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26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
27 <a name="math_toolkit.history2"></a><a class="link" href="history2.html" title="History and What's New">History and What's New</a>
28 </h2></div></div></div>
29 <p>
30       Currently open bug reports can be viewed <a href="https://svn.boost.org/trac/boost/query?status=assigned&amp;status=new&amp;status=reopened&amp;component=math&amp;col=id&amp;col=summary&amp;col=status&amp;col=type&amp;col=milestone&amp;col=component&amp;order=priority" target="_top">here</a>.
31     </p>
32 <p>
33       All bug reports including closed ones can be viewed <a href="https://svn.boost.org/trac/boost/query?status=assigned&amp;status=closed&amp;status=new&amp;status=reopened&amp;component=math&amp;col=id&amp;col=summary&amp;col=status&amp;col=type&amp;col=milestone&amp;col=component&amp;order=priority" target="_top">here</a>.
34     </p>
35 <h5>
36 <a name="math_toolkit.history2.h0"></a>
37       <span class="phrase"><a name="math_toolkit.history2.math_2_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
38       (boost-1.57.0)</a>
39     </h5>
40 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
41 <li class="listitem">
42           Added <a class="link" href="dist_ref/dists/hyperexponential_dist.html" title="Hyperexponential Distribution">Hyperexponential
43           Distribution</a>.
44         </li>
45 <li class="listitem">
46           Fix some spurious overflows in the incomplete gamma functions (with thanks
47           to Rocco Romeo).
48         </li>
49 <li class="listitem">
50           Fix bug in derivative of incomplete beta when a = b = 0.5 - this also effects
51           several non-central distributions, see <a href="https://svn.boost.org/trac/boost/ticket/10480" target="_top">10480</a>.
52         </li>
53 <li class="listitem">
54           Fixed some corner cases in <a class="link" href="rounding/round.html" title="Rounding Functions">round</a>.
55         </li>
56 <li class="listitem">
57           Don't support 80-bit floats in cstdfloat.hpp if standard library support
58           is broken.
59         </li>
60 </ul></div>
61 <h5>
62 <a name="math_toolkit.history2.h1"></a>
63       <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
64       (Boost-1.56.0)</a>
65     </h5>
66 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
67 <li class="listitem">
68           <span class="bold"><strong>Breaking change</strong></span>: moved a number of non-core
69           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
70           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>,
71           <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>,
72           <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
73           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
74           path.
75         </li>
76 <li class="listitem">
77           <span class="bold"><strong>Breaking change</strong></span>: A number of distributions
78           and special functions were returning the maximum finite value rather than
79           raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>,
80           this has now been fixed, which means these functions now behave as documented.
81           However, since the default behavior on raising an <a class="link" href="error_handling.html#math_toolkit.error_handling.overflow_error">overflow_error</a>
82           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
83           which have come to reply rely on these functions not throwing may experience
84           exceptions where they did not before. The special functions involved are
85           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>,
86           <a class="link" href="sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>,
87           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
88           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inva</a>,
89           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>,
90           <a class="link" href="sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>,
91           <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
92           involved are <a class="link" href="dist_ref/dists/pareto.html" title="Pareto Distribution">Pareto
93           Distribution</a>, <a class="link" href="dist_ref/dists/beta_dist.html" title="Beta Distribution">Beta
94           Distribution</a>, <a class="link" href="dist_ref/dists/geometric_dist.html" title="Geometric Distribution">Geometric
95           Distribution</a>, <a class="link" href="dist_ref/dists/negative_binomial_dist.html" title="Negative Binomial Distribution">Negative
96           Binomial Distribution</a>, <a class="link" href="dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
97           Distribution</a>, <a class="link" href="dist_ref/dists/chi_squared_dist.html" title="Chi Squared Distribution">Chi
98           Squared Distribution</a>, <a class="link" href="dist_ref/dists/gamma_dist.html" title="Gamma (and Erlang) Distribution">Gamma
99           Distribution</a>, <a class="link" href="dist_ref/dists/inverse_chi_squared_dist.html" title="Inverse Chi Squared Distribution">Inverse
100           chi squared Distribution</a>, <a class="link" href="dist_ref/dists/inverse_gamma_dist.html" title="Inverse Gamma Distribution">Inverse
101           Gamma Distribution</a>. See <a href="https://svn.boost.org/trac/boost/ticket/10111" target="_top">#10111</a>.
