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24</div>
25<div class="section">
26<div class="titlepage"><div><div><h2 class="title" style="clear: both">
27<a name="math_toolkit.history2"></a><a class="link" href="history2.html" title="History and What's New">History and What's New</a>
28</h2></div></div></div>
29<p>
30      Currently open bug reports can be viewed <a href="https://github.com/boostorg/math/issues" target="_top">here</a>
31      on GitHub.
32    </p>
33<p>
34      All old bug reports including closed ones can be viewed on Trac <a href="https://svn.boost.org/trac/boost/query?status=assigned&amp;status=closed&amp;status=new&amp;status=reopened&amp;component=math&amp;col=id&amp;col=summary&amp;col=status&amp;col=type&amp;col=milestone&amp;col=component&amp;order=priority" target="_top">here</a>.
35    </p>
36<p>
37      Recent issues on GitHub <a href="https://github.com/boostorg/math/issues?utf8=%E2%9C%93&amp;q=is%3Aissue" target="_top">here</a>.
38    </p>
39<h5>
40<a name="math_toolkit.history2.h0"></a>
41      <span class="phrase"><a name="math_toolkit.history2.math_2_12_0_boost_1_73"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_12_0_boost_1_73">Math-2.12.0
42      (Boost-1.73)</a>
43    </h5>
44<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
45<li class="listitem">
46          IMPORTANT: C++03 support is now deprecated and will be removed from March
47          2021.
48        </li>
49<li class="listitem">
50          Added <a class="link" href="cubic_hermite.html" title="Cubic Hermite interpolation">Cubic Hermite Interpolation.</a>
51        </li>
52<li class="listitem">
53          Added <a class="link" href="makima.html" title="Modified Akima interpolation">Modified Akima Interpolation.</a>
54        </li>
55<li class="listitem">
56          Added <a class="link" href="pchip.html" title="PCHIP interpolation">PCHIP Interpolation.</a>
57        </li>
58<li class="listitem">
59          Added <a class="link" href="quintic_hermite.html" title="Quintic Hermite interpolation">Quintic Hermite Interpolation.</a>
60        </li>
61<li class="listitem">
62          Added entropy to numerous distributions.
63        </li>
64<li class="listitem">
65          Allow trivial quadrature case where the two end points are equal, and in
66          addition allow bounds to be interchanged.
67        </li>
68<li class="listitem">
69          Fix exp_sinh quadrature to work with complex types over a non-native range.
70        </li>
71<li class="listitem">
72          Fix miscellaneous compiler warnings in factorial.hpp.
73        </li>
74<li class="listitem">
75          Use std::chrono rather than boost::chrono in timed pFq calculations.
76        </li>
77<li class="listitem">
78          Remove much of the old boost::mpl dependencies to improve constexpr support.
79        </li>
80</ul></div>
81<h5>
82<a name="math_toolkit.history2.h1"></a>
83      <span class="phrase"><a name="math_toolkit.history2.math_2_11_0_boost_1_72"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_11_0_boost_1_72">Math-2.11.0
84      (Boost-1.72)</a>
85    </h5>
86<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
87<li class="listitem">
88          Added Hypergeometric functions <a class="link" href="hypergeometric/hypergeometric_1f0.html" title="Hypergeometric 1F0">1F0</a>,
89          <a class="link" href="hypergeometric/hypergeometric_0f1.html" title="Hypergeometric 0F1">0F1</a>,
90          <a class="link" href="hypergeometric/hypergeometric_2f0.html" title="Hypergeometric 2F0">2F0</a>,
91          <a class="link" href="hypergeometric/hypergeometric_1f1.html" title="Hypergeometric 1F1">1F1</a>
92          and <a class="link" href="hypergeometric/hypergeometric_pfq.html" title="Hypergeometric pFq">pFq</a>.
93        </li>
94<li class="listitem">
95          Added <a class="link" href="sf_poly/jacobi.html" title="Jacobi Polynomials">Jacobi polynomial</a>
96          (and derivatives) evaluation.
97        </li>
98<li class="listitem">
99          Added <a class="link" href="sf_poly/gegenbauer.html" title="Gegenbauer Polynomials">Gegenbauer polynomial</a>
100          (and derivatives) evaluation.
101        </li>
102<li class="listitem">
103          Added <a class="link" href="sf_poly/cardinal_b_splines.html" title="Cardinal B-splines">Cardinal
104          B-Splines</a> (and derivatives) as polynomial functions in their own
105          right.
106        </li>
107<li class="listitem">
108          Added <a class="link" href="cardinal_trigonometric.html" title="Cardinal Trigonometric interpolation">Cardinal Trigonometric
109          Interpolation</a>.
110        </li>
111<li class="listitem">
112          Added new statistics sub-section.
113        </li>
114<li class="listitem">
115          Added <a class="link" href="t_test.html" title="t-tests">One Sample Student's T Test</a>.
116        </li>
117<li class="listitem">
118          Added <a class="link" href="anderson_darling.html" title="The Anderson-Darling Test">Anderson Darling test
119          for normality</a>.
120        </li>
121<li class="listitem">
122          Added <a class="link" href="ljung_box.html" title="The Ljung-Box Test">Ljung Box test for auto-correlation</a>.
123        </li>
124<li class="listitem">
125          Added <a class="link" href="runs_test.html" title="Runs tests">Runs test for random sequences</a>.
126        </li>
127<li class="listitem">
128          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>,
129          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>
130          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>.
131        </li>
132<li class="listitem">
133          Added <a class="link" href="dist_ref/dists/empirical_cdf.html" title="Empirical Cumulative Distribution Function">The Empirical
134          CDF distribution</a>.
135        </li>
136<li class="listitem">
137          Reworked the Sterling approximation used by multiprecision gamma functions
138          to be applicable to all the function that use the Lanczos approximation
139          at regular precision. Also extended Lanczos approximations up to 100 decimal
140          digit precision.
141        </li>
142</ul></div>
143<h5>
144<a name="math_toolkit.history2.h2"></a>
145      <span class="phrase"><a name="math_toolkit.history2.math_2_10_0_boost_1_71"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_10_0_boost_1_71">Math-2.10.0
146      (Boost-1.71)</a>
147    </h5>
148<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
149<li class="listitem">
150          Catmull-Rom interpolator now works in C++11.
151        </li>
152<li class="listitem">
153          Cardinal quadratic B-spline interpolation.
154        </li>
155<li class="listitem">
156          Domain of elliptic integrals extended.
157        </li>
158<li class="listitem">
159          sin_pi and cos_pi performance improvements.
