk/1482128/" target="_top">Fast and accurate
          parallel computation of quantile functions for random number generation,
          Doctorial Thesis 2016</a>. <a href="http://discovery.ucl.ac.uk/1463470/" target="_top">Efficient
          and Accurate Parallel Inversion of the Gamma Distribution, Thomas Luu</a>
        </p>
<h5>
<a name="math_toolkit.history1.h19"></a>
          <span class="phrase"><a name="math_toolkit.history1.boost_1_54"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_54">Boost-1.54</a>
        </h5>
</li>
<li class="listitem">
          Major reorganization to incorporate other Boost.Math like Integer Utilities
          Integer Utilities (Greatest Common Divisor and Least Common Multiple),
          quaternions and octonions. Making new chapter headings.
        </li>
<li class="listitem">
          Added many references to Boost.Multiprecision and <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>
          as an example of a User-defined Type (UDT).
        </li>
<li class="listitem">
          Added Clang to list of supported compilers.
        </li>
<li class="listitem">
          Fixed constants to use a thread-safe cache of computed values when used
          at arbitrary precision.
        </li>
<li class="listitem">
          Added finding zeros of Bessel functions <code class="computeroutput"><span class="identifier">cyl_bessel_j_zero</span></code>,
          <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
          Christopher Kormanyos).
        </li>
<li class="listitem">
          More accuracy improvements to the Bessel J and Y functions from Rocco Romeo.
        </li>
<li class="listitem">
          Fixed nasty cyclic dependency bug that caused some headers to not compile
          <a href="https://svn.boost.org/trac/boost/ticket/7999" target="_top">#7999</a>.
        </li>
<li class="listitem">
          Fixed bug in <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
          that caused spurious overflow for arguments between 142.5 and 143.
        </li>
<li class="listitem">
          Fixed bug in raise_rounding_error that caused it to return an incorrect
          result when throwing an exception is turned off <a href="https://svn.boost.org/trac/boost/ticket/7905" target="_top">#7905</a>.
        </li>
<li class="listitem">
          Added minimal __float128 support.
        </li>
<li class="listitem">
          Fixed bug in edge-cases of poisson quantile <a href="https://svn.boost.org/trac/boost/ticket/8308" target="_top">#8308</a>.
        </li>
<li class="listitem">
          Adjusted heuristics used in Halley iteration to cope with inverting the
          incomplete beta in tricky regions where the derivative is flatlining. Example
          is computing the quantile of the Fisher F distribution for probabilities
          smaller than machine epsilon. See ticket <a href="https://svn.boost.org/trac/boost/ticket/8314" target="_top">#8314</a>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h20"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_53"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_53">Boost-1.53</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/7325" target="_top">#7325</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7415" target="_top">#7415</a>
          and <a href="https://svn.boost.org/trac/boost/ticket/7416" target="_top">#7416</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7183" target="_top">#7183</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7649" target="_top">#7649</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7694" target="_top">#7694</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/4445" target="_top">#4445</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7492" target="_top">#7492</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7891" target="_top">#7891</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7429" target="_top">#7429</a>.
        </li>
<li class="listitem">
          Fixed mistake in calculating pooled standard deviation in two-sample students
          t example <a href="https://svn.boost.org/trac/boost/ticket/7402" target="_top">#7402</a>.
        </li>
<li class="listitem">
          Improve complex acos/asin/atan, see <a href="https://svn.boost.org/trac/boost/ticket/7290" target="_top">#7290</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7291" target="_top">#7291</a>.
        </li>
<li class="listitem">
          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>
          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>
          thanks to suggestions from Rocco Romeo.
        </li>
<li class="listitem">
          Improve accuracy of Bessel J and Y for integer orders thanks to suggestions
          from Rocco Romeo.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h21"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_52"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_52">Boost-1.52</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Corrected moments for small degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7177" target="_top">#7177</a>
          (reported by Thomas Mang).
        </li>
<li class="listitem">
          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>.
        </li>
<li class="listitem">
          Corrected failure to detect bad parameters in many distributions <a href="https://svn.boost.org/trac/boost/ticket/6934" target="_top">#6934</a> (reported
          by Florian Schoppmann) by adding a function check_out_of_range to test
          many possible bad parameters. This test revealed several distributions
          where the checks for bad parameters were ineffective, and these have been
          rectified.
        </li>
<li class="listitem">
          Fixed issue in Hankel functions that causes incorrect values to be returned
          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>.
        </li>
<li class="listitem">
          Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/6517" target="_top">#6517</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/6362" target="_top">#6362</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7053" target="_top">#7053</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/2693" target="_top">#2693</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/6937" target="_top">#6937</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/7099" target="_top">#7099</a>.
        </li>
<li class="listitem">
          Permitted infinite degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>
          implemented using the normal distribution (requested by Thomas Mang).
