[boost-doc-zh] r325 committed - 转换至1.40.0，第8批，完成以下库：...

From: codesite-noreply@xxxxxxxxxx
To: boost-doc-zh-notify@xxxxxxxxxxxxx
Date: Thu, 10 Sep 2009 03:10:47 +0000

Revision: 325
Author: alai04
Date: Wed Sep  9 20:09:56 2009
Log: 转换至1.40.0，第8批，完成以下库：
math
math/common_factor
math/complex number algorithms
math/octonion
math/quaternion
math/special_functions
math/statistical distributions
http://code.google.com/p/boost-doc-zh/source/detail?r=325

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=======================================
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+++ /trunk/libs/math/doc/distexplorer/html/index.html Wed Sep 9 20:09:562009

@@ -0,0 +1,216 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Statistical Distribution Explorer</title>

+<link rel="stylesheet" href="../../../../../doc/html/boostbook.css"type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">

+<link rel="home" href="index.html" title="Statistical DistributionExplorer">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../index.html">Home</a></td>

+<td align="center"><ahref="../../../../../libs/libraries.htm">Libraries</a></td>+<td align="center"><ahref="http://www.boost.org/users/people.html";>People</a></td>+<td align="center"><ahref="http://www.boost.org/users/faq.html";>FAQ</a></td>

+<td align="center"><a href="../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav"></div>
+<div class="article" lang="en">
+<div class="titlepage">
+<div>
+<div><h2 class="title">

+<a name="statistical_distribution_explorer"></a>Statistical DistributionExplorer</h2></div>

+<div><div class="authorgroup">
+<div class="author"><h3 class="author">
+<span class="firstname">Paul A.</span> <span class="surname">Bristow</span>
+</h3></div>
+<div class="author"><h3 class="author">
+<span class="firstname">John</span> <span class="surname">Maddock</span>
+</h3></div>
+</div></div>

+<div><div class="legalnotice">
+<a name="id770834"></a><p>

+ Distributed under the Boost Software License, Version 1.0. (Seeaccompanying+ file LICENSE_1_0.txt or copy at <ahref="http://www.boost.org/LICENSE_1_0.txt";target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)

+      </p>
+</div></div>
+</div>
+<hr>
+</div>
+<p>

+ A Windows utility to show the properties of statistical distributionsusing parameters

+    provided interactively by the user.
+  </p>
+<p>
+    The distributions provided are:
+  </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+      bernoulli
+    </li>
+<li>
+      beta_distribution
+    </li>
+<li>
+      binomial_distribution
+    </li>
+<li>
+      cauchy
+    </li>
+<li>
+      chi_squared
+    </li>
+<li>
+      exponential
+    </li>
+<li>
+      extreme_value
+    </li>
+<li>
+      fisher_f
+    </li>
+<li>
+      gamma_distribution
+    </li>
+<li>
+      lognormal_distribution
+    </li>
+<li>
+      negative_binomial_distribution
+    </li>
+<li>
+      normal_distribution
+    </li>
+<li>
+      pareto
+    </li>
+<li>
+      poisson
+    </li>
+<li>
+      rayleigh
+    </li>
+<li>
+      students_t
+    </li>
+<li>
+      triangular
+    </li>
+<li>
+      uniform
+    </li>
+<li>
+      weibull
+    </li>
+</ul></div>
+<p>
+    Properties of distributions computed are:
+  </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+      mean
+    </li>
+<li>
+      mode
+    </li>
+<li>
+      median
+    </li>
+<li>
+      variance
+    </li>
+<li>
+      standard deviation
+    </li>
+<li>
+      coefficient of variation,
+    </li>
+<li>
+      skewness
+    </li>
+<li>
+      kurtosis
+    </li>
+<li>
+      excess
+    </li>
+<li>
+      range supported
+    </li>
+</ul></div>
+<p>
+    Calculated, from values provided, are:
+  </p>
+<div class="itemizedlist"><ul type="disc">
+<li>
+      probability density (or mass) function (PDF)
+    </li>
+<li>
+      cumulative distribution function (CDF), and complement
+    </li>
+<li>

+ Quantiles (percentiles) are calculated for typical risk (alpha)probabilities+ (0.001, 0.01, 0.5, 0.1, 0.333) and for additional probabilitiesprovided by

+      the user.
+    </li>
+</ul></div>
+<p>

+ Results can be saved to text files using Save or SaveAs. All thevalues on the+ four tabs are output to the file chosen, and are tab separated toassist input

+    to other programs, for example, spreadsheets or text editors.
+  </p>
+<p>

+ Note: Excel (for example), only shows 10 decimal digits, by default:to display+ the maximum possible precision (abotu 15 decimal digits), it isnecessary to+ format all cells to display this precision. Although unusuallyaccurate, not+ all values computed by Distexplorer will be as accurate as this.Values shown+ as NaN cannot be calculated from the value(s) given, most commonlybecause the

+    value input is outside the range for the distribution.
+  </p>
+<p>
+    For more information, including downloads, see
+  </p>
+<p>

+ <a href="http://distexplorer.sourceforge.net/";target="_top">Distexplorer at Sourceforge</a>

+  </p>
+<p>

+ This Microsoft Windows 32 package distribution.exe was generated froma C# program+ and uses a boost_math.dll generated using the Boost.Math C++ sourcecode from+ the Boost.Math Toolkit, compiled in CLI mode, containing theunderlying statistical

+    distribution classes and functions.
+  </p>
+<p>

+ All source code is freely available for view and use under the <ahref="http://www.boost.org/LICENSE_1_0.txt"; target="_top">Boost

+    Open Source License</a>.
+  </p>
+<p>

+ <ahref="https://svn.boost.org/svn/boost/sandbox%5Cmath_toolkit%5Clibs%5Cmath%5Cdot_net_example";target="_top">Math+ Toolkit C++ source code</a> to produce boost_math.dll is in the mostrecent+ <a href="http://www.boost.org"; target="_top">Boost</a> release,initially 1.35.0.

+  </p>
+<p>

+ It is distributed as a single Windows Installer packageSetupdistex.msi. Unzip+ the distexplorer.zip to a temporary location of your choice and runsetup.exe.

+  </p>
+<p>

+ (Note that .NET framework 2.0 and VCredist are requirements for thisprogram.+ Most recent and updated Windows environments will already have these,but they+ are quickly, easily and safely installed from the Microsoft site ifrequired.)

+  </p>
+<p>

+ (The package cannot be run on other platforms at present but it shouldbe possible+ to build an equivalent utility on any C/C++ platform if anyone wouldlike to

+    undertake this task.)
+  </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>+<td align="left">Last revised: February 26, 2009 at 17:08:18GMT</td>

+<td align="right"><div class="copyright-footer"></div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav"></div>
+</body>
+</html>
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+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/hypergeometric_dist.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,344 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Hypergeometric Distribution</title>

+<link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
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+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../../../boost.png"></td>+<td align="center"><ahref="../../../../../../../../../index.html">Home</a></td>+<td align="center"><ahref="../../../../../../../../../libs/libraries.htm">Libraries</a></td>+<td align="center"><ahref="http://www.boost.org/users/people.html";>People</a></td>+<td align="center"><ahref="http://www.boost.org/users/faq.html";>FAQ</a></td>+<td align="center"><ahref="../../../../../../../../../more/index.htm">More</a></td>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="gamma_dist.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../dists.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="laplace_dist.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">

+<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist"></a><aclass="link" href="hypergeometric_dist.html" title="HypergeometricDistribution">

+          Hypergeometric Distribution</a>
+</h5></div></div></div>
+<p>
+
+</p>

+<p>
+          </p>

+<pre class="programlisting">namespace <spanclass="identifier">boost{ <spanclass="keyword">namespace math<spanclass="special">{

+template <spanclass="special"><class <spanclass="identifier">RealType = <spanclass="keyword">double,+ class <a class="link"href="../../../policy.html" title="Policies">Policy</a> <spanclass="special">= <a class="link"href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy ClassReference">policies::policy<></a> >+class <spanclass="identifier">hypergeometric_distribution<spanclass="special">;

+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>

+ typedef <spanclass="identifier">RealType <spanclass="identifier">value_type;+ typedef <spanclass="identifier">Policy <spanclass="identifier">policy_type;

+   <span class="comment">// Construct:

+ hypergeometric_distribution<spanclass="special">(unsigned <spanclass="identifier">r, <spanclass="keyword">unsigned n<spanclass="special">, unsigned <spanclass="identifier">N);

+   <span class="comment">// Accessors:

+ unsigned <spanclass="identifier">total()<spanclass="keyword">const;+ unsigned <spanclass="identifier">defective()<spanclass="keyword">const;+ unsigned <spanclass="identifier">sample_count()<spanclass="keyword">const;

+<span class="special">};</span>
+

+typedef <spanclass="identifier">hypergeometric_distribution<spanclass="special"><> <spanclass="identifier">hypergeometric;

+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>

+ The hypergeometric distribution describes the numberof "events"+ k from a sample <spanclass="emphasis">n drawn from+ a total population Nwithout replacement.

+          </p>
+<p>

+ Imagine we have a sample of <spanclass="emphasis">N objects of which+ r are "defective" andN-r are "not

+            defective" (the terms "success/failure" or "red/blue"

+ are also used). If we sample <spanclass="emphasis">n items without+ replacement then what is the probability thatexactly k+ items in the sample are defective? The answer is given by thepdf of+ the hypergeometric distribution <codeclass="computeroutput">f<spanclass="special">(k<spanclass="special">; r<spanclass="special">, n<spanclass="special">, N<spanclass="special">)</code>, whilst the probability of <spanclass="emphasis">k+ defectives or fewer is given by F(k; r, n, N), where F(k) isthe CDF

+            of the hypergeometric distribution.
+          </p>
+<div class="note"><table border="0" summary="Note">
+<tr>

+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]"src="../../../../../../../../../doc/html/images/note.png"></td>

+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>

+ Unlike almost all of the other distributions in thislibrary, the hypergeometric+ distribution is strictly discrete: it can not be extended toreal valued

+              arguments of its parameters or random variable.
+            </p></td></tr>
+</table></div>
+<p>

+ The following graph shows how the distribution changes as theproportion

+            of "defective" items changes, while keeping the population
+            and sample sizes constant:
+          </p>
+<p>

+ <imgsrc="../../../../../graphs/hypergeometric_pdf_1.png" align="middle">

+          </p>
+<p>

+ Note that since the distribution is symmetrical in parametersn+ and r, if we change thesample size and keep the

+            population and proportion "defective" the same then we obtain
+            basically the same graphs:
+          </p>
+<p>

+ <imgsrc="../../../../../graphs/hypergeometric_pdf_2.png" align="middle">

+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions"></a><h5>

+<a name="id776835"></a>

+ <a class="link"href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions">Member

+            Functions</a>
+          </h5>

+<pre class="programlisting"><spanclass="identifier">hypergeometric_distribution<spanclass="special">(unsigned <spanclass="identifier">r, <spanclass="keyword">unsigned n<spanclass="special">, unsigned <spanclass="identifier">N);

+</pre>
+<p>

+ Constructs a hypergeometric distribution with with apopulation of N+ objects, of which r aredefective, and from which

+            <span class="emphasis"><em>n</em></span> are sampled.
+          </p>

+<pre class="programlisting">unsigned <spanclass="identifier">total()<spanclass="keyword">const;

+</pre>
+<p>

+ Returns the total number of objects <spanclass="emphasis">N.

+          </p>

+<pre class="programlisting">unsigned <spanclass="identifier">defective()<spanclass="keyword">const;

+</pre>
+<p>

+ Returns the number of objects <spanclass="emphasis">r in population <spanclass="emphasis">N

+            which are defective.
+          </p>

+<pre class="programlisting">unsigned <spanclass="identifier">sample_count()<spanclass="keyword">const;

+</pre>
+<p>

+ Returns the number of objects <spanclass="emphasis">n which are sampled

+            from the population <span class="emphasis"><em>N</em></span>.
+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors"></a><h5>

+<a name="id777014"></a>

+ <a class="link"href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors">Non-member

+            Accessors</a>
+          </h5>
+<p>

+ All the <a class="link" href="../nmp.html" title="Non-MemberProperties">usual non-member+ accessor functions</a> that are generic to all distributionsare supported:+ <a class="link" href="../nmp.html#math.dist.cdf">CumulativeDistribution Function</a>,+ <a class="link" href="../nmp.html#math.dist.pdf">ProbabilityDensity Function</a>, <a class="link"href="../nmp.html#math.dist.quantile">Quantile</a>, <a class="link"href="../nmp.html#math.dist.hazard">Hazard+ Function</a>, <a class="link"href="../nmp.html#math.dist.chf">Cumulative Hazard Function</a>,+ <a class="link" href="../nmp.html#math.dist.mean">mean</a>, <aclass="link" href="../nmp.html#math.dist.median">median</a>,+ <a class="link" href="../nmp.html#math.dist.mode">mode</a>, <aclass="link" href="../nmp.html#math.dist.variance">variance</a>,+ <a class="link" href="../nmp.html#math.dist.sd">standarddeviation</a>, <a class="link"href="../nmp.html#math.dist.skewness">skewness</a>,+ <a class="link"href="../nmp.html#math.dist.kurtosis">kurtosis</a>, <a class="link"href="../nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>,+ <a class="link" href="../nmp.html#math.dist.range">range</a>and <a class="link" href="../nmp.html#math.dist.support">support</a>.

