Boost-Commit :

Date view	Thread view	Subject view	Author view

Subject: [Boost-commit] svn:boost r50647 - in sandbox/mp_math: boost/mp_math/mp_int libs/mp_math/doc libs/mp_math/doc/html libs/mp_math/doc/html/mp_int libs/mp_math/doc/html/mp_int_ libs/mp_math/test
From: baraclese_at_[hidden]
Date: 2009-01-16 18:53:23

Next message: baraclese_at_[hidden]: "[Boost-commit] svn:boost r50648 - in sandbox/mp_math/libs/mp_math/doc: . html html/mp_int"
Previous message: fmhess_at_[hidden]: "[Boost-commit] svn:boost r50646 - sandbox/thread_safe_signals/trunk/libs/signals2/doc"

Author: baraclese
Date: 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
New Revision: 50647
URL: http://svn.boost.org/trac/boost/changeset/50647

Log:
Updated documentation.

Added:
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/bibliography.html (contents, props changed)
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/implementation_notes.html (contents, props changed)
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/mp_int_reference.html (contents, props changed)
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/mp_int_traits_reference.html (contents, props changed)
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/performance.html (contents, props changed)
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/primality_tests_reference.html (contents, props changed)
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/tutorial.html (contents, props changed)
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/uniform_mp_int_bits_reference.html (contents, props changed)
   sandbox/mp_math/libs/mp_math/doc/html/mp_int/uniform_mp_int_reference.html (contents, props changed)
Removed:
   sandbox/mp_math/libs/mp_math/doc/html/mp_int_/
Text files modified:
   sandbox/mp_math/boost/mp_math/mp_int/operators.hpp | 34 +-
   sandbox/mp_math/libs/mp_math/doc/html/index.html | 74 +++---
   sandbox/mp_math/libs/mp_math/doc/mp_int.qbk | 6
   sandbox/mp_math/libs/mp_math/doc/mp_int_reference.qbk | 397 ++++++++++++++++-----------------------
   sandbox/mp_math/libs/mp_math/doc/primality_tests_reference.qbk | 4
   sandbox/mp_math/libs/mp_math/test/integral_ops.cpp | 7
   6 files changed, 233 insertions(+), 289 deletions(-)

Modified: sandbox/mp_math/boost/mp_math/mp_int/operators.hpp
==============================================================================
--- sandbox/mp_math/boost/mp_math/mp_int/operators.hpp (original)
+++ sandbox/mp_math/boost/mp_math/mp_int/operators.hpp 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -1,4 +1,4 @@
-// Copyright Kevin Sopp 2008.
+// Copyright Kevin Sopp 2008 - 2009.
// Distributed under the Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)
@@ -32,7 +32,7 @@
 return true;
 if (lhs.size() > rhs.size())
 return false;
-
+
 if (lhs.is_negative())
 return std::lexicographical_compare(
 rhs.rbegin(), rhs.rend(), lhs.rbegin(), lhs.rend());
@@ -136,7 +136,7 @@
inline bool
operator >= (const mp_int<A,T>& lhs, const charT* rhs) { return lhs >= mp_int<A,T>(rhs); }

-// compare const char* to mp_int
+// compare const charT* to mp_int
template<class A, class T, typename charT>
inline bool
operator == (const charT* lhs, const mp_int<A,T>& rhs) { return mp_int<A,T>(lhs) == rhs; }
@@ -260,7 +260,7 @@

 /* shift any bit count < valid_bits */
 const digit_type d = static_cast<digit_type>(b % valid_bits);
-
+
 if (d)
 {
 /* bitmask for carries */
@@ -281,7 +281,7 @@
 /* set the carry to the carry bits of the current word */
 carry = carry_cur;
 }
-
+
 if (carry)
 push(carry);
 }
@@ -368,16 +368,16 @@
 {
 grow_capacity(rhs.size_);
 // result has opposite sign from *this
- set_sign(is_positive() ? -1 : 1);
+ set_sign(is_positive() ? -1 : 1);
 x = &rhs;
 y = this;
 }
-
+
 ops_type::sub_smaller_magnitude(digits_, x->digits_, x->size_,
 y->digits_, y->size_);

 size_ = x->size_;
-
+
 clamp();

 if (!*this)
@@ -394,7 +394,7 @@
 sqr();
 return *this;
 }
-
+
 const int neg = (sign() == rhs.sign()) ? 1 : -1;
 const size_type min = std::min(size_, rhs.size_);

@@ -406,7 +406,7 @@
 {
 mp_int tmp;
 tmp.grow_capacity(size_ + rhs.size_);
-
+
 if (size_ == rhs.size_)
 ops_type::comba_mul(tmp.digits(), digits(), rhs.digits(), size_);
 else
@@ -466,13 +466,13 @@
 px = size_;
 x = this;
 }
-
+
 for (size_type i = 0; i < px; ++i)
 tmp[i] |= (*x)[i];
-
+
 tmp.clamp();
 swap(tmp);
-
+
 return *this;
}

@@ -498,12 +498,12 @@

 for (size_type i = 0; i < px; ++i)
 tmp[i] &= (*x)[i];
-
+
 /* zero digits above the last from the smallest mp_int */
 std::memset(tmp.digits_ + px, 0, (tmp.size_ - px) * sizeof(digit_type));
 tmp.clamp();
 swap(tmp);
-
+
 return *this;
}

@@ -529,10 +529,10 @@

 for (size_type i = 0; i < px; ++i)
 tmp[i] ^= (*x)[i];
-
+
 tmp.clamp();
 swap(tmp);
-
+
 return *this;
}

Modified: sandbox/mp_math/libs/mp_math/doc/html/index.html
==============================================================================
--- sandbox/mp_math/libs/mp_math/doc/html/index.html (original)
+++ sandbox/mp_math/libs/mp_math/doc/html/index.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -3,9 +3,9 @@
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<title>Chapter 1. mp_int</title>
<link rel="stylesheet" href="boostbook.css" type="text/css">
-<meta name="generator" content="DocBook XSL Stylesheets V1.73.2">
-<link rel="start" href="index.html" title="Chapter 1. mp_int">
-<link rel="next" href="mp_int_/tutorial.html" title="Tutorial">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="index.html" title="Chapter 1. mp_int">
+<link rel="next" href="mp_int/tutorial.html" title="Tutorial">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
@@ -17,62 +17,64 @@
<td align="center">More</td>
</tr></table>
<hr>
-<div class="spirit-nav"><a accesskey="n" href="mp_int_/tutorial.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a></div>
+<div class="spirit-nav"><a accesskey="n" href="mp_int/tutorial.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a></div>
<div class="chapter" lang="en">
<div class="titlepage"><div>
<div><h2 class="title">
-<a name="mp_int"></a>Chapter 1. mp_int </h2></div>
+<a name="mp_int"></a>Chapter 1. mp_int</h2></div>
<div><div class="author"><h3 class="author">
Kevin Sopp
</h3></div></div>
-<div>Copyright © 2008 Kevin Sopp</div>
+<div>Copyright © 2008 - 2009 Kevin Sopp</div>
<div><div class="legalnotice">
-<a name="id2693145"></a>
- All code and documentation is in the public domain
+<a name="id3102140"></a>
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
 
</div></div>
</div></div>
<div class="toc">
Table of Contents
<dl>
-<dt>Introduction</dt>
-<dt>Tutorial</dt>
+<dt>Introduction</dt>
+<dt>Tutorial</dt>
<dd><dl>
-<dt>General use</dt>
-<dt><a href="mp_int_/tutorial.html#mp_int_.tutorial.random_number_generation">Random number
+<dt>General use</dt>
+<dt><a href="mp_int/tutorial.html#mp_int.tutorial.random_number_generation">Random number
 generation</a></dt>
-<dt>Primality testing</dt>
-<dt><a href="mp_int_/tutorial.html#mp_int_.tutorial.prime_number_generation">Prime number
+<dt>Primality testing</dt>
+<dt><a href="mp_int/tutorial.html#mp_int.tutorial.prime_number_generation">Prime number
 generation</a></dt>
</dl></dd>
-<dt>Performance</dt>
+<dt>Performance</dt>
<dd><dl>
-<dt>Tips</dt>
-<dt>Measurements</dt>
+<dt>Tips</dt>
+<dt>Measurements</dt>
</dl></dd>
-<dt>Implementation notes</dt>
+<dt>Implementation notes</dt>
<dd><dl>
-<dt><a href="mp_int_/implementation_notes.html#mp_int_.implementation_notes.mp_int_structure">mp_int
+<dt><a href="mp_int/implementation_notes.html#mp_int.implementation_notes.mp_int_structure">mp_int
 structure</a></dt>
-<dt>Semantics</dt>
+<dt>Semantics</dt>
</dl></dd>
-<dt>mp_int reference</dt>
-<dt>mp_int_traits reference</dt>
-<dt>uniform_mp_int reference</dt>
-<dt><a href="mp_int_/uniform_mp_int_bits_reference.html">uniform_mp_int_bits
+<dt>mp_int reference</dt>
+<dt>mp_int_traits reference</dt>
+<dt>uniform_mp_int reference</dt>
+<dt><a href="mp_int/uniform_mp_int_bits_reference.html">uniform_mp_int_bits
 reference</a></dt>
-<dt>Primality Tests reference</dt>
+<dt>Primality Tests reference</dt>
<dd><dl>
-<dt>primality_division_test</dt>
-<dt>primality_fermat_test</dt>
-<dt>primality_miller_rabin_test</dt>
+<dt>primality_division_test</dt>
+<dt>primality_fermat_test</dt>
+<dt>primality_miller_rabin_test</dt>
</dl></dd>
-<dt>Bibliography</dt>
+<dt>Bibliography</dt>
</dl>
</div>
<div class="section" lang="en">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
-<a name="mp_int_.introduction"></a><a class="link" href="index.html#mp_int_.introduction" title="Introduction">Introduction</a>
+<a name="mp_int.introduction"></a><a class="link" href="index.html#mp_int.introduction" title="Introduction">Introduction</a>
</h2></div></div></div>

 This library provides the <code class="computeroutput">mp_int</code>
@@ -81,9 +83,9 @@
 for the implementation of public key cryptography such as prime generation
 are provided.
 
-<a name="mp_int_.introduction.acknowledgement"></a><h4>
-<a name="id2733685"></a>
- <a class="link" href="index.html#mp_int_.introduction.acknowledgement">Acknowledgement</a>
+<a name="mp_int.introduction.acknowledgement"></a><h4>
+<a name="id3141691"></a>
+ <a class="link" href="index.html#mp_int.introduction.acknowledgement">Acknowledgement</a>
 </h4>

 This library originally started as a port of the C code of libtommath. Without
@@ -96,14 +98,12 @@
 domain as well.
 