        </li>
<li class="listitem">
          Much enhanced accuracy for large degrees of freedom &#957; and/or large non-centrality
          &#948;
by switching to use the Students t distribution (or Normal distribution
          for infinite degrees of freedom) centered at delta, when &#948; / (4 * &#957;) &lt;
          epsilon for the floating-point type in use. <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>.
          It was found that the incomplete beta was suffering from serious cancellation
          errors when degrees of freedom was very large. (That has now been fixed
          in our code, but any code based on Didonato and Morris's original papers
          (probably every implementation out there actually) will have the same issue).
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h22"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_51"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_51">Boost-1.51</a>
    </h5>
<p>
      See Boost-1.52 - some items were added but not listed in time for the release.
    </p>
<h5>
<a name="math_toolkit.history1.h23"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_50"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_50">Boost-1.50</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Promoted math constants to be 1st class citizens, including convenient
          access to the most widely used built-in float, double, long double via
          three namespaces.
        </li>
<li class="listitem">
          Added the Owen's T function and Skew Normal distribution written by Benjamin
          Sobotta: see <a class="link" href="owens_t.html" title="Owen's T function">Owens T</a> and skew_normal_distrib.
        </li>
<li class="listitem">
          Added Hankel functions <a class="link" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a>,
          <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>.
        </li>
<li class="listitem">
          Corrected issue <a href="https://svn.boost.org/trac/boost/ticket/6627" target="_top">#6627
          nonfinite_num_put formatting of 0.0 is incorrect</a> based on a patch
          submitted by K R Walker.
        </li>
<li class="listitem">
          Changed constant initialization mechanism so that it is thread safe even
          for user-defined types, also so that user defined types get the full precision
          of the constant, even when <code class="computeroutput"><span class="keyword">long</span>
          <span class="keyword">double</span></code> does not. So for example
          128-bit rational approximations will work with UDT's and do the right thing,
          even though <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
          may be only 64 or 80 bits.
        </li>
<li class="listitem">
          Fixed issue in <code class="computeroutput"><span class="identifier">bessel_jy</span></code>
          which causes Y<sub>8.5</sub>(4&#960;) to yield a NaN.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h24"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_49"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_49">Boost-1.49</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Deprecated wrongly named <code class="computeroutput"><span class="identifier">twothirds</span></code>
          math constant in favour of <code class="computeroutput"><span class="identifier">two_thirds</span></code>
          (with underscore separator). (issue <a href="https://svn.boost.org/trac/boost/ticket/6199" target="_top">#6199</a>).
        </li>
<li class="listitem">
          Refactored test data and some special function code to improve support
          for arbitary precision and/or expression-template-enabled types.
        </li>
<li class="listitem">
          Added new faster zeta function evaluation method.
        </li>
</ul></div>
<p>
      Fixed issues:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Corrected CDF complement for Laplace distribution (issue <a href="https://svn.boost.org/trac/boost/ticket/6151" target="_top">#6151</a>).
        </li>
<li class="listitem">
          Corrected branch cuts on the complex inverse trig functions, to handle
          signed zeros (issue <a href="https://svn.boost.org/trac/boost/ticket/6171" target="_top">#6171</a>).
        </li>
<li class="listitem">
          Fixed bug in <code class="computeroutput"><span class="identifier">bessel_yn</span></code>
          which caused incorrect overflow errors to be raised for negative <span class="emphasis"><em>n</em></span>
          (issue <a href="https://svn.boost.org/trac/boost/ticket/6367" target="_top">#6367</a>).
        </li>
<li class="listitem">
          Also fixed minor/cosmetic/configuration issues <a href="https://svn.boost.org/trac/boost/ticket/6120" target="_top">#6120</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/6191" target="_top">#6191</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/6130" target="_top">#6130</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/6234" target="_top">#6234</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/6307" target="_top">#6307</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/6192" target="_top">#6192</a>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h25"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_48"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_48">Boost-1.48</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added new series evaluation methods to the cyclic Bessel I, J, K and Y
          functions. Also taken great care to avoid spurious over and underflow of
          these functions. Fixes issue <a href="https://svn.boost.org/trac/boost/ticket/5560" target="_top">#5560</a>
        </li>
<li class="listitem">
          Added an example of using Inverse Chi-Squared distribution for Bayesian
          statistics, provided by Thomas Mang.
        </li>
<li class="listitem">
          Added tests to use improved version of lexical_cast which handles C99 nonfinites
          without using globale facets.
        </li>
<li class="listitem">
          Corrected wrong out-of-bound uniform distribution CDF complement values
          <a href="https://svn.boost.org/trac/boost/ticket/5733" target="_top">#5733</a>.