+          </p>
+<p>

+ The domain of the random variable is the unsigned integers inthe range+ [max(0, n + r - N), min(n, r)]. A <a class="link"href="../../../main_overview/error_handling.html#domain_error">domain_error</a>+ is raised if the random variable is outside this range, or isnot an

+            integral value.
+          </p>
+<div class="caution"><table border="0" summary="Caution">
+<tr>

+<td rowspan="2" align="center" valign="top" width="25"><imgalt="[Caution]"src="../../../../../../../../../doc/html/images/caution.png"></td>

+<th align="left">Caution</th>
+</tr>
+<tr><td align="left" valign="top">
+<p>

+ The quantile function will by default return an integerresult that+ has been roundedoutwards. That is to say lower+ quantiles (where the probability is less than 0.5) arerounded downward,+ and upper quantiles (where the probability is greater than0.5) are+ rounded upwards. This behaviour ensures that if an X%quantile is requested,+ then at least therequested coverage will be present+ in the central region, and nomore than the requested

+              coverage will be present in the tails.
+            </p>
+<p>

+ This behaviour can be changed so that the quantile functionsare rounded+ differently using <a class="link"href="../../../policy/pol_overview.html" title="PolicyOverview">Policies</a>.+ It is strongly recommended that you read the tutorial <aclass="link" href="../../../policy/pol_tutorial/understand_dis_quant.html"title="Understanding Quantiles of Discrete Distributions">Understanding+ Quantiles of Discrete Distributions</a> before using thequantile+ function on the Hypergeometric distribution. The <aclass="link" href="../../../policy/pol_ref/discrete_quant_ref.html"title="Discrete Quantile Policies">reference+ docs</a> describe how to change the rounding policy forthese distributions.

+            </p>
+<p>

+ However, note that the implementation method of the quantilefunction+ always returns an integral value, therefore attempting touse a <a class="link" href="../../../policy.html"title="Policies">Policy</a> that requires (or produces)

+              a real valued result will result in a compile time error.
+            </p>
+</td></tr>
+</table></div>

+<aname="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy"></a><h5>

+<a name="id777164"></a>

+ <a class="link"href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy">Accuracy</a>

+          </h5>
+<p>

+ For small N such that <code class="computeroutput"><spanclass="identifier">N < <spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">max_factorial<spanclass="special"><RealType<spanclass="special">>::value</code>+ then table based lookup of the results gives an accuracy to afew epsilon.+ <code class="computeroutput"><spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">max_factorial<spanclass="special"><RealType<spanclass="special">>::value</code>is 170 at double or long double

+            precision.
+          </p>
+<p>

+ For larger N such that <code class="computeroutput"><spanclass="identifier">N < <spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">prime(<spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">max_prime)</code>then only basic arithmetic is required+ for the calculation and the accuracy is typically < 20epsilon. This

+            takes care of N up to 104729.
+          </p>
+<p>

+ For <code class="computeroutput"><spanclass="identifier">N >+ boost<spanclass="special">::math<spanclass="special">::prime<spanclass="special">(boost<spanclass="special">::math<spanclass="special">::max_prime<spanclass="special">)</code>+ then accuracy quickly degrades, with 5 or 6 decimal digitsbeing lost

+            for N = 110000.
+          </p>
+<p>

+ In general for very large N, the user should expect to looselog10N decimal+ digits of precision during the calculation, with the resultsbecoming

+            meaningless for N &gt;= 10<sup>15</sup>.
+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing"></a><h5>

+<a name="id780004"></a>

+ <a class="link"href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing">Testing</a>

+          </h5>
+<p>

+ There are three sets of tests: our implementation is testedagainst a+ table of values produced by Mathematica's implementation ofthis distribution.+ We also sanity check our implementation against some spotvalues computed+ using the online calculator here <ahref="http://stattrek.com/Tables/Hypergeometric.aspx";target="_top">http://stattrek.com/Tables/Hypergeometric.aspx</a>.+ Finally we test accuracy against some high precision test datausing

+            this implementation and NTL::RR.
+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation"></a><h5>

+<a name="id780028"></a>

+ <a class="link"href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation">Implementation</a>

+          </h5>
+<p>
+            The PDF can be calculated directly using the formula:
+          </p>
+<p>

+ <imgsrc="../../../../../equations/hypergeometric1.png">

+          </p>
+<p>

+ However, this can only be used directly when the largest ofthe factorials+ is guaranteed not to overflow the floating pointrepresentation used.+ This formula is used directly when <codeclass="computeroutput">N+ < <spanclass="identifier">max_factorial<spanclass="special"><RealType<spanclass="special">>::value</code>+ in which case table lookup of the factorials gives a rapid andaccurate

+            implementation method.
+          </p>
+<p>

+ For larger N the methoddescribed in "An Accurate

+            Computation of the Hypergeometric Distribution Function", Trong

+ Wu, ACM Transactions on Mathematical Software, Vol. 19, No. 1,March+ 1993, Pages 33-43 is used. The method relies on the fact thatthere is+ an easy method for factorising a factorial into the product ofprime

+            numbers:
+          </p>
+<p>

+ <imgsrc="../../../../../equations/hypergeometric2.png">

+          </p>
+<p>

+ Where pi is the i'th prime number, andei is a small positive integer or

+            zero, which can be calculated via:
+          </p>
+<p>

+ <imgsrc="../../../../../equations/hypergeometric3.png">

+          </p>
+<p>

+ Further we can combine the factorials in the expression forthe PDF to

+            yield the PDF directly as the product of prime numbers:
+          </p>
+<p>

+ <imgsrc="../../../../../equations/hypergeometric4.png">

+          </p>
+<p>

+ With this time the exponents ei being eitherpositive, negative or zero.+ Indeed such a degree of cancellation occurs in the calculationof the+ ei that many are zero, and typically most have amagnitude or no more

+            than 1 or 2.
+          </p>
+<p>

+ Calculation of the product of the primes requires some care toprevent+ numerical overflow, we use a novel recursive method whichsplits the+ calculation into a series of sub-products, with a newsub-product started+ each time the next multiplication would cause either overflowor underflow.+ The sub-products are stored in a linked list on the programstack, and+ combined in an order that will guarantee no overflow orunnecessary-underflow

+            once the last sub-product has been calculated.
+          </p>
+<p>

+ This method can be used as long as N is smaller than thelargest prime+ number we have stored in our table of primes (currently104729). The+ method is relatively slow (calculating the exponents requiresthe most+ time), but requires only a small number of arithmeticoperations to calculate+ the result (indeed there is no shorter method involving onlybasic arithmetic+ once the exponents have been found), the method is thereforemuch more

+            accurate than the alternatives.
+          </p>
+<p>

+ For much larger N, we can calculate the PDF from thefactorials using+ either lgamma, or by directly combining lanczos approximationsto avoid+ calculating via logarithms. We use the latter method, as it isusually+ 1 or 2 decimal digits more accurate than computing vialogarithms with+ lgamma. However, in this area where N > 104729, the usershould expect+ to loose around log10N decimal digits during thecalculation in the worst

+            case.
+          </p>
+<p>

+ The CDF and its complement is calculated by directly summingthe PDF's.+ We start by deciding whether the CDF, or its complement, islikely to+ be the smaller of the two and then calculate the PDF at <spanclass="emphasis">k+ (or k+1 if we'recalculating the complement) and

+            calculate successive PDF values via the recurrence relations:
+          </p>
+<p>

+ <imgsrc="../../../../../equations/hypergeometric5.png">

+          </p>
+<p>

+ Until we either reach the end of the distributions domain, orthe next

+            PDF value to be summed would be too small to affect the result.
+          </p>
+<p>

+ The quantile is calculated in a similar manner to the CDF: wefirst guess+ which end of the distribution we're nearer to, and then sumPDFs starting+ from the end of the distribution this time, until we have somevalue+ k that gives therequired CDF.

+          </p>
+<p>

+ The median is simply the quantile at 0.5, and the remainingproperties

+            are calculated via:
+          </p>
+<p>

+ <imgsrc="../../../../../equations/hypergeometric6.png">

+          </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/laplace_dist.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,370 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Laplace Distribution</title>

+<link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">

+<link rel="prev" href="hypergeometric_dist.html" title="HypergeometricDistribution">

+<link rel="next" href="logistic_dist.html" title="Logistic Distribution">
+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="hypergeometric_dist.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../dists.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="logistic_dist.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">

+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist"></a><aclass="link" href="laplace_dist.html" title="Laplace Distribution"> Laplace

+          Distribution</a>
+</h5></div></div></div>
+<p>
+
+</p>

+<p>
+          </p>

+template <spanclass="special"><class <spanclass="identifier">RealType = <spanclass="keyword">double,+ class <a class="link"href="../../../policy.html" title="Policies">Policy</a> <spanclass="special">= <a class="link"href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy ClassReference">policies::policy<></a> >+class <spanclass="identifier">laplace_distribution;

+typedef <spanclass="identifier">laplace_distribution<spanclass="special"><> <spanclass="identifier">laplace;

+template <spanclass="special"><class <spanclass="identifier">RealType, <spanclass="keyword">class <a class="link" href="../../../policy.html"title="Policies">Policy</a>>+class <spanclass="identifier">laplace_distribution

+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>

+   <span class="comment">// Construct:

+ laplace_distribution<spanclass="special">(RealType <spanclass="identifier">location = <spanclass="number">0, <spanclass="identifier">RealType scale= 1<spanclass="special">);

+   <span class="comment">// Accessors:

+ RealType <spanclass="identifier">location()<spanclass="keyword">const;+ RealType <spanclass="identifier">scale()<spanclass="keyword">const;

+<span class="special">};</span>
+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>

+ Laplace distribution is the distribution of differencesbetween two independent+ variates with identical exponential distributions (Abramowitzand Stegun+ 1972, p. 930). It is also called the double exponentialdistribution.

+          </p>
+<p>

+ For location parameter μ and scale parameter σ it isdefined by the probability

+            density function:
+          </p>
+<p>

+ <imgsrc="../../../../../equations/laplace_pdf.png">

+          </p>
+<p>

+ The location and scale parameters are equivalent to the meanand standard

+            deviation of the normal or Gaussian distribution.
+          </p>
+<p>

+ The following graph illustrates the effect of the locationparameter+ μ on the PDF. Note that the range of the random variableremains [-∞,+∞]

+            irrespective of the value of the location parameter:
+          </p>
+<p>

+ <imgsrc="../../../../../graphs/laplace_pdf_mu.png" align="middle">

+          </p>
+<p>

+ The next graph illustrates the effect of the scale parameterσ on the PDF:

+          </p>
+<p>

+ <imgsrc="../../../../../graphs/laplace_pdf_sigma.png" align="middle">

+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions"></a><h5>

+<a name="id780786"></a>

+ <a class="link"href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions">Member

+            Functions</a>
+          </h5>

+<pre class="programlisting"><spanclass="identifier">laplace_distribution<spanclass="special">(RealType <spanclass="identifier">location = <spanclass="number">0, <spanclass="identifier">RealType scale= 1<spanclass="special">);

+</pre>
+<p>

+ Constructs a laplace distribution with location <spanclass="emphasis">location

+            and scale <span class="emphasis"><em>scale</em></span>.
+          </p>
+<p>

+ The location parameter is the same as the mean of the randomvariate.

+          </p>
+<p>

+ The scale parameter is proportional to the standard deviationof the

+            random variate.
+          </p>
+<p>

+ Requires that the scale parameter is greater than zero,otherwise calls+ <a class="link"href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.

+          </p>

+<pre class="programlisting">RealType <spanclass="identifier">location()<spanclass="keyword">const;

+</pre>
+<p>

+ Returns the locationparameter of this distribution.

+          </p>

+<pre class="programlisting">RealType <spanclass="identifier">scale()<spanclass="keyword">const;

+</pre>
+<p>

+ Returns the scaleparameter of this distribution.

+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors"></a><h5>

+<a name="id780948"></a>

+ <a class="link"href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors">Non-member

+            Accessors</a>
+          </h5>
+<p>

+          </p>
+<p>
+            The domain of the random variable is [-&#8734;,+&#8734;].
+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy"></a><h5>
+<a name="id781045"></a>

+ <a class="link"href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy">Accuracy</a>

+          </h5>
+<p>

+ The laplace distribution is implemented in terms of thestandard library+ log and exp functions and as such should have very smallerrors.

+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.laplace_dist.implementation"></a><h5>

+<a name="id781064"></a>

+ <a class="link"href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.implementation">Implementation</a>

+          </h5>
+<p>

+ In the following table μ is the location parameter of thedistribution,+ σ is its scale parameter, <spanclass="emphasis">x is the random variate,+ p is the probabilityand its complement q

+            = 1-p</em></span>.
+          </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>

+ Using the relation: pdf = e-abs(x-μ) /σ / (2 * σ)

+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relations:
+                  </p>
+                  <p>

+ x < μ : p = e(x-μ)/σ /σ

+                  </p>
+                  <p>

+ x >= μ : p = 1 - e(μ-x)/σ / σ

+
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>

+ -x < μ : q = e(-x-μ)/σ /σ

+                  </p>
+                  <p>

+ -x >= μ : q = 1 - e(μ+x)/σ / σ

+
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relations:
+                  </p>
+                  <p>
+                    p &lt; 0.5 : x = &#956; + &#963; * log(2*p)
+                  </p>
+                  <p>
+                    p &gt;= 0.5 : x = &#956; - &#963; * log(2-2*p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation:
+                  </p>
+                  <p>
+                    q &gt; 0.5: x = &#956; + &#963;*log(2-2*q)
+                  </p>
+                  <p>
+                    q &lt;=0.5: x = &#956; - &#963;*log( 2*q )
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#956;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    2 * &#963;<sup>2</sup>
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    &#956;
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    6
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    3
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.references"></a><h5>
+<a name="id781372"></a>

+ <a class="link"href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.references">References</a>

+          </h5>
+<div class="itemizedlist"><ul type="disc">
+<li>

+<a href="http://mathworld.wolfram.com/LaplaceDistribution.html";target="_top">Weisstein,

+              Eric W. "Laplace Distribution."</a> From MathWorld--A
+              Wolfram Web Resource.
+            </li>

+<li><a href="http://en.wikipedia.org/wiki/Laplace_distribution";target="_top">Laplace

+              Distribution</a></li>
+<li>

+ M. Abramowitz and I. A. Stegun, Handbook of MathematicalFunctions,

+              1972, p. 930.
+            </li>
+</ul></div>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/dist_ref/dists/logistic_dist.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,302 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Logistic Distribution</title>

+<link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../dists.html" title="Distributions">
+<link rel="prev" href="laplace_dist.html" title="Laplace Distribution">

+<link rel="next" href="lognormal_dist.html" title="Log NormalDistribution">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="laplace_dist.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../dists.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="lognormal_dist.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">

+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist"></a><aclass="link" href="logistic_dist.html" title="Logistic Distribution">

+          Logistic Distribution</a>
+</h5></div></div></div>
+<p>
+
+</p>

+<p>
+          </p>

+template <spanclass="special"><class <spanclass="identifier">RealType = <spanclass="keyword">double,+ class <a class="link"href="../../../policy.html" title="Policies">Policy</a> <spanclass="special">= <a class="link"href="../../../policy/pol_ref/pol_ref_ref.html" title="Policy ClassReference">policies::policy<></a> >+class <spanclass="identifier">logistic_distribution<spanclass="special">;

+<span class="special">{</span>
+<span class="keyword">public</span><span class="special">:</span>

+   <span class="comment">// Construct:

+ logistic_distribution<spanclass="special">(RealType <spanclass="identifier">location = <spanclass="number">0, <spanclass="identifier">RealType scale= 1<spanclass="special">);

+   <span class="comment">// Accessors:

+ RealType <spanclass="identifier">location()<spanclass="keyword">const; <spanclass="comment">// location.+ RealType <spanclass="identifier">scale()<spanclass="keyword">const; <spanclass="comment">// scale.