</div>
-
- 
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
-<td align="left">Last revised: October 06, 2008 at 11:40:14 GMT</td>
+<td align="left">Last revised: January 16, 2009 at 23:54:32 GMT</td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>
-<div class="spirit-nav"><a accesskey="n" href="mp_int_/tutorial.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a></div>
+<div class="spirit-nav"><a accesskey="n" href="mp_int/tutorial.html"><img src="../../../../doc/html/images/next.png" alt="Next"></a></div>
</body>
</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/bibliography.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/bibliography.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,73 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Bibliography</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="primality_tests_reference.html" title="Primality Tests reference">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="primality_tests_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h2 class="title" style="clear: both">
+<a name="mp_int.bibliography"></a><a class="link" href="bibliography.html" title="Bibliography">Bibliography</a>
+</h2></div></div></div>
+<a name="mp_int.bibliography.gmp__gnu_multiple_precision_arithmetic_library_"></a><h4>
+<a name="id3197812"></a>
+ <a class="link" href="bibliography.html#mp_int.bibliography.gmp__gnu_multiple_precision_arithmetic_library_">GMP
+ (GNU Multiple Precision Arithmetic Library)</a>
+ </h4>
+<div class="itemizedlist"><ul type="disc"><li>http://gmplib.org/</li></ul></div>
+<a name="mp_int.bibliography.handbook_of_applied_cryptogtaphy"></a><h4>
+<a name="id3197847"></a>
+ <a class="link" href="bibliography.html#mp_int.bibliography.handbook_of_applied_cryptogtaphy">Handbook
+ of Applied Cryptogtaphy</a>
+ </h4>
+<div class="itemizedlist"><ul type="disc"><li>http://www.cacr.math.uwaterloo.ca/hac/</li></ul></div>
+<a name="mp_int.bibliography.libtommath"></a><h4>
+<a name="id3197881"></a>
+ <a class="link" href="bibliography.html#mp_int.bibliography.libtommath">libtommath</a>
+ </h4>
+<div class="itemizedlist"><ul type="disc">
+<li>
+http://libtom.org/<code class="computeroutput">// this link seems to be down lately (10/26/2008)</code>
+</li>
+<li>
+http://math.libtomcrypt.com/<code class="computeroutput">// this works but is out of date</code>
+</li>
+</ul></div>
+<a name="mp_int.bibliography.miller_rabin_primality_test"></a><h4>
+<a name="id3197947"></a>
+ <a class="link" href="bibliography.html#mp_int.bibliography.miller_rabin_primality_test">Miller-Rabin
+ Primality Test</a>
+ </h4>
+<div class="itemizedlist"><ul type="disc"><li>http://www.bitnuts.de/rienhardt/docs/miller_rabin.pdf</li></ul></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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="primality_tests_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a>
+</div>
+</body>
+</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/implementation_notes.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/implementation_notes.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,100 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Implementation notes</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="performance.html" title="Performance">
+<link rel="next" href="mp_int_reference.html" title="mp_int reference">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="performance.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mp_int_reference.html"><img src="../../../../../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="mp_int.implementation_notes"></a><a class="link" href="implementation_notes.html" title="Implementation notes">Implementation notes</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt><a href="implementation_notes.html#mp_int.implementation_notes.mp_int_structure">mp_int
+ structure</a></dt>
+<dt>Semantics</dt>
+</dl></div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.implementation_notes.mp_int_structure"></a><a class="link" href="implementation_notes.html#mp_int.implementation_notes.mp_int_structure" title="mp_int structure">mp_int
+ structure</a>
+</h3></div></div></div>
+
+ An <code class="computeroutput">mp_int</code> is handled in a
+ sign plus magnitude representation which looks like this:
+ 
+<pre class="programlisting">struct mp_int
+{
+ digit_type* digits_;
+ size_type used_, capacity_;
+ int sign_;
+};
+</pre>
+
+ The least significant digit of the number always lives at <code class="computeroutput">digits_[0]</code>
+ while the most significant lives at <code class="computeroutput">digits_[used_ - 1]</code>.
+ 
+
+ Libtommath on which this code is ultimately based chose a <code class="computeroutput">digit_type</code>
+ representation which does not use all of its bits, instead some bits are
+ reserved to hold carries in intermediate results. This allows very fast multiplication
+ routines. I chose a different representation which uses all the bits in the
+ <code class="computeroutput">digit_type</code> but needs explicit
+ carry handling in the code. This makes normal c++ code a tad slower. However
+ it makes it much easier to write assembler routines since most CPUs provide
+ instructions that allow the handling of carries in place. This is what GMP
+ does as well. It is possible that a <code class="computeroutput">digit_type</code>
+ representation similar to libtommath's returns someday which can then be
+ enabled via a different <code class="computeroutput">mp_int_traits</code>
+ class template.
+ 
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.implementation_notes.semantics"></a><a class="link" href="implementation_notes.html#mp_int.implementation_notes.semantics" title="Semantics">Semantics</a>
+</h3></div></div></div>
+<div class="itemizedlist"><ul type="disc">
+<li>
+ An integer with a value of zero has a <code class="computeroutput">used_</code>
+ count of 1 and <code class="computeroutput">digits_[0]</code>
+ holds the value 0.
+ </li>
+<li>
+ An unitialized integer has no value and all operations on it except for
+ initializing or swapping are undefined.
+ </li>
+</ul></div>
+</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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="performance.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mp_int_reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/mp_int_reference.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/mp_int_reference.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,2057 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>mp_int reference</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="implementation_notes.html" title="Implementation notes">
+<link rel="next" href="mp_int_traits_reference.html" title="mp_int_traits reference">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="implementation_notes.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mp_int_traits_reference.html"><img src="../../../../../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="mp_int.mp_int_reference"></a><a class="link" href="mp_int_reference.html" title="mp_int reference">mp_int reference</a>
+</h2></div></div></div>
+<a name="mp_int.mp_int_reference.synopsis"></a><h4>
+<a name="id3153688"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.synopsis">Synopsis</a>
+ </h4>
+<pre class="programlisting">// <boost/mp_math/mp_int.hpp>
+namespace boost {
+namespace mp_math {
+
+template<
+ class Allocator = std::allocator<void>,
+ class Traits = mp_int_traits<>
+>
+struct mp_int
+{
+ typedef Allocator allocator_type;
+ typedef Traits traits_type;
+ typedef typename base_allocator_type::size_type size_type;
+
+ // ctor/cctor/dtor/assign
+ mp_int();
+
+ explicit mp_int(const allocator_type& a);
+
+ template<typename IntegralT>
+ mp_int(IntegralT,
+ const allocator_type& a = allocator_type(),
+ typename enable_if<is_integral<IntegralT> >::type* dummy = 0);
+
+ template<typename charT>
+ mp_int(const charT*, const allocator_type& a = allocator_type());
+
+ template<typename charT>
+ mp_int(const charT*,
+ std::ios_base::fmtflags,
+ const allocator_type& a = allocator_type());
+
+ template<typename charT, class traits, class Alloc>
+ mp_int(const std::basic_string<charT,traits,Alloc>&,
+ const allocator_type& a = allocator_type());
+
+ template<typename charT, class traits, class Alloc>
+ mp_int(const std::basic_string<charT,traits,Alloc>&,
+ std::ios_base::fmtflags,
+ const allocator_type& a = allocator_type());
+
+ template<typename RandomAccessIterator>
+ mp_int(RandomAccessIterator first,
+ RandomAccessIterator last,
+ const allocator_type& a = allocator_type());
+
+ template<typename RandomAccessIterator>
+ mp_int(RandomAccessIterator first,
+ RandomAccessIterator last,
+ std::ios_base::fmtflags f,
+ const allocator_type& a = allocator_type());
+
+ mp_int(const mp_int& copy);
+
+ #ifdef BOOST_HAS_RVALUE_REFS
+ mp_int(mp_int&& copy);
+ #endif
+
+ ~mp_int();
+
+ mp_int& operator = (const mp_int& rhs);
+
+ #ifdef BOOST_HAS_RVALUE_REFS
+ mp_int& operator = (mp_int&& rhs);
+ #endif
+
+ template<typename IntegralT>
+ mp_int& operator = (IntegralT rhs);
+
+ template<typename charT>
+ mp_int& operator = (const charT*);
+
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator = (const std::basic_string<charT,traits,Alloc>&);
+
+ template<typename charT>
+ void assign(const charT*, std::ios_base::fmtflags);
+
+ template<typename charT, class traits, class Alloc>
+ void assign(const std::basic_string<charT,traits,Alloc>&,
+ std::ios_base::fmtflags);
+
+ template<typename RandomAccessIterator>
+ void assign(RandomAccessIterator first, RandomAccessIterator last,
+ std::ios_base::fmtflags);
+
+ // modifiers
+ #ifdef BOOST_HAS_RVALUE_REFS
+ void swap(mp_int&& other);
+ #else
+ void swap(mp_int& other);
+ #endif
+
+ // increment/decrement
+ mp_int& operator ++();
+ mp_int& operator --();
+ mp_int operator ++(int);
+ mp_int operator --(int);
+
+ // shifting
+ mp_int& operator <<= (size_type);
+ mp_int& operator >>= (size_type);
+
+ // unary negate
+ mp_int& operator - ();
+
+ // arithmetic operators
+ mp_int& operator += (const mp_int& x);
+ mp_int& operator -= (const mp_int& x);
+ mp_int& operator *= (const mp_int& x);
+ mp_int& operator /= (const mp_int& x);
+ mp_int& operator %= (const mp_int& x);
+
+ // bitwise operators
+ mp_int& operator |= (const mp_int& x);
+ mp_int& operator &= (const mp_int& x);
+ mp_int& operator ^= (const mp_int& x);
+
+ // operators involving integral types
+ template<typename IntegralT> mp_int& operator += (IntegralT x);
+ template<typename IntegralT> mp_int& operator -= (IntegralT x);
+ template<typename IntegralT> mp_int& operator *= (IntegralT x);
+ template<typename IntegralT> mp_int& operator /= (IntegralT x);
+ template<typename IntegralT> mp_int& operator %= (IntegralT x);
+ template<typename IntegralT> mp_int& operator |= (IntegralT x);
+ template<typename IntegralT> mp_int& operator &= (IntegralT x);
+ template<typename IntegralT> mp_int& operator ^= (IntegralT x);
+
+ // operators involving character strings
+ template<typename charT> mp_int& operator += (const charT*);
+ template<typename charT> mp_int& operator -= (const charT*);
+ template<typename charT> mp_int& operator *= (const charT*);
+ template<typename charT> mp_int& operator /= (const charT*);
+ template<typename charT> mp_int& operator %= (const charT*);
+ template<typename charT> mp_int& operator |= (const charT*);
+ template<typename charT> mp_int& operator &= (const charT*);
+ template<typename charT> mp_int& operator ^= (const charT*);
+
+ // operators involving std::basic_string
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator += (const std::basic_string<charT,traits,Alloc>& s);
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator -= (const std::basic_string<charT,traits,Alloc>& s);
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator *= (const std::basic_string<charT,traits,Alloc>& s);
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator /= (const std::basic_string<charT,traits,Alloc>& s);
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator %= (const std::basic_string<charT,traits,Alloc>& s);
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator |= (const std::basic_string<charT,traits,Alloc>& s);
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator &= (const std::basic_string<charT,traits,Alloc>& s);
+ template<typename charT, class traits, class Alloc>
+ mp_int& operator ^= (const std::basic_string<charT,traits,Alloc>& s);
+
+ // observers
+ allocator_type get_allocator() const;
+
+ bool is_even() const;
+ bool is_odd () const;
+
+ bool is_positive() const;
+ bool is_negative() const;
+
+ size_type precision() const;
+
+ operator unspecified_bool_type() const;
+
+ std::string to_string(std::ios_base::fmtflags f = std::ios_base::dec) const;
+
+ template<typename IntegralT>
+ IntegralT to_integral() const;
+
+ // low level access
+ typedef traits_type::digit_type digit_type;
+ typedef traits_type::word_type word_type;
+
+ digit_type& operator[](size_type i);
+ const digit_type& operator[](size_type i) const;
+
+ digit_type& at(size_type i);
+ const digit_type& at(size_type i) const;
+};
+
+
+// non-member functions
+
+#ifdef BOOST_HAS_RVALUE_REFS
+template<class A, class T>
+void swap(mp_int<A,T>&&, mp_int<A,T>&&);
+#else
+void swap(mp_int<A,T>&, mp_int<A,T>&);
+#endif
+
+template<class A, class T>
+mp_int<A,T> operator << (const mp_int<A,T>&, typename mp_int<A,T>::size_type);
+
+template<class A, class T>
+mp_int<A,T> operator >> (const mp_int<A,T>&, typename mp_int<A,T>::size_type);
+
+template<class A, class T>
+mp_int<A,T> operator - (const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator + (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator - (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator * (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator / (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator % (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator | (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator & (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator ^ (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator + (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator - (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator * (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator / (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator % (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator | (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator & (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator ^ (const mp_int<A,T>&, IntegralT);
+
+
+// Comparison operators
+
+template<class A, class T>
+bool operator == (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator != (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator < (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator > (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator <= (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator >= (const mp_int<A,T>&, const mp_int<A,T>&);
+
+// Comparison between mp_int and std::basic_string
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator == (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator != (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator < (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator > (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator <= (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator >= (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+// Comparison between std::basic_string and mp_int
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator == (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator != (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator < (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator > (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator <= (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator >= (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+// Comparison between mp_int and const charT*
+
+template<class A, class T>
+bool operator == (const mp_int<A,T>&, const charT*);
+
+template<class A, class T>
+bool operator != (const mp_int<A,T>&, const charT*);
+
+template<class A, class T>
+bool operator < (const mp_int<A,T>&, const charT*);
+
+template<class A, class T>
+bool operator > (const mp_int<A,T>&, const charT*);
+
+template<class A, class T>
+bool operator <= (const mp_int<A,T>&, const charT*);
+
+template<class A, class T>
+bool operator >= (const mp_int<A,T>&, const charT*);
+
+// Comparison between const charT* and mp_int
+
+template<class A, class T>
+bool operator == (const charT*, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator != (const charT*, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator < (const charT*, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator > (const charT*, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator <= (const charT*, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator >= (const charT*, const mp_int<A,T>&);
+
+// Comparison between mp_int and integral type
+
+template<class A, class T, typename IntegralT>
+bool operator == (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator != (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator < (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator > (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator <= (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator >= (const mp_int<A,T>&, IntegralT);
+
+// Comparison between integral type and mp_int
+
+template<class A, class T, typename IntegralT>
+bool operator == (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator != (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator < (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator > (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator <= (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator >= (IntegralT, const mp_int<A,T>&);
+
+
+// Stream I/O
+
+template<class A, class T, typename charT, class traits>
+std::basic_istream<charT, traits>&
+operator >> (std::basic_istream<charT, traits>& is, mp_int<A,T>& x);
+
+template<class A, class T, typename charT, class traits>
+std::basic_ostream<charT, traits>&
+operator << (std::basic_ostream<charT, traits>& os, const mp_int<A,T>& x);
+
+
+// Special functions
+
+template<class A, class T>
+mp_int<A,T> abs(const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> gcd(const mp_int<A,T>& a, const mp_int<A,T>& b);
+
+template<class A, class T>
+mp_int<A,T> lcm(const mp_int<A,T>& a, const mp_int<A,T>& b);
+
+template<class A, class T>
+int jacobi(const mp_int<A,T>& a, const mp_int<A,T>& p);
+
+template<class A, class T>
+mp_int<A,T> pow(const mp_int<A,T>& x, typename mp_int<A,T>::digit_type n);
+
+template<class A, class T>
+mp_int<A,T> pow(const mp_int<A,T>& x, const mp_int<A,T>& n);
+
+template<class A, class T>
+mp_int<A,T> modpow(const mp_int<A,T>& base, const mp_int<A,T>& exp, const mp_int<A,T>& mod);
+
+template<class A, class T>
+mp_int<A,T> sqrt(const mp_int<A,T>& x);
+
+template<class A, class T>
+mp_int<A,T> nth_root(const mp_int<A,T>& x, typename mp_int<A,T>::digit_type n);
+
+template<class A, class T>
+mp_int<A,T> nth_root(const mp_int<A,T>& x, const mp_int<A,T>& n);
+
+
+} // namespace mp_math
+} // namespace boost
+</pre>
+<a name="mp_int.mp_int_reference.construction_from___assignment_to_a_string_object"></a><h4>
+<a name="id3169608"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.construction_from___assignment_to_a_string_object">Construction
+ from / assignment to a string object</a>
+ </h4>
+
+ In a constructor or assignment operation without the possibility to specify
+ the base of the string argument the base of the number is deduced from the
+ string. If the string starts with <code class="computeroutput">0x</code> or <code class="computeroutput">0X</code> then the number will be treated as hexadecimal
+ value. If the string starts with <code class="computeroutput">0</code>
+ then the number will be treated as octal value else it will be treated as decimal
+ value. An optional <code class="computeroutput">-</code> sign is allowed
+ as the first character in the string to indicate a negative value.
+ 
+
+ In a constructor or assignment operation with the ability to specify the format
+ of the string argument via a <code class="computeroutput">std::ios_base::fmtflags</code>
+ parameter, possible formatting flags are:
+ 
+<div class="itemizedlist"><ul type="disc">
+<li><code class="computeroutput">std::ios_base::showbase</code></li>
+<li><code class="computeroutput">std::ios_base::dec</code></li>
+<li><code class="computeroutput">std::ios_base::hex</code></li>
+<li><code class="computeroutput">std::ios_base::oct</code></li>
+</ul></div>
+<a name="mp_int.mp_int_reference.construct_copy_destroy_assign"></a><h4>
+<a name="id3169858"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.construct_copy_destroy_assign">Construct/Copy/Destroy/Assign</a>
+ </h4>
+<pre class="programlisting">mp_int();
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Constructs an empty <code class="computeroutput">mp_int</code> object, such an uninitialized <code class="computeroutput">mp_int</code> has no value, i.e. it is not
+ zero.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">explicit mp_int(const allocator_type& a);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Constructs an empty <code class="computeroutput">mp_int</code> object and initializes its allocator
+ with <code class="computeroutput">a</code>, such an uninitialized
+ <code class="computeroutput">mp_int</code> has no value, i.e.
+ it is not zero.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT>
+mp_int(IntegralT x,
+ const allocator_type& a = allocator_type(),
+ typename enable_if<is_integral<IntegralT> >::type* dummy = 0);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from an integral type. The value of the object is that of the integral