102         </li>
103 <li class="listitem">
104           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
105           be used with integer arguments, see <a href="https://svn.boost.org/trac/boost/ticket/10066" target="_top">#10066</a>.
106         </li>
107 <li class="listitem">
108           Fix Halley iteration to handle zero derivative (with non-zero second derivative),
109           see <a href="https://svn.boost.org/trac/boost/ticket/10046" target="_top">#10046</a>.
110         </li>
111 </ul></div>
112 <h5>
113 <a name="math_toolkit.history2.h2"></a>
114       <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>
115     </h5>
116 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
117 <li class="listitem">
118           Fix Geometric distribution use of Policies, see <a href="https://svn.boost.org/trac/boost/ticket/9833" target="_top">#9833</a>.
119         </li>
120 <li class="listitem">
121           Fix corner cases in the negative binomial distribution, see <a href="https://svn.boost.org/trac/boost/ticket/9834" target="_top">#9834</a>.
122         </li>
123 <li class="listitem">
124           Fix compilation failures on Mac OS.
125         </li>
126 </ul></div>
127 <h5>
128 <a name="math_toolkit.history2.h3"></a>
129       <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>
130     </h5>
131 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
132 <li class="listitem">
133           Changed version number to new Boost.Math specific version now that we're
134           in the modular Boost world.
135         </li>
136 <li class="listitem">
137           Added <a class="link" href="number_series/bernoulli_numbers.html" title="Bernoulli Numbers">Bernoulli
138           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
139           approximation (from Nikhar Agrawal).
140         </li>
141 <li class="listitem">
142           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>,
143           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_neumann_prime</a>,
144           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_i_prime</a>,
145           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">cyl_bessel_k_prime</a>,
146           <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_bessel_prime</a>
147           and <a class="link" href="bessel/bessel_derivatives.html" title="Derivatives of the Bessel Functions">sph_neumann_prime</a>
148           (from Anton Bikineev).
149         </li>
150 <li class="listitem">
151           Fixed buggy Student's t example code, along with docs for testing sample
152           means for equivalence.
153         </li>
154 <li class="listitem">
155           Documented <code class="computeroutput"><span class="identifier">max_iter</span></code> parameter
156           in root finding code better, see <a href="https://svn.boost.org/trac/boost/ticket/9225" target="_top">#9225</a>.
157         </li>
158 <li class="listitem">
159           Add option to explicitly enable/disable use of __float128 in constants
160           code, see <a href="https://svn.boost.org/trac/boost/ticket/9240" target="_top">#9240</a>.
161         </li>
162 <li class="listitem">
163           Cleaned up handling of negative values in Bessel I0 and I1 code (removed
164           dead code), see <a href="https://svn.boost.org/trac/boost/ticket/9512" target="_top">#9512</a>.
165         </li>
166 <li class="listitem">
167           Fixed handling of very small values passed to <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
168           and <a class="link" href="sf_gamma/lgamma.html" title="Log Gamma">lgamma</a> so they
169           don't generate spurious overflows (thanks to Rocco Romeo).
170         </li>
171 <li class="listitem">
172           <a href="https://svn.boost.org/trac/boost/ticket/9672" target="_top">#9672 PDF and
173           CDF of a Laplace distribution throwing domain_error</a> Random variate
174           can now be infinite.
175         </li>
176 <li class="listitem">
177           Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
178           <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
179           and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
180           with thanks to Rocco Romeo.
181         </li>
182 <li class="listitem">
183           Fixed several corner cases in <a class="link" href="factorials/sf_rising_factorial.html" title="Rising Factorial">rising_factorial</a>,
184           <a class="link" href="factorials/sf_falling_factorial.html" title="Falling Factorial">falling_factorial</a>
185           and <a class="link" href="sf_gamma/gamma_ratios.html" title="Ratios of Gamma Functions">tgamma_delta_ratio</a>
186           (thanks to Rocco Romeo).
187         </li>
188 <li class="listitem">
189           Removed constant <code class="computeroutput"><span class="identifier">pow23_four_minus_pi</span>
190           </code> whose value did not match the name (and was unused by Boost.Math),
191           see <a href="https://svn.boost.org/trac/boost/ticket/9712" target="_top">#9712</a>.