+</span>
+<span class="special">};</span>
+

+typedef <spanclass="identifier">logistic_distribution<spanclass="special"><> <spanclass="identifier">logistic;

+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<p>

+ The logistic distribution is a continous probabilitydistribution. It+ has two parameters - location and scale. The cumulativedistribution+ function of the logistic distribution appears in logisticregression+ and feedforward neural networks. Among other applications,United State

+            Chess Federation and FIDE use it to calculate chess ratings.
+          </p>
+<p>

+ The following graph shows how the distribution changes as theparameters

+            change:
+          </p>
+<p>

+ <imgsrc="../../../../../graphs/logistic_pdf.png" align="middle">

+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions"></a><h5>

+<a name="id781851"></a>

+ <a class="link"href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions">Member

+            Functions</a>
+          </h5>

+<pre class="programlisting"><spanclass="identifier">logistic_distribution<spanclass="special">(RealType <spanclass="identifier">u = <spanclass="number">0, <spanclass="identifier">RealType s <spanclass="special">= 1<spanclass="special">);

+</pre>
+<p>

+ Constructs a logistic distribution with location <spanclass="emphasis">u

+            and scale <span class="emphasis"><em>s</em></span>.
+          </p>
+<p>

+ Requires <code class="computeroutput"><spanclass="identifier">scale >+ 0</code>, otherwise a <aclass="link"href="../../../main_overview/error_handling.html#domain_error">domain_error</a>

+            is raised.
+          </p>

+</pre>
+<p>
+            Returns the location of this distribution.
+          </p>

+</pre>
+<p>
+            Returns the scale of this distribution.
+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors"></a><h5>

+<a name="id782017"></a>

+ <a class="link"href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors">Non-member

+            Accessors</a>
+          </h5>
+<p>

+          </p>
+<p>

+ The domain of the random variable is [-[max_value],+[min_value]]. However,

+            the pdf and cdf support inputs of +&#8734; and -&#8734;
+as special cases if RealType
+            permits.
+          </p>
+<p>

+ At <code class="computeroutput"><spanclass="identifier">p=<spanclass="number">1</code> and <code class="computeroutput"><spanclass="identifier">p=<spanclass="number">0</code>, the+ quantile function returns the result of +<a class="link"href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>+ and -<a class="link"href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>,while the+ complement quantile function returns the result of -<aclass="link"href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>+ and +<a class="link"href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a>respectively.

+          </p>
+<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy"></a><h5>
+<a name="id782184"></a>

+ <a class="link"href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy">Accuracy</a>

+          </h5>
+<p>

+ The logistic distribution is implemented in terms of the <codeclass="computeroutput">std<spanclass="special">::exp</code> and the<code class="computeroutput">std<spanclass="special">::log</code>+ functions, so its accuracy is related to the accurateimplementations+ of those functions on a given platform. When calculating thequantile+ with a non-zero <spanclass="emphasis">position parameter catastrophic+ cancellation errors can occur: in such cases, only a low <spanclass="emphasis">absolute

+            error</em></span> can be guarenteed.
+          </p>

+<aname="math_toolkit.dist.dist_ref.dists.logistic_dist.implementation"></a><h5>

+<a name="id782239"></a>

+ <a class="link"href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.implementation">Implementation</a>

+          </h5>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+                  <p>
+                    Function
+                  </p>
+                  </th>
+<th>
+                  <p>
+                    Implementation Notes
+                  </p>
+                  </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+                  <p>
+                    pdf
+                  </p>
+                  </td>
+<td>
+                  <p>

+ Using the relation: pdf = e-(x-u)/s /(s*(1+e-(x-u)/s)2)

+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: p = 1/(1+e<sup>-(x-u)/s</sup>)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    cdf complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: q = 1/(1+e<sup>(x-u)/s</sup>)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = u - s*log(1/p-1)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    quantile from the complement
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    Using the relation: x = u + s*log(p/1-p)
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mean
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    u
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    mode
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    The same as the mean.
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    skewness
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    0
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    kurtosis excess
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    6/5
+                  </p>
+                  </td>
+</tr>
+<tr>
+<td>
+                  <p>
+                    variance
+                  </p>
+                  </td>
+<td>
+                  <p>
+                    (&#960;*s)<sup>2</sup> / 3
+                  </p>
+                  </td>
+</tr>
+</tbody>
+</table></div>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/complements.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,136 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>

+<meta http-equiv="Content-Type" content="text/html;charset=UTF-8"><title>Complements are supported too - and when to usethem</title>

+<link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../overview.html" title="Overview of Distributions">

+<link rel="prev" href="generic.html" title="Generic operations common toall distributions are non-member functions">+<link rel="next" href="parameters.html" title="Parameters can becalculated">

+</head>

+<body style="color: black; background-color: white;" alink="#0000ff"link="#0000ff" vlink="#840084">

+<table cellpadding="2" width="100%">
+<tbody>
+<tr>

+<td valign="top"><img alt="Boost C++ Libraries"src="../../../../../../../../../boost.png" height="86" width="277"></td>+<td align="center"><ahref="../../../../../../../../../index.html">Home</a></td>+<td align="center"><ahref="../../../../../../../../../libs/libraries.htm">Libraries</a></td>+<td align="center"><ahref="http://www.boost.org/users/people.html";>People</a></td>+<td align="center"><ahref="http://www.boost.org/users/faq.html";>FAQ</a></td>+<td align="center"><ahref="../../../../../../../../../more/index.htm">More</a></td>

+</tr>
+</tbody>
+</table>
+<hr>

+<div class="spirit-nav"><a accesskey="p" href="generic.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../overview.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="parameters.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage">
+<div>
+<div>

+<h5 class="title"><aname="math_toolkit.dist.stat_tut.overview.complements"></a><a class="link"href="complements.html" title="Complements are supported too - and when touse them">

+补集也得到支持 - 何时使用它们</a>
+</h5>
+</div>
+</div>
+</div>

+你经常不想得到CDF的值，而是它的补集的值，也就是说你想得到<codeclass="computeroutput">1<spanclass="special">-p</code> 而不是<code class="computeroutput">p</code>。+你可以计算CDF 然后用<code class="computeroutput"><spanclass="number">1</code>减去这个结果，但是如果<codeclass="computeroutput">p</code>

+非常接近于<code class="computeroutput"><span class="number">1</span></code>

+，那么消去错误(cancellation error)将会使用你丢失有效数字。在极端的情况下，<code class="computeroutput">p</code>+可能实际上等于 <code class="computeroutput"><spanclass="number">1</code>，即使补集的真值( true

+value)是非零的。. </p>

+<a href="complements.html#why_complements">参见<spanclass="emphasis">"为什么有补集( complements)?"</a>

+</p>

+在这个库中，无论何时你想要得到一个补集(complement)，把所有的函数参数包装在对函数<code class="computeroutput"><spanclass="identifier">complement<spanclass="special">(...)</code>的调用之中，例如： +<pre class="programlisting">students_tdist(<spanclass="number">5); <spanclass="identifier">cout << <spanclass="string">"CDF at t = 1 is " <spanclass="special"><< cdf<spanclass="special">(dist<spanclass="special">, 1.0<spanclass="special">) << <spanclass="identifier">endl; <spanclass="identifier">cout << <spanclass="string">"Complement of CDF at t = 1 is " <spanclass="special"><< cdf<spanclass="special">(complement<spanclass="special">(dist<spanclass="special">, 1.0<spanclass="special">)) << <spanclass="identifier">endl;

+</pre>

+但请等一下，现在我们有一个补集(complement)，我们必须也能够使用它。任何的接受一个概率作为参数的函数同样也可以接受将+所有的参数包装在对函数 <code class="computeroutput"><spanclass="identifier">complement<spanclass="special">(...)</code>中产生的补集，例如：+<pre class="programlisting">students_tdist(<spanclass="number">5); <spanclass="keyword">for(<spanclass="keyword">double i <spanclass="special">= 10<spanclass="special">; i <spanclass="special">< 1e10<spanclass="special">; i <spanclass="special">*= 10<spanclass="special">) { <spanclass="comment">// 计算1 in i chance中的分位点: <spanclass="keyword">double t <spanclass="special">= quantile<spanclass="special">(complement<spanclass="special">(dist<spanclass="special">, 1<spanclass="special">/i<spanclass="special">)); // 打印出来 : cout <spanclass="special"><< "Quantile ofstudents-t with 5 degrees of freedom\n" <spanclass="string">"for a 1 in " <<i <<" chance is " <spanclass="special"><< t <spanclass="special"><< endl<spanclass="special">; }

+</pre>
+<div class="tip">
+<table summary="Tip" border="0">
+<tbody>
+<tr>

+<td rowspan="2" align="middle" valign="top" width="25"><img alt="[Tip]"src="../../../../../../../../../doc/html/images/tip.png"></td>

+<th align="left">提示</th>
+</tr>
+<tr>
+<td align="left" valign="top">
+<p></p>
+<p><span class="bold"><strong>临界值
+(Critical values)就是分位点(quantiles)</strong></span> </p>

+一些资料谈及quantiles，另一些资料谈及临界值( critical values)，基本原则是：

+<p><span class="emphasis"><em>下临界值(Lower
+critical values)</em></span> 与分位点(quantile)是相同的。</p>
+<p><span class="emphasis"><em>上临界值(Upper
+critical values)</em></span> 与概率补集的分位点(quantile)是相同的。</p>
+<p>例如，我们有一个伯努利过程(Bernoulli process)，产生一个成功比(success

+ratio)为0.1且总共100次试验的伯努利分布(binomial distribution)。概率为0.05的下临界值(lower critical value)

+由下面给定：</p>

+<code class="computeroutput"><spanclass="identifier">quantile(<spanclass="identifier">binomial(<spanclass="number">100, <spanclass="number">0.1), <spanclass="number">0.05)</code> 

+<p><span class="emphasis"><em>上临界值(upper
+critical value</em></span>) 由下面给定：</p>

+<code class="computeroutput"><spanclass="identifier">quantile(<spanclass="identifier">complement(<spanclass="identifier">binomial(<spanclass="number">100, <spanclass="number">0.1), <spanclass="number">0.05))</code> 

+<p>分别返回4.82 和14.63。</p>
+</td>
+</tr>
+</tbody>
+</table>
+</div>
+<a name="why_complements"></a>
+<p></p>
+<div class="tip">
+<table summary="Tip" border="0">
+<tbody>
+<tr>

+<td rowspan="2" align="middle" valign="top" width="25"><img alt="[Tip]"src="../../../../../../../../../doc/html/images/tip.png"></td>

+<th align="left">提示</th>
+</tr>
+<tr>
+<td align="left" valign="top">
+<p></p>
+<p><span class="bold"><strong>为什么要担心
+(bother)补集(complements)?</strong></span> </p>

+省掉补集(complements)是非常诱人的，并且在需要的时候只是简单地用1减去概率。然而，考虑当概率非常常于1+时会发生什么：假设概率以浮点数表示为 <code class="computeroutput"><spanclass="number">0.999999940f</code>，那么<codeclass="computeroutput">1+- 0.999999940f= 5.96046448e

+-008，</span></code>但是结果实际上只精确到<span class="emphasis"><em>一
+个bit</em></span>： 没有消去(cancel out)的唯一一个bit! </p>

+或者以另一种方式来看待这个问题：假定我们想要在一个样本大小为10,000的学生t分布(student's t+distribution)中错误拒绝(reject)虚假设(null-hypothesis)的风险(risk)为十亿分之一。这给出的概率为 1+- 10-9，当以float精度计算时刚好为1。在这种情况下，使用补集来计算分位点+(quantile)巧妙地解决了这个问题，例如：<code class="computeroutput"><spanclass="identifier">quantile(<spanclass="identifier">complement(<spanclass="identifier">students_t(<spanclass="number">10000), <spanclass="number">1e-9))</code> +返回期望的 t-statistic <code class="computeroutput"><spanclass="number">6.00336</code>，因为：+<code class="computeroutput"><spanclass="identifier">quantile(<spanclass="identifier">students_t(<spanclass="number">10000), <spanclass="number">1-<spanclass="number">1e-9f)</code> 

+<p>产生一个溢出错误，因为它与 下面等价：</p>

+<code class="computeroutput"><spanclass="identifier">quantile(<spanclass="identifier">students_t(<spanclass="number">10000), <spanclass="number">1)</code> 

+<p>这就没有有限值的结果。</p>
+</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%">

+<tbody>
+<tr>
+<td align="left"></td>
+<td align="right">
+<div class="copyright-footer">Copyright © 2006 ,
+2007, 2008, 2009 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang
+Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg
+<p> Distributed under the Boost Software License, Version