+ type.
+ </li>
+<li>
+Complexity: O(N) where N is the number of
+ bits of IntegralT.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename charT>
+mp_int(const charT* s, const allocator_type& a = allocator_type());
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">s</code>
+ points to a valid number formatted as string or to an empty string.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from a string.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<typename charT>
+mp_int(const charT* s,
+ std::ios_base::fmtflags f,
+ const allocator_type& a = allocator_type());
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">s</code>
+ points to a valid number formatted according to the flags in <code class="computeroutput">f</code> or <code class="computeroutput">s</code>
+ is an empty string.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from a string.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character or if an unrecognized formatting flag was set.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<typename charT, class traits, class Alloc>
+mp_int(const std::basic_string<charT,traits,Alloc>& s,
+ const allocator_type& a = allocator_type());
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">s</code>
+ contains a valid number formatted as string or <code class="computeroutput">s</code>
+ is an empty string.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from a string.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<typename charT, class traits, class Alloc>
+mp_int(const std::basic_string<charT,traits,Alloc>& s,
+ std::ios_base::fmtflags f,
+ const allocator_type& a = allocator_type());
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">s</code>
+ contains a valid number formatted according to the flags in <code class="computeroutput">f</code> or <code class="computeroutput">s</code>
+ is an empty string.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from a string.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character or if an unrecognized formatting flag was set.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<typename RandomAccessIterator>
+mp_int(RandomAccessIterator first,
+ RandomAccessIterator last,
+ const allocator_type& a = allocator_type());
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">first</code>
+ and <code class="computeroutput">last</code> are iterators into
+ a string.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from two iterators.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<typename RandomAccessIterator>
+mp_int(RandomAccessIterator first,
+ RandomAccessIterator last,
+ std::ios_base::fmtflags f,
+ const allocator_type& a = allocator_type());
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">first</code>
+ and <code class="computeroutput">last</code> are iterators into
+ a string formatted according to the formatting flags in <code class="computeroutput">f</code>.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from two iterators.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character or if an unrecognized formatting flag was set.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">mp_int(const mp_int& copy);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Constructs a copy of a given <code class="computeroutput">mp_int</code>.
+ </li>
+<li>
+Complexity: O(N), where N is the number
+ of digits in <code class="computeroutput">copy</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int(mp_int&& copy);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ by moving <code class="computeroutput">copy</code> into <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">~mp_int();
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Destroys <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator = (const mp_int& rhs);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Copies the value of <code class="computeroutput">rhs</code> into <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator = (mp_int&& rhs);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: <code class="computeroutput">*this</code> obtains the value of <code class="computeroutput">rhs</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT>
+mp_int& operator = (IntegralT rhs);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: <code class="computeroutput">*this</code> obtains the value of <code class="computeroutput">rhs</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: basic.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename charT>
+mp_int& operator = (const charT* s);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">s</code>
+ points to a valid number formatted as string or to an empty string.
+ </li>
+<li>
+Effects:<code class="computeroutput">*this = mp_int(s);</code>.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+<li>
+Exception safety: basic.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename charT, class traits, class Alloc>
+mp_int& operator = (const std::basic_string<charT,traits,Alloc>& s);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">s</code>
+ points to a valid number formatted as string or to an empty string.
+ </li>
+<li>
+Effects:<code class="computeroutput">*this = mp_int(s);</code>.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+<li>
+Exception safety: basic.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename charT>
+void assign(const charT* s, std::ios_base::fmtflags);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">s</code>
+ points to a valid number formatted according to the flags in <code class="computeroutput">f</code> or <code class="computeroutput">s</code>
+ is an empty string.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from a string.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character or if an unrecognized formatting flag was set.
+ </li>
+</ul></div>
+</li>
+<li>
+Exception safety: basic.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename charT, class traits, class Alloc>
+void assign(const std::basic_string<charT,traits,Alloc>& s, std::ios_base::fmtflags f);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">s</code>
+ contains a valid number formatted according to the flags in <code class="computeroutput">f</code> or <code class="computeroutput">s</code>
+ is an empty string.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from a string.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character or if an unrecognized formatting flag was set.
+ </li>
+</ul></div>
+</li>
+<li>
+Exception safety: basic.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename RandomAccessIterator>
+void assign(RandomAccessIterator first, RandomAccessIterator last, std::ios_base::fmtflags f);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">first</code>
+ and <code class="computeroutput">last</code> are iterators into
+ a string formatted according to the formatting flags in <code class="computeroutput">f</code>.
+ </li>
+<li>
+Effects: Constructs an <code class="computeroutput">mp_int</code>
+ object from two iterators.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character or if an unrecognized formatting flag was set.
+ </li>
+</ul></div>
+</li>
+<li>
+Exception safety: basic.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.modifiers"></a><h4>
+<a name="id3173944"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.modifiers">Modifiers</a>
+ </h4>
+<pre class="programlisting">void swap(mp_int&& other);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Swaps the value of <code class="computeroutput">other</code> and <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Exception safety: nothrow.
+ </li>
+</ul></div>
+<pre class="programlisting">void swap(mp_int& other);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Swaps the value of <code class="computeroutput">other</code> and <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Exception safety: nothrow.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.increment_decrement"></a><h4>
+<a name="id3174161"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.increment_decrement">Increment/decrement</a>
+ </h4>
+<pre class="programlisting">mp_int& operator ++();
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects:<pre class="programlisting">*this += 1;
+return *this;
+</pre>
+</li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: best case is O(1), worst case
+ is O(N) - this happens when the addition causes a carry bit to ripple through
+ all digits subsequently.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator --();
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects:<pre class="programlisting">*this -= 1;
+return *this;
+</pre>
+</li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: best case is O(1), worst case
+ is O(N) - this happens when the subtraction causes a borrow bit to ripple
+ through all digits subsequently.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int operator ++(int);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects:<pre class="programlisting">mp_int tmp(*this);
+*this += 1;
+return tmp;
+</pre>
+</li>
+<li>
+Returns: The value of <code class="computeroutput">*this</code> before incrementation.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int operator --(int);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects:<pre class="programlisting">mp_int tmp(*this);
+*this -= 1;
+return tmp;
+</pre>
+</li>
+<li>
+Returns: The value of <code class="computeroutput">*this</code> before decrementation.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.shifting"></a><h4>
+<a name="id3174889"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.shifting">Shifting</a>
+ </h4>
+<pre class="programlisting">mp_int& operator <<= (size_type x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Shift <code class="computeroutput">*this</code> by <code class="computeroutput">x</code>
+ bits to the left.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator >>= (size_type x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Shift <code class="computeroutput">*this</code> by <code class="computeroutput">x</code>
+ bits to the right.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.unary_negate"></a><h4>
+<a name="id3175224"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.unary_negate">Unary negate</a>
+ </h4>
+<pre class="programlisting">mp_int& operator - ();
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Negates <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Exception safety: nothrow.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.arithmetic_operators"></a><h4>
+<a name="id3175350"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.arithmetic_operators">Arithmetic operators</a>
+ </h4>
+<pre class="programlisting">mp_int& operator += (const mp_int& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Adds <code class="computeroutput">x</code>
+ to <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator -= (const mp_int& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Subtracts <code class="computeroutput">x</code>
+ from <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator *= (const mp_int& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Multiplies <code class="computeroutput">*this</code> by <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: If <code class="computeroutput">&x == this</code>
+ then a squaring algorithm will be used. Different multiplication algorithms
+ are chosen for numbers of different size. The thresholds can be tuned via
+ the <code class="computeroutput">mp_int_traits</code> class template
+ parameter.
+ <div class="itemizedlist"><ul type="circle">
+<li>
+ Small numbers: Comba algorithm O(N^2).
+ </li>
+<li>
+ Midsize numbers: Karatsuba algorithm O(N^log2(3)) ~ O(N^1.585).
+ </li>
+<li>
+ Large numbers: Toom-Cook algorithm O(N^(log(5)/log(3))) ~ O(N^1.465).
+ </li>
+</ul></div>
+</li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator /= (const mp_int& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">x
+ != 0</code>.
+ </li>
+<li>
+Effects: Divides <code class="computeroutput">*this</code> by <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::domain_error</code> if <code class="computeroutput">x
+ == 0</code>.
+ </li>
+</ul></div>
+</li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator %= (const mp_int& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">x
+ != 0</code>.
+ </li>
+<li>
+Effects: Modulus <code class="computeroutput">*this</code> by <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::domain_error</code> if <code class="computeroutput">x
+ == 0</code>.
+ </li>
+</ul></div>
+</li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.bitwise_operators"></a><h4>
+<a name="id3176409"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.bitwise_operators">Bitwise operators</a>
+ </h4>
+<pre class="programlisting">mp_int& operator |= (const mp_int& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: <code class="computeroutput">*this</code> OR <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator &= (const mp_int& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: <code class="computeroutput">*this</code> AND <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">mp_int& operator ^= (const mp_int& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: <code class="computeroutput">*this</code> XOR <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.operators_involving_integral_types"></a><h4>
+<a name="id3176932"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.operators_involving_integral_types">Operators
+ involving integral types</a>
+ </h4>
+<pre class="programlisting">template<typename IntegralT> mp_int& operator += (IntegralT x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Adds <code class="computeroutput">x</code>
+ to <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT> mp_int& operator -= (IntegralT x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Subtracts <code class="computeroutput">x</code>
+ to <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT> mp_int& operator *= (IntegralT x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Multiplies <code class="computeroutput">*this</code> by <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT> mp_int& operator /= (IntegralT x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Divides <code class="computeroutput">*this</code> by <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT> mp_int& operator %= (IntegralT x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: <code class="computeroutput">*this</code> modulo <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT> mp_int& operator |= (IntegralT x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Applies the bitwise or operation
+ on <code class="computeroutput">*this</code>
+ and the absolute of <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT> mp_int& operator &= (IntegralT x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Applies the bitwise and operation
+ on <code class="computeroutput">*this</code>
+ and the absolute of <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT> mp_int& operator ^= (IntegralT x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Applies the bitwise xor operation
+ on <code class="computeroutput">*this</code>
+ and the absolute of <code class="computeroutput">x</code>.
+ </li>
+<li>
+Returns: <code class="computeroutput">*this</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.operators_involving_chart_strings"></a><h4>
+<a name="id3178345"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.operators_involving_chart_strings">Operators
+ involving charT strings</a>
+ </h4>
+<pre class="programlisting">template<typename charT> mp_int& operator += (const charT* s);
+template<typename charT> mp_int& operator -= (const charT* s);
+template<typename charT> mp_int& operator *= (const charT* s);
+template<typename charT> mp_int& operator /= (const charT* s);
+template<typename charT> mp_int& operator %= (const charT* s);
+template<typename charT> mp_int& operator |= (const charT* s);
+template<typename charT> mp_int& operator &= (const charT* s);
+template<typename charT> mp_int& operator ^= (const charT* s);
+</pre>
+<a name="mp_int.mp_int_reference.operators_involving_std__basic_string"></a><h4>
+<a name="id3178991"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.operators_involving_std__basic_string">Operators
+ involving std::basic_string</a>
+ </h4>
+<pre class="programlisting">template<typename charT, class traits, class Alloc>
+mp_int& operator += (const std::basic_string<charT,traits,Alloc>& s);
+template<typename charT, class traits, class Alloc>
+mp_int& operator -= (const std::basic_string<charT,traits,Alloc>& s);
+template<typename charT, class traits, class Alloc>
+mp_int& operator *= (const std::basic_string<charT,traits,Alloc>& s);
+template<typename charT, class traits, class Alloc>
+mp_int& operator /= (const std::basic_string<charT,traits,Alloc>& s);
+template<typename charT, class traits, class Alloc>
+mp_int& operator %= (const std::basic_string<charT,traits,Alloc>& s);
+template<typename charT, class traits, class Alloc>
+mp_int& operator |= (const std::basic_string<charT,traits,Alloc>& s);
+template<typename charT, class traits, class Alloc>
+mp_int& operator &= (const std::basic_string<charT,traits,Alloc>& s);
+template<typename charT, class traits, class Alloc>
+mp_int& operator ^= (const std::basic_string<charT,traits,Alloc>& s);
+</pre>
+<a name="mp_int.mp_int_reference.observers"></a><h4>
+<a name="id3180185"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.observers">Observers</a>
+ </h4>
+<pre class="programlisting">allocator_type get_allocator() const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: A copy of the allocator.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing if allocator copy constructor
+ is nothrow.
+ </li>
+</ul></div>
+<pre class="programlisting">bool is_even() const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">bool is_odd () const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">bool is_positive() const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">bool is_negative() const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">size_type precision() const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: The number of bits used by the
+ absolute value of *this.
+ </li>
+<li>
+Complexity: O(N).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">operator unspecified_bool_type() const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: <code class="computeroutput">*this != 0</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">std::string to_string(std::ios_base::fmtflags f = std::ios_base::dec) const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Converts <code class="computeroutput">*this</code> to a <code class="computeroutput">std::string</code>,
+ formatting of the string is done according to the <code class="computeroutput">std::ios_base::fmtflags</code>
+ parameter. Possible formatting flags are:
+ <div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::ios_base::showpos</code></li>
+<li><code class="computeroutput">std::ios_base::showbase</code></li>
+<li><code class="computeroutput">std::ios_base::dec</code></li>
+<li><code class="computeroutput">std::ios_base::hex</code></li>
+<li><code class="computeroutput">std::ios_base::oct</code></li>
+<li><code class="computeroutput">std::ios_base::uppercase</code></li>
+</ul></div>
+</li>
+<li>
+Returns: <code class="computeroutput">*this</code> converted to a <code class="computeroutput">std::string</code>
+ object.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<pre class="programlisting">template<typename IntegralT>
+IntegralT to_integral() const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: <code class="computeroutput">*this</code> converted to an object of type <code class="computeroutput">IntegralT</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::overflow_error</code>
+ if <code class="computeroutput">IntegralT</code> does not have
+ enough precision to hold the result.
+ </li>
+<li>
+Exception safety: strong.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.non_member_functions"></a><h4>
+<a name="id3181249"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.non_member_functions">Non-member functions</a>
+ </h4>
+<pre class="programlisting">template<class A, class T>
+void swap(mp_int<A,T>&&, mp_int<A,T>&&);
+
+template<class A, class T>
+mp_int<A,T> operator << (const mp_int<A,T>&, typename mp_int<A,T>::size_type);
+
+template<class A, class T>
+mp_int<A,T> operator >> (const mp_int<A,T>&, typename mp_int<A,T>::size_type);
+
+template<class A, class T>
+mp_int<A,T> operator - (const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator + (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator - (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator * (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator / (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator % (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator | (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator & (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+mp_int<A,T> operator ^ (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator + (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator - (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator * (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator / (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator % (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator | (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator & (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+mp_int<A,T> operator ^ (const mp_int<A,T>&, IntegralT);
+</pre>
+
+ These functions are implemented in terms of their respective member functions.
+ 
+<a name="mp_int.mp_int_reference.comparison_operators"></a><h4>