160        </li>
161<li class="listitem">
162          Forward-mode automatic differentiation.
163        </li>
164<li class="listitem">
165          Vector valued barycentric rational interpolation.
166        </li>
167<li class="listitem">
168          Ooura's method for evaluation of Fourier integrals.
169        </li>
170<li class="listitem">
171          Multiple compatibility issues with Multiprecision fixed.
172        </li>
173<li class="listitem">
174          Lambert-W fixed on a rare architecture.
175        </li>
176</ul></div>
177<h5>
178<a name="math_toolkit.history2.h3"></a>
179      <span class="phrase"><a name="math_toolkit.history2.math_2_9_0_boost_1_70"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_9_0_boost_1_70">Math-2.9.0
180      (Boost-1.70)</a>
181    </h5>
182<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
183<li class="listitem">
184          Add Lanczos smoothing derivatives
185        </li>
186<li class="listitem">
187          Move <code class="computeroutput"><span class="identifier">numerical_differentiation</span><span class="special">.</span><span class="identifier">hpp</span></code>
188          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>
189          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>.
190        </li>
191<li class="listitem">
192          Add mean, variance, skewness, kurtosis, median, Gini coefficient, and median
193          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>.
194        </li>
195<li class="listitem">
196          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>
197        </li>
198<li class="listitem">
199          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
200          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>.
201        </li>
202<li class="listitem">
203          Add total variation, l0, l1, l2, and sup norms, as well as corresponding
204          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>.
205        </li>
206<li class="listitem">
207          Add move constructors for polynomials, support complex coefficients, add
208          <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>
209          methods.
210        </li>
211<li class="listitem">
212          Add <code class="computeroutput"><span class="identifier">quadratic_roots</span></code> to
213          <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>.
214        </li>
215<li class="listitem">
216          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>.
217        </li>
218<li class="listitem">
219          Add Catmull-Rom interpolator.
220        </li>
221<li class="listitem">
222          Fix bug in <code class="computeroutput"><span class="identifier">newton_raphson_iterate</span></code>
223          where we could terminate incorrectly under certain exceptional cases.
224        </li>
225<li class="listitem">
226          Suppressed warnings from use of <code class="computeroutput"><span class="identifier">Q</span></code>
227          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>
228          <span class="special">-</span><span class="identifier">pedantic</span></code>.
229        </li>
230</ul></div>
231<h5>
232<a name="math_toolkit.history2.h4"></a>
233      <span class="phrase"><a name="math_toolkit.history2.math_2_8_0_boost_1_69"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_8_0_boost_1_69">Math-2.8.0
234      (Boost-1.69)</a>
235    </h5>
236<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
237<li class="listitem">
238          Add LambertW functions.
239        </li>
240<li class="listitem">
241          Update integration routines to support complex valued integrands and contour
242          integrals.
243        </li>
244<li class="listitem">
245          Added the derivative of the Barycentric rational approximation.
246        </li>
247<li class="listitem">
248          Updated continued fraction and series evaluation code to support complex
249          types.
250        </li>
251<li class="listitem">
252          Minor fixes to better support variable precision floating point types.
253        </li>
254<li class="listitem">
255          Removed use of deprecated Boost.Endian in favour of Predef.
256        </li>
257<li class="listitem">
258          Prevent logic error leading to infinite loop in toms748_solve. See <a href="https://github.com/boostorg/math/issues/138" target="_top">#138</a>.
259        </li>
260<li class="listitem">
261          Fix mean and standard_deviation for extreme_value_distribution. See <a href="https://github.com/boostorg/math/issues/139" target="_top">#139</a>.
262        </li>
263<li class="listitem">
264          Improve heuristics used in newton_raphson_iterate. See <a href="https://github.com/boostorg/math/issues/145" target="_top">#145</a>.
265        </li>
266<li class="listitem">
267          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>.
268          See <a href="https://github.com/boostorg/math/issues/141" target="_top">#141</a>.
269        </li>
270<li class="listitem">
271          Big push to reduce GCC warnings. See <a href="https://github.com/boostorg/math/issues/136" target="_top">#136</a>.
272        </li>
273<li class="listitem">
274          Refactor polynomial addition. See <a href="https://github.com/boostorg/math/pull/132" target="_top">PR132</a>.
275        </li>
276<li class="listitem">
277          Fix for vxWorks having a <code class="computeroutput"><span class="identifier">real</span></code>
278          function in the global namespace. See <a href="https://github.com/boostorg/math/pull/131" target="_top">PR131</a>.
279        </li>
280<li class="listitem">
281          Improve <code class="computeroutput"><span class="identifier">sinc</span></code> approximations
282          and add better tests.
283        </li>
284<li class="listitem">
285          Fix typo in Student's T hypothesis testing documentation, see <a href="https://github.com/boostorg/math/issues/143" target="_top">#143</a>.
286        </li>
287</ul></div>
288<h5>
289<a name="math_toolkit.history2.h5"></a>
290      <span class="phrase"><a name="math_toolkit.history2.math_2_7_1_boost_1_68"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_7_1_boost_1_68">Math-2.7.1
291      (Boost-1.68)</a>
292    </h5>
293<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
294<li class="listitem">
295          Continue to improve numerical integration routines, and in particular add
296          support for contour integrals.
297        </li>
298<li class="listitem">
299          Improve accuracy of erfc function's rational approximations.
300        </li>
301</ul></div>
302<h5>
303<a name="math_toolkit.history2.h6"></a>
304      <span class="phrase"><a name="math_toolkit.history2.math_2_7_0_boost_1_66"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_7_0_boost_1_66">Math-2.7.0
305      (Boost-1.66)</a>
306    </h5>
307<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
308<li class="listitem">
309          Add Gauss and Gauss-Kronrod quadrature routines.
310        </li>
311<li class="listitem">
312          Add double-exponential (tanh-sinh, exp-sinh and sinh-sinh) quadrature routines.
313        </li>
314<li class="listitem">
315          Add Chebyshev polynomial evaluation, roots, integration, differentiation,
316          and interpolation routines.
317        </li>
318</ul></div>
319<h5>
320<a name="math_toolkit.history2.h7"></a>
321      <span class="phrase"><a name="math_toolkit.history2.math_2_6_0_boost_1_65"></a></span><a class="link" href="history2.html#math_toolkit.history2.math_2_6_0_boost_1_65">Math-2.6.0
322      (Boost-1.65)</a>
323    </h5>
324<p>
325      New Features:
326    </p>
327<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
328<li class="listitem">
329          Add <a class="link" href="cardinal_cubic_b.html" title="Cardinal Cubic B-spline interpolation">Cardinal cubic B-Spline
330          interpolation functions</a>, with thanks to Nick Thompson.
331        </li>
332<li class="listitem">
333          Add <a class="link" href="barycentric.html" title="Barycentric Rational Interpolation">barycentric rational interpolation
334          functions</a>, with thanks to Nick Thompson.
335        </li>
336<li class="listitem">
337          Add <a class="link" href="trapezoidal.html" title="Trapezoidal Quadrature">adaptive trapezoidal quadrature</a>,
338          with thanks to Nick Thompson.