192         </li>
193 </ul></div>
194 <h5>
195 <a name="math_toolkit.history2.h4"></a>
196       <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>
197     </h5>
198 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
199 <li class="listitem">
200           Suppress numerous warnings (mostly from GCC-4.8 and MSVC) <a href="https://svn.boost.org/trac/boost/ticket/8384" target="_top">#8384</a>,
201           <a href="https://svn.boost.org/trac/boost/ticket/8855" target="_top">#8855</a>,
202           <a href="https://svn.boost.org/trac/boost/ticket/9107" target="_top">#9107</a>,
203           <a href="https://svn.boost.org/trac/boost/ticket/9109" target="_top">#9109</a>..
204         </li>
205 <li class="listitem">
206           Fixed PGI compilation issue <a href="https://svn.boost.org/trac/boost/ticket/8333" target="_top">#8333</a>.
207         </li>
208 <li class="listitem">
209           Fixed PGI constant value initialization issue that caused erf to generate
210           incorrect results <a href="https://svn.boost.org/trac/boost/ticket/8621" target="_top">#8621</a>.
211         </li>
212 <li class="listitem">
213           Prevent macro expansion of some C99 macros that are also C++ functions
214           <a href="https://svn.boost.org/trac/boost/ticket/8732" target="_top">#8732</a>
215           and <a href="https://svn.boost.org/trac/boost/ticket/8733" target="_top">#8733</a>..
216         </li>
217 <li class="listitem">
218           Fixed Student's T distribution to behave correctly with huge degrees of
219           freedom (larger than the largest representable integer) <a href="https://svn.boost.org/trac/boost/ticket/8837" target="_top">#8837</a>.
220         </li>
221 <li class="listitem">
222           Make some core functions usable with <code class="computeroutput"><span class="keyword">long</span>
223           <span class="keyword">double</span></code> even when the platform has
224           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>.
225         </li>
226 <li class="listitem">
227           Fix error handling of distributions to catch invalid scale and location
228           parameters when the random variable is infinite <a href="https://svn.boost.org/trac/boost/ticket/9042" target="_top">#9042</a>
229           and <a href="https://svn.boost.org/trac/boost/ticket/9126" target="_top">#9126</a>.
230         </li>
231 <li class="listitem">
232           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>.
233         </li>
234 <li class="listitem">
235           Improve consistency of argument reduction in the elliptic integrals <a href="https://svn.boost.org/trac/boost/ticket/9104" target="_top">#9104</a>.
236         </li>
237 <li class="listitem">
238           Fix bug in inverse incomplete beta that results in cancellation errors
239           when the beta function is really an arcsine or Student's T distribution.
240         </li>
241 <li class="listitem">
242           Fix issue in Bessel I and K function continued fractions that causes spurious
243           over/underflow.
244         </li>
245 <li class="listitem">
246           Add improvement to non-central chi squared distribution quantile due to
247           Thomas Luu.
248         </li>
249 </ul></div>
250 <h5>
251 <a name="math_toolkit.history2.h5"></a>
252       <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>
253     </h5>
254 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
255 <li class="listitem">
256           Major reorganization to incorporate other Boost.Math like Integer Utilities
257           Integer Utilities (Greatest Common Divisor and Least Common Multiple),
258           quaternions and octonions. Making new chapter headings.
259         </li>
260 <li class="listitem">
261           Added many references to Boost.Multiprecision and <code class="computeroutput"><span class="identifier">cpp_dec_float_50</span></code>
262           as an example of a User-defined Type (UDT).
263         </li>
264 <li class="listitem">
265           Added Clang to list of supported compilers.
266         </li>
267 <li class="listitem">
268           Fixed constants to use a thread-safe cache of computed values when used
269           at arbitrary precision.
270         </li>
271 <li class="listitem">
272           Added finding zeros of Bessel functions <code class="computeroutput"><span class="identifier">cyl_bessel_j_zero</span></code>,
273           <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
274           Christopher Kormanyos).
275         </li>
276 <li class="listitem">
277           More accuracy improvements to the Bessel J and Y functions from Rocco Romeo.
278         </li>
279 <li class="listitem">
280           Fixed nasty cyclic dependency bug that caused some headers to not compile
281           <a href="https://svn.boost.org/trac/boost/ticket/7999" target="_top">#7999</a>.
282         </li>
283 <li class="listitem">
284           Fixed bug in <a class="link" href="sf_gamma/tgamma.html" title="Gamma">tgamma</a>
285           that caused spurious overflow for arguments between 142.5 and 143.
286         </li>
287 <li class="listitem">
288           Fixed bug in raise_rounding_error that caused it to return an incorrect
289           result when throwing an exception is turned off <a href="https://svn.boost.org/trac/boost/ticket/7905" target="_top">#7905</a>.