+<a name="id3184214"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.comparison_operators">Comparison operators</a>
+ </h4>
+<pre class="programlisting">template<class A, class T>
+bool operator == (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator != (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator < (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator > (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator <= (const mp_int<A,T>&, const mp_int<A,T>&);
+
+template<class A, class T>
+bool operator >= (const mp_int<A,T>&, const mp_int<A,T>&);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: These operators compare the numeric
+ value of their arguments and return a truth value based on that evaluation.
+ </li>
+<li>
+Throws: Nothing.
+ </li>
+</ul></div>
+<pre class="programlisting">template<class A, class T, class charT, class Traits, class Alloc>
+bool operator == (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator != (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator < (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator > (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator <= (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator >= (const mp_int<A,T>&, const std::basic_string<charT,Traits,Alloc>&);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Converts the string argument to
+ an <code class="computeroutput">mp_int</code> object and compares
+ it to the object on the left side of the expression.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<class A, class T, class charT, class Traits, class Alloc>
+bool operator == (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator != (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator < (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator > (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator <= (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+
+template<class A, class T, class charT, class Traits, class Alloc>
+bool operator >= (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Converts the string argument to
+ an <code class="computeroutput">mp_int</code> object and compares
+ it to the object on the right side of the expression.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<class A, class T, typename charT>
+bool operator == (const mp_int<A,T>&, const charT*);
+
+template<class A, class T, typename charT>
+bool operator != (const mp_int<A,T>&, const charT*);
+
+template<class A, class T, typename charT>
+bool operator < (const mp_int<A,T>&, const charT*);
+
+template<class A, class T, typename charT>
+bool operator > (const mp_int<A,T>&, const charT*);
+
+template<class A, class T, typename charT>
+bool operator <= (const mp_int<A,T>&, const charT*);
+
+template<class A, class T, typename charT>
+bool operator >= (const mp_int<A,T>&, const charT*);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Converts the string argument to
+ an <code class="computeroutput">mp_int</code> object and compares
+ it to the object on the left side of the expression.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<class A, class T, typename charT>
+bool operator == (const charT*, const mp_int<A,T>&);
+
+template<class A, class T, typename charT>
+bool operator != (const charT*, const mp_int<A,T>&);
+
+template<class A, class T, typename charT>
+bool operator < (const charT*, const mp_int<A,T>&);
+
+template<class A, class T, typename charT>
+bool operator > (const charT*, const mp_int<A,T>&);
+
+template<class A, class T, typename charT>
+bool operator <= (const charT*, const mp_int<A,T>&);
+
+template<class A, class T, typename charT>
+bool operator >= (const charT*, const mp_int<A,T>&);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Converts the string argument to
+ an <code class="computeroutput">mp_int</code> object and compares
+ it to the object on the right side of the expression.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::invalid_argument</code> if the string contains
+ an invalid character.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<class A, class T, typename IntegralT>
+bool operator == (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator != (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator < (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator > (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator <= (const mp_int<A,T>&, IntegralT);
+
+template<class A, class T, typename IntegralT>
+bool operator >= (const mp_int<A,T>&, IntegralT);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Converts the integral argument
+ to an <code class="computeroutput">mp_int</code> object and compares
+ it to the object on the left side of the expression.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<pre class="programlisting">template<class A, class T, typename IntegralT>
+bool operator == (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator != (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator < (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator > (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator <= (IntegralT, const mp_int<A,T>&);
+
+template<class A, class T, typename IntegralT>
+bool operator >= (IntegralT, const mp_int<A,T>&);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Effects: Converts the integral argument
+ to an <code class="computeroutput">mp_int</code> object and compares
+ it to the object on the right side of the expression.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<a name="mp_int.mp_int_reference.stream_i_o"></a><h4>
+<a name="id3190887"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.stream_i_o">Stream I/O</a>
+ </h4>
+<pre class="programlisting">template<class A, class T, typename charT, class traits>
+std::basic_istream<charT, traits>&
+operator >> (std::basic_istream<charT, traits>& is, mp_int<A,T>& x);
+
+template<class A, class T, typename charT, class traits>
+std::basic_ostream<charT, traits>&
+operator << (std::basic_ostream<charT, traits>& os, const mp_int<A,T>& x);
+</pre>
+<a name="mp_int.mp_int_reference.special_functions"></a><h4>
+<a name="id3191347"></a>
+ <a class="link" href="mp_int_reference.html#mp_int.mp_int_reference.special_functions">Special functions</a>
+ </h4>
+<pre class="programlisting">template<class A, class T>
+mp_int<A,T> abs(const mp_int<A,T>& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: The positive value of <code class="computeroutput">x</code>.
+ </li>
+<li>
+Complexity: O(1).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<pre class="programlisting">template<class A, class T>
+mp_int<A,T> gcd(const mp_int<A,T>& a, const mp_int<A,T>& b);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: The greatest common divisor of
+ <code class="computeroutput">a</code> and <code class="computeroutput">b</code>.
+ </li>
+<li>
+Complexity: O((log2(AB))^2).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<pre class="programlisting">template<class A, class T>
+mp_int<A,T> lcm(const mp_int<A,T>& a, const mp_int<A,T>& b);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: The least common multiple of <code class="computeroutput">a</code> and <code class="computeroutput">b</code>.
+ </li>
+<li>
+Complexity: O((log2(AB))^2).
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<pre class="programlisting">template<class A, class T>
+int jacobi(const mp_int<A,T>& a, const mp_int<A,T>& p);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: The Jacobi symbol of integer <code class="computeroutput">a</code> and positive odd integer <code class="computeroutput">p</code>.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::domain_error</code> if <code class="computeroutput">p</code>
+ is negative.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<class A, class T>
+mp_int<A,T> pow(const mp_int<A,T>& x, typename mp_int<A,T>::digit_type n);
+
+template<class A, class T>
+mp_int<A,T> pow(const mp_int<A,T>& x, const mp_int<A,T>& n);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: The <code class="computeroutput">n</code>th
+ power of <code class="computeroutput">x</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<pre class="programlisting">template<class A, class T>
+mp_int<A,T> modpow(const mp_int<A,T>& base,
+ const mp_int<A,T>& exp,
+ const mp_int<A,T>& mod);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: <code class="computeroutput">(base ^ exp) %
+ mod</code>.
+ </li>
+<li>
+Throws: <code class="computeroutput">std::bad_alloc</code>.
+ </li>
+</ul></div>
+<pre class="programlisting">template<class A, class T>
+mp_int<A,T> sqrt(const mp_int<A,T>& x);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: The square root of <code class="computeroutput">x</code>.
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::domain_error</code> if <code class="computeroutput">x</code>
+ is negative.
+ </li>
+</ul></div>
+</li>
+</ul></div>
+<pre class="programlisting">template<class A, class T>
+mp_int<A,T> nth_root(const mp_int<A,T>& x, typename mp_int<A,T>::digit_type n);
+
+template<class A, class T>
+mp_int<A,T> nth_root(const mp_int<A,T>& x, const mp_int<A,T>& n);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Returns: The <code class="computeroutput">n</code>th
+ root of <code class="computeroutput">x</code>.
+ </li>
+<li>
+Complexity: O(log(N)).
+ </li>
+<li>
+Throws:<div class="itemizedlist"><ul type="circle">
+<li><code class="computeroutput">std::bad_alloc</code></li>
+<li>
+<code class="computeroutput">std::domain_error</code> if <code class="computeroutput">x</code>
+ is negative and <code class="computeroutput">n</code> is
+ odd.
+ </li>
+</ul></div>
+</li>
+</ul></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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="implementation_notes.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mp_int_traits_reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/mp_int_traits_reference.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/mp_int_traits_reference.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,80 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>mp_int_traits reference</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="mp_int_reference.html" title="mp_int reference">
+<link rel="next" href="uniform_mp_int_reference.html" title="uniform_mp_int reference">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="mp_int_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="uniform_mp_int_reference.html"><img src="../../../../../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="mp_int.mp_int_traits_reference"></a><a class="link" href="mp_int_traits_reference.html" title="mp_int_traits reference">mp_int_traits reference</a>
+</h2></div></div></div>
+
+ The second template parameter to mp_int is a type which allows to customize
+ some of mp_int's internal workings.
+ 
+<a name="mp_int.mp_int_traits_reference.synopsis"></a><h4>
+<a name="id3193705"></a>
+ <a class="link" href="mp_int_traits_reference.html#mp_int.mp_int_traits_reference.synopsis">Synopsis</a>
+ </h4>
+
+
+
+<pre class="programlisting">// <boost/mp_math/mp_int/traits.hpp>
+namespace boost {
+namespace mp_math {
+
+template<
+ typename Digit = implementation defined,
+ typename Word = implementation defined
+>
+struct mp_int_traits
+{
+ typedef std::size_t size_type;
+ typedef Digit digit_type;
+ typedef Word word_type;
+
+ static size_type toom_mul_cutoff; // default: 350
+ static size_type toom_sqr_cutoff; // default: 400
+ static size_type karatsuba_mul_cutoff; // default: 80
+ static size_type karatsuba_sqr_cutoff; // default: 120
+};
+
+} // namespace mp_math
+} // namespace boost
+</pre>
+
+ 
+</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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="mp_int_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="uniform_mp_int_reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/performance.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/performance.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,230 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Performance</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="tutorial.html" title="Tutorial">
+<link rel="next" href="implementation_notes.html" title="Implementation notes">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tutorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="implementation_notes.html"><img src="../../../../../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="mp_int.performance"></a><a class="link" href="performance.html" title="Performance">Performance</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt>Tips</dt>
+<dt>Measurements</dt>
+</dl></div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.performance.tips"></a><a class="link" href="performance.html#mp_int.performance.tips" title="Tips">Tips</a>
+</h3></div></div></div>
+<div class="itemizedlist"><ul type="disc">
+<li>
+ A statement like
+<pre class="programlisting">x = a + b;</pre>
+ involves the creation of a temporary <code class="computeroutput">mp_int</code>
+ inside <code class="computeroutput">operator +</code>
+ because it is not able to write the result directly into <code class="computeroutput">x</code> which may already have enough memory
+ allocated to hold the result. Instead rewrite it into
+<pre class="programlisting">x = a;
+x += b;
+</pre>
+ This trick proves to be useful only for simple operations like addition
+ and subtraction.
+ </li>
+<li>
+ In operations involving built in integral types, try to use unsigned types,
+ preferrably unsigned types that are as large or smaller than mp_int<>::digit_type.
+ </li>
+<li>
+ Use hexadecimal digits for input and output. Conversion from/to power of
+ two bases uses a O(n) algorithm which is not possible for base 10.
+ </li>
+</ul></div>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.performance.measurements"></a><a class="link" href="performance.html#mp_int.performance.measurements" title="Measurements">Measurements</a>
+</h3></div></div></div>
+<div class="toc"><dl><dt><a href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_">AMD
+ Athlon XP 2000+</a></dt></dl></div>
+
+ A benchmark program is supplied with Boost.Mp_math under libs/mp_math/tools/benchmark.
+ This benchmark compares some primitive operations of different multi precision
+ integer libraries. It creates detailed result files and uses gnuplot
+ to create graphs.
+ 
+
+ Example invocations:
+ 
+<pre class="programlisting">benchmark // runs all benches
+benchmark --help
+benchmark --ops="add subtract multiply" --libs="boost.mp_math libtommath"
+</pre>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_"></a><a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_" title="AMD Athlon XP 2000+">AMD
+ Athlon XP 2000+</a>
+</h4></div></div></div>
+<pre class="programlisting">Operating System: Arch Linux (i686), Kernel 2.6.26, glibc 2.8
+Compiler: gcc-4.3.2
+</pre>
+
+ Libraries being compared:
+ 
+<div class="itemizedlist"><ul type="disc">
+<li>
+ Boost.Mp_math-1_37
+ <div class="itemizedlist"><ul type="circle"><li>
+ switches used: -ftemplate-depth-128 -O3 -finline-functions -march=i686
+ -mtune=generic -std=c++0x
+ </li></ul></div>
+</li>
+<li>
+ libtommath-0.41
+ <div class="itemizedlist"><ul type="circle"><li>
+ switches used: -ftemplate-depth-128 -O3 -finline-functions -march=i686
+ -mtune=generic
+ </li></ul></div>
+</li>
+<li>
+ gmp-4.2.2 (precompiled distribution package, uses generic i386 asm and
+ Intel P6 (Pentium Pro) asm where available)
+ <div class="itemizedlist"><ul type="circle"><li>
+ switches used: -march=i686 -mtune=generic -O2
+ </li></ul></div>
+</li>
+</ul></div>
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.input_vectors"></a><h4>
+<a name="id3152872"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.input_vectors">Input
+ vectors</a>
+ </h4>
+
+ Operand size is measured in number of bits. I chose to vary the operand
+ size for the benchmarks a little to see how well the operation handles
+ inputs of differing sizes. Benchmarks that use only one operand use operand
+ 1. <img src="../benchmark_imgs/k7/input_vecs.png" alt="input_vecs">
+ 
+
+ While input operand 1 grows linearly, input operand 2's size is determined
+ by a modified sine function.
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.construct_from_decimal_string"></a><h4>
+<a name="id3152920"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.construct_from_decimal_string">Construct
+ from decimal string</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/ctor_dec.png" alt="ctor_dec">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.construct_from_hex_string"></a><h4>
+<a name="id3152959"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.construct_from_hex_string">Construct
+ from hex string</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/ctor_hex.png" alt="ctor_hex">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.conversion_to_decimal_string"></a><h4>
+<a name="id3152999"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.conversion_to_decimal_string">Conversion
+ to decimal string</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/to_dec.png" alt="to_dec">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.conversion_to_hex_string"></a><h4>
+<a name="id3153038"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.conversion_to_hex_string">Conversion
+ to hex string</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/to_hex.png" alt="to_hex">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.add"></a><h4>
+<a name="id3153077"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.add">Add</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/add.png" alt="add">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.subtract"></a><h4>
+<a name="id3153113"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.subtract">Subtract</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/subtract.png" alt="subtract">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.multiply"></a><h4>
+<a name="id3153150"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.multiply">Multiply</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/multiply.png" alt="multiply">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.divide"></a><h4>
+<a name="id3153186"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.divide">Divide</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/divide.png" alt="divide">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.modulo"></a><h4>
+<a name="id3153223"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.modulo">Modulo</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/modulo.png" alt="modulo">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.square"></a><h4>
+<a name="id3153259"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.square">Square</a>
+ </h4>
+
+ <img src="../benchmark_imgs/k7/square.png" alt="square">
+ 
+<a name="mp_int.performance.measurements.amd_athlon_xp_2000_.modular_power"></a><h4>
+<a name="id3153296"></a>
+ <a class="link" href="performance.html#mp_int.performance.measurements.amd_athlon_xp_2000_.modular_power">Modular
+ Power</a>
+ </h4>
+
+ The operation looks like this: <code class="computeroutput">dest
+ = (op1 ^ op1) % op2</code>.
+ This graph uses a logarithmic scale. <img src="../benchmark_imgs/k7/modpow.png" alt="modpow">
+ 
+</div>
+</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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="tutorial.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="implementation_notes.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/primality_tests_reference.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/primality_tests_reference.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,211 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Primality Tests reference</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="uniform_mp_int_bits_reference.html" title="uniform_mp_int_bits reference">
+<link rel="next" href="bibliography.html" title="Bibliography">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="uniform_mp_int_bits_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="bibliography.html"><img src="../../../../../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="mp_int.primality_tests_reference"></a><a class="link" href="primality_tests_reference.html" title="Primality Tests reference">Primality Tests reference</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt>primality_division_test</dt>
+<dt>primality_fermat_test</dt>
+<dt>primality_miller_rabin_test</dt>
+</dl></div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.primality_tests_reference.primality_division_test"></a><a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_division_test" title="primality_division_test">primality_division_test</a>
+</h3></div></div></div>
+
+ This function object tests a candidate <code class="computeroutput">p</code>
+ by repeatedly dividing it by small primes (2, 3, 5, 7, 11...). This is a
+ test that should be used before other more complex tests because it quickly
+ sieves out composite numbers. For example, testing for 2, 5, 7 will eliminate
+ 54% of all numbers, testing for all primes less than 100 eliminates 70%,
+ for all primes less than 256 it is 80%.
+ 
+<a name="mp_int.primality_tests_reference.primality_division_test.synopsis"></a><h5>
+<a name="id3099918"></a>
+ <a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_division_test.synopsis">Synopsis</a>
+ </h5>
+<pre class="programlisting">// <boost/mp_math/mp_int.hpp>
+struct primality_division_test
+{
+ typedef bool result_type;
+
+ template<class A, class T>
+ bool operator()(const mp_int<A,T>& p) const;
+};
+</pre>
+<a name="mp_int.primality_tests_reference.primality_division_test.members"></a><h4>
+<a name="id3195994"></a>
+ <a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_division_test.members">Members</a>
+ </h4>