339        </li>
340<li class="listitem">
341          Add <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">support for the zeros
342          and derivatives of Legendre polynomials</a>, with thanks to Nick Thompson.
343        </li>
344</ul></div>
345<p>
346      Patches:
347    </p>
348<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
349<li class="listitem">
350          Improve polynomial GCD algorithms, with thanks to Jeremy Murphy.
351        </li>
352<li class="listitem">
353          Removed gcd/lcm routines from Boost.Math - these are now in Boost.Integer.
354        </li>
355</ul></div>
356<h5>
357<a name="math_toolkit.history2.h8"></a>
358      <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
359      (Boost-1.64)</a>
360    </h5>
361<p>
362      Patches:
363    </p>
364<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
365<li class="listitem">
366          Big push to ensure all functions in also in C99 are compatible with Annex
367          F.
368        </li>
369<li class="listitem">
370          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>.
371        </li>
372</ul></div>
373<h5>
374<a name="math_toolkit.history2.h9"></a>
375      <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
376      (Boost-1.63)</a>
377    </h5>
378<p>
379      Patches:
380    </p>
381<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
382<li class="listitem">
383          Fixed evaluation of zero polynomial in polynomial.hpp, see <a href="https://svn.boost.org/trac/boost/ticket/12532" target="_top">12532</a>.
384        </li>
385<li class="listitem">
386          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>.
387        </li>
388</ul></div>
389<h5>
390<a name="math_toolkit.history2.h10"></a>
391      <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
392      (Boost-1.62)</a>
393    </h5>
394<p>
395      New Features:
396    </p>
397<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
398          Enabled all the special function code to work correctly with types whose
399          precision can change at runtime: for example type <code class="computeroutput"><span class="identifier">mpfr_float</span></code>
400          from Boost.Multiprecision.
401        </li></ul></div>
402<p>
403      Patches:
404    </p>
405<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
406<li class="listitem">
407          Fix tgamma_delta_ratio for cases where the delta is small compared to the
408          base.
409        </li>
410<li class="listitem">
411          Fix misc GCC-4.4 test failures.
412        </li>
413</ul></div>
414<h5>
415<a name="math_toolkit.history2.h11"></a>
416      <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
417      (Boost-1.61)</a>
418    </h5>
419<p>
420      New Features:
421    </p>
422<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
423          Polynomial arithmetic added to tools.
424        </li></ul></div>
425<h5>
426<a name="math_toolkit.history2.h12"></a>
427      <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
428      (Boost-1.60)</a>
429    </h5>
430<p>
431      New Features:
432    </p>
433<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
434<li class="listitem">
435          Promote the root finding and function minimization code to first class
436          citizens - these are now officially supported as part of the library.
437        </li>
438<li class="listitem">
439          Allow the library to be used and tested with compiler exception handling
440          support turned off. To better facilitate this the default error handling
441          policies have been changed to <span class="emphasis"><em>errno_on_error</em></span> but only
442          when the compiler has no exception handling support.
443        </li>
444</ul></div>
445<p>
446      Patches:
447    </p>
448<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
449<li class="listitem">
450          Fix behaviour of the non-central chi-squared distribution when the non-centrality
451          parameter is zero to match the chi-squared, see <a href="https://svn.boost.org/trac/boost/ticket/11557" target="_top">11557</a>.
452        </li>
453<li class="listitem">
454          Fix comments in code for the hypergeometric to match what it actually does,
455          also fixes the parameter access functions to return the correct values.
456          See <a href="https://svn.boost.org/trac/boost/ticket/11556" target="_top">11556</a>.
457        </li>
458<li class="listitem">
459          Stopped using hidden visibility library build with the Oracle compiler
460          as it leads to unresolved externals from the C++ standard library. See
461          <a href="https://svn.boost.org/trac/boost/ticket/11547" target="_top">11547</a>.
462        </li>
463<li class="listitem">
464          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>.
465        </li>
466<li class="listitem">
467          Fix corner case bug in root bracketing code, see <a href="https://svn.boost.org/trac/boost/ticket/11532" target="_top">11532</a>.
468        </li>
469<li class="listitem">
470          Add some missing typecasts in arguments to std::max in Bernoulli code.
471          See <a href="https://svn.boost.org/trac/boost/ticket/11453" target="_top">11453</a>.
472        </li>
473<li class="listitem">
474          Fix mistaken assumptions about the possible values for FLT_EVAL_METHOD.
475          See <a href="https://svn.boost.org/trac/boost/ticket/11429" target="_top">11429</a>.
476        </li>
477<li class="listitem">
478          Completely revamped performance testing and error-rate measuring code so
479          we can more easily document how well (or not!) we're doing. This information
480          will hopefully get more frequently updated in future as it's more or less
481          automatically generated - see the <span class="emphasis"><em>reporting</em></span> sub-directory
482          for more information.
483        </li>
484<li class="listitem">
485          Fix some corner cases in the beta, incomplete beta, and incomplete beta
486          derivative. With thanks to Rocco Romeo.
487        </li>
488<li class="listitem">
489          Reorganized the Bessel functions internally to improve the performance
490          of Jn and Yn.
491        </li>
492<li class="listitem">
493          Fixed skewness formula for triangular distribution, see <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">#11768</a>.
494        </li>
495<li class="listitem">
496          Fixed some examples so they compile on Unix platforms which have an ::exception
497          struct declared, see <a href="https://svn.boost.org/trac/boost/ticket/11827" target="_top">#11827</a>.
498        </li>
499<li class="listitem">
500          Correct mistake in triangular distribution skewness formula <a href="https://svn.boost.org/trac/boost/ticket/11768" target="_top">11768</a>,
501          reported by Juan Leni.
502        </li>
503</ul></div>
504<h5>
505<a name="math_toolkit.history2.h13"></a>
506      <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>
507    </h5>
508<p>
509      Patch release for Boost-1.58:
510    </p>
511<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
512<li class="listitem">
513          Minor <a href="https://github.com/boostorg/math/pull/13#issuecomment-98905579" target="_top">patch
514          for Haiku support.</a>
515        </li>
516<li class="listitem">
517          Fix the decimal digit count for 128-bit floating point types.
518        </li>
519<li class="listitem">
520          Fix a few documentation typos.
521        </li>
522</ul></div>
523<h5>
524<a name="math_toolkit.history2.h14"></a>
525      <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
526      (boost-1.58.0)</a>
527    </h5>
528<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
529<li class="listitem">
530          Added two new special functions - <a class="link" href="sf_gamma/trigamma.html" title="Trigamma">trigamma</a>
531          and <a class="link" href="sf_gamma/polygamma.html" title="Polygamma">polygamma</a>.