290         </li>
291 <li class="listitem">
292           Added minimal __float128 support.
293         </li>
294 <li class="listitem">
295           Fixed bug in edge-cases of poisson quantile <a href="https://svn.boost.org/trac/boost/ticket/8308" target="_top">#8308</a>.
296         </li>
297 <li class="listitem">
298           Adjusted heuristics used in Halley iteration to cope with inverting the
299           incomplete beta in tricky regions where the derivative is flatlining. Example
300           is computing the quantile of the Fisher F distribution for probabilities
301           smaller than machine epsilon. See ticket <a href="https://svn.boost.org/trac/boost/ticket/8314" target="_top">#8314</a>.
302         </li>
303 </ul></div>
304 <h5>
305 <a name="math_toolkit.history2.h6"></a>
306       <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>
307     </h5>
308 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
309 <li class="listitem">
310           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/7325" target="_top">#7325</a>,
311           <a href="https://svn.boost.org/trac/boost/ticket/7415" target="_top">#7415</a>
312           and <a href="https://svn.boost.org/trac/boost/ticket/7416" target="_top">#7416</a>,
313           <a href="https://svn.boost.org/trac/boost/ticket/7183" target="_top">#7183</a>,
314           <a href="https://svn.boost.org/trac/boost/ticket/7649" target="_top">#7649</a>,
315           <a href="https://svn.boost.org/trac/boost/ticket/7694" target="_top">#7694</a>,
316           <a href="https://svn.boost.org/trac/boost/ticket/4445" target="_top">#4445</a>,
317           <a href="https://svn.boost.org/trac/boost/ticket/7492" target="_top">#7492</a>,
318           <a href="https://svn.boost.org/trac/boost/ticket/7891" target="_top">#7891</a>,
319           <a href="https://svn.boost.org/trac/boost/ticket/7429" target="_top">#7429</a>.
320         </li>
321 <li class="listitem">
322           Fixed mistake in calculating pooled standard deviation in two-sample students
323           t example <a href="https://svn.boost.org/trac/boost/ticket/7402" target="_top">#7402</a>.
324         </li>
325 <li class="listitem">
326           Improve complex acos/asin/atan, see <a href="https://svn.boost.org/trac/boost/ticket/7290" target="_top">#7290</a>,
327           <a href="https://svn.boost.org/trac/boost/ticket/7291" target="_top">#7291</a>.
328         </li>
329 <li class="listitem">
330           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>
331           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>
332           thanks to suggestions from Rocco Romeo.
333         </li>
334 <li class="listitem">
335           Improve accuracy of Bessel J and Y for integer orders thanks to suggestions
336           from Rocco Romeo.
337         </li>
338 </ul></div>
339 <h5>
340 <a name="math_toolkit.history2.h7"></a>
341       <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>
342     </h5>
343 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
344 <li class="listitem">
345           Corrected moments for small degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7177" target="_top">#7177</a>
346           (reported by Thomas Mang).
347         </li>
348 <li class="listitem">
349           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>.
350         </li>
351 <li class="listitem">
352           Corrected failure to detect bad parameters in many distributions <a href="https://svn.boost.org/trac/boost/ticket/6934" target="_top">#6934</a> (reported
353           by Florian Schoppmann) by adding a function check_out_of_range to test
354           many possible bad parameters. This test revealed several distributions
355           where the checks for bad parameters were ineffective, and these have been
356           rectified.
357         </li>
358 <li class="listitem">
359           Fixed issue in Hankel functions that causes incorrect values to be returned
360           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>.
361         </li>
362 <li class="listitem">
363           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/6517" target="_top">#6517</a>,
364           <a href="https://svn.boost.org/trac/boost/ticket/6362" target="_top">#6362</a>,
365           <a href="https://svn.boost.org/trac/boost/ticket/7053" target="_top">#7053</a>,
366           <a href="https://svn.boost.org/trac/boost/ticket/2693" target="_top">#2693</a>,
367           <a href="https://svn.boost.org/trac/boost/ticket/6937" target="_top">#6937</a>,
368           <a href="https://svn.boost.org/trac/boost/ticket/7099" target="_top">#7099</a>.
369         </li>
370 <li class="listitem">
371           Permitted infinite degrees of freedom <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>
372           implemented using the normal distribution (requested by Thomas Mang).