+<pre class="programlisting">template<class A, class T>
+bool operator()(const mp_int<A,T>& p) const;
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Effects: Returns true if <code class="computeroutput">p</code> is probably prime. Returns false if
+ <code class="computeroutput">p</code> is definitely composite.
+ </li></ul></div>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.primality_tests_reference.primality_fermat_test"></a><a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_fermat_test" title="primality_fermat_test">primality_fermat_test</a>
+</h3></div></div></div>
+
+ This test is based on Fermat's little theorem which states that if an integer
+ <code class="computeroutput">p</code> is prime, then for all
+ integers <code class="computeroutput">a</code> where 0 <
+ <code class="computeroutput">a</code> < <code class="computeroutput">p</code>
+ 
+
+ <code class="computeroutput">a**(p-1) = 1
+ (mod
+ p)</code>
+ 
+
+ an alternative formulation is
+ 
+
+ <code class="computeroutput">a**p = a
+ (mod
+ p)</code>
+ 
+
+ For each round the test creates a random base <code class="computeroutput">a</code>
+ and checks if the condition holds. There is a class of pseudoprimes called
+ carmichael numbers which are less likely though not impossible with enough
+ rounds to be detected by this test.
+ 
+<a name="mp_int.primality_tests_reference.primality_fermat_test.synopsis"></a><h5>
+<a name="id3196375"></a>
+ <a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_fermat_test.synopsis">Synopsis</a>
+ </h5>
+<pre class="programlisting">// <boost/mp_math/mp_int.hpp>
+template<class Distribution = uniform_mp_int<> >
+struct primality_fermat_test
+{
+ typedef Distribution distribution_type;
+ typedef bool result_type;
+
+ explicit primality_fermat_test(unsigned int rounds);
+
+ template<class Engine, class A, class T>
+ bool operator()(Engine& e, const mp_int<A,T>& p) const;
+};
+</pre>
+<a name="mp_int.primality_tests_reference.primality_fermat_test.members"></a><h4>
+<a name="id3196700"></a>
+ <a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_fermat_test.members">Members</a>
+ </h4>
+<pre class="programlisting">explicit primality_fermat_test(unsigned int r);
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Effects: Constructs a <code class="computeroutput">primality_fermat_test</code>
+ object with the number of test rounds given by <code class="computeroutput">r</code>.
+ </li></ul></div>
+<pre class="programlisting">template<class Engine, class A, class T>
+bool operator()(Engine& e, const mp_int<A,T>& p) const;
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Effects: Returns true if <code class="computeroutput">p</code> is probably prime. Returns false if
+ <code class="computeroutput">p</code> is definitely composite.
+ </li></ul></div>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.primality_tests_reference.primality_miller_rabin_test"></a><a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_miller_rabin_test" title="primality_miller_rabin_test">primality_miller_rabin_test</a>
+</h3></div></div></div>
+
+ This test is an improved version of the Fermat primality test that will also
+ detect carmichael numbers.
+ 
+<a name="mp_int.primality_tests_reference.primality_miller_rabin_test.synopsis"></a><h5>
+<a name="id3197010"></a>
+ <a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_miller_rabin_test.synopsis">Synopsis</a>
+ </h5>
+<pre class="programlisting">// <boost/mp_math/mp_int.hpp>
+template<class Distribution = uniform_mp_int<> >
+struct primality_miller_rabin_test
+{
+ typedef Distribution distribution_type;
+ typedef bool result_type;
+
+ explicit primality_miller_rabin_test(unsigned int r = 0);
+
+ template<class Engine, class A, class T>
+ bool operator()(Engine& e, const mp_int<A,T>& p) const;
+
+ static unsigned int recommended_number_of_rounds(unsigned bits);
+};
+</pre>
+<a name="mp_int.primality_tests_reference.primality_miller_rabin_test.members"></a><h4>
+<a name="id3197388"></a>
+ <a class="link" href="primality_tests_reference.html#mp_int.primality_tests_reference.primality_miller_rabin_test.members">Members</a>
+ </h4>
+<pre class="programlisting">explicit primality_miller_rabin_test(unsigned int r = 0);
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Effects: Constructs a <code class="computeroutput">primality_miller_rabin_test</code>
+ object with the number of test rounds given by <code class="computeroutput">r</code>.
+ If <code class="computeroutput">r ==
+ 0</code> then each invocation of this function
+ object will use the recommended number of rounds.
+ </li></ul></div>
+<pre class="programlisting">template<class Engine, class A, class T>
+bool operator()(Engine& e, const mp_int<A,T>& p) const;
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">p</code>
+ is odd.
+ </li>
+<li>
+Effects: Returns true if <code class="computeroutput">p</code> is probably prime. Returns false if
+ <code class="computeroutput">p</code> is definitely composite.
+ </li>
+</ul></div>
+<pre class="programlisting">unsigned int recommended_number_of_rounds(unsigned bits);
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Effects: Returns the recommended number
+ of rounds for a number of precision <code class="computeroutput">bits</code>
+ so that the probability of error is less than 2^-96.
+ </li></ul></div>
+</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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="uniform_mp_int_bits_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="bibliography.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/tutorial.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/tutorial.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,264 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>Tutorial</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="../index.html" title="Chapter 1. mp_int">
+<link rel="next" href="performance.html" title="Performance">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../index.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="performance.html"><img src="../../../../../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="mp_int.tutorial"></a><a class="link" href="tutorial.html" title="Tutorial">Tutorial</a>
+</h2></div></div></div>
+<div class="toc"><dl>
+<dt>General use</dt>
+<dt><a href="tutorial.html#mp_int.tutorial.random_number_generation">Random number
+ generation</a></dt>
+<dt>Primality testing</dt>
+<dt><a href="tutorial.html#mp_int.tutorial.prime_number_generation">Prime number
+ generation</a></dt>
+</dl></div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.tutorial.general_use"></a><a class="link" href="tutorial.html#mp_int.tutorial.general_use" title="General use">General use</a>
+</h3></div></div></div>
+
+ The only header you need to include to use the library is <code class="computeroutput"><boost/mp_math/mp_int.hpp></code>.
+ This is a header-only library so deployment is easy. All functions and objects
+ of this library live in namespace <code class="computeroutput">boost::mp_math</code>.
+ 
+<pre class="programlisting">#include <iostream>
+#include <string>
+#include <boost/mp_math/mp_int.hpp>
+
+using namespace boost::mp_math;
+using namespace std;
+
+int main()
+{
+ // init from string
+ mp_int<> x("93423894782394782347823947289374");
+ // init from integral type
+ mp_int<> y = 2340;
+ mp_int<> z = x * y;
+
+ // stream output reacts to stream flags
+ cout << hex << z << endl;
+
+ // automatic detection of radix using the base prefix 0x
+ z = "0xaaaabbbbccccddddeeeeffff222255557777";
+
+ z /= y;
+
+ // explicit conversion to string according to formatting flags
+ string s = z.to_string<string>(ios::hex | ios::showbase);
+ cout << s << endl;
+
+ z -= z;
+
+ // explicit conversion to built in integral types - this will throw
+ // std::overflow_error if int does not have enough precision to hold the
+ // result
+ int result = z.to_integral<int>();
+
+ return result;
+}
+</pre>
+
+ In most cases the <code class="computeroutput">mp_int</code>
+ type will behave like a built in integral type.
+ 
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.tutorial.random_number_generation"></a><a class="link" href="tutorial.html#mp_int.tutorial.random_number_generation" title="Random number generation">Random number
+ generation</a>
+</h3></div></div></div>
+
+ The random number generators have interfaces similar to Boost.Random. Including
+ <code class="computeroutput"><boost/random.hpp></code>
+ is not necessary because it is used internally by the <code class="computeroutput">mp_int</code>
+ random machinery. The random number engine <code class="computeroutput">mt19937</code>
+ that we use from here on lives in namespace <code class="computeroutput">boost</code>.
+ 
+<pre class="programlisting">const mp_int<> min(0U);
+const mp_int<> max("0x8974651231456456564");
+
+uniform_mp_int<> generator(min, max);
+
+// Choose a random number engine.
+mt19937 e;
+
+// Now generate a random number.
+mp_int<> r = generator(e);
+</pre>
+
+ Another probably more useful alternative is to generate random numbers of
+ a certain precision measured in bits.
+ 
+<pre class="programlisting">// A generator for 2048 bit integers.
+uniform_mp_int_bits<> generator(2048);
+
+mt19937 e;
+mp_int<> r = generator(e);
+</pre>
+
+ Note that the numbers will always be 2048 bits large, i.e. the 2048th bit
+ is always set to 1.
+ 
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.tutorial.primality_testing"></a><a class="link" href="tutorial.html#mp_int.tutorial.primality_testing" title="Primality testing">Primality testing</a>
+</h3></div></div></div>
+
+ Currently all primality tests in this library are probabilistic. A probabilistic
+ primality test cannot ascertain that a prime candidate p is really prime.
+ It can however ascertain that it is a composite number.
+ 
+
+ Here we will learn how to test a number <code class="computeroutput">p</code>
+ for primality using the fermat primality test. We use boost::bind to bind
+ the random number engine to the test functor. That is necessary because the
+ test functor's function invocation operator needs the random number engine.
+ The operator looks like this:
+ 
+<pre class="programlisting">bool operator()(Engine& e, const mp_int<>& p) const;
+</pre>
+
+ We need to bind the random number engine to the first parameter slot. Let's
+ do it!
+ 
+<pre class="programlisting">// Create the fermat test functor with 4 rounds of testing.
+primality_fermat_test<> test(4);
+
+// Create a random number engine.
+mt19937 rng;
+
+// Create a random 1024 bit candidate number.
+mp_int<> p = uniform_mp_int_bits<>(1024)(rng);
+
+bool is_p_prime = is_prime(p, bind(test, rng, _1));
+</pre>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h3 class="title">
+<a name="mp_int.tutorial.prime_number_generation"></a><a class="link" href="tutorial.html#mp_int.tutorial.prime_number_generation" title="Prime number generation">Prime number
+ generation</a>
+</h3></div></div></div>
+<div class="toc"><dl>
+<dt>prime_generator</dt>
+<dt>safe_prime_generator</dt>
+</dl></div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="mp_int.tutorial.prime_number_generation.prime_generator"></a><a class="link" href="tutorial.html#mp_int.tutorial.prime_number_generation.prime_generator" title="prime_generator">prime_generator</a>
+</h4></div></div></div>
+
+ First we will look at how to generate prime numbers using a simple trial
+ division test. What this means is that the prime generator creates a random
+ number and then repeatedly divides it by small primes until it finds a
+ number that passes this test.
+ 
+<pre class="programlisting">// Create a generator for 2048 bit primes.
+prime_generator<primality_division_test> generator(2048);
+
+// Create a random number engine.
+mt19937 rng;
+
+// Now create a prime.
+mp_int<> prime = generator(rng);
+</pre>
+</div>
+<div class="section" lang="en">
+<div class="titlepage"><div><div><h4 class="title">
+<a name="mp_int.tutorial.prime_number_generation.safe_prime_generator"></a><a class="link" href="tutorial.html#mp_int.tutorial.prime_number_generation.safe_prime_generator" title="safe_prime_generator">safe_prime_generator</a>
+</h4></div></div></div>
+
+ A safe prime is a prime <code class="computeroutput">p</code>
+ for which <code class="computeroutput">(p-1)/2</code> is also prime. Such prime numbers are much
+ rarer and thus take longer to generate.
+ 
+
+ Now we will look at how to use a more sophisticated primality test like
+ <code class="computeroutput">primality_miller_rabin_test</code>
+ for prime number generation. It is very useful to combine this test with
+ the <code class="computeroutput">primality_division_test</code>.
+ This will involve a bit of code, mostly because <code class="computeroutput">primality_miller_rabin_test</code>
+ and <code class="computeroutput">safe_prime_generator</code>
+ require a random number generator. The latter needs randomness to create
+ a candidate to test for primality and the miller rabin test needs randomness
+ to test the candidate effectively.
+ 
+<pre class="programlisting">// Define a function object that checks a prime candidate p first with a trial
+// division and then with the miller-rabin algorithm. For ease of use we give
+// it default template arguments.
+// It does not hold a reference to the random number engine because that could
+// lead to lifetime problems.
+template<
+ class Engine = mt19937,
+ class Distribution = uniform_mp_int_bits<>
+>
+struct primality_test
+{
+ primality_division_test test1;
+ primality_miller_rabin_test<Distribution> test2;
+ Engine rng;
+
+ explicit tester(const Engine& e = Engine()) : rng(e) {}
+
+ bool operator()(const mp_int<>& p)
+ {
+ return test1(p) && test2(rng, p);
+ }
+};
+
+// Create a random number engine that we will feed to the different
+// algorithms.
+mt19937 rng;
+
+// Create a generator for safe primes with 128 bits precision.
+typedef safe_prime_generator<primality_test<>, uniform_mp_int_bits<> >
+ generator_type;
+
+generator_type generator(128, primality_test<>(rng));
+
+mp_int<> prime = generator(rng);
+</pre>
+
+ Remember, the generated numbers are probably prime.
+ 
+</div>
+</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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="../index.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="performance.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/uniform_mp_int_bits_reference.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/uniform_mp_int_bits_reference.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,104 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>uniform_mp_int_bits reference</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="uniform_mp_int_reference.html" title="uniform_mp_int reference">
+<link rel="next" href="primality_tests_reference.html" title="Primality Tests reference">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="uniform_mp_int_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="primality_tests_reference.html"><img src="../../../../../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="mp_int.uniform_mp_int_bits_reference"></a><a class="link" href="uniform_mp_int_bits_reference.html" title="uniform_mp_int_bits reference">uniform_mp_int_bits
+ reference</a>
+</h2></div></div></div>
+<a name="mp_int.uniform_mp_int_bits_reference.synopsis"></a><h4>
+<a name="id3194915"></a>
+ <a class="link" href="uniform_mp_int_bits_reference.html#mp_int.uniform_mp_int_bits_reference.synopsis">Synopsis</a>
+ </h4>
+<pre class="programlisting">// <boost/mp_math/mp_int.hpp>
+template<class MpInt = mp_int<> >
+struct uniform_mp_int_bits
+{
+ typedef MpInt input_type;
+ typedef MpInt result_type;
+
+ static const bool has_fixed_range = false;
+
+ uniform_mp_int_bits(typename MpInt::size_type bits);
+
+ result_type min() const;
+ result_type max() const;
+
+ void reset();
+
+ template<class UniformRandomNumberGenerator>
+ result_type operator()(UniformRandomNumberGenerator& urng);
+};
+</pre>
+<a name="mp_int.uniform_mp_int_bits_reference.members"></a><h4>
+<a name="id3195263"></a>
+ <a class="link" href="uniform_mp_int_bits_reference.html#mp_int.uniform_mp_int_bits_reference.members">Members</a>
+ </h4>
+<pre class="programlisting">uniform_mp_int_bits(typename MpInt::size_type x);
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Effects: Constructs a <code class="computeroutput">uniform_mp_int_bits</code>
+ object. All numbers generated by this object will be <code class="computeroutput">x</code>
+ bits in size.
+ </li></ul></div>
+<pre class="programlisting">result_type min() const;
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Returns: The least value of the distribution.
+ </li></ul></div>
+<pre class="programlisting">result_type max() const;
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Returns: The greatest value of the distribution.
+ </li></ul></div>
+<pre class="programlisting">void reset();
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Effects: Resets the state of the distribution
+ function.
+ </li></ul></div>
+<pre class="programlisting">template<class UniformRandomNumberGenerator>
+result_type operator()(UniformRandomNumberGenerator& urng);
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Returns: A uniform random number <code class="computeroutput">x</code> in the range <code class="computeroutput">min
+ <= x
+ <= max</code>.
+ </li></ul></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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="uniform_mp_int_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="primality_tests_reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Added: sandbox/mp_math/libs/mp_math/doc/html/mp_int/uniform_mp_int_reference.html
==============================================================================
--- (empty file)
+++ sandbox/mp_math/libs/mp_math/doc/html/mp_int/uniform_mp_int_reference.html 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -0,0 +1,110 @@
+<html>
+<head>
+<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
+<title>uniform_mp_int reference</title>
+<link rel="stylesheet" href="../boostbook.css" type="text/css">
+<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
+<link rel="home" href="../index.html" title="Chapter 1. mp_int">
+<link rel="up" href="../index.html" title="Chapter 1. mp_int">
+<link rel="prev" href="mp_int_traits_reference.html" title="mp_int_traits reference">
+<link rel="next" href="uniform_mp_int_bits_reference.html" title="uniform_mp_int_bits reference">
+</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">Home</td>
+<td align="center">Libraries</td>
+<td align="center">People</td>
+<td align="center">FAQ</td>
+<td align="center">More</td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="mp_int_traits_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="uniform_mp_int_bits_reference.html"><img src="../../../../../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="mp_int.uniform_mp_int_reference"></a><a class="link" href="uniform_mp_int_reference.html" title="uniform_mp_int reference">uniform_mp_int reference</a>
+</h2></div></div></div>
+<a name="mp_int.uniform_mp_int_reference.synopsis"></a><h4>
+<a name="id3194095"></a>
+ <a class="link" href="uniform_mp_int_reference.html#mp_int.uniform_mp_int_reference.synopsis">Synopsis</a>
+ </h4>
+<pre class="programlisting">// <boost/mp_math/mp_int.hpp>
+template<class MpInt = mp_int<> >
+struct uniform_mp_int
+{
+ typedef MpInt input_type;
+ typedef MpInt result_type;
+
+ static const bool has_fixed_range = false;
+
+ uniform_mp_int(const MpInt& min, const MpInt& max);
+
+ result_type min() const;
+ result_type max() const;
+
+ void reset();
+
+ template<class UniformRandomNumberGenerator>
+ result_type operator()(UniformRandomNumberGenerator& urng);
+};
+</pre>
+<a name="mp_int.uniform_mp_int_reference.members"></a><h4>
+<a name="id3194464"></a>
+ <a class="link" href="uniform_mp_int_reference.html#mp_int.uniform_mp_int_reference.members">Members</a>
+ </h4>
+<pre class="programlisting">uniform_mp_int(const MpInt& min, const MpInt& max);
+</pre>
+<div class="itemizedlist"><ul type="disc">
+<li>
+Requires: <code class="computeroutput">min
+ <= max</code>
+</li>
+<li>
+Effects: Constructs a <code class="computeroutput">uniform_mp_int</code>
+ object. <code class="computeroutput">min</code> and <code class="computeroutput">max</code> are the parameters of the distribution.
+ </li>
+</ul></div>
+<pre class="programlisting">result_type min() const;
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Returns: The <code class="computeroutput">min</code>
+ parameter of the distribution.
+ </li></ul></div>
+<pre class="programlisting">result_type max() const;
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Returns: The <code class="computeroutput">max</code>
+ parameter of the distribution.
+ </li></ul></div>
+<pre class="programlisting">void reset();
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Effects: Resets the state of the distribution
+ function.
+ </li></ul></div>
+<pre class="programlisting">template<class UniformRandomNumberGenerator>
+result_type operator()(UniformRandomNumberGenerator& urng);
+</pre>
+<div class="itemizedlist"><ul type="disc"><li>
+Returns: A uniform random number <code class="computeroutput">x</code> in the range <code class="computeroutput">min
+ <= x
+ <= max</code>.
+ </li></ul></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 © 2008 - 2009 Kevin Sopp
+ Distributed under the Boost Software License, Version 1.0. (See accompanying
+ file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt
+ [source-mode c++
+ 
+</div></td>
+</tr></table>
+<hr>
+<div class="spirit-nav">
+<a accesskey="p" href="mp_int_traits_reference.html"><img src="../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="uniform_mp_int_bits_reference.html"><img src="../../../../../doc/html/images/next.png" alt="Next"></a>
+</div>
+</body>
+</html>