532        </li>
533<li class="listitem">
534          Fixed namespace scope constants so they are constexpr on conforming compilers,
535          see https://svn.boost.org/trac/boost/ticket/10901.
536        </li>
537<li class="listitem">
538          Fixed various cases of spurious under/overflow in the incomplete beta and
539          gamma functions, plus the elliptic integrals, with thanks to Rocco Romeo.
540        </li>
541<li class="listitem">
542          Fix 3-arg <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_p</a>
543          and <a class="link" href="sf_poly/legendre.html" title="Legendre (and Associated) Polynomials">legendre_q</a> functions
544          to not call the policy based overload if the final argument is not actually
545          a policy.
546        </li>
547<li class="listitem">
548          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>.
549        </li>
550<li class="listitem">
551          Fixed extreme-value pdf for large valued inputs, see <a href="https://svn.boost.org/trac/boost/ticket/10938" target="_top">#10938</a>.
552        </li>
553<li class="listitem">
554          Large update to the Elliptic integral code to use Carlson's latest algorithms
555          - these should be more stable, more accurate and slightly faster than before.
556          Also added support for Carlson's RG integral.
557        </li>
558<li class="listitem">
559          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
560          integrals.
561        </li>
562<li class="listitem">
563          Switched documentation to use SVG rather than PNG graphs and equations
564          - browsers seem to have finally caught up!
565        </li>
566</ul></div>
567<h5>
568<a name="math_toolkit.history2.h15"></a>
569      <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
570      (boost-1.57.0)</a>
571    </h5>
572<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
573<li class="listitem">
574          Added <a class="link" href="dist_ref/dists/hyperexponential_dist.html" title="Hyperexponential Distribution">Hyperexponential
575          Distribution</a>.
576        </li>
577<li class="listitem">
578          Fix some spurious overflows in the incomplete gamma functions (with thanks
579          to Rocco Romeo).
580        </li>
581<li class="listitem">
582          Fix bug in derivative of incomplete beta when a = b = 0.5 - this also effects
583          several non-central distributions, see <a href="https://svn.boost.org/trac/boost/ticket/10480" target="_top">10480</a>.
584        </li>
585<li class="listitem">
586          Fixed some corner cases in <a class="link" href="rounding/round.html" title="Rounding Functions">round</a>.
587        </li>
588<li class="listitem">
589          Don't support 80-bit floats in cstdfloat.hpp if standard library support
590          is broken.
591        </li>
592</ul></div>
593<h5>
594<a name="math_toolkit.history2.h16"></a>
595      <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
596      (Boost-1.56.0)</a>
597    </h5>
598<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
599<li class="listitem">
600          <span class="bold"><strong>Breaking change</strong></span>: moved a number of non-core
601          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
602          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>,
603          <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>,
604          <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
605          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
606          path.
607        </li>
608<li class="listitem">
609          <span class="bold"><strong>Breaking change</strong></span>: A number of distributions
610          and special functions were returning the maximum finite value rather than
611          raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>,
612          this has now been fixed, which means these functions now behave as documented.
613          However, since the default behavior on raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>
614          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
615          which have come to reply rely on these functions not throwing may experience
616          exceptions where they did not before. The special functions involved are
617          <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>,
618          <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>,
619          <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
620          <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
621          <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>,
622          <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>,
623          <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
624          involved are <a class="link" href="dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto
625          Distribution</a>, <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta
626          Distribution</a>, <a class="link" href="dist_ref/dists/geometric_dist.html" title="Geometric Distribution">Geometric
627          Distribution</a>, <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
628          Binomial Distribution</a>, <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
629          Distribution</a>, <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
630          Squared Distribution</a>, <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
631          Distribution</a>, <a class="link" href="dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">Inverse
632          chi squared Distribution</a>, <a class="link" href="dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution">Inverse
633          Gamma Distribution</a>. See <a href="https://svn.boost.org/trac/boost/ticket/10111" target="_top">#10111</a>.
634        </li>
635<li class="listitem">
636          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
637          be used with integer arguments, see <a href="https://svn.boost.org/trac/boost/ticket/10066" target="_top">#10066</a>.
638        </li>
639<li class="listitem">
640          Fix Halley iteration to handle zero derivative (with non-zero second derivative),
641          see <a href="https://svn.boost.org/trac/boost/ticket/10046" target="_top">#10046</a>.
642        </li>
643</ul></div>
644<h5>
645<a name="math_toolkit.history2.h17"></a>
646      <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>
647    </h5>
648<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
649<li class="listitem">
650          Fix Geometric distribution use of Policies, see <a href="https://svn.boost.org/trac/boost/ticket/9833" target="_top">#9833</a>.
651        </li>
652<li class="listitem">
653          Fix corner cases in the negative binomial distribution, see <a href="https://svn.boost.org/trac/boost/ticket/9834" target="_top">#9834</a>.
654        </li>
655<li class="listitem">
656          Fix compilation failures on Mac OS.
657        </li>
658</ul></div>
659<h5>
660<a name="math_toolkit.history2.h18"></a>
661      <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>
662    </h5>
663<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
664<li class="listitem">
665          Changed version number to new Boost.Math specific version now that we're
666          in the modular Boost world.
667        </li>
668<li class="listitem">
669          Added <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
670          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
671          approximation (from Nikhar Agrawal).
672        </li>
673<li class="listitem">
674          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>,
675          <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_neumann_prime</a>,
676          <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_i_prime</a>,
677          <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_k_prime</a>,
678          <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_bessel_prime</a>
679          and <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_neumann_prime</a>
680          (from Anton Bikineev).
681        </li>
682<li class="listitem">
683          Fixed buggy Student's t example code, along with docs for testing sample
684          means for equivalence.
685        </li>
686<li class="listitem">
687          Documented <code class="computeroutput"><span class="identifier">max_iter</span></code> parameter
688          in root finding code better, see <a href="https://svn.boost.org/trac/boost/ticket/9225" target="_top">#9225</a>.
689        </li>
690<li class="listitem">
691          Add option to explicitly enable/disable use of __float128 in constants
692          code, see <a href="https://svn.boost.org/trac/boost/ticket/9240" target="_top">#9240</a>.
693        </li>
694<li class="listitem">
695          Cleaned up handling of negative values in Bessel I0 and I1 code (removed
696          dead code), see <a href="https://svn.boost.org/trac/boost/ticket/9512" target="_top">#9512</a>.
697        </li>
698<li class="listitem">
699          Fixed handling of very small values passed to <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
700          and <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> so they
701          don't generate spurious overflows (thanks to Rocco Romeo).
702        </li>
703<li class="listitem">
704          <a href="https://svn.boost.org/trac/boost/ticket/9672" target="_top">#9672 PDF and
705          CDF of a Laplace distribution throwing domain_error</a> Random variate
706          can now be infinite.