+1.0. (See accompanying file LICENSE_1_0.txt or copy at <ahref="http://www.boost.org/LICENSE_1_0.txt";target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)

+</p>
+</div>
+</td>
+</tr>
+</tbody>
+</table>
+<hr>

+</div>
+</body></html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/generic.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,178 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>

+<meta http-equiv="Content-Type" content="text/html;charset=UTF-8"><title>Generic operations common to all distributions are

+non-member functions</title>
+

+<link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../overview.html" title="Overview of Distributions">
+<link rel="prev" href="objects.html" title="Distributions are Objects">

+<link rel="next" href="complements.html" title="Complements are supportedtoo - and when to use them">

+</head>

+<body style="color: black; background-color: white;" alink="#0000ff"link="#0000ff" vlink="#840084">

+<table cellpadding="2" width="100%">
+<tbody>
+<tr>

+</tr>
+</tbody>
+</table>
+<hr>

+<div class="spirit-nav"><a accesskey="p" href="objects.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../overview.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="complements.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage">
+<div>
+<div>

+<h5 class="title"><aname="math_toolkit.dist.stat_tut.overview.generic"></a><a class="link"href="generic.html" title="Generic operations common to all distributionsare non-member functions">

+对所有分布都通用的操作是非成员函数</a>
+</h5>
+</div>
+</div>
+</div>
+<p>想要计算一个分布的PDF (概率密度函数)吗? 没问题，使用：</p>

+<pre class="programlisting">pdf<spanclass="special">(my_dist<spanclass="special">, x<spanclass="special">); // 返回分布my_dist在点x处的PDF(密度). </pre>

+<p>或者计算CDF (累积分布函数)：</p>

+<pre class="programlisting">cdf<spanclass="special">(my_dist<spanclass="special">, x<spanclass="special">); // 返回分布my_dist的CDF (积分形式 -从无穷到点x处) </pre>

+<p>分位点(quantiles)也是一样的：</p>

+<pre class="programlisting">quantile<spanclass="special">(my_dist<spanclass="special">, p<spanclass="special">); // 返回返回变量x的值 // 满足 cdf(my_dist, x) ==p. </pre>+如果你在考虑为什么这些函数不是成员函数，原因是使得这个库更容易扩展：如果你想要添加通用的操作－比方说第n个矩 n'thmoment－+那么所有你需要做的仅仅是添加合适的非成员函数，针对每个实现的分布类型进行重载。

+<div class="tip">
+<table summary="Tip" border="0">
+<tbody>
+<tr>

+<td rowspan="2" align="middle" valign="top" width="25"><img alt="[Tip]"src="../../../../../../../../../doc/html/images/tip.png"></td>

+<th align="left">提示</th>
+</tr>
+<tr>
+<td align="left" valign="top">
+<p></p>
+<p><span class="bold"><strong>近似于分布的分位点(<strong>Quantile</strong>)
+的随机数(Random numbers)</strong></span></p>

+如果你想获得以一种特定方式分布的随机数，例如，以均匀，正态或三角形方式分布，参考<a href="http://www.boost.org/libs/random/";target="_top">Boost.Random</a>.

+</p>
+<p>然而，在原理上没有什么能阻止你使用分位点函数(quantile

+function)来将均匀分布的随机数转换成另外一种分布。实际上，存在更高效的随机数生成算法。

+</td>
+</tr>
+</tbody>
+</table>
+</div>

+例如，二项分布(binomial distribution)有两个参数： n (试验次数) 和 p (单次试验的成功概率)。+<code class="computeroutput"><spanclass="identifier">binomial_distribution</code>

+构造函数有两个参数：</p>

+<code class="computeroutput"><spanclass="identifier">binomial_distribution<spanclass="special">(RealType+n, <spanclass="identifier">RealType+p);</code>+对于这个分布，随机变量是 k：观测到的成功试验数。概率密度/质量函数(pdf) 写作：f(k; n, p).

+</p>
+<div class="note">
+<table summary="Note" border="0">
+<tbody>
+<tr>

+<td rowspan="2" align="middle" valign="top" width="25"><img alt="[Note]"src="../../../../../../../../../doc/html/images/note.png"></td>

+<th align="left">注意</th>
+</tr>
+<tr>
+<td align="left" valign="top">
+<p></p>
+<p><span class="bold"><strong>随机变量和分布参数</strong></span>
+</p>

+<a href="http://en.wikipedia.org/wiki/Random_variate"; target="_top">随机变量</a> 和 <a href="http://en.wikipedia.org/wiki/Parameter";target="_top">分+布参数</a> 按照惯例进行区分 (例如在 Wikipedia 和 Wolfram MathWorld通过在随机变量后面放置一个+semi-colon (或者有时是vertical bar)，来区分随机变量与定义这个分布形状的形状参数(shape parameter)。

+</td>
+</tr>
+</tbody>
+</table>
+</div>

+就像上面提到的那样，非成员函数<code class="computeroutput"><spanclass="identifier">pdf</code>有一个分布类型的参数，以及+另一个随机变量类型的参数。以二项分布为例( binomial distribution)，我们可以写出如下代码：+<code class="computeroutput">pdf<spanclass="special">(<spanclass="identifier">binomial_distribution<spanclass="special"><RealType<spanclass="special">>(n<spanclass="special">,+p), <spanclass="identifier">k);</code> +允许和支持的随机变量值的范围可以通过<code class="computeroutput"><spanclass="identifier">range</code> 和<code class="computeroutput"><spanclass="identifier">support</code>这

+两个函数来测试。</p>

+在一个范围上分布 (实际上是随机变量)是得到 "支持的" 就是说<ahref="http://en.wikipedia.org/wiki/Probability_distribution";target="_top">"补集的概率为0的最小的封闭集合"</a>. MathWorld+对这个范围使用词语 '定义(defined)' 。非数学家( Non-mathematicians)可能会说它的含义是：随机变量 x+的'interesting'最小范围，使得函数cdf的值从零到单位元素(unity)。在这个范围之外是"uninteresting

+zones"，函数pdf 的值为0，且函数cdf的为0或单位元素(unity)。</p>

+对于大多数的分布，具有概率分布函数的分布可以描述为“ 运行良好的(well-behaved) ”， 如果端点是不连续的，我+们认为对支持的范围排除类似于刚好为0的值是很有帮助的。例如，随着随机变量x朝0递减，韦泊尔分布(Weibull+Distribution)(尺度参数为1，形状参数为1)顺利地(smoothly)向单位元素(unity)推进。但在x =+zero处，依照定义，函数pdf的值突然变为0。如果你在为pdf函数绘图(plot)，或计算pdf函数，对于支持的下限，0并不是最有用的值，就像+我们发现的那样。因此对于这个分布，以及类似的分布，我们决定将最接近0的值min_value作为支持的范围的下限在数值上是很有用的。(范围仍然是从+0开始，因此你仍会得到<code class="computeroutput"><spanclass="identifier">pdf(<spanclass="identifier">weibull, <spanclass="number">0) <spanclass="special">==

+<span class="number">0</span></code>)。(指数分布和γ分布
+也有类似的不连续函数)。</p>

+在数学上，对于(+ 或 -)无穷值这些函数是有意义的，但是除了一些特殊情况(在柯西分布和正态分布中)，这个库的实现将对于<code class="computeroutput"><spanclass="identifier">RealType</code>类+型的随机变量的值限定为从<code class="computeroutput"><spanclass="identifier">max</code> 到 <code class="computeroutput"><spanclass="identifier">min+的</code>有限值。 (参考<ahref="../../../backgrounders/implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">处

+理浮点类型无限值</a> 了解原理)。</p>
+<div class="note">
+<table summary="Note" border="0">
+<tbody>
+<tr>

+<td rowspan="2" align="middle" valign="top" width="25"><img style="width:24px; height: 24px;" alt="[Note]"src="../../../../../../../../../doc/html/images/note.png"></td>

+<th align="left">注意</th>
+</tr>
+<tr>
+<td align="left" valign="top">
+<p></p>
+<p><span class="bold"><strong>离散概率分布</strong></span>
+</p>

+注意<ahref="http://en.wikipedia.org/wiki/Discrete_probability_distribution";target="_top">离散概率分布(discrete distributions)</a>，包括二项分布

+(binomial distribution)， 负二项分布(negative binomial distribution)，
+泊松分布(Poisson distribution ) &amp; 伯努利分布(Bernoulli

+distribution)，都在数学上定义为离散函数( discrete functions)：也就是说函数<code class="computeroutput">cdf</code>

+和 <code class="computeroutput"><span class="identifier">pdf</span></code>
+只针对于整数的随机变量进行定义。</p>

+然而，因为计算方法经常使用连续函数，所以把它们当作“好像是”连续函数来对待会带来方便，并且允许它们的参数为非整数

+值。</p>

+用户想要确保一个严格的数学模型，可以在调用这个分布函数之前使用函数<codeclass="computeroutput">floor</code>

+或 <code class="computeroutput"><span class="identifier">ceil</span></code>
+。</p>
+<p>这些分布的分位点函数(quantile

+functions)在某种程度上很难一直满足所有人的需要而得到具体指定。缺省的行为是返回一个将结果向外舍入(outwards)整+数值：这就是说，下分位点(lower quantiles)－概率小于0.5是向下舍入，而对于上分位点(upper+quantile)－概率大于0.5是向上舍入。这种行为确保如果返回一个X%分位点值，那么至少标的覆盖范围将会在中心区域显示，不是要求的覆盖范围将

+会在尾部(tails)显示。</p>

+这种行为可以改变，使得分位点函数可以进行不同的舍入，或者甚至使用<atitle="Policy Overview" href="../../../policy/pol_overview.html">策+略</a>来返回一个实值(real-valued)。在你使用二项分布的分位点函数之前，强烈推荐你阅读<a title="Understanding Quantiles of Discrete Distributions"href="../../../policy/pol_tutorial/understand_dis_quant.html">理+解分布的分位点</a> 。<a title="Discrete Quantile Policies"href="../../../policy/pol_ref/discrete_quant_ref.html">参考文档</a>

+描述了如何为这些分布改变舍入策略。</p>
+<p>出于类似的原因，对于参数类似于“自由度(degree of

+freedom)”为整数的连续分布，参数被当作实数看待(如果需要的话，会从整数提升为浮点数)。然而在这种情况下，有少数的情况，非整数自由度

+(degree of freedom)的确有一个真实的含义( genuine meaning)。</p>
+</td>
+</tr>
+</tbody>
+</table>
+</div>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%">

+<tbody>
+<tr>
+<td align="left"></td>
+<td align="right">
+<div class="copyright-footer">Copyright © 2006 ,
+2007, 2008, 2009 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang
+Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg
+<p> Distributed under the Boost Software License, Version

+1.0. (See accompanying file LICENSE_1_0.txt or copy at <ahref="http://www.boost.org/LICENSE_1_0.txt";target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)

+</p>
+</div>
+</td>
+</tr>
+</tbody>
+</table>
+<hr>

+</div>
+</body></html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/headers.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,49 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+

+<title>Headers and Namespaces</title><link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../overview.html" title="Overview of Distributions">
+<link rel="prev" href="../overview.html" title="Overview of Distributions">

+<link rel="next" href="objects.html" title="Distributions areObjects"></head>+<body alink="#0000ff" bgcolor="white" link="#0000ff" text="black"vlink="#840084">

+<table cellpadding="2" width="100%"><tbody><tr>

+</tr></tbody></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="../overview.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../overview.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="objects.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">

+<a name="math_toolkit.dist.stat_tut.overview.headers"></a><a class="link"href="headers.html" title="Headers and Namespaces"> 头文件和名字空间</a>

+</h5></div></div></div>
+<p>这个库的所有代码都在boost::math名字空间中。</p>
+<p>为了使用一个分布<span class="emphasis"><em>my_distribution</em></span>

+，你需要包含头文件<boost/math/distributions/my_distribution.hpp>或"包含所有(include

+everything)"头文件：&lt;boost/math/distributions.hpp&gt;。</p>
+<p>例如，为了使用学生t分布(Students-t
+distribution)，包含头文件&lt;boost/math/distributions/students_t.hpp&gt; 或
+&lt;boost/math/distributions.hpp&gt;</p></div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tbody><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></tbody></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body></html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/objects.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,71 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+

+<title>Distributions are Objects</title><link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../overview.html" title="Overview of Distributions">
+<link rel="prev" href="headers.html" title="Headers and Namespaces">

+<link rel="next" href="generic.html" title="Generic operations common toall distributions are non-member functions"></head>+<body alink="#0000ff" bgcolor="white" link="#0000ff" text="black"vlink="#840084">

+<table cellpadding="2" width="100%"><tbody><tr>

+</tr></tbody></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="headers.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../overview.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="generic.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">

+<a name="math_toolkit.dist.stat_tut.overview.objects"></a><a class="link"href="objects.html" title="Distributions are Objects"> 分布都是对象</a>

+</h5></div></div></div>
+<p>每一种分布在这个库中都是一个类类型(class type)。</p>

+<a title="Policies" href="../../../policy.html">策略</a>提供了对这些类的行为的更好粒度(fine-grained)的控制，允许用户定制这些类的行为：例如，如何处理错误，

+离散分布的分位点(quantiles)如何工作(behave)。</p>
+<div class="tip">
+<table summary="Tip" border="0">
+<tbody>
+<tr>

+<td rowspan="2" align="middle" valign="top" width="25"><img style="width:25px; height: 24px;" alt="[Tip]"src="../../../../../../../../../doc/html/images/tip.png"></td>

+<th align="left">提示</th></tr>
+<tr>
+<td align="left" valign="top">

+如果你很熟悉使用函数而不是对象的统计类库，而且 '统计作为对象(Distributions as Objects)' 看起来很陌生，参考<a title="Comparison with C,R, FORTRAN-style Free Functions" href="../weg/nag_library.html">与其它统计类库的比较</a> 。</td></tr></tbody></table></div>

+<p>将统计作为类类型(class type)完成了两件事情：</p>
+<div class="itemizedlist">

+<ul type="disc"><li>它将统计类型封装在C++类型系统中;因此，例如，学生t分布(Students-t distributions)与χ方形分布(Chi-Squared