Modified: sandbox/mp_math/libs/mp_math/doc/mp_int.qbk
==============================================================================
--- sandbox/mp_math/libs/mp_math/doc/mp_int.qbk (original)
+++ sandbox/mp_math/libs/mp_math/doc/mp_int.qbk 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -1,13 +1,13 @@
-[/ Copyright Kevin Sopp 2008.
+[/ Copyright Kevin Sopp 2008 - 2009.
  / Distributed under the Boost Software License, Version 1.0.
  / (See accompanying file LICENSE_1_0.txt or copy at
  / http://www.boost.org/LICENSE_1_0.txt)]

-[library mp_int
+[library mp_int
   [quickbook 1.4]
   [id mp_int]
   [dirname mp_int]
- [copyright 2008 Kevin Sopp]
+ [copyright 2008 - 2009 Kevin Sopp]
   [purpose multi precision integer arithmetic]
   [authors [Sopp, Kevin]]
   [license Distributed under the Boost Software License, Version 1.0.

Modified: sandbox/mp_math/libs/mp_math/doc/mp_int_reference.qbk
==============================================================================
--- sandbox/mp_math/libs/mp_math/doc/mp_int_reference.qbk (original)
+++ sandbox/mp_math/libs/mp_math/doc/mp_int_reference.qbk 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -1,4 +1,4 @@
-[/ Copyright Kevin Sopp 2008.
+[/ Copyright Kevin Sopp 2008 - 2009.
 / Distributed under the Boost Software License, Version 1.0.
 / (See accompanying file LICENSE_1_0.txt or copy at
 / http://www.boost.org/LICENSE_1_0.txt)]
@@ -17,40 +17,54 @@
>
 struct mp_int
 {
- typedef Allocator allocator_type;
- typedef Traits traits_type;
- typedef typename traits_type::size_type size_type;
+ typedef Allocator allocator_type;
+ typedef Traits traits_type;
+ typedef typename base_allocator_type::size_type size_type;