707        </li>
708<li class="listitem">
709          Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
710          <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
711          and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
712          with thanks to Rocco Romeo.
713        </li>
714<li class="listitem">
715          Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
716          <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
717          and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
718          (thanks to Rocco Romeo).
719        </li>
720<li class="listitem">
721          Removed constant <code class="computeroutput"><span class="identifier">pow23_four_minus_pi</span>
722          </code> whose value did not match the name (and was unused by Boost.Math),
723          see <a href="https://svn.boost.org/trac/boost/ticket/9712" target="_top">#9712</a>.
724        </li>
725</ul></div>
726<h5>
727<a name="math_toolkit.history2.h19"></a>
728      <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>
729    </h5>
730<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
731<li class="listitem">
732          Suppress numerous warnings (mostly from GCC-4.8 and MSVC) <a href="https://svn.boost.org/trac/boost/ticket/8384" target="_top">#8384</a>,
733          <a href="https://svn.boost.org/trac/boost/ticket/8855" target="_top">#8855</a>,
734          <a href="https://svn.boost.org/trac/boost/ticket/9107" target="_top">#9107</a>,
735          <a href="https://svn.boost.org/trac/boost/ticket/9109" target="_top">#9109</a>..
736        </li>
737<li class="listitem">
738          Fixed PGI compilation issue <a href="https://svn.boost.org/trac/boost/ticket/8333" target="_top">#8333</a>.
739        </li>
740<li class="listitem">
741          Fixed PGI constant value initialization issue that caused erf to generate
742          incorrect results <a href="https://svn.boost.org/trac/boost/ticket/8621" target="_top">#8621</a>.
743        </li>
744<li class="listitem">
745          Prevent macro expansion of some C99 macros that are also C++ functions
746          <a href="https://svn.boost.org/trac/boost/ticket/8732" target="_top">#8732</a>
747          and <a href="https://svn.boost.org/trac/boost/ticket/8733" target="_top">#8733</a>..
748        </li>
749<li class="listitem">
750          Fixed Student's T distribution to behave correctly with huge degrees of
751          freedom (larger than the largest representable integer) <a href="https://svn.boost.org/trac/boost/ticket/8837" target="_top">#8837</a>.
752        </li>
753<li class="listitem">
754          Make some core functions usable with <code class="computeroutput"><span class="keyword">long</span>
755          <span class="keyword">double</span></code> even when the platform has
756          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>.
757        </li>
758<li class="listitem">
759          Fix error handling of distributions to catch invalid scale and location
760          parameters when the random variable is infinite <a href="https://svn.boost.org/trac/boost/ticket/9042" target="_top">#9042</a>
761          and <a href="https://svn.boost.org/trac/boost/ticket/9126" target="_top">#9126</a>.
762        </li>
763<li class="listitem">
764          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>.
765        </li>
766<li class="listitem">
767          Improve consistency of argument reduction in the elliptic integrals <a href="https://svn.boost.org/trac/boost/ticket/9104" target="_top">#9104</a>.
768        </li>
769<li class="listitem">
770          Fix bug in inverse incomplete beta that results in cancellation errors
771          when the beta function is really an arcsine or Student's T distribution.
772        </li>
773<li class="listitem">
774          Fix issue in Bessel I and K function continued fractions that causes spurious
775          over/underflow.
776        </li>
777<li class="listitem">
778<p class="simpara">
779          Add improvement to non-central chi squared distribution quantile due to
780          Thomas Luu, <a href="http://discovery.ucl.ac.uk/1482128/" target="_top">Fast and accurate
781          parallel computation of quantile functions for random number generation,
782          Doctoral Thesis 2016</a>. <a href="http://discovery.ucl.ac.uk/1463470/" target="_top">Efficient
783          and Accurate Parallel Inversion of the Gamma Distribution, Thomas Luu</a>
784        </p>
785<h5>
786<a name="math_toolkit.history2.h20"></a>
787          <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>
788        </h5>
789</li>
790<li class="listitem">
791          Major reorganization to incorporate other Boost.Math like Integer Utilities
792          Integer Utilities (Greatest Common Divisor and Least Common Multiple),
793          quaternions and octonions. Making new chapter headings.
794        </li>
795<li class="listitem">
796          Added many references to Boost.Multiprecision and <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>
797          as an example of a User-defined Type (UDT).
798        </li>
799<li class="listitem">
800          Added Clang to list of supported compilers.
801        </li>
802<li class="listitem">
803          Fixed constants to use a thread-safe cache of computed values when used
804          at arbitrary precision.
805        </li>
806<li class="listitem">
807          Added finding zeros of Bessel functions <code class="computeroutput"><span class="identifier">cyl_bessel_j_zero</span></code>,
808          <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
809          Christopher Kormanyos).
810        </li>
811<li class="listitem">
812          More accuracy improvements to the Bessel J and Y functions from Rocco Romeo.
813        </li>
814<li class="listitem">
815          Fixed nasty cyclic dependency bug that caused some headers to not compile
816          <a href="https://svn.boost.org/trac/boost/ticket/7999" target="_top">#7999</a>.
817        </li>
818<li class="listitem">
819          Fixed bug in <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
820          that caused spurious overflow for arguments between 142.5 and 143.
821        </li>
822<li class="listitem">
823          Fixed bug in raise_rounding_error that caused it to return an incorrect
824          result when throwing an exception is turned off <a href="https://svn.boost.org/trac/boost/ticket/7905" target="_top">#7905</a>.
825        </li>
826<li class="listitem">
827          Added minimal __float128 support.
828        </li>
829<li class="listitem">
830          Fixed bug in edge-cases of poisson quantile <a href="https://svn.boost.org/trac/boost/ticket/8308" target="_top">#8308</a>.
831        </li>
832<li class="listitem">
833          Adjusted heuristics used in Halley iteration to cope with inverting the
834          incomplete beta in tricky regions where the derivative is flatlining. Example
835          is computing the quantile of the Fisher F distribution for probabilities
836          smaller than machine epsilon. See ticket <a href="https://svn.boost.org/trac/boost/ticket/8314" target="_top">#8314</a>.
837        </li>
838</ul></div>
839<h5>
840<a name="math_toolkit.history2.h21"></a>
841      <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>
842    </h5>
843<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
844<li class="listitem">
845          Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/7325" target="_top">#7325</a>,
846          <a href="https://svn.boost.org/trac/boost/ticket/7415" target="_top">#7415</a>
847          and <a href="https://svn.boost.org/trac/boost/ticket/7416" target="_top">#7416</a>,
848          <a href="https://svn.boost.org/trac/boost/ticket/7183" target="_top">#7183</a>,
849          <a href="https://svn.boost.org/trac/boost/ticket/7649" target="_top">#7649</a>,
850          <a href="https://svn.boost.org/trac/boost/ticket/7694" target="_top">#7694</a>,
851          <a href="https://svn.boost.org/trac/boost/ticket/4445" target="_top">#4445</a>,
852          <a href="https://svn.boost.org/trac/boost/ticket/7492" target="_top">#7492</a>,
853          <a href="https://svn.boost.org/trac/boost/ticket/7891" target="_top">#7891</a>,
854          <a href="https://svn.boost.org/trac/boost/ticket/7429" target="_top">#7429</a>.