        </li>
<li class="listitem">
          Enabled long double support on OpenBSD (issue <a href="https://svn.boost.org/trac/boost/ticket/6014" target="_top">#6014</a>).
        </li>
<li class="listitem">
          Changed nextafter and related functions to behave in the same way as other
          implementations - so that nextafter(+INF, 0) is a finite value (issue
          <a href="https://svn.boost.org/trac/boost/ticket/5823" target="_top">#5832</a>).
        </li>
<li class="listitem">
          Changed tuple include configuration to fix issue when using in conjunction
          with Boost.Tr1 (issue <a href="https://svn.boost.org/trac/boost/ticket/5934" target="_top">#5934</a>).
        </li>
<li class="listitem">
          Changed class eps_tolerance to behave correctly when both ends of the range
          are zero (issue <a href="https://svn.boost.org/trac/boost/ticket/6001" target="_top">#6001</a>).
        </li>
<li class="listitem">
          Fixed missing include guards on prime.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5927" target="_top">#5927</a>).
        </li>
<li class="listitem">
          Removed unused/undocumented constants from constants.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>).
        </li>
<li class="listitem">
          Fixed missing std:: prefix in nonfinite_num_facets.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5914" target="_top">#5914</a>).
        </li>
<li class="listitem">
          Minor patches for Cray compiler compatibility.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h26"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_47"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_47">Boost-1.47</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added changesign function to sign.hpp to facilitate addition of nonfinite
          facets.
        </li>
<li class="listitem">
          Addition of nonfinite facets from Johan Rade, with tests, examples of use
          for C99 format infinity and NaN, and documentation.
        </li>
<li class="listitem">
          Added tests and documentation of changesign from Johan Rade.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h27"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_46_1"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_46_1">Boost-1.46.1</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
          Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5095</a>,
          <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
        </li></ul></div>
<h5>
<a name="math_toolkit.history1.h28"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_46_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_46_0">Boost-1.46.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added Wald, Inverse Gaussian and geometric distributions.
        </li>
<li class="listitem">
          Added information about configuration macros.
        </li>
<li class="listitem">
          Added support for mpreal as a real-numbered type.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h29"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_45_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_45_0">Boost-1.45.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added warnings about potential ambiguity with std random library in distribution
          and function names.
        </li>
<li class="listitem">
          Added inverse gamma distribution and inverse chi_square and scaled inverse
          chi_square.
        </li>
<li class="listitem">
          Editorial revision of documentation, and added FAQ.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h30"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_44_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_44_0">Boost-1.44.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Fixed incorrect range and support for Rayleigh distribution.
        </li>
<li class="listitem">
          Fixed numerical error in the quantile of the Student's T distribution:
          the function was returning garbage values for non-integer degrees of freedom
          between 2 and 3.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h31"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_41_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_41_0">Boost-1.41.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
          Significantly improved performance for the incomplete gamma function and
          its inverse.
        </li></ul></div>
<h5>
<a name="math_toolkit.history1.h32"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_40_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_40_0">Boost-1.40.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added support for MPFR as a bignum type.
        </li>
<li class="listitem">
          Added some full specializations of the policy classes to reduce compile
          times.
        </li>
<li class="listitem">
          Added logistic and hypergeometric distributions, from Gautam Sewani's Google
          Summer of Code project.
        </li>
<li class="listitem">
          Added Laplace distribution submitted by Thijs van den Berg.
        </li>
<li class="listitem">
          Updated performance test code to include new distributions, and improved
          the performance of the non-central distributions.
        </li>
<li class="listitem">
          Added SSE2 optimised <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
          code, from Gautam Sewani's Google Summer of Code project.
        </li>
<li class="listitem">
          Fixed bug in cyl_bessel_i that used an incorrect approximation for &#957; = 0.5,
          also effects the non-central Chi Square Distribution when &#957; = 3, see bug
          report <a href="https://svn.boost.org/trac/boost/ticket/2877" target="_top">#2877</a>.
        </li>
<li class="listitem">
          Fixed minor bugs <a href="https://svn.boost.org/trac/boost/ticket/2873" target="_top">#2873</a>.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h33"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_38_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_38_0">Boost-1.38.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added Johan R&#229;de's optimised floating point classification routines.
        </li>
<li class="listitem">
          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>).
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h34"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_37_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_37_0">Boost-1.37.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
          Improved accuracy and testing of the inverse hypergeometric functions.
        </li></ul></div>
<h5>
<a name="math_toolkit.history1.h35"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_36_0"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_36_0">Boost-1.36.0</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added Noncentral Chi Squared Distribution.
        </li>
<li class="listitem">
          Added Noncentral Beta Distribution.
        </li>
<li class="listitem">
          Added Noncentral F Distribution.
        </li>
<li class="listitem">
          Added Noncentral T Distribution.
        </li>
<li class="listitem">
          Added Exponential Integral Functions.