 // ctor/cctor/dtor/assign
 mp_int();

+ explicit mp_int(const allocator_type& a);
+
 template<typename IntegralT>
- mp_int(IntegralT x, typename enable_if<is_integral<IntegralT> >::type* dummy = 0);
-
- mp_int(const char* s);
- mp_int(const wchar_t* s);
+ mp_int(IntegralT,
+ const allocator_type& a = allocator_type(),
+ typename enable_if<is_integral<IntegralT> >::type* dummy = 0);
+
+ template<typename charT>
+ mp_int(const charT*, const allocator_type& a = allocator_type());
+
+ template<typename charT>
+ mp_int(const charT*,
+ std::ios_base::fmtflags,
+ const allocator_type& a = allocator_type());

 template<typename charT, class traits, class Alloc>
- mp_int(const std::basic_string<charT,traits,Alloc>& s);
-
- template<typename RandomAccessIterator>
- mp_int(RandomAccessIterator first, RandomAccessIterator last);
-
- mp_int(const char* s, std::ios_base::fmtflags f);
- mp_int(const wchar_t* s, std::ios_base::fmtflags f);
+ mp_int(const std::basic_string<charT,traits,Alloc>&,
+ const allocator_type& a = allocator_type());

 template<typename charT, class traits, class Alloc>
- mp_int(const std::basic_string<charT,traits,Alloc>& s, std::ios_base::fmtflags f);
-
+ mp_int(const std::basic_string<charT,traits,Alloc>&,
+ std::ios_base::fmtflags,
+ const allocator_type& a = allocator_type());
+
+ template<typename RandomAccessIterator>
+ mp_int(RandomAccessIterator first,
+ RandomAccessIterator last,
+ const allocator_type& a = allocator_type());
+
 template<typename RandomAccessIterator>
- mp_int(RandomAccessIterator first, RandomAccessIterator last, std::ios_base::fmtflags f);
+ mp_int(RandomAccessIterator first,
+ RandomAccessIterator last,
+ std::ios_base::fmtflags f,
+ const allocator_type& a = allocator_type());

 mp_int(const mp_int& copy);

 #ifdef BOOST_HAS_RVALUE_REFS
 mp_int(mp_int&& copy);
 #endif
-
+
 ~mp_int();

 mp_int& operator = (const mp_int& rhs);
@@ -58,26 +72,26 @@
 #ifdef BOOST_HAS_RVALUE_REFS
 mp_int& operator = (mp_int&& rhs);
 #endif
-
+
 template<typename IntegralT>
 mp_int& operator = (IntegralT rhs);

- mp_int& operator = (const char* s);
-
- mp_int& operator = (const wchar_t* s);
+ template<typename charT>
+ mp_int& operator = (const charT*);

 template<typename charT, class traits, class Alloc>
- mp_int& operator = (const std::basic_string<charT,traits,Alloc>& s);
+ mp_int& operator = (const std::basic_string<charT,traits,Alloc>&);

- void assign(const char* s, std::ios_base::fmtflags f);
-
- void assign(const wchar_t* s, std::ios_base::fmtflags f);
+ template<typename charT>
+ void assign(const charT*, std::ios_base::fmtflags);

 template<typename charT, class traits, class Alloc>
- void assign(const std::basic_string<charT,traits,Alloc>& s, std::ios_base::fmtflags f);
-
+ void assign(const std::basic_string<charT,traits,Alloc>&,
+ std::ios_base::fmtflags);
+
 template<typename RandomAccessIterator>
- void assign(RandomAccessIterator first, RandomAccessIterator last, std::ios_base::fmtflags f);
+ void assign(RandomAccessIterator first, RandomAccessIterator last,
+ std::ios_base::fmtflags);

 // modifiers
 #ifdef BOOST_HAS_RVALUE_REFS
@@ -121,25 +135,15 @@
 template<typename IntegralT> mp_int& operator &= (IntegralT x);
 template<typename IntegralT> mp_int& operator ^= (IntegralT x);

- // operators involving char strings
- mp_int& operator += (const char* s);
- mp_int& operator -= (const char* s);
- mp_int& operator *= (const char* s);
- mp_int& operator /= (const char* s);
- mp_int& operator %= (const char* s);
- mp_int& operator |= (const char* s);
- mp_int& operator &= (const char* s);
- mp_int& operator ^= (const char* s);
-
- // operators involving wchar_t strings
- mp_int& operator += (const wchar_t* s);
- mp_int& operator -= (const wchar_t* s);
- mp_int& operator *= (const wchar_t* s);
- mp_int& operator /= (const wchar_t* s);
- mp_int& operator %= (const wchar_t* s);
- mp_int& operator |= (const wchar_t* s);
- mp_int& operator &= (const wchar_t* s);
- mp_int& operator ^= (const wchar_t* s);
+ // operators involving character strings
+ template<typename charT> mp_int& operator += (const charT*);
+ template<typename charT> mp_int& operator -= (const charT*);
+ template<typename charT> mp_int& operator *= (const charT*);
+ template<typename charT> mp_int& operator /= (const charT*);
+ template<typename charT> mp_int& operator %= (const charT*);
+ template<typename charT> mp_int& operator |= (const charT*);
+ template<typename charT> mp_int& operator &= (const charT*);
+ template<typename charT> mp_int& operator ^= (const charT*);

 // operators involving std::basic_string
 template<typename charT, class traits, class Alloc>
@@ -181,11 +185,9 @@
 typedef traits_type::digit_type digit_type;
 typedef traits_type::word_type word_type;

- bool is_zero() const;
-
 digit_type& operator[](size_type i);
 const digit_type& operator[](size_type i) const;
-
+
 digit_type& at(size_type i);
 const digit_type& at(size_type i) const;
 };
@@ -318,85 +320,45 @@
 template<class A, class T, class charT, class Traits, class Alloc>
 bool operator >= (const std::basic_string<charT,Traits,Alloc>&, const mp_int<A,T>&);

- // Comparison between mp_int and const char*
-
- template<class A, class T>
- bool operator == (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator != (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator < (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator > (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator <= (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator >= (const mp_int<A,T>&, const char*);
-
- // Comparison between const char* and mp_int
-
- template<class A, class T>
- bool operator == (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator != (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator < (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator > (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator <= (const char*, const mp_int<A,T>&);
+ // Comparison between mp_int and const charT*

 template<class A, class T>
- bool operator >= (const char*, const mp_int<A,T>&);
-
- // Comparison between mp_int and const wchar_t*
+ bool operator == (const mp_int<A,T>&, const charT*);

 template<class A, class T>
- bool operator == (const mp_int<A,T>&, const wchar_t*);
+ bool operator != (const mp_int<A,T>&, const charT*);

 template<class A, class T>
- bool operator != (const mp_int<A,T>&, const wchar_t*);
+ bool operator < (const mp_int<A,T>&, const charT*);

 template<class A, class T>
- bool operator < (const mp_int<A,T>&, const wchar_t*);
+ bool operator > (const mp_int<A,T>&, const charT*);

 template<class A, class T>
- bool operator > (const mp_int<A,T>&, const wchar_t*);
+ bool operator <= (const mp_int<A,T>&, const charT*);

 template<class A, class T>
- bool operator <= (const mp_int<A,T>&, const wchar_t*);
+ bool operator >= (const mp_int<A,T>&, const charT*);