855        </li>
856<li class="listitem">
857          Fixed mistake in calculating pooled standard deviation in two-sample students
858          t example <a href="https://svn.boost.org/trac/boost/ticket/7402" target="_top">#7402</a>.
859        </li>
860<li class="listitem">
861          Improve complex acos/asin/atan, see <a href="https://svn.boost.org/trac/boost/ticket/7290" target="_top">#7290</a>,
862          <a href="https://svn.boost.org/trac/boost/ticket/7291" target="_top">#7291</a>.
863        </li>
864<li class="listitem">
865          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>
866          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>
867          thanks to suggestions from Rocco Romeo.
868        </li>
869<li class="listitem">
870          Improve accuracy of Bessel J and Y for integer orders thanks to suggestions
871          from Rocco Romeo.
872        </li>
873</ul></div>
874<h5>
875<a name="math_toolkit.history2.h22"></a>
876      <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>
877    </h5>
878<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
879<li class="listitem">
880          Corrected moments for small degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7177" target="_top">#7177</a>
881          (reported by Thomas Mang).
882        </li>
883<li class="listitem">
884          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>.
885        </li>
886<li class="listitem">
887          Corrected failure to detect bad parameters in many distributions <a href="https://svn.boost.org/trac/boost/ticket/6934" target="_top">#6934</a> (reported
888          by Florian Schoppmann) by adding a function check_out_of_range to test
889          many possible bad parameters. This test revealed several distributions
890          where the checks for bad parameters were ineffective, and these have been
891          rectified.
892        </li>
893<li class="listitem">
894          Fixed issue in Hankel functions that causes incorrect values to be returned
895          for <span class="emphasis"><em>x &lt; 0</em></span> and ν odd, see <a href="https://svn.boost.org/trac/boost/ticket/7135" target="_top">#7135</a>.
896        </li>
897<li class="listitem">
898          Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/6517" target="_top">#6517</a>,
899          <a href="https://svn.boost.org/trac/boost/ticket/6362" target="_top">#6362</a>,
900          <a href="https://svn.boost.org/trac/boost/ticket/7053" target="_top">#7053</a>,
901          <a href="https://svn.boost.org/trac/boost/ticket/2693" target="_top">#2693</a>,
902          <a href="https://svn.boost.org/trac/boost/ticket/6937" target="_top">#6937</a>,
903          <a href="https://svn.boost.org/trac/boost/ticket/7099" target="_top">#7099</a>.
904        </li>
905<li class="listitem">
906          Permitted infinite degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>
907          implemented using the normal distribution (requested by Thomas Mang).
908        </li>
909<li class="listitem">
910          Much enhanced accuracy for large degrees of freedom ν and/or large non-centrality
911          δ
912by switching to use the Students t distribution (or Normal distribution
913          for infinite degrees of freedom) centered at delta, when δ / (4 * ν) &lt;
914          epsilon for the floating-point type in use. <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>.
915          It was found that the incomplete beta was suffering from serious cancellation
916          errors when degrees of freedom was very large. (That has now been fixed
917          in our code, but any code based on Didonato and Morris's original papers
918          (probably every implementation out there actually) will have the same issue).
919        </li>
920</ul></div>
921<h5>
922<a name="math_toolkit.history2.h23"></a>
923      <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>
924    </h5>
925<p>
926      See Boost-1.52 - some items were added but not listed in time for the release.
927    </p>
928<h5>
929<a name="math_toolkit.history2.h24"></a>
930      <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>
931    </h5>
932<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
933<li class="listitem">
934          Promoted math constants to be 1st class citizens, including convenient
935          access to the most widely used built-in float, double, long double via
936          three namespaces.
937        </li>
938<li class="listitem">
939          Added the Owen's T function and Skew Normal distribution written by Benjamin
940          Sobotta: see <a class="link" href="owens_t.html" title="Owen's T function">Owens T</a> and skew_normal_distrib.
941        </li>
942<li class="listitem">
943          Added Hankel functions <a class="link" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a>,
944          <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>.
945        </li>
946<li class="listitem">
947          Corrected issue <a href="https://svn.boost.org/trac/boost/ticket/6627" target="_top">#6627
948          nonfinite_num_put formatting of 0.0 is incorrect</a> based on a patch
949          submitted by K R Walker.
950        </li>
951<li class="listitem">
952          Changed constant initialization mechanism so that it is thread safe even
953          for user-defined types, also so that user defined types get the full precision
954          of the constant, even when <code class="computeroutput"><span class="keyword">long</span>
955          <span class="keyword">double</span></code> does not. So for example
956          128-bit rational approximations will work with UDT's and do the right thing,
957          even though <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
958          may be only 64 or 80 bits.
959        </li>
960<li class="listitem">
961          Fixed issue in <code class="computeroutput"><span class="identifier">bessel_jy</span></code>
962          which causes Y<sub>8.5</sub>(4π) to yield a NaN.
963        </li>
964</ul></div>
965<h5>
966<a name="math_toolkit.history2.h25"></a>
967      <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>
968    </h5>
969<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
970<li class="listitem">
971          Deprecated wrongly named <code class="computeroutput"><span class="identifier">twothirds</span></code>
972          math constant in favour of <code class="computeroutput"><span class="identifier">two_thirds</span></code>
973          (with underscore separator). (issue <a href="https://svn.boost.org/trac/boost/ticket/6199" target="_top">#6199</a>).
974        </li>
975<li class="listitem">
976          Refactored test data and some special function code to improve support
977          for arbitrary precision and/or expression-template-enabled types.
978        </li>
979<li class="listitem">
980          Added new faster zeta function evaluation method.
981        </li>
982</ul></div>
983<p>
984      Fixed issues:
985    </p>
986<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
987<li class="listitem">
988          Corrected CDF complement for Laplace distribution (issue <a href="https://svn.boost.org/trac/boost/ticket/6151" target="_top">#6151</a>).
989        </li>
990<li class="listitem">
991          Corrected branch cuts on the complex inverse trig functions, to handle
992          signed zeros (issue <a href="https://svn.boost.org/trac/boost/ticket/6171" target="_top">#6171</a>).
993        </li>
994<li class="listitem">
995          Fixed bug in <code class="computeroutput"><span class="identifier">bessel_yn</span></code>
996          which caused incorrect overflow errors to be raised for negative <span class="emphasis"><em>n</em></span>
997          (issue <a href="https://svn.boost.org/trac/boost/ticket/6367" target="_top">#6367</a>).