+distributions)永远都是不同的类型。

+</li><li>分布对象存储了与这个分布相关的任何参数：例如，学生t分布(Students-t distributions)有一个自由度参数(degree of+freedom)用于控制分布的形状。当构造学生t分布对象时必须提供自由度参数(<spanclass="emphasis">degrees of

+freedom</em></span> parameter) 。 </li></ul></div>

+虽然在这个库中的所有分布类都是模板，但提供了关于类型<spanclass="emphasis">double+的使用分布的常见名字的typedef (除了与一个具有相同名字的函数发生冲突：beta和 gamma，在这种情况下，使用缺省的模板参数- <codeclass="computeroutput">RealType <spanclass="special">= double -+</code>也差不多方便)。可能有95%的使用情况由这些typedefs覆盖。<pre class="programlisting">using <spanclass="keyword">namespace boost<spanclass="special">::math<spanclass="special">; // 使用自由度(degreeof freedom)为4来构造一个学生t分布(students_t distribution): <spanclass="identifier">students_t <spanclass="identifier">d1(<spanclass="number">4); <spanclass="comment">// 构造一个double精度的β分布(beta distribution) // 参数为 a = 10， b = 20 <spanclass="identifier">beta_distribution<spanclass="special"><> d2<spanclass="special">(10<spanclass="special">, 20<spanclass="special">); // 注意:_distribution<> 下标(suffix) ! </pre>+如果你想要使用一个不是double类型的分布对象，那么你可以直接实例化这个模板：模板的名字与double typedef是相同的，但是附加了一个+<code class="computeroutput"><spanclass="identifier">_distribution</code>+后缀，例如：<a title="Students t Distribution"href="../../dist_ref/dists/students_t_dist.html">Students tDistribution</a> 或 <a title="Binomial Distribution"href="../../dist_ref/dists/binomial_dist.html">BinomialDistribution</a>：<pre class="programlisting">//构造一个float类型的学生t分布(student t distribution)， //自由度数(degreeof freedom)为4 <spanclass="identifier">students_t_distribution<spanclass="special"><float<spanclass="special">> d3<spanclass="special">(4<spanclass="special">); // 构造一个longdouble类型的二项分布(binomial distribution)， <spanclass="comment">// 概率分数(probability of success)为 0.3 <spanclass="comment">// 总共20次试验: <spanclass="identifier">binomial_distribution<spanclass="special"><long <spanclass="keyword">double> <spanclass="identifier">d4(<spanclass="number">20, <spanclass="number">0.3);

+</pre>

+传递给这些分布的参数可以通过成员获取函数(getter member functions)来访问：<pre class="programlisting">d1<spanclass="special">.<spanclass="identifier">degrees_of_freedom<spanclass="special">(); // 返回 4.0 </pre>+这是很好的，但是到目前为止还不是很有用。我们经常想要做的是对这些分布计算累积分布函数(cumulative distributionfunctions+)和分位点(quantiles )等等。</div>+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tbody><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></tbody></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body></html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/parameters.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,51 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+

+<title>Parameters can be calculated</title><link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../overview.html" title="Overview of Distributions">

+<link rel="prev" href="complements.html" title="Complements are supportedtoo - and when to use them">

+<link rel="next" href="summary.html" title="Summary"></head>

+<body alink="#0000ff" bgcolor="white" link="#0000ff" text="black"vlink="#840084">

+<table cellpadding="2" width="100%"><tbody><tr>

+</tr></tbody></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="complements.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../overview.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="summary.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">

+<a name="math_toolkit.dist.stat_tut.overview.parameters"></a><aclass="link" href="parameters.html" title="Parameters can be calculated">

+          参数可以被计算</a>
+</h5></div></div></div>

+有时你需要查找定义这个分布的参数。假设，例如，你已经针对相等均值并且结果是边界(borderline)构造了一个学生t分布

+(Student's t

+Distribution)。或许你的两个样本彼此不同，或许它们不是彼此不同;基于计算的结果你并不能确定。一个合理的问题是“在我获得一个样本的区别+是真实的概率为X%时我需要进行多少次的测量？”参数查找可以回答这个问题，并且对于每个分布的回答都不同。它们作为分布的静态成员函数来实现。例如：<preclass="programlisting">students_t<spanclass="special">::<spanclass="identifier">find_degrees_of_freedom<spanclass="special">( 1.3<spanclass="special">, // 要检测的与真实均值的差值(difference from true mean to detect) <spanclass="number">0.05, <spanclass="comment">// 错误否决虚假设的最大风险值(maximum risk of falselyrejecting the null-hypothesis). <spanclass="number">0.1, <spanclass="comment">// 错误否决虚假设的最大风险值(maximum risk of falselyfailing to reject the null-hypothesis). <spanclass="number">0.13); <spanclass="comment">// 样本标准差(sample standard deviation) </pre>+获得在均值中观测到的差值没有下降到偶然的独立事件(chance alone)的概率为95%时所需要的自由度(degree of

+freedom)。在这种情况下，边界( borderline )学生t分布测试(Students-t

+test)结果已经在前面获得，这可以用来估算在观测的差值被认为是有效的之前，样本的大小应当变为多大。这需要假设，当然，

+样本均值与标准差对于样本大小是不变的。</p></div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tbody><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></tbody></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body></html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/overview/summary.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,50 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
+<html><head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+

+<title>Summary</title><link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../overview.html" title="Overview of Distributions">

+<link rel="prev" href="parameters.html" title="Parameters can becalculated">

+<link rel="next" href="../weg.html" title="Worked Examples"></head>

+<body alink="#0000ff" bgcolor="white" link="#0000ff" text="black"vlink="#840084">

+<table cellpadding="2" width="100%"><tbody><tr>

+</tr></tbody></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="parameters.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../overview.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="../weg.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">
+<a name="math_toolkit.dist.stat_tut.overview.summary"></a> 总结

+</h5></div></div></div><div class="itemizedlist"><ul type="disc"><li>分布都是对象，使用分布所需要的参数来构造。

+</li><li>成员函数允许你获得分布的参数。

+</li><li>通用的非成员函数提供对所有的分布都通用的属性的访问(PDF, CDF,quantile 等等).+</li><li>通过将函数的参数包装在对函数<code class="computeroutput"><spanclass="identifier">complement<spanclass="special">(...)</code>的调用中来计算概率的补集。+</li><li>接受概率作为参数的函数也可以接受概率的补集作为参数，通过将函数的参数包装在对函数<code class="computeroutput"><spanclass="identifier">complement<spanclass="special">(...)</code>的调用之中。

+
+</li><li>静态成员函数允许使用其它信息来查找分布的参数。 </li></ul></div>
+<p>现在你了解了所有的基本信息，下一部分查看一些可运行的例子。</p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tbody><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></tbody></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body></html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/dist/stat_tut/weg/c_sharp.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,58 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Using the Distributions from Within C#</title>

+<link rel="stylesheet"href="../../../../../../../../../doc/html/boostbook.css" type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../../../index.html" title="Math Toolkit">
+<link rel="up" href="../weg.html" title="Worked Examples">

+<link rel="prev" href="nag_library.html" title="Comparison with C, R,FORTRAN-style Free Functions">+<link rel="next" href="../variates.html" title="Random Variates andDistribution Parameters">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="nag_library.html"><imgsrc="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../weg.html"><imgsrc="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../../../index.html"><imgsrc="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="../variates.html"><imgsrc="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h5 class="title">

+<a name="math_toolkit.dist.stat_tut.weg.c_sharp"></a><a class="link"href="c_sharp.html" title="Using the Distributions from Within C#"> Usingthe

+          Distributions from Within C#</a>
+</h5></div></div></div>
+<p>

+ The distributions in this library can be used from the C#programming+ language when they are built using Microsofts Common LanguageRuntime

+            option.
+          </p>
+<p>

+ An example of this kind of usage is given in the <ahref="../../../../../../distexplorer/html/index.html"target="_top">distribution_explorer</a>+ example: see <codeclass="literal">boost-root/libs/math/dot_net_example</code>+ for the source code: the application consists of a C++ dllthat contains+ the actual distributions, and a C# GUI that allows you toexplore their

+            properties.
+          </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++ /trunk/libs/math/doc/sf_and_dist/html/math_toolkit/extern_c.html WedSep 9 20:09:56 2009

@@ -0,0 +1,51 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<title>TR1 and C99 external "C" Functions</title>

+<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">+<meta name="generator" content="DocBook XSL StylesheetsVsnapshot_2006-12-17_0120">

+<link rel="start" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">

+<link rel="prev" href="next_float/float_advance.html" title="Advancing aFloating Point Value by a Specific Representation Distance (ULP)float_advance">+<link rel="next" href="extern_c/tr1.html" title="C99 and TR1 C FunctionsOverview">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../../../index.html">Home</a></td>

+<td align="center"><ahref="../../../../../../../libs/libraries.htm">Libraries</a></td>+<td align="center"><ahref="http://www.boost.org/users/people.html";>People</a></td>+<td align="center"><ahref="http://www.boost.org/users/faq.html";>FAQ</a></td>+<td align="center"><ahref="../../../../../../../more/index.htm">More</a></td>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="next_float/float_advance.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../special.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="extern_c/tr1.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div>
+  <h3 class="title">

+<a name="math_toolkit.special.extern_c"></a><a href="extern_c.html"title='TR1 and C99 external "C" Functions'> TR1 和 C99 中的外部"C" 函数</a>

+</h3>
+</div></div></div>
+<div class="toc"><dl>

+<dt><a href="extern_c/tr1.html"> C99中TR1中的C函数概览</a></dt>+<dt><a href="extern_c/c99.html"> C99中的C函数</a></dt>+<dt><a href="extern_c/tr1_ref.html"> TR1中的C函数快速参考</a></dt>

+</dl></div>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+<td align="right"><div class="copyright-footer">Copyright ?2006 , 2007,2008 John Maddock, Paul A. Bristow, Hubert

+      Holin, Xiaogang Zhang and Bruno Lalande<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/main_overview/building.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,156 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>If and How to Build the Library and its Examples and Tests</title>

+<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../main_overview.html" title="Overview">
+<link rel="prev" href="perf_over.html" title="Performance">
+<link rel="next" href="history1.html" title="History and What's New">
+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../../../index.html">Home</a></td>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="perf_over.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../main_overview.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="history1.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">

+<a name="math_toolkit.main_overview.building"></a><a class="link"href="building.html" title="If and How to Build the Library and itsExamples and Tests"> If and How to Build

+      the Library and its Examples and Tests</a>
+</h3></div></div></div>
+<a name="math_toolkit.main_overview.building.building_the_library"></a><h5>
+<a name="id662842"></a>

+ <a class="link"href="building.html#math_toolkit.main_overview.building.building_the_library">Building

+        the Library</a>
+      </h5>
+<p>

+ The first thing you need to ask yourself is "Do I need to buildanything+ at all?" as the bulk of this library is header only: meaning youcan+ use it just by #including the necessary header(s). Refer to <aclass="link" href="../extern_c.html" title='TR1 and C99 external "C"Functions'>C99+ and C++ TR1 C-style Functions</a> for pros and cons of using theTR1 components

+        as opposed to the header only ones.
+      </p>
+<p>

+ The only time you <spanclass="emphasis">need to build+ the library is if you want to use the <codeclass="computeroutput">extern

+        <span class="string">"C"</span></code> functions declared in

+ <code class="computeroutput"><spanclass="special"><boost<spanclass="special">/math<spanclass="special">/tr1<spanclass="special">.hpp<spanclass="special">></code>. To build this using Boost.Build, from

+        a commandline boost-root directory issue a command like:
+      </p>

+</pre>
+<p>
+        will do the job on Linux, while:
+      </p>

+<pre class="programlisting">bjam <spanclass="identifier">toolset=<spanclass="identifier">msvc --<spanclass="identifier">with-<spanclass="identifier">math --<spanclass="identifier">build-<spanclass="identifier">type=<spanclass="identifier">complete stage

+</pre>
+<p>

+ will work better on Windows (leaving libraries built in sub-folder<code class="computeroutput">/<spanclass="identifier">stage</code>+ below your Boost root directory). Either way you should consultthe <ahref="http://www.boost.org/doc/libs/release/more/getting_started/index.html";target="_top">getting

+        started guide</a> for more information.
+      </p>
+<p>

+ You can also build the libraries from your favourite IDE orcommand line+ tool: each <code class="computeroutput"><spanclass="keyword">extern "C"</code>+ function declared in <code class="computeroutput"><spanclass="special"><boost<spanclass="special">/math<spanclass="special">/tr1<spanclass="special">.hpp<spanclass="special">></code> has its own source file with the same+ name in <code class="computeroutput"><spanclass="identifier">libs/<spanclass="identifier">math/<spanclass="identifier">src/<spanclass="identifier">tr1</code>. Just+ select the sources corresponding to the functions you are usingand build+ them into a library, or else add them directly to your project.Note that+ the directory <code class="computeroutput"><spanclass="identifier">libs/<spanclass="identifier">math/<spanclass="identifier">src/<spanclass="identifier">tr1</code> will+ need to be in your compiler's #include path as well as theboost-root directory+ (MSVC Tools, Options, Projects and Solutions, VC++ Directories,Include files).

+      </p>
+<div class="note"><table border="0" summary="Note">
+<tr>

+<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]"src="../../../../../../../doc/html/images/note.png"></td>

+<th align="left">Note</th>
+</tr>
+<tr><td align="left" valign="top"><p>

+ If you are using a Windows compiler that supports auto-linkingand you+ have built the sources yourself (or added them directly to yourproject)+ then you will need to prevent <code class="computeroutput"><spanclass="special"><boost<spanclass="special">/math<spanclass="special">/tr1<spanclass="special">.hpp<spanclass="special">></code>+ from trying to auto-link to the binaries that Boost.Buildgenerates. You+ can do this by defining either BOOST_MATH_NO_LIB orBOOST_ALL_NO_LIB at+ project level (so the defines get passed to each compilerinvocation).