373         </li>
374 <li class="listitem">
375           Much enhanced accuracy for large degrees of freedom &#957; and/or large non-centrality
376           &#948;
377 by switching to use the Students t distribution (or Normal distribution
378           for infinite degrees of freedom) centered at delta, when &#948; / (4 * &#957;) &lt;
379           epsilon for the floating-point type in use. <a href="https://svn.boost.org/trac/boost/ticket/7259" target="_top">#7259</a>.
380           It was found that the incomplete beta was suffering from serious cancellation
381           errors when degrees of freedom was very large. (That has now been fixed
382           in our code, but any code based on Didonato and Morris's original papers
383           (probably every implementation out there actually) will have the same issue).
384         </li>
385 </ul></div>
386 <h5>
387 <a name="math_toolkit.history2.h8"></a>
388       <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>
389     </h5>
390 <p>
391       See Boost-1.52 - some items were added but not listed in time for the release.
392     </p>
393 <h5>
394 <a name="math_toolkit.history2.h9"></a>
395       <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>
396     </h5>
397 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
398 <li class="listitem">
399           Promoted math constants to be 1st class citizens, including convenient
400           access to the most widely used built-in float, double, long double via
401           three namespaces.
402         </li>
403 <li class="listitem">
404           Added the Owen's T function and Skew Normal distribution written by Benjamin
405           Sobotta: see <a class="link" href="owens_t.html" title="Owen's T function">Owens T</a> and skew_normal_distrib.
406         </li>
407 <li class="listitem">
408           Added Hankel functions <a class="link" href="hankel/cyl_hankel.html" title="Cyclic Hankel Functions">cyl_hankel_1</a>,
409           <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>.
410         </li>
411 <li class="listitem">
412           Corrected issue <a href="https://svn.boost.org/trac/boost/ticket/6627" target="_top">#6627
413           nonfinite_num_put formatting of 0.0 is incorrect</a> based on a patch
414           submitted by K R Walker.
415         </li>
416 <li class="listitem">
417           Changed constant initialization mechanism so that it is thread safe even
418           for user-defined types, also so that user defined types get the full precision
419           of the constant, even when <code class="computeroutput"><span class="keyword">long</span>
420           <span class="keyword">double</span></code> does not. So for example
421           128-bit rational approximations will work with UDT's and do the right thing,
422           even though <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>
423           may be only 64 or 80 bits.
424         </li>
425 <li class="listitem">
426           Fixed issue in <code class="computeroutput"><span class="identifier">bessel_jy</span></code>
427           which causes Y<sub>8.5</sub>(4&#960;) to yield a NaN.
428         </li>
429 </ul></div>
430 <h5>
431 <a name="math_toolkit.history2.h10"></a>
432       <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>
433     </h5>
434 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
435 <li class="listitem">
436           Deprecated wrongly named <code class="computeroutput"><span class="identifier">twothirds</span></code>
437           math constant in favour of <code class="computeroutput"><span class="identifier">two_thirds</span></code>
438           (with underscore separator). (issue <a href="https://svn.boost.org/trac/boost/ticket/6199" target="_top">#6199</a>).
439         </li>
440 <li class="listitem">
441           Refactored test data and some special function code to improve support
442           for arbitary precision and/or expression-template-enabled types.
443         </li>
444 <li class="listitem">
445           Added new faster zeta function evaluation method.
446         </li>
447 </ul></div>
448 <p>
449       Fixed issues:
450     </p>
451 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
452 <li class="listitem">
453           Corrected CDF complement for Laplace distribution (issue <a href="https://svn.boost.org/trac/boost/ticket/6151" target="_top">#6151</a>).
454         </li>
455 <li class="listitem">
456           Corrected branch cuts on the complex inverse trig functions, to handle
457           signed zeros (issue <a href="https://svn.boost.org/trac/boost/ticket/6171" target="_top">#6171</a>).
458         </li>
459 <li class="listitem">
460           Fixed bug in <code class="computeroutput"><span class="identifier">bessel_yn</span></code>
461           which caused incorrect overflow errors to be raised for negative <span class="emphasis"><em>n</em></span>
462           (issue <a href="https://svn.boost.org/trac/boost/ticket/6367" target="_top">#6367</a>).