998        </li>
999<li class="listitem">
1000          Also fixed minor/cosmetic/configuration issues <a href="https://svn.boost.org/trac/boost/ticket/6120" target="_top">#6120</a>,
1001          <a href="https://svn.boost.org/trac/boost/ticket/6191" target="_top">#6191</a>,
1002          <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>,
1003          <a href="https://svn.boost.org/trac/boost/ticket/6130" target="_top">#6130</a>,
1004          <a href="https://svn.boost.org/trac/boost/ticket/6234" target="_top">#6234</a>,
1005          <a href="https://svn.boost.org/trac/boost/ticket/6307" target="_top">#6307</a>,
1006          <a href="https://svn.boost.org/trac/boost/ticket/6192" target="_top">#6192</a>.
1007        </li>
1008</ul></div>
1009<h5>
1010<a name="math_toolkit.history2.h26"></a>
1011      <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>
1012    </h5>
1013<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1014<li class="listitem">
1015          Added new series evaluation methods to the cyclic Bessel I, J, K and Y
1016          functions. Also taken great care to avoid spurious over and underflow of
1017          these functions. Fixes issue <a href="https://svn.boost.org/trac/boost/ticket/5560" target="_top">#5560</a>
1018        </li>
1019<li class="listitem">
1020          Added an example of using Inverse Chi-Squared distribution for Bayesian
1021          statistics, provided by Thomas Mang.
1022        </li>
1023<li class="listitem">
1024          Added tests to use improved version of lexical_cast which handles C99 nonfinites
1025          without using globale facets.
1026        </li>
1027<li class="listitem">
1028          Corrected wrong out-of-bound uniform distribution CDF complement values
1029          <a href="https://svn.boost.org/trac/boost/ticket/5733" target="_top">#5733</a>.
1030        </li>
1031<li class="listitem">
1032          Enabled long double support on OpenBSD (issue <a href="https://svn.boost.org/trac/boost/ticket/6014" target="_top">#6014</a>).
1033        </li>
1034<li class="listitem">
1035          Changed nextafter and related functions to behave in the same way as other
1036          implementations - so that nextafter(+INF, 0) is a finite value (issue
1037          <a href="https://svn.boost.org/trac/boost/ticket/5823" target="_top">#5832</a>).
1038        </li>
1039<li class="listitem">
1040          Changed tuple include configuration to fix issue when using in conjunction
1041          with Boost.Tr1 (issue <a href="https://svn.boost.org/trac/boost/ticket/5934" target="_top">#5934</a>).
1042        </li>
1043<li class="listitem">
1044          Changed class eps_tolerance to behave correctly when both ends of the range
1045          are zero (issue <a href="https://svn.boost.org/trac/boost/ticket/6001" target="_top">#6001</a>).
1046        </li>
1047<li class="listitem">
1048          Fixed missing include guards on prime.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5927" target="_top">#5927</a>).
1049        </li>
1050<li class="listitem">
1051          Removed unused/undocumented constants from constants.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>).
1052        </li>
1053<li class="listitem">
1054          Fixed missing std:: prefix in nonfinite_num_facets.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5914" target="_top">#5914</a>).
1055        </li>
1056<li class="listitem">
1057          Minor patches for Cray compiler compatibility.
1058        </li>
1059</ul></div>
1060<h5>
1061<a name="math_toolkit.history2.h27"></a>
1062      <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>
1063    </h5>
1064<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1065<li class="listitem">
1066          Added changesign function to sign.hpp to facilitate addition of nonfinite
1067          facets.
1068        </li>
1069<li class="listitem">
1070          Addition of nonfinite facets from Johan Rade, with tests, examples of use
1071          for C99 format infinity and NaN, and documentation.
1072        </li>
1073<li class="listitem">
1074          Added tests and documentation of changesign from Johan Rade.
1075        </li>
1076</ul></div>
1077<h5>
1078<a name="math_toolkit.history2.h28"></a>
1079      <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>
1080    </h5>
1081<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
1082          Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5095</a>,
1083          <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
1084        </li></ul></div>
1085<h5>
1086<a name="math_toolkit.history2.h29"></a>
1087      <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>
1088    </h5>
1089<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1090<li class="listitem">
1091          Added Wald, Inverse Gaussian and geometric distributions.
1092        </li>
1093<li class="listitem">
1094          Added information about configuration macros.
1095        </li>
1096<li class="listitem">
1097          Added support for mpreal as a real-numbered type.
1098        </li>
1099</ul></div>
1100<h5>
1101<a name="math_toolkit.history2.h30"></a>
1102      <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>
1103    </h5>
1104<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1105<li class="listitem">
1106          Added warnings about potential ambiguity with std random library in distribution
1107          and function names.
1108        </li>
1109<li class="listitem">
1110          Added inverse gamma distribution and inverse chi_square and scaled inverse
1111          chi_square.
1112        </li>
1113<li class="listitem">
1114          Editorial revision of documentation, and added FAQ.
1115        </li>
1116</ul></div>
1117<h5>
1118<a name="math_toolkit.history2.h31"></a>
1119      <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>
1120    </h5>
1121<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1122<li class="listitem">
1123          Fixed incorrect range and support for Rayleigh distribution.
1124        </li>
1125<li class="listitem">
1126          Fixed numerical error in the quantile of the Student's T distribution:
1127          the function was returning garbage values for non-integer degrees of freedom
1128          between 2 and 3.
1129        </li>
1130</ul></div>
1131<h5>
1132<a name="math_toolkit.history2.h32"></a>
1133      <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>
1134    </h5>
1135<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
1136          Significantly improved performance for the incomplete gamma function and
1137          its inverse.
1138        </li></ul></div>
1139<h5>
1140<a name="math_toolkit.history2.h33"></a>
1141      <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>
1142    </h5>
1143<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1144<li class="listitem">
1145          Added support for MPFR as a bignum type.
1146        </li>
1147<li class="listitem">
1148          Added some full specializations of the policy classes to reduce compile
1149          times.
1150        </li>
1151<li class="listitem">
1152          Added logistic and hypergeometric distributions, from Gautam Sewani's Google
1153          Summer of Code project.
1154        </li>
1155<li class="listitem">
1156          Added Laplace distribution submitted by Thijs van den Berg.
1157        </li>
1158<li class="listitem">
1159          Updated performance test code to include new distributions, and improved
1160          the performance of the non-central distributions.
1161        </li>
1162<li class="listitem">
1163          Added SSE2 optimised <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
1164          code, from Gautam Sewani's Google Summer of Code project.