+        </p></td></tr>
+</table></div>
+<p>

+ Optionally the sources in <code class="computeroutput"><spanclass="identifier">libs/<spanclass="identifier">math/<spanclass="identifier">src/<spanclass="identifier">tr1</code>+ have support for using <code class="computeroutput"><spanclass="identifier">libs/<spanclass="identifier">math/<spanclass="identifier">src/<spanclass="identifier">tr1/<spanclass="identifier">pch.<spanclass="identifier">hpp</code> as a precompiled header <spanclass="emphasis">if+ your compiler supports precompiled headers. Note thatnormally+ this header is a do-nothing include: to activate the header sothat it #includes+ everything required by all the sources you will need to defineBOOST_BUILD_PCH_ENABLED+ on the command line, both when building the pre-compiled headerand when+ building the sources. Boost.Build will do this automatically whenappropriate.

+      </p>

+<aname="math_toolkit.main_overview.building.building_the_examples"></a><h5>

+<a name="id663287"></a>

+ <a class="link"href="building.html#math_toolkit.main_overview.building.building_the_examples">Building

+        the Examples</a>
+      </h5>
+<p>

+ The examples are all located in <code class="computeroutput"><spanclass="identifier">libs/<spanclass="identifier">math/<spanclass="identifier">example</code>, they can all be built without+ reference to any external libraries, either with Boost.Build usingthe supplied+ Jamfile, or from your compiler's command line. The onlyrequirement is that

+        the Boost headers are in your compilers #include search path.
+      </p>
+<a name="math_toolkit.main_overview.building.building_the_tests"></a><h5>
+<a name="id663328"></a>

+ <a class="link"href="building.html#math_toolkit.main_overview.building.building_the_tests">Building

+        the Tests</a>
+      </h5>
+<p>

+ The tests are located in <code class="computeroutput"><spanclass="identifier">libs/<spanclass="identifier">math/<spanclass="identifier">test</code> and are best built using Boost.Build+ and the supplied Jamfile. If you plan to build them separatelyfrom your+ favourite IDE then you will need to add <codeclass="computeroutput">libs<spanclass="special">/math<spanclass="special">/test</code> to thelist of your compiler's search

+        paths.
+      </p>
+<p>

+ You will also need to build and link to the Boost.Regex libraryfor many+ of the tests: this can built from the command line by followingthe <ahref="http://www.boost.org/doc/libs/release/more/getting_started/index.html";target="_top">getting

+        started guide</a>, using a command such as:
+      </p>

+</pre>
+<p>
+        or
+      </p>

+<pre class="programlisting">bjam <spanclass="identifier">toolset=<spanclass="identifier">msvc --<spanclass="identifier">with-<spanclass="identifier">regex --<spanclass="identifier">build-<spanclass="identifier">type=<spanclass="identifier">complete stage

+</pre>
+<p>
+        depending on whether you are on Linux or Windows.
+      </p>
+<p>

+ Many of the tests have optional precompiled header support usingthe header+ <code class="computeroutput"><spanclass="identifier">libs/<spanclass="identifier">math/<spanclass="identifier">test/<spanclass="identifier">pch.<spanclass="identifier">hpp</code>. Note that normally this header is+ a do-nothing include: to activate the header so that it #includeseverything+ required by all the sources you will need to defineBOOST_BUILD_PCH_ENABLED+ on the command line, both when building the pre-compiled headerand when+ building the sources. Boost.Build will do this automatically whenappropriate.

+      </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/using_udt/use_mpfr.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,90 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">

+<title>Using With MPFR / GMP - a High-Precision Floating-PointLibrary</title>+<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../index.html" title="Math Toolkit">

+<link rel="up" href="../using_udt.html" title="Use with User-DefinedFloating-Point Types">+<link rel="prev" href="use_ntl.html" title="Using With NTL - aHigh-Precision Floating-Point Library">+<link rel="next" href="concepts.html" title="Conceptual Requirements forReal Number Types">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../../../index.html">Home</a></td>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="use_ntl.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../using_udt.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="concepts.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">

+<a name="math_toolkit.using_udt.use_mpfr"></a><a class="link"href="use_mpfr.html" title="Using With MPFR / GMP - a High-PrecisionFloating-Point Library"> Using With MPFR / GMP

+      - a High-Precision Floating-Point Library</a>
+</h3></div></div></div>
+<p>

+ The special functions and tools in this library can be used with<a href="http://www.mpfr.org"; target="_top">MPFR+ (an arbitrary precision number type based on the GMP library)</a>,via+ the bindings in <ahref="../../../../../../../boost/math/bindings/mpfr.hpp"target="_top">boost/math/bindings/mpfr.hpp</a>.

+      </p>
+<p>

+ In order to use these binings you will need to have installed <ahref="http://www.mpfr.org"; target="_top">MPFR</a>+ plus it's dependency the <a href="http://gmplib.org";target="_top">GMP library</a>+ and the C++ wrapper for MPFR known as <ahref="http://math.berkeley.edu/~wilken/code/gmpfrxx/"; target="_top">gmpfrxx

+        (or mpfr_class)</a>.
+      </p>
+<p>

+ Unfortunately <code class="computeroutput"><spanclass="identifier">mpfr_class</code>+ doesn't quite satisfy our conceptual requirements, so there is avery thin+ set of additional interfaces and some helper traits defined in <ahref="../../../../../../../boost/math/bindings/mpfr.hpp"target="_top">boost/math/bindings/mpfr.hpp</a>+ that you should use in place of including 'gmpfrxx.h' directly.The existing+ mpfr_class is then usable unchanged once this header is included,so it's+ performance-enhancing expression templates are preserved and fullysupported

+        by this library:
+      </p>

+<pre class="programlisting">#include<boost<spanclass="special">/math<spanclass="special">/bindings<spanclass="special">/mpfr<spanclass="special">.hpp<spanclass="special">>+#include <spanclass="special"><boost<spanclass="special">/math<spanclass="special">/<spanclass="identifier">special_functions<spanclass="special">/gamma<spanclass="special">.hpp<spanclass="special">>

+int main<spanclass="special">()

+<span class="special">{</span>

+ mpfr_class<spanclass="special">::set_dprec<spanclass="special">(500<spanclass="special">); // 500 bit precision

+</span>   <span class="comment">//

+ // Note that the argument to tgamma is anexpression template,

+</span>   <span class="comment">// that's just fine here:
+</span>   <span class="comment">//

+ mpfr_class <spanclass="identifier">v = <spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">tgamma(<spanclass="identifier">sqrt(<spanclass="identifier">mpfr_class(<spanclass="number">2)));+ std::<spanclass="identifier">cout << <spanclass="identifier">std::<spanclass="identifier">setprecision(<spanclass="number">50) <spanclass="special"><< v <spanclass="special"><< std<spanclass="special">::endl<spanclass="special">;

+<span class="special">}</span>
+</pre>
+<p>

+ For those functions that are based upon the <a class="link"href="../backgrounders/lanczos.html" title="The LanczosApproximation">Lanczos+ approximation</a>, the bindings defines a series of approximationswith+ up to 61 terms and accuracy up to approximately 3e-113. Thistherefore sets+ the upper limit for accuracy to the majority of functions definedthis library+ when used with <code class="computeroutput"><spanclass="identifier">mpfr_class</code>.

+      </p>
+<p>

+ There is a concept checking test program for mpfr support <ahref="../../../../../../../libs/math/test/mpfr_concept_check.cpp"target="_top">here</a>.

+      </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++ /trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/fpclass.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,221 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<title>Floating-Point Classification: Infinities and NaN's</title>

+<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">+<meta name="generator" content="DocBook XSL StylesheetsVsnapshot_2006-12-17_0120">

+<link rel="start" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">

+<link rel="prev" href="rounding/modf.html" title="Integer and FractionalPart Splitting (modf)">+<link rel="next" href="next_float.html" title="Floating-PointRepresentation Distance (ULP), and Finding Adjacent Floating-Point Values">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../../../index.html">Home</a></td>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="rounding/modf.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../special.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="next_float.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div>
+  <h3 class="title">

+<a name="math_toolkit.special.fpclass"></a><a href="fpclass.html"title="Floating-Point Classification: Infinities and NaN's"> 浮点数分类:

+      无限数和非数字(Infinities and NaN's)</a>
+</h3>
+</div></div></div>
+<a name="math_toolkit.special.fpclass.synopsis"></a>
+<h5>
+<a name="id740192"></a>

+ <a href="fpclass.html#math_toolkit.special.fpclass.synopsis">概要</a></h5>+<pre class="programlisting">#defineFP_ZERO /* 依据实现特定的值 */+#define <spanclass="identifier">FP_NORMAL /* 依据实现特定的值 */+#define <spanclass="identifier">FP_INFINITE /* 依据实现特定的值 */+#define <spanclass="identifier">FP_NAN /* 依据实现特定的值 */+#define <spanclass="identifier">FP_SUBNORMAL /* 依据实现特定的值 */

+template <spanclass="special"><class <spanclass="identifier">T>+bool <spanclass="identifier">isfinite(<spanclass="identifier">T z<spanclass="special">); // 既不是无限数又不是NaN(Not a Number : 不是一个数字).

+</span>

+</span>

+</span>

+
+包含头文件
+</span>

+#include <spanclass="special"><boost<spanclass="special">\math<spanclass="special">\<spanclass="identifier">special_functions<spanclass="special">\fpclassify<spanclass="special">.hpp<spanclass="special">>

+</pre>
+<p>
+        来使用这些函数</p>
+<a name="math_toolkit.special.fpclass.description"></a>
+<h5>
+<a name="id740726"></a>

+ <a href="fpclass.html#math_toolkit.special.fpclass.description">描述</a>

+  </h5>
+<p>

+ 这些函数与C99中的同名宏提供相同的功能,实际上,如果C99中的宏是可用的，那么这些函数就使用这些宏来实现。否则的话这些函数依赖于std::numeric_limits<>。

+<p>

+ 注意：在那些已经以宏的形式提供这些函数的平台上，这些函数的定义并没有覆盖(suppress:抑制)由头文件math.h以宏的形式定义的这些名字。这意味着下面的代码具有不同的含义:

+  </p>

+<pre class="programlisting">using <spanclass="keyword">namespace boost<spanclass="special">::math<spanclass="special">;

+
+<span class="comment">//如果定义了的话,那么下面的代码可能会调用一个全局宏

+//但是如果类型Z没有得到标准库中的的支持，那么下面的代码可能无法编译+isnan<spanclass="special">(z<spanclass="special">);

+<span class="comment">//
+</span><span class="comment">// 下面的代码调用Boost版本的isnan
+</span><span class="comment">// (通过"using namespace boost::math"来找到)

+// 对于任何具有numeric_limits支持的任何类型Z，Boost版本的isnan都可以正常工作:+(<spanclass="identifier">isnan)(<spanclass="identifier">z);

+<span class="comment">//
+</span><span class="comment">// 和上面一样，但是使用了名字空间限定.

+(<spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">isnan)(<spanclass="identifier">z);

+<span class="comment">//

+// 如果isnan是一个本地宏，那么下面的代码将会导致一个编译错误:+boost<spanclass="special">::math<spanclass="special">::isnan<spanclass="special">(z<spanclass="special">);

+<span class="comment">//所以请一直使用下面的形式:

+<span class="comment">//

+// 你也可以使用一个.cpp文件中使用一个全局的using声明,+// 也可以在一个.hpp文件中的函数中使用一个局部的using声明.+using <spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">isnan;

+<span class="comment">// 那么你的代码可以写得理简短也更整洁一些

+(<spanclass="identifier">isnan)(<spanclass="identifier">z)+// 但是与上面一样，如果 isnan 是一个本地宏,那么上面的代码会产生一个编译错误+// 因为宏永远最先获得这个名字, 除非包含在一对()里面。</pre>

+<p>
+        这些函数的详细描述如下:
+  </p>

+</pre>
+<p>
+        返回一个将<span class="emphasis"><em>t</em></span>的值分类的整数:
+  </p>
+<div class="informaltable"><table class="table">
+<colgroup>
+<col>
+<col>
+</colgroup>
+<thead><tr>
+<th>
+              <p>
+                fp 的分类值 </p>
+          </th>
+<th>
+              <p>
+                t的类别.
+             </p>
+          </th>
+</tr></thead>
+<tbody>
+<tr>
+<td>
+              <p>
+                FP_ZERO
+              </p>
+          </td>
+<td>
+              <p>
+                如果<span class="emphasis"><em> t</em></span> 的值为0.
+              </p>
+          </td>
+</tr>
+<tr>
+<td>
+              <p>
+                FP_NORMAL
+              </p>
+          </td>
+<td>
+              <p>

+ 如果 t 是非零的, 并且是规范化的有限值

+          </td>
+</tr>
+<tr>
+<td>
+              <p>
+                FP_INFINITE
+              </p>
+          </td>
+<td>
+              <p>

+ 如果 t 是正无穷或是负无穷

+          </td>
+</tr>
+<tr>
+<td>
+              <p>
+                FP_NAN
+              </p>
+          </td>
+<td>
+              <p>

+ 如果 t 是一个NaN(Not a Number)

+          </td>
+</tr>
+<tr>
+<td>
+              <p>
+                FP_SUBNORMAL
+              </p>
+          </td>
+<td>

+ 如果 <spanclass="emphasis">t 是一个非规范化的数字 

+          </td>
+</tr>
+</tbody>
+</table></div>

+</pre>
+<p>

+ 仅当z 的值不是无穷的且不是NaN是才返回true.

+  </p>

+</pre>
+<p>

+ 仅当z 的值是下无穷或是负无穷时才返回true.

+  </p>

+</pre>

+ 仅当 z 的值是<ahref="http://en.wikipedia.org/wiki/NaN"; target="_top">NaN</a> 才返回true.