463         </li>
464 <li class="listitem">
465           Also fixed minor/cosmetic/configuration issues <a href="https://svn.boost.org/trac/boost/ticket/6120" target="_top">#6120</a>,
466           <a href="https://svn.boost.org/trac/boost/ticket/6191" target="_top">#6191</a>,
467           <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>,
468           <a href="https://svn.boost.org/trac/boost/ticket/6130" target="_top">#6130</a>,
469           <a href="https://svn.boost.org/trac/boost/ticket/6234" target="_top">#6234</a>,
470           <a href="https://svn.boost.org/trac/boost/ticket/6307" target="_top">#6307</a>,
471           <a href="https://svn.boost.org/trac/boost/ticket/6192" target="_top">#6192</a>.
472         </li>
473 </ul></div>
474 <h5>
475 <a name="math_toolkit.history2.h11"></a>
476       <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>
477     </h5>
478 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
479 <li class="listitem">
480           Added new series evaluation methods to the cyclic Bessel I, J, K and Y
481           functions. Also taken great care to avoid spurious over and underflow of
482           these functions. Fixes issue <a href="https://svn.boost.org/trac/boost/ticket/5560" target="_top">#5560</a>
483         </li>
484 <li class="listitem">
485           Added an example of using Inverse Chi-Squared distribution for Bayesian
486           statistics, provided by Thomas Mang.
487         </li>
488 <li class="listitem">
489           Added tests to use improved version of lexical_cast which handles C99 nonfinites
490           without using globale facets.
491         </li>
492 <li class="listitem">
493           Corrected wrong out-of-bound uniform distribution CDF complement values
494           <a href="https://svn.boost.org/trac/boost/ticket/5733" target="_top">#5733</a>.
495         </li>
496 <li class="listitem">
497           Enabled long double support on OpenBSD (issue <a href="https://svn.boost.org/trac/boost/ticket/6014" target="_top">#6014</a>).
498         </li>
499 <li class="listitem">
500           Changed nextafter and related functions to behave in the same way as other
501           implementations - so that nextafter(+INF, 0) is a finite value (issue
502           <a href="https://svn.boost.org/trac/boost/ticket/5823" target="_top">#5832</a>).
503         </li>
504 <li class="listitem">
505           Changed tuple include configuration to fix issue when using in conjunction
506           with Boost.Tr1 (issue <a href="https://svn.boost.org/trac/boost/ticket/5934" target="_top">#5934</a>).
507         </li>
508 <li class="listitem">
509           Changed class eps_tolerance to behave correctly when both ends of the range
510           are zero (issue <a href="https://svn.boost.org/trac/boost/ticket/6001" target="_top">#6001</a>).
511         </li>
512 <li class="listitem">
513           Fixed missing include guards on prime.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5927" target="_top">#5927</a>).
514         </li>
515 <li class="listitem">
516           Removed unused/undocumented constants from constants.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5982" target="_top">#5982</a>).
517         </li>
518 <li class="listitem">
519           Fixed missing std:: prefix in nonfinite_num_facets.hpp (issue <a href="https://svn.boost.org/trac/boost/ticket/5914" target="_top">#5914</a>).
520         </li>
521 <li class="listitem">
522           Minor patches for Cray compiler compatibility.
523         </li>
524 </ul></div>
525 <h5>
526 <a name="math_toolkit.history2.h12"></a>
527       <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>
528     </h5>
529 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
530 <li class="listitem">
531           Added changesign function to sign.hpp to facilitate addition of nonfinite
532           facets.
533         </li>
534 <li class="listitem">
535           Addition of nonfinite facets from Johan Rade, with tests, examples of use
536           for C99 format infinity and NaN, and documentation.
537         </li>
538 <li class="listitem">
539           Added tests and documentation of changesign from Johan Rade.
540         </li>
541 </ul></div>
542 <h5>
543 <a name="math_toolkit.history2.h13"></a>
544       <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>
545     </h5>
546 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
547           Fixed issues <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5095</a>,
548           <a href="https://svn.boost.org/trac/boost/ticket/5095" target="_top">#5113</a>.
549         </li></ul></div>
550 <h5>
551 <a name="math_toolkit.history2.h14"></a>
552       <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>
553     </h5>
554 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
555 <li class="listitem">
556           Added Wald, Inverse Gaussian and geometric distributions.
557         </li>
558 <li class="listitem">
559           Added information about configuration macros.
560         </li>
561 <li class="listitem">
562           Added support for mpreal as a real-numbered type.
563         </li>
564 </ul></div>
565 <h5>
566 <a name="math_toolkit.history2.h15"></a>
567       <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>
568     </h5>
569 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
570 <li class="listitem">
571           Added warnings about potential ambiguity with std random library in distribution
572           and function names.