        </li>
<li class="listitem">
          Added Zeta Function.
        </li>
<li class="listitem">
          Added Rounding and Truncation functions.
        </li>
<li class="listitem">
          Added Compile time powers of runtime bases.
        </li>
<li class="listitem">
          Added SSE2 optimizations for Lanczos evaluation.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h36"></a>
      <span class="phrase"><a name="math_toolkit.history1.boost_1_35_0_post_review_first_o"></a></span><a class="link" href="history1.html#math_toolkit.history1.boost_1_35_0_post_review_first_o">Boost-1.35.0:
      Post Review First Official Release</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Added Policy based framework that allows fine grained control over function
          behaviour.
        </li>
<li class="listitem">
          <span class="bold"><strong>Breaking change:</strong></span> Changed default behaviour
          for domain, pole and overflow errors to throw an exception (based on review
          feedback), this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
        </li>
<li class="listitem">
          <span class="bold"><strong>Breaking change:</strong></span> Changed exception thrown
          when an internal evaluation error occurs to boost::math::evaluation_error.
        </li>
<li class="listitem">
          <span class="bold"><strong>Breaking change:</strong></span> Changed discrete quantiles
          to return an integer result: this is anything up to 20 times faster than
          finding the true root, this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;20.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
        </li>
<li class="listitem">
          Polynomial/rational function evaluation is now customisable and hopefully
          faster than before.
        </li>
<li class="listitem">
          Added performance test program.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h37"></a>
      <span class="phrase"><a name="math_toolkit.history1.milestone_4_second_review_candid"></a></span><a class="link" href="history1.html#math_toolkit.history1.milestone_4_second_review_candid">Milestone
      4: Second Review Candidate (1st March 2007)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
          them into line with the rest of the code.
        </li>
<li class="listitem">
          Added C# "Distribution Explorer" demo application.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h38"></a>
      <span class="phrase"><a name="math_toolkit.history1.milestone_3_first_review_candida"></a></span><a class="link" href="history1.html#math_toolkit.history1.milestone_3_first_review_candida">Milestone
      3: First Review Candidate (31st Dec 2006)</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Implemented the main probability distribution and density functions.
        </li>
<li class="listitem">
          Implemented digamma.
        </li>
<li class="listitem">
          Added more factorial functions.
        </li>
<li class="listitem">
          Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
          harmonic functions from TR1.
        </li>
<li class="listitem">
          Moved Xiaogang Zhang's elliptic integral code into the library, and brought
          them into line with the rest of the code.
        </li>
<li class="listitem">
          Moved Hubert Holin's existing Boost.Math special functions into this library
          and brought them into line with the rest of the code.
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h39"></a>
      <span class="phrase"><a name="math_toolkit.history1.milestone_2_released_september_1"></a></span><a class="link" href="history1.html#math_toolkit.history1.milestone_2_released_september_1">Milestone
      2: Released September 10th 2006</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Implement preview release of the statistical distributions.
        </li>
<li class="listitem">
          Added statistical distributions tutorial.
        </li>
<li class="listitem">
          Implemented root finding algorithms.
        </li>
<li class="listitem">
          Implemented the inverses of the incomplete gamma and beta functions.
        </li>
<li class="listitem">
          Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
        </li>
<li class="listitem">
          Integrated the statistical results generated from the test data with Boost.Test:
          uses a database of expected results, indexed by test, floating point type,
          platform, and compiler.
        </li>
<li class="listitem">
          Improved lgamma near 1 and 2 (rational approximations).
        </li>
<li class="listitem">
          Improved erf/erfc inverses (rational approximations).
        </li>
<li class="listitem">
          Implemented Rational function generation (the Remez method).
        </li>
</ul></div>
<h5>
<a name="math_toolkit.history1.h40"></a>
      <span class="phrase"><a name="math_toolkit.history1.milestone_1_released_march_31st_"></a></span><a class="link" href="history1.html#math_toolkit.history1.milestone_1_released_march_31st_">Milestone
      1: Released March 31st 2006</a>
    </h5>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          Implement gamma/beta/erf functions along with their incomplete counterparts.
        </li>
<li class="listitem">
          Generate high quality test data, against which future improvements can
          be judged.
        </li>
<li class="listitem">
          Provide tools for the evaluation of infinite series, continued fractions,
          and rational functions.
        </li>
<li class="listitem">
          Provide tools for testing against tabulated test data, and collecting statistics
          on error rates.
        </li>
<li class="listitem">
          Provide sufficient docs for people to be able to find their way around
          the library.
        </li>
</ul></div>
<p>
      SVN Revisions:
    </p>
<p>
      Sandbox and trunk last synchonised at revision: .
    </p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
      R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
      Daryle Walker and Xiaogang Zhang<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
</div></td>
</tr></table>
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