+  </p>

+</pre>
+<p>

+ 仅当z 是一个常规的数字 (非零,

+        非无限, 非NaN, 或是规范化的)时才返回true.
+  </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+<td align="right"><div class="copyright-footer">Copyright ?2006 , 2007,2008 John Maddock, Paul A. Bristow, Hubert

+      Holin, Xiaogang Zhang and Bruno Lalande<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/next_float.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,69 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">

+<title>Floating-Point Representation Distance (ULP), and Finding AdjacentFloating-Point Values</title>+<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">+<meta name="generator" content="DocBook XSL StylesheetsVsnapshot_2006-12-17_0120">

+<link rel="start" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">

+<link rel="prev" href="fpclass.html" title="Floating-Point Classification:Infinities and NaN's">+<link rel="next" href="next_float/nextafter.html" title="Finding the NextRepresentable Value in a Specific Direction (nextafter)">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../../../index.html">Home</a></td>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="fpclass.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../special.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="next_float/nextafter.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div>
+  <h3 class="title">

+<a name="math_toolkit.special.next_float"></a><a href="next_float.html"title="Floating-Point Representation Distance (ULP), and Finding AdjacentFloating-Point Values"> 浮点表示距离 (ULP), 以及查找邻近的浮点值 </a>

+</h3>
+</div></div></div>
+<div class="toc"><dl>

+<dt><a href="next_float/nextafter.html"> 在一个特定的方向上查找下一个可以表示的浮点值 (nextafter)</a></dt>+<dt><a href="next_float/float_next.html"> 查找下一个查找的浮点值 (float_next)</a></dt>+<dt><a href="next_float/float_prior.html"> 查找下一个查找的浮点值 (float_prior)</a></dt>+<dt><a href="next_float/float_distance.html"> 计算两个浮点数之间的浮点距离 (ULP) </a></dt>+<dt><a href="next_float/float_advance.html"> 将一个浮点值增加一个特定的浮点距离 (ULP)</a></dt>

+</dl></div>
+<p>

+ <a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place";target="_top">最小精度单元或上一个位置单元</a> 是两个不同的，但是尽可能接近的浮点值的间隙

+<p>

+ 大多数的十进制值, 例如 0.1, 无法由浮点数精确的表示, 但是将会由最邻近的可表示的浮点值来存储.

+      </p>
+<p>

+ 这些函数用于查找邻近的较大的或较小的浮点值, 以及估算任意两个浮点数之间的间隔的个数.

+      </p>
+<p>
+        浮点类型FPT的表示中必须有固定的比特位数.

+ 具体的比特数个数可以在运行时设定, 但是比特的个数对于所有的浮点数必须是一样的.例如, <a href="http://shoup.net/ntl/doc/quad_float.txt";target="_top">NTL::quad_float</a>+ 类型 (固定的 128-bit 表示) 或者 <ahref="http://shoup.net/ntl/doc/RR.txt"; target="_top">NTL::RR</a>+ 类型 (任意的比特数但是具有固定的十进制数字, 缺省为 150) 但 <spanclass="bold">不是+ 一个为了精确的描述任意数字而扩展浮点表示的类型, 例如<ahref="http://keithbriggs.info/xrc.html"; target="_top">XRC

+        eXact Real in C</a>.
+      </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+<td align="right"><div class="copyright-footer">Copyright ?2006 , 2007,2008 John Maddock, Paul A. Bristow, Hubert

+      Holin, Xiaogang Zhang and Bruno Lalande<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++ /trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/rounding.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,51 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
+<title>Rounding Truncation and Integer Conversion</title>

+<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">+<meta name="generator" content="DocBook XSL StylesheetsVsnapshot_2006-12-17_0120">

+<link rel="start" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../special.html" title="Special Functions">
+<link rel="prev" href="inv_hyper/atanh.html" title="atanh">
+<link rel="next" href="rounding/round.html" title="Rounding Functions">
+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../../../index.html">Home</a></td>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="inv_hyper/atanh.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../special.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="rounding/round.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div>
+  <h3 class="title">

+<a name="math_toolkit.special.rounding"></a><a href="rounding.html"title="Rounding Truncation and Integer Conversion"> 舍入截断和整数转换 </a>

+</h3>
+</div></div></div>
+<div class="toc"><dl>

+<dt><a href="rounding/round.html"> 舍入函数</a></dt>+<dt><a href="rounding/trunc.html"> 截断函数</a></dt>+<dt><a href="rounding/modf.html"> 整数部分和小数部分切分 (modf函数)</a></dt>

+</dl></div>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+<td align="right"><div class="copyright-footer">Copyright ?2006 , 2007,2008 John Maddock, Paul A. Bristow, Hubert

+      Holin, Xiaogang Zhang and Bruno Lalande<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils/sign_functions.htmlWed Sep 9 20:09:56 2009

@@ -0,0 +1,98 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Sign Manipulation Functions</title>

+<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../../index.html" title="Math Toolkit">
+<link rel="up" href="../utils.html" title="Floating Point Utilities">

+<link rel="prev" href="fpclass.html" title="Floating-Point Classification:Infinities and NaN's">+<link rel="next" href="next_float.html" title="Floating-PointRepresentation Distance (ULP), and Finding Adjacent Floating-Point Values">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../../../index.html">Home</a></td>

+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="fpclass.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../utils.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="next_float.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">

+<a name="math_toolkit.utils.sign_functions"></a><a class="link"href="sign_functions.html" title="Sign Manipulation Functions"> SignManipulation

+      Functions</a>
+</h3></div></div></div>
+<a name="math_toolkit.utils.sign_functions.synopsis"></a><h5>
+<a name="id904917"></a>

+ <a class="link"href="sign_functions.html#math_toolkit.utils.sign_functions.synopsis">Synopsis</a>

+      </h5>
+<p>
+
+</p>

+</pre>
+<p>
+      </p>

+template <spanclass="special"><class <spanclass="identifier">T>+inline int <spanclass="identifier">sign (<spanclass="keyword">const T<spanclass="special">& z<spanclass="special">);

+template <spanclass="special"><class <spanclass="identifier">T>+inline Tcopysign <spanclass="special">(const <spanclass="identifier">T& <spanclass="identifier">x, <spanclass="keyword">const T<spanclass="special">& y<spanclass="special">);

+
+<span class="special">}}</span> <span class="comment">// namespaces
+</span></pre>
+<a name="math_toolkit.utils.sign_functions.description"></a><h5>
+<a name="id905211"></a>

+ <a class="link"href="sign_functions.html#math_toolkit.utils.sign_functions.description">Description</a>

+      </h5>

+</pre>
+<p>

+ Returns a non-zero value if the sign bit is set in variable <spanclass="emphasis">x,+ otherwise <code class="computeroutput"><spanclass="number">0</code>.

+      </p>

+<pre class="programlisting">template <spanclass="special"><class <spanclass="identifier">T>+inline int <spanclass="identifier">sign (<spanclass="keyword">const T<spanclass="special">& z<spanclass="special">);

+</pre>
+<p>

+ Returns <code class="computeroutput"><spanclass="number">1</code> if <code class="computeroutput"><spanclass="identifier">x+ > <spanclass="number">0</code>,+ <code class="computeroutput">-<spanclass="number">1</code>+ if <code class="computeroutput">x<+ 0</code>, and <codeclass="computeroutput">0</code>

+        if x is zero.
+      </p>

+<pre class="programlisting">template <spanclass="special"><class <spanclass="identifier">T>+inline Tcopysign <spanclass="special">(const <spanclass="identifier">T& <spanclass="identifier">x, <spanclass="keyword">const T<spanclass="special">& y<spanclass="special">);

+</pre>
+<p>

+ Sets the sign of x to bethe same as the sign of y.

+      </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++ /trunk/libs/math/doc/sf_and_dist/html/math_toolkit/utils.html Wed Sep9 20:09:56 2009

@@ -0,0 +1,75 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Floating Point Utilities</title>

+<link rel="stylesheet" href="../../../../../../doc/html/boostbook.css"type="text/css">

+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Math Toolkit">
+<link rel="up" href="../index.html" title="Math Toolkit">
+<link rel="prev" href="special/inv_hyper/atanh.html" title="atanh">

+<link rel="next" href="utils/rounding.html" title="Rounding Truncation andInteger Conversion">

+</head>

+<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

+<table cellpadding="2" width="100%"><tr>

+<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../boost.png"></td>

+<td align="center"><a href="../../../../../../index.html">Home</a></td>

+<td align="center"><ahref="../../../../../../libs/libraries.htm">Libraries</a></td>+<td align="center"><ahref="http://www.boost.org/users/people.html";>People</a></td>+<td align="center"><ahref="http://www.boost.org/users/faq.html";>FAQ</a></td>

+<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+<a accesskey="p" href="special/inv_hyper/atanh.html"><imgsrc="../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../index.html"><imgsrc="../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../index.html"><imgsrc="../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="utils/rounding.html"><imgsrc="../../../../../../doc/html/images/next.png" alt="Next"></a>

+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">

+<a name="math_toolkit.utils"></a><a class="link" href="utils.html"title="Floating Point Utilities"> Floating Point Utilities</a>

+</h2></div></div></div>
+<div class="toc"><dl>

+<dt><a href="utils/rounding.html"> RoundingTruncation and

+      Integer Conversion</a></span></dt>
+<dd><dl>

+<dt><a href="utils/rounding/round.html"> RoundingFunctions</a></dt>+<dt><a href="utils/rounding/trunc.html"> TruncationFunctions</a></dt>+<dt><a href="utils/rounding/modf.html"> Integer andFractional

+        Part Splitting (modf)</a></span></dt>
+</dl></dd>

+<dt><a href="utils/fpclass.html"> Floating-PointClassification:

+      Infinities and NaN's</a></span></dt>

+<dt><a href="utils/sign_functions.html"> SignManipulation

+      Functions</a></span></dt>

+<dt><a href="utils/next_float.html"> Floating-PointRepresentation+ Distance (ULP), and Finding Adjacent Floating-PointValues</a></dt>

+<dd><dl>

+<dt><a href="utils/next_float/nextafter.html">Finding the+ Next Representable Value in a Specific Direction(nextafter)</a></dt>+<dt><a href="utils/next_float/float_next.html">Finding

+        the Next Greater Representable Value (float_next)</a></span></dt>

+<dt><a href="utils/next_float/float_prior.html">Finding

+        the Next Smaller Representable Value (float_prior)</a></span></dt>

+<dt><a href="utils/next_float/float_distance.html">Calculating+ the Representation Distance Between Two Floating Point Values(ULP) float_distance</a></dt>+<dt><a href="utils/next_float/float_advance.html">Advancing+ a Floating Point Value by a Specific Representation Distance (ULP)float_advance</a></dt>

+</dl></dd>
+</dl></div>
+<p>
+    </p>
+</div>

+<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

+<td align="left"></td>

+      and Thijs van den Berg<p>

+      </p>
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">

+</div>
+</body>
+</html>
=======================================
--- /dev/null

+++ /trunk/libs/math/dot_net_example/distribution_explorer/boost.png WedSep 9 20:09:56 2009

Binary file, no diff available.
=======================================

---/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/extern_c.htmlSat Dec 6 05:06:05 2008

+++ /dev/null
@@ -1,51 +0,0 @@
-<html>
-<head>
-<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
-<title>TR1 and C99 external "C" Functions</title>

-<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">-<meta name="generator" content="DocBook XSL StylesheetsVsnapshot_2006-12-17_0120">

-<link rel="start" href="../../index.html" title="Math Toolkit">
-<link rel="up" href="../special.html" title="Special Functions">

-<link rel="prev" href="next_float/float_advance.html" title="Advancing aFloating Point Value by a Specific Representation Distance (ULP)float_advance">-<link rel="next" href="extern_c/tr1.html" title="C99 and TR1 C FunctionsOverview">

-</head>

-<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

-<table cellpadding="2" width="100%"><tr>

-<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

-<td align="center"><a href="../../../../../../../index.html">Home</a></td>

-<td align="center"><ahref="../../../../../../../libs/libraries.htm">Libraries</a></td>-<td align="center"><ahref="http://www.boost.org/users/people.html";>People</a></td>-<td align="center"><ahref="http://www.boost.org/users/faq.html";>FAQ</a></td>-<td align="center"><ahref="../../../../../../../more/index.htm">More</a></td>

-</tr></table>
-<hr>
-<div class="spirit-nav">

-<a accesskey="p" href="next_float/float_advance.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../special.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="extern_c/tr1.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

-</div>
-<div class="section" lang="en">
-<div class="titlepage"><div><div>
-  <h3 class="title">

-<a name="math_toolkit.special.extern_c"></a><a href="extern_c.html"title='TR1 and C99 external "C" Functions'> TR1 和 C99 中的外部"C" 函数</a>

-</h3>
-</div></div></div>
-<div class="toc"><dl>

-<dt><a href="extern_c/tr1.html"> C99中TR1中的C函数概览</a></dt>-<dt><a href="extern_c/c99.html"> C99中的C函数</a></dt>-<dt><a href="extern_c/tr1_ref.html"> TR1中的C函数快速参考</a></dt>

-</dl></div>
-</div>

-<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

-<td align="left"></td>

-<td align="right"><div class="copyright-footer">Copyright ?2006 , 2007,2008 John Maddock, Paul A. Bristow, Hubert

-      Holin, Xiaogang Zhang and Bruno Lalande<p>

- Distributed under the Boost Software License, Version 1.0. (Seeaccompanying- file LICENSE_1_0.txt or copy at <ahref="http://www.boost.org/LICENSE_1_0.txt";target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)

-      </p>
-</div></td>
-</tr></table>
-<hr>
-<div class="spirit-nav">

-</div>
-</body>
-</html>
=======================================

--- /trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/fpclass.htmlSat Dec 6 05:06:05 2008

+++ /dev/null
@@ -1,221 +0,0 @@
-<html>
-<head>
-<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
-<title>Floating-Point Classification: Infinities and NaN's</title>

-<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">-<meta name="generator" content="DocBook XSL StylesheetsVsnapshot_2006-12-17_0120">

-<link rel="start" href="../../index.html" title="Math Toolkit">
-<link rel="up" href="../special.html" title="Special Functions">

-<link rel="prev" href="rounding/modf.html" title="Integer and FractionalPart Splitting (modf)">-<link rel="next" href="next_float.html" title="Floating-PointRepresentation Distance (ULP), and Finding Adjacent Floating-Point Values">

-</head>

-<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

-<table cellpadding="2" width="100%"><tr>

-<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

-<td align="center"><a href="../../../../../../../index.html">Home</a></td>

-</tr></table>
-<hr>
-<div class="spirit-nav">

-<a accesskey="p" href="rounding/modf.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../special.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="next_float.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

-</div>
-<div class="section" lang="en">
-<div class="titlepage"><div><div>
-  <h3 class="title">

-<a name="math_toolkit.special.fpclass"></a><a href="fpclass.html"title="Floating-Point Classification: Infinities and NaN's"> 浮点数分类:

-      无限数和非数字(Infinities and NaN's)</a>
-</h3>
-</div></div></div>
-<a name="math_toolkit.special.fpclass.synopsis"></a>
-<h5>
-<a name="id740192"></a>

- <a href="fpclass.html#math_toolkit.special.fpclass.synopsis">概要</a></h5>-<pre class="programlisting">#defineFP_ZERO /* 依据实现特定的值 */-#define <spanclass="identifier">FP_NORMAL /* 依据实现特定的值 */-#define <spanclass="identifier">FP_INFINITE /* 依据实现特定的值 */-#define <spanclass="identifier">FP_NAN /* 依据实现特定的值 */-#define <spanclass="identifier">FP_SUBNORMAL /* 依据实现特定的值 */

-template <spanclass="special"><class <spanclass="identifier">T>-int <spanclass="identifier">fpclassify(<spanclass="identifier">T t<spanclass="special">);

-template <spanclass="special"><class <spanclass="identifier">T>-bool <spanclass="identifier">isfinite(<spanclass="identifier">T z<spanclass="special">); // 既不是无限数又不是NaN(Not a Number : 不是一个数字).