573         </li>
574 <li class="listitem">
575           Added inverse gamma distribution and inverse chi_square and scaled inverse
576           chi_square.
577         </li>
578 <li class="listitem">
579           Editorial revision of documentation, and added FAQ.
580         </li>
581 </ul></div>
582 <h5>
583 <a name="math_toolkit.history2.h16"></a>
584       <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>
585     </h5>
586 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
587 <li class="listitem">
588           Fixed incorrect range and support for Rayleigh distribution.
589         </li>
590 <li class="listitem">
591           Fixed numerical error in the quantile of the Student's T distribution:
592           the function was returning garbage values for non-integer degrees of freedom
593           between 2 and 3.
594         </li>
595 </ul></div>
596 <h5>
597 <a name="math_toolkit.history2.h17"></a>
598       <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>
599     </h5>
600 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
601           Significantly improved performance for the incomplete gamma function and
602           its inverse.
603         </li></ul></div>
604 <h5>
605 <a name="math_toolkit.history2.h18"></a>
606       <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>
607     </h5>
608 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
609 <li class="listitem">
610           Added support for MPFR as a bignum type.
611         </li>
612 <li class="listitem">
613           Added some full specializations of the policy classes to reduce compile
614           times.
615         </li>
616 <li class="listitem">
617           Added logistic and hypergeometric distributions, from Gautam Sewani's Google
618           Summer of Code project.
619         </li>
620 <li class="listitem">
621           Added Laplace distribution submitted by Thijs van den Berg.
622         </li>
623 <li class="listitem">
624           Updated performance test code to include new distributions, and improved
625           the performance of the non-central distributions.
626         </li>
627 <li class="listitem">
628           Added SSE2 optimised <a class="link" href="lanczos.html" title="The Lanczos Approximation">Lanczos approximation</a>
629           code, from Gautam Sewani's Google Summer of Code project.
630         </li>
631 <li class="listitem">
632           Fixed bug in cyl_bessel_i that used an incorrect approximation for &#957; = 0.5,
633           also effects the non-central Chi Square Distribution when &#957; = 3, see bug
634           report <a href="https://svn.boost.org/trac/boost/ticket/2877" target="_top">#2877</a>.
635         </li>
636 <li class="listitem">
637           Fixed minor bugs <a href="https://svn.boost.org/trac/boost/ticket/2873" target="_top">#2873</a>.
638         </li>
639 </ul></div>
640 <h5>
641 <a name="math_toolkit.history2.h19"></a>
642       <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>
643     </h5>
644 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
645 <li class="listitem">
646           Added Johan R&#229;de's optimised floating point classification routines.
647         </li>
648 <li class="listitem">
649           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>).
650         </li>
651 </ul></div>
652 <h5>
653 <a name="math_toolkit.history2.h20"></a>
654       <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>
655     </h5>
656 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
657           Improved accuracy and testing of the inverse hypergeometric functions.
658         </li></ul></div>
659 <h5>
660 <a name="math_toolkit.history2.h21"></a>
661       <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>
662     </h5>
663 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
664 <li class="listitem">
665           Added Noncentral Chi Squared Distribution.
666         </li>
667 <li class="listitem">
668           Added Noncentral Beta Distribution.
669         </li>
670 <li class="listitem">
671           Added Noncentral F Distribution.
672         </li>
673 <li class="listitem">
674           Added Noncentral T Distribution.
675         </li>
676 <li class="listitem">
677           Added Exponential Integral Functions.
678         </li>
679 <li class="listitem">
680           Added Zeta Function.
681         </li>
682 <li class="listitem">
683           Added Rounding and Truncation functions.
684         </li>
685 <li class="listitem">
686           Added Compile time powers of runtime bases.
687         </li>
688 <li class="listitem">
689           Added SSE2 optimizations for Lanczos evaluation.
690         </li>
691 </ul></div>
692 <h5>
693 <a name="math_toolkit.history2.h22"></a>
694       <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:
695       Post Review First Official Release</a>
696     </h5>
697 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
698 <li class="listitem">
699           Added Policy based framework that allows fine grained control over function
700           behaviour.
701         </li>
702 <li class="listitem">
703           <span class="bold"><strong>Breaking change:</strong></span> Changed default behaviour
704           for domain, pole and overflow errors to throw an exception (based on review
705           feedback), this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
706         </li>
707 <li class="listitem">
708           <span class="bold"><strong>Breaking change:</strong></span> Changed exception thrown
709           when an internal evaluation error occurs to boost::math::evaluation_error.