1165        </li>
1166<li class="listitem">
1167          Fixed bug in cyl_bessel_i that used an incorrect approximation for ν = 0.5,
1168          also effects the non-central Chi Square Distribution when ν = 3, see bug
1169          report <a href="https://svn.boost.org/trac/boost/ticket/2877" target="_top">#2877</a>.
1170        </li>
1171<li class="listitem">
1172          Fixed minor bugs <a href="https://svn.boost.org/trac/boost/ticket/2873" target="_top">#2873</a>.
1173        </li>
1174</ul></div>
1175<h5>
1176<a name="math_toolkit.history2.h34"></a>
1177      <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>
1178    </h5>
1179<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1180<li class="listitem">
1181          Added Johan Råde's optimised floating point classification routines.
1182        </li>
1183<li class="listitem">
1184          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>).
1185        </li>
1186</ul></div>
1187<h5>
1188<a name="math_toolkit.history2.h35"></a>
1189      <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>
1190    </h5>
1191<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
1192          Improved accuracy and testing of the inverse hypergeometric functions.
1193        </li></ul></div>
1194<h5>
1195<a name="math_toolkit.history2.h36"></a>
1196      <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>
1197    </h5>
1198<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1199<li class="listitem">
1200          Added Noncentral Chi Squared Distribution.
1201        </li>
1202<li class="listitem">
1203          Added Noncentral Beta Distribution.
1204        </li>
1205<li class="listitem">
1206          Added Noncentral F Distribution.
1207        </li>
1208<li class="listitem">
1209          Added Noncentral T Distribution.
1210        </li>
1211<li class="listitem">
1212          Added Exponential Integral Functions.
1213        </li>
1214<li class="listitem">
1215          Added Zeta Function.
1216        </li>
1217<li class="listitem">
1218          Added Rounding and Truncation functions.
1219        </li>
1220<li class="listitem">
1221          Added Compile time powers of runtime bases.
1222        </li>
1223<li class="listitem">
1224          Added SSE2 optimizations for Lanczos evaluation.
1225        </li>
1226</ul></div>
1227<h5>
1228<a name="math_toolkit.history2.h37"></a>
1229      <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:
1230      Post Review First Official Release</a>
1231    </h5>
1232<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1233<li class="listitem">
1234          Added Policy based framework that allows fine grained control over function
1235          behaviour.
1236        </li>
1237<li class="listitem">
1238          <span class="bold"><strong>Breaking change:</strong></span> Changed default behaviour
1239          for domain, pole and overflow errors to throw an exception (based on review
1240          feedback), this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
1241        </li>
1242<li class="listitem">
1243          <span class="bold"><strong>Breaking change:</strong></span> Changed exception thrown
1244          when an internal evaluation error occurs to boost::math::evaluation_error.
1245        </li>
1246<li class="listitem">
1247          <span class="bold"><strong>Breaking change:</strong></span> Changed discrete quantiles
1248          to return an integer result: this is anything up to 20 times faster than
1249          finding the true root, this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
1250        </li>
1251<li class="listitem">
1252          Polynomial/rational function evaluation is now customisable and hopefully
1253          faster than before.
1254        </li>
1255<li class="listitem">
1256          Added performance test program.
1257        </li>
1258</ul></div>
1259<h5>
1260<a name="math_toolkit.history2.h38"></a>
1261      <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
1262      4: Second Review Candidate (1st March 2007)</a>
1263    </h5>
1264<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1265<li class="listitem">
1266          Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
1267          them into line with the rest of the code.
1268        </li>
1269<li class="listitem">
1270          Added C# "Distribution Explorer" demo application.
1271        </li>
1272</ul></div>
1273<h5>
1274<a name="math_toolkit.history2.h39"></a>
1275      <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
1276      3: First Review Candidate (31st Dec 2006)</a>
1277    </h5>
1278<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1279<li class="listitem">
1280          Implemented the main probability distribution and density functions.
1281        </li>
1282<li class="listitem">
1283          Implemented digamma.
1284        </li>
1285<li class="listitem">
1286          Added more factorial functions.
1287        </li>
1288<li class="listitem">
1289          Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
1290          harmonic functions from TR1.
1291        </li>
1292<li class="listitem">
1293          Moved Xiaogang Zhang's elliptic integral code into the library, and brought
1294          them into line with the rest of the code.
1295        </li>
1296<li class="listitem">
1297          Moved Hubert Holin's existing Boost.Math special functions into this library
1298          and brought them into line with the rest of the code.
1299        </li>
1300</ul></div>
1301<h5>
1302<a name="math_toolkit.history2.h40"></a>
1303      <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
1304      2: Released September 10th 2006</a>
1305    </h5>
1306<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1307<li class="listitem">
1308          Implement preview release of the statistical distributions.
1309        </li>
1310<li class="listitem">
1311          Added statistical distributions tutorial.
1312        </li>
1313<li class="listitem">
1314          Implemented root finding algorithms.
1315        </li>
1316<li class="listitem">
1317          Implemented the inverses of the incomplete gamma and beta functions.
1318        </li>
1319<li class="listitem">
1320          Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
1321        </li>
1322<li class="listitem">
1323          Integrated the statistical results generated from the test data with Boost.Test:
1324          uses a database of expected results, indexed by test, floating point type,
1325          platform, and compiler.
1326        </li>
1327<li class="listitem">
1328          Improved lgamma near 1 and 2 (rational approximations).
1329        </li>
1330<li class="listitem">
1331          Improved erf/erfc inverses (rational approximations).
1332        </li>
1333<li class="listitem">
1334          Implemented Rational function generation (the Remez method).
1335        </li>
1336</ul></div>
1337<h5>
1338<a name="math_toolkit.history2.h41"></a>
1339      <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
1340      1: Released March 31st 2006</a>
1341    </h5>
1342<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
1343<li class="listitem">
1344          Implement gamma/beta/erf functions along with their incomplete counterparts.
1345        </li>
1346<li class="listitem">
1347          Generate high quality test data, against which future improvements can
1348          be judged.
1349        </li>
1350<li class="listitem">
1351          Provide tools for the evaluation of infinite series, continued fractions,
1352          and rational functions.
1353        </li>
1354<li class="listitem">
1355          Provide tools for testing against tabulated test data, and collecting statistics
1356          on error rates.
1357        </li>
1358<li class="listitem">
1359          Provide sufficient docs for people to be able to find their way around
1360          the library.
1361        </li>
1362</ul></div>
1363<p>
1364      SVN Revisions:
1365    </p>
1366<p>
1367      Sandbox and trunk last synchonised at revision: .
1368    </p>
1369</div>
1370<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
1371<td align="left"></td>
1372<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
1373      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
1374      Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
1375      Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
1376      Daryle Walker and Xiaogang Zhang<p>
1377        Distributed under the Boost Software License, Version 1.0. (See accompanying
1378        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>)
1379      </p>
1380</div></td>
1381</tr></table>
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