-</span>

-template <spanclass="special"><class <spanclass="identifier">T>-bool <spanclass="identifier">isinf(<spanclass="identifier">T t<spanclass="special">); // 无限数 (+ 或 -).

-</span>

-template <spanclass="special"><class <spanclass="identifier">T>-bool <spanclass="identifier">isnan(<spanclass="identifier">T t<spanclass="special">); // NaN.

-</span>

-template <spanclass="special"><class <spanclass="identifier">T>-bool <spanclass="identifier">isnormal(<spanclass="identifier">T t<spanclass="special">); // 有限的并且是规格化的.

-
-包含头文件
-</span>

-#include <spanclass="special"><boost<spanclass="special">\math<spanclass="special">\<spanclass="identifier">special_functions<spanclass="special">\fpclassify<spanclass="special">.hpp<spanclass="special">>

-</pre>
-<p>
-        来使用这些函数</p>
-<a name="math_toolkit.special.fpclass.description"></a>
-<h5>
-<a name="id740726"></a>

- <a href="fpclass.html#math_toolkit.special.fpclass.description">描述</a>

-  </h5>
-<p>

- 这些函数与C99中的同名宏提供相同的功能,实际上,如果C99中的宏是可用的，那么这些函数就使用这些宏来实现。否则的话这些函数依赖于std::numeric_limits<>。

-<p>

- 注意：在那些已经以宏的形式提供这些函数的平台上，这些函数的定义并没有覆盖(suppress:抑制)由头文件math.h以宏的形式定义的这些名字。这意味着下面的代码具有不同的含义:

-  </p>

-<pre class="programlisting">using <spanclass="keyword">namespace boost<spanclass="special">::math<spanclass="special">;

-
-<span class="comment">//如果定义了的话,那么下面的代码可能会调用一个全局宏

-//但是如果类型Z没有得到标准库中的的支持，那么下面的代码可能无法编译-isnan<spanclass="special">(z<spanclass="special">);

-<span class="comment">//
-</span><span class="comment">// 下面的代码调用Boost版本的isnan
-</span><span class="comment">// (通过"using namespace boost::math"来找到)

-// 对于任何具有numeric_limits支持的任何类型Z，Boost版本的isnan都可以正常工作:-(<spanclass="identifier">isnan)(<spanclass="identifier">z);

-<span class="comment">//
-</span><span class="comment">// 和上面一样，但是使用了名字空间限定.

-(<spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">isnan)(<spanclass="identifier">z);

-<span class="comment">//

-// 如果isnan是一个本地宏，那么下面的代码将会导致一个编译错误:-boost<spanclass="special">::math<spanclass="special">::isnan<spanclass="special">(z<spanclass="special">);

-<span class="comment">//所以请一直使用下面的形式:

-<span class="comment">//

-// 你也可以使用一个.cpp文件中使用一个全局的using声明,-// 也可以在一个.hpp文件中的函数中使用一个局部的using声明.-using <spanclass="identifier">boost::<spanclass="identifier">math::<spanclass="identifier">isnan;

-<span class="comment">// 那么你的代码可以写得理简短也更整洁一些

-(<spanclass="identifier">isnan)(<spanclass="identifier">z)-// 但是与上面一样，如果 isnan 是一个本地宏,那么上面的代码会产生一个编译错误-// 因为宏永远最先获得这个名字, 除非包含在一对()里面。</pre>

-<p>
-        这些函数的详细描述如下:
-  </p>

-<pre class="programlisting">template <spanclass="special"><class <spanclass="identifier">T>-int <spanclass="identifier">fpclassify(<spanclass="identifier">T t<spanclass="special">);

-</pre>
-<p>
-        返回一个将<span class="emphasis"><em>t</em></span>的值分类的整数:
-  </p>
-<div class="informaltable"><table class="table">
-<colgroup>
-<col>
-<col>
-</colgroup>
-<thead><tr>
-<th>
-              <p>
-                fp 的分类值 </p>
-          </th>
-<th>
-              <p>
-                t的类别.
-             </p>
-          </th>
-</tr></thead>
-<tbody>
-<tr>
-<td>
-              <p>
-                FP_ZERO
-              </p>
-          </td>
-<td>
-              <p>
-                如果<span class="emphasis"><em> t</em></span> 的值为0.
-              </p>
-          </td>
-</tr>
-<tr>
-<td>
-              <p>
-                FP_NORMAL
-              </p>
-          </td>
-<td>
-              <p>

- 如果 t 是非零的, 并且是规范化的有限值

-          </td>
-</tr>
-<tr>
-<td>
-              <p>
-                FP_INFINITE
-              </p>
-          </td>
-<td>
-              <p>

- 如果 t 是正无穷或是负无穷

-          </td>
-</tr>
-<tr>
-<td>
-              <p>
-                FP_NAN
-              </p>
-          </td>
-<td>
-              <p>

- 如果 t 是一个NaN(Not a Number)

-          </td>
-</tr>
-<tr>
-<td>
-              <p>
-                FP_SUBNORMAL
-              </p>
-          </td>
-<td>

- 如果 <spanclass="emphasis">t 是一个非规范化的数字 

-          </td>
-</tr>
-</tbody>
-</table></div>

-<pre class="programlisting">template <spanclass="special"><class <spanclass="identifier">T>-bool <spanclass="identifier">isfinite(<spanclass="identifier">T z<spanclass="special">);

-</pre>
-<p>

- 仅当z 的值不是无穷的且不是NaN是才返回true.

-  </p>

-<pre class="programlisting">template <spanclass="special"><class <spanclass="identifier">T>-bool <spanclass="identifier">isinf(<spanclass="identifier">T t<spanclass="special">);

-</pre>
-<p>

- 仅当z 的值是下无穷或是负无穷时才返回true.

-  </p>

-<pre class="programlisting">template <spanclass="special"><class <spanclass="identifier">T>-bool <spanclass="identifier">isnan(<spanclass="identifier">T t<spanclass="special">);

-</pre>

- 仅当 z 的值是<ahref="http://en.wikipedia.org/wiki/NaN"; target="_top">NaN</a> 才返回true.

-  </p>

-<pre class="programlisting">template <spanclass="special"><class <spanclass="identifier">T>-bool <spanclass="identifier">isnormal(<spanclass="identifier">T t<spanclass="special">);

-</pre>
-<p>

- 仅当z 是一个常规的数字 (非零,

-        非无限, 非NaN, 或是规范化的)时才返回true.
-  </p>
-</div>

-<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

-<td align="left"></td>

-<td align="right"><div class="copyright-footer">Copyright ?2006 , 2007,2008 John Maddock, Paul A. Bristow, Hubert

-      Holin, Xiaogang Zhang and Bruno Lalande<p>

-      </p>
-</div></td>
-</tr></table>
-<hr>
-<div class="spirit-nav">

-</div>
-</body>
-</html>
=======================================

---/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/next_float.htmlSat Dec 6 05:06:05 2008

+++ /dev/null
@@ -1,69 +0,0 @@
-<html>
-<head>
-<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">

-<title>Floating-Point Representation Distance (ULP), and Finding AdjacentFloating-Point Values</title>-<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css"type="text/css">-<meta name="generator" content="DocBook XSL StylesheetsVsnapshot_2006-12-17_0120">

-<link rel="start" href="../../index.html" title="Math Toolkit">
-<link rel="up" href="../special.html" title="Special Functions">

-<link rel="prev" href="fpclass.html" title="Floating-Point Classification:Infinities and NaN's">-<link rel="next" href="next_float/nextafter.html" title="Finding the NextRepresentable Value in a Specific Direction (nextafter)">

-</head>

-<body bgcolor="white" text="black" link="#0000FF" vlink="#840084"alink="#0000FF">

-<table cellpadding="2" width="100%"><tr>

-<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86"src="../../../../../../../boost.png"></td>

-<td align="center"><a href="../../../../../../../index.html">Home</a></td>

-</tr></table>
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-<a accesskey="p" href="fpclass.html"><imgsrc="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><aaccesskey="u" href="../special.html"><imgsrc="../../../../../../../doc/html/images/up.png" alt="Up"></a><aaccesskey="h" href="../../index.html"><imgsrc="../../../../../../../doc/html/images/home.png" alt="Home"></a><aaccesskey="n" href="next_float/nextafter.html"><imgsrc="../../../../../../../doc/html/images/next.png" alt="Next"></a>

-</div>
-<div class="section" lang="en">
-<div class="titlepage"><div><div>
-  <h3 class="title">

-<a name="math_toolkit.special.next_float"></a><a href="next_float.html"title="Floating-Point Representation Distance (ULP), and Finding AdjacentFloating-Point Values"> 浮点表示距离 (ULP), 以及查找邻近的浮点值 </a>

-</h3>
-</div></div></div>
-<div class="toc"><dl>

-<dt><a href="next_float/nextafter.html"> 在一个特定的方向上查找下一个可以表示的浮点值 (nextafter)</a></dt>-<dt><a href="next_float/float_next.html"> 查找下一个查找的浮点值 (float_next)</a></dt>-<dt><a href="next_float/float_prior.html"> 查找下一个查找的浮点值 (float_prior)</a></dt>-<dt><a href="next_float/float_distance.html"> 计算两个浮点数之间的浮点距离 (ULP) </a></dt>-<dt><a href="next_float/float_advance.html"> 将一个浮点值增加一个特定的浮点距离 (ULP)</a></dt>

-</dl></div>
-<p>

- <a href="http://en.wikipedia.org/wiki/Unit_in_the_last_place";target="_top">最小精度单元或上一个位置单元</a> 是两个不同的，但是尽可能接近的浮点值的间隙

-<p>

- 大多数的十进制值, 例如 0.1, 无法由浮点数精确的表示, 但是将会由最邻近的可表示的浮点值来存储.

-      </p>
-<p>

- 这些函数用于查找邻近的较大的或较小的浮点值, 以及估算任意两个浮点数之间的间隔的个数.

-      </p>
-<p>
-        浮点类型FPT的表示中必须有固定的比特位数.

- 具体的比特数个数可以在运行时设定, 但是比特的个数对于所有的浮点数必须是一样的.例如, <a href="http://shoup.net/ntl/doc/quad_float.txt";target="_top">NTL::quad_float</a>- 类型 (固定的 128-bit 表示) 或者 <ahref="http://shoup.net/ntl/doc/RR.txt"; target="_top">NTL::RR</a>- 类型 (任意的比特数但是具有固定的十进制数字, 缺省为 150) 但 <spanclass="bold">不是- 一个为了精确的描述任意数字而扩展浮点表示的类型, 例如<ahref="http://keithbriggs.info/xrc.html"; target="_top">XRC

-        eXact Real in C</a>.
-      </p>
-</div>

-<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

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-<td align="right"><div class="copyright-footer">Copyright ?2006 , 2007,2008 John Maddock, Paul A. Bristow, Hubert

-      Holin, Xiaogang Zhang and Bruno Lalande<p>

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---/trunk/libs/math/doc/sf_and_dist/html/math_toolkit/special/rounding.htmlSat Dec 6 05:06:05 2008

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-  <h3 class="title">

-<a name="math_toolkit.special.rounding"></a><a href="rounding.html"title="Rounding Truncation and Integer Conversion"> 舍入截断和整数转换 </a>

-</h3>
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-<div class="toc"><dl>

-<dt><a href="rounding/round.html"> 舍入函数</a></dt>-<dt><a href="rounding/trunc.html"> 截断函数</a></dt>-<dt><a href="rounding/modf.html"> 整数部分和小数部分切分 (modf函数)</a></dt>

-</dl></div>
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-<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision";width="100%"><tr>

-<td align="left"></td>

-<td align="right"><div class="copyright-footer">Copyright ?2006 , 2007,2008 John Maddock, Paul A. Bristow, Hubert

-      Holin, Xiaogang Zhang and Bruno Lalande<p>

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--- /trunk/libs/math/doc/sf_and_dist/graphs/acosh.png Thu Sep 4 22:46:362008+++ /trunk/libs/math/doc/sf_and_dist/graphs/acosh.png Wed Sep 9 20:09:562009

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[boost-doc-zh] r325 committed - 转换至1.40.0，第8批，完成以下库：...

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