710         </li>
711 <li class="listitem">
712           <span class="bold"><strong>Breaking change:</strong></span> Changed discrete quantiles
713           to return an integer result: this is anything up to 20 times faster than
714           finding the true root, this behaviour can be customised using <a class="link" href="../policy.html" title="Chapter&#160;14.&#160;Policies: Controlling Precision, Error Handling etc">Policy</a>'s.
715         </li>
716 <li class="listitem">
717           Polynomial/rational function evaluation is now customisable and hopefully
718           faster than before.
719         </li>
720 <li class="listitem">
721           Added performance test program.
722         </li>
723 </ul></div>
724 <h5>
725 <a name="math_toolkit.history2.h23"></a>
726       <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
727       4: Second Review Candidate (1st March 2007)</a>
728     </h5>
729 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
730 <li class="listitem">
731           Moved Xiaogang Zhang's Bessel Functions code into the library, and brought
732           them into line with the rest of the code.
733         </li>
734 <li class="listitem">
735           Added C# "Distribution Explorer" demo application.
736         </li>
737 </ul></div>
738 <h5>
739 <a name="math_toolkit.history2.h24"></a>
740       <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
741       3: First Review Candidate (31st Dec 2006)</a>
742     </h5>
743 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
744 <li class="listitem">
745           Implemented the main probability distribution and density functions.
746         </li>
747 <li class="listitem">
748           Implemented digamma.
749         </li>
750 <li class="listitem">
751           Added more factorial functions.
752         </li>
753 <li class="listitem">
754           Implemented the Hermite, Legendre and Laguerre polynomials plus the spherical
755           harmonic functions from TR1.
756         </li>
757 <li class="listitem">
758           Moved Xiaogang Zhang's elliptic integral code into the library, and brought
759           them into line with the rest of the code.
760         </li>
761 <li class="listitem">
762           Moved Hubert Holin's existing Boost.Math special functions into this library
763           and brought them into line with the rest of the code.
764         </li>
765 </ul></div>
766 <h5>
767 <a name="math_toolkit.history2.h25"></a>
768       <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
769       2: Released September 10th 2006</a>
770     </h5>
771 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
772 <li class="listitem">
773           Implement preview release of the statistical distributions.
774         </li>
775 <li class="listitem">
776           Added statistical distributions tutorial.
777         </li>
778 <li class="listitem">
779           Implemented root finding algorithms.
780         </li>
781 <li class="listitem">
782           Implemented the inverses of the incomplete gamma and beta functions.
783         </li>
784 <li class="listitem">
785           Rewrite erf/erfc as rational approximations (valid to 128-bit precision).
786         </li>
787 <li class="listitem">
788           Integrated the statistical results generated from the test data with Boost.Test:
789           uses a database of expected results, indexed by test, floating point type,
790           platform, and compiler.
791         </li>
792 <li class="listitem">
793           Improved lgamma near 1 and 2 (rational approximations).
794         </li>
795 <li class="listitem">
796           Improved erf/erfc inverses (rational approximations).
797         </li>
798 <li class="listitem">
799           Implemented Rational function generation (the Remez method).
800         </li>
801 </ul></div>
802 <h5>
803 <a name="math_toolkit.history2.h26"></a>
804       <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
805       1: Released March 31st 2006</a>
806     </h5>
807 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
808 <li class="listitem">
809           Implement gamma/beta/erf functions along with their incomplete counterparts.
810         </li>
811 <li class="listitem">
812           Generate high quality test data, against which future improvements can
813           be judged.
814         </li>
815 <li class="listitem">
816           Provide tools for the evaluation of infinite series, continued fractions,
817           and rational functions.
818         </li>
819 <li class="listitem">
820           Provide tools for testing against tabulated test data, and collecting statistics
821           on error rates.
822         </li>
823 <li class="listitem">
824           Provide sufficient docs for people to be able to find their way around
825           the library.
826         </li>
827 </ul></div>
828 <p>
829       SVN Revisions:
830     </p>
831 <p>
832       Sandbox and trunk last synchonised at revision: .
833     </p>
834 </div>
835 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
836 <td align="left"></td>
837 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
838       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
839       Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
840       Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
841         Distributed under the Boost Software License, Version 1.0. (See accompanying
842         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>)
843       </p>
844 </div></td>
845 </tr></table>
846 <hr>
847 <div class="spirit-nav">
848 <a accesskey="p" href="../status.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../status.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="issues.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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850 </body>
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