- template<class A, class T>
- bool operator >= (const mp_int<A,T>&, const wchar_t*);
-
- // Comparison between const wchar_t* and mp_int
+ // Comparison between const charT* and mp_int

 template<class A, class T>
- bool operator == (const wchar_t*, const mp_int<A,T>&);
+ bool operator == (const charT*, const mp_int<A,T>&);

 template<class A, class T>
- bool operator != (const wchar_t*, const mp_int<A,T>&);
+ bool operator != (const charT*, const mp_int<A,T>&);

 template<class A, class T>
- bool operator < (const wchar_t*, const mp_int<A,T>&);
+ bool operator < (const charT*, const mp_int<A,T>&);

 template<class A, class T>
- bool operator > (const wchar_t*, const mp_int<A,T>&);
+ bool operator > (const charT*, const mp_int<A,T>&);

 template<class A, class T>
- bool operator <= (const wchar_t*, const mp_int<A,T>&);
+ bool operator <= (const charT*, const mp_int<A,T>&);

 template<class A, class T>
- bool operator >= (const wchar_t*, const mp_int<A,T>&);
+ bool operator >= (const charT*, const mp_int<A,T>&);

 // Comparison between mp_int and integral type

@@ -468,6 +430,9 @@
 mp_int<A,T> pow(const mp_int<A,T>& x, typename mp_int<A,T>::digit_type n);

 template<class A, class T>
+ mp_int<A,T> pow(const mp_int<A,T>& x, const mp_int<A,T>& n);
+
+ template<class A, class T>
 mp_int<A,T> modpow(const mp_int<A,T>& base, const mp_int<A,T>& exp, const mp_int<A,T>& mod);

 template<class A, class T>
@@ -476,6 +441,9 @@
 template<class A, class T>
 mp_int<A,T> nth_root(const mp_int<A,T>& x, typename mp_int<A,T>::digit_type n);

+ template<class A, class T>
+ mp_int<A,T> nth_root(const mp_int<A,T>& x, const mp_int<A,T>& n);
+

 } // namespace mp_math
 } // namespace boost
@@ -509,8 +477,18 @@
* [*Throws:] Nothing.

+ explicit mp_int(const allocator_type& a);
+
+* [*Effects:] Constructs an empty `mp_int` object and initializes its allocator
+with `a`, such an uninitialized `mp_int` has no value, i.e. it is /not/ zero.
+* [*Complexity:] O(1).
+* [*Throws:] Nothing.
+
+
 template<typename IntegralT>
- mp_int(IntegralT x, typename enable_if<boost::is_integral<IntegralT> >::type* dummy = 0);
+ mp_int(IntegralT x,
+ const allocator_type& a = allocator_type(),
+ typename enable_if<is_integral<IntegralT> >::type* dummy = 0);

* [*Effects:] Constructs an `mp_int` object from an integral type. The value of
the object is that of the integral type.
@@ -518,8 +496,8 @@
* [*Throws: ] `std::bad_alloc`.

- mp_int(const char* s);
- mp_int(const wchar_t* s);
+ template<typename charT>
+ mp_int(const charT* s, const allocator_type& a = allocator_type());

* [*Requires: ] `s` points to a valid number formatted as string or to an empty
string.
@@ -529,31 +507,38 @@
 * `std::invalid_argument` if the string contains an invalid character.

- template<typename charT, class traits, class Alloc>
- mp_int(const std::basic_string<charT,traits,Alloc>& s);
+ template<typename charT>
+ mp_int(const charT* s,
+ std::ios_base::fmtflags f,
+ const allocator_type& a = allocator_type());

-* [*Requires: ] `s` contains a valid number formatted as string or `s` is an
-empty string.
+* [*Requires: ] `s` points to a valid number formatted according to the flags in
+`f` or `s` is an empty string.
* [*Effects:] Constructs an `mp_int` object from a string.
* [*Throws:]
 * `std::bad_alloc`
- * `std::invalid_argument` if the string contains an invalid character.
+ * `std::invalid_argument` if the string contains an invalid character or if an
+ unrecognized formatting flag was set.

- template<typename RandomAccessIterator>
- mp_int(RandomAccessIterator first, RandomAccessIterator last);
+ template<typename charT, class traits, class Alloc>
+ mp_int(const std::basic_string<charT,traits,Alloc>& s,
+ const allocator_type& a = allocator_type());

-* [*Requires: ] `first` and `last` are iterators into a string.
-* [*Effects:] Constructs an `mp_int` object from two iterators.
+* [*Requires: ] `s` contains a valid number formatted as string or `s` is an
+empty string.
+* [*Effects:] Constructs an `mp_int` object from a string.
* [*Throws:]
 * `std::bad_alloc`
 * `std::invalid_argument` if the string contains an invalid character.

- mp_int(const char* s, std::ios_base::fmtflags f);
- mp_int(const wchar_t* s, std::ios_base::fmtflags f);
+ template<typename charT, class traits, class Alloc>
+ mp_int(const std::basic_string<charT,traits,Alloc>& s,
+ std::ios_base::fmtflags f,
+ const allocator_type& a = allocator_type());

-* [*Requires: ] `s` points to a valid number formatted according to the flags in
+* [*Requires: ] `s` contains a valid number formatted according to the flags in
`f` or `s` is an empty string.
* [*Effects:] Constructs an `mp_int` object from a string.
* [*Throws:]
@@ -562,20 +547,23 @@
 unrecognized formatting flag was set.

- template<typename charT, class traits, class Alloc>
- mp_int(const std::basic_string<charT,traits,Alloc>& s, std::ios_base::fmtflags f);
+ template<typename RandomAccessIterator>
+ mp_int(RandomAccessIterator first,
+ RandomAccessIterator last,
+ const allocator_type& a = allocator_type());

-* [*Requires: ] `s` contains a valid number formatted according to the flags in
-`f` or `s` is an empty string.
-* [*Effects:] Constructs an `mp_int` object from a string.
+* [*Requires: ] `first` and `last` are iterators into a string.
+* [*Effects:] Constructs an `mp_int` object from two iterators.
* [*Throws:]
 * `std::bad_alloc`
- * `std::invalid_argument` if the string contains an invalid character or if an
- unrecognized formatting flag was set.
+ * `std::invalid_argument` if the string contains an invalid character.

 template<typename RandomAccessIterator>
- mp_int(RandomAccessIterator first, RandomAccessIterator last, std::ios_base::fmtflags f);
+ mp_int(RandomAccessIterator first,
+ RandomAccessIterator last,
+ std::ios_base::fmtflags f,
+ const allocator_type& a = allocator_type());

* [*Requires: ] `first` and `last` are iterators into a string formatted
according to the formatting flags in `f`.
@@ -592,13 +580,13 @@
* [*Complexity:] O(N), where N is the number of digits in `copy`.
* [*Throws: ] `std::bad_alloc`.

-
+
 mp_int(mp_int&& copy);

* [*Effects:] Constructs an `mp_int` by moving `copy` into `*this`.
* [*Complexity:] O(1).
* [*Throws:] Nothing.
-
+

 ~mp_int();

@@ -615,7 +603,7 @@
* [*Throws: ] `std::bad_alloc`.
* [*Exception safety:] strong.

-
+
 mp_int& operator = (mp_int&& rhs);

* [*Effects: ] `*this` obtains the value of `rhs`.
@@ -632,8 +620,9 @@
* [*Throws: ] `std::bad_alloc`.
* [*Exception safety:] basic.

- mp_int& operator = (const char* s);
- mp_int& operator = (const wchar_t* s);
+
+ template<typename charT>
+ mp_int& operator = (const charT* s);

* [*Requires: ] `s` points to a valid number formatted as string or to an empty
string.
@@ -656,8 +645,8 @@
* [*Exception safety:] basic.

- void assign(const char* s, std::ios_base::fmtflags f);
- void assign(const wchar_t* s, std::ios_base::fmtflags f);
+ template<typename charT>
+ void assign(const charT* s, std::ios_base::fmtflags);

* [*Requires: ] `s` points to a valid number formatted according to the flags in
`f` or `s` is an empty string.
@@ -670,7 +659,7 @@

 template<typename charT, class traits, class Alloc>
- void assign(const std::basic_string<charT,traits,Alloc>& s, std::ios_base::fmtflags f);
+ void assign(const std::basic_string<charT,traits,Alloc>& s, std::ios_base::fmtflags f);

* [*Requires: ] `s` contains a valid number formatted according to the flags in
`f` or `s` is an empty string.
@@ -837,7 +826,7 @@

 mp_int& operator /= (const mp_int& x);

-* [*Requires: ] `x != 0`.
+* [*Requires: ] `x != 0`.
* [*Effects:] Divides `*this` by `x`.
* [*Returns: ] `*this`.
* [*Throws: ]
@@ -849,7 +838,7 @@

 mp_int& operator %= (const mp_int& x);

-* [*Requires: ] `x != 0`.
+* [*Requires: ] `x != 0`.
* [*Effects:] Modulus `*this` by `x`.
* [*Returns: ] `*this`.
* [*Throws: ]
@@ -954,24 +943,16 @@
* [*Exception safety:] strong.

-[heading Operators involving char/wchar_t strings]
+[heading Operators involving charT strings]

- mp_int& operator += (const char* s);
- mp_int& operator += (const wchar_t* s);
- mp_int& operator -= (const char* s);
- mp_int& operator -= (const wchar_t* s);
- mp_int& operator *= (const char* s);
- mp_int& operator *= (const wchar_t* s);
- mp_int& operator /= (const char* s);
- mp_int& operator /= (const wchar_t* s);
- mp_int& operator %= (const char* s);
- mp_int& operator %= (const wchar_t* s);
- mp_int& operator |= (const char* s);
- mp_int& operator |= (const wchar_t* s);
- mp_int& operator &= (const char* s);
- mp_int& operator &= (const wchar_t* s);
- mp_int& operator ^= (const char* s);
- mp_int& operator ^= (const wchar_t* s);
+ template<typename charT> mp_int& operator += (const charT* s);
+ template<typename charT> mp_int& operator -= (const charT* s);
+ template<typename charT> mp_int& operator *= (const charT* s);
+ template<typename charT> mp_int& operator /= (const charT* s);
+ template<typename charT> mp_int& operator %= (const charT* s);
+ template<typename charT> mp_int& operator |= (const charT* s);
+ template<typename charT> mp_int& operator &= (const charT* s);
+ template<typename charT> mp_int& operator ^= (const charT* s);

[heading Operators involving std::basic_string]

@@ -1207,73 +1188,23 @@
 * `std::invalid_argument` if the string contains an invalid character.

- template<class A, class T>
- bool operator == (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator != (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator < (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator > (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator <= (const mp_int<A,T>&, const char*);
-
- template<class A, class T>
- bool operator >= (const mp_int<A,T>&, const char*);
-
-* [*Effects:] Converts the string argument to an `mp_int` object and compares it
-to the object on the left side of the expression.
-* [*Throws:]
- * `std::bad_alloc`
- * `std::invalid_argument` if the string contains an invalid character.
-
-
- template<class A, class T>
- bool operator == (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator != (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator < (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator > (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator <= (const char*, const mp_int<A,T>&);
-
- template<class A, class T>
- bool operator >= (const char*, const mp_int<A,T>&);
-
-* [*Effects:] Converts the string argument to an `mp_int` object and compares it
-to the object on the right side of the expression.
-* [*Throws:]
- * `std::bad_alloc`
- * `std::invalid_argument` if the string contains an invalid character.
-
-
- template<class A, class T>
- bool operator == (const mp_int<A,T>&, const wchar_t*);
+ template<class A, class T, typename charT>
+ bool operator == (const mp_int<A,T>&, const charT*);

- template<class A, class T>
- bool operator != (const mp_int<A,T>&, const wchar_t*);
+ template<class A, class T, typename charT>
+ bool operator != (const mp_int<A,T>&, const charT*);

- template<class A, class T>
- bool operator < (const mp_int<A,T>&, const wchar_t*);
+ template<class A, class T, typename charT>
+ bool operator < (const mp_int<A,T>&, const charT*);

- template<class A, class T>
- bool operator > (const mp_int<A,T>&, const wchar_t*);
+ template<class A, class T, typename charT>
+ bool operator > (const mp_int<A,T>&, const charT*);

- template<class A, class T>
- bool operator <= (const mp_int<A,T>&, const wchar_t*);
+ template<class A, class T, typename charT>
+ bool operator <= (const mp_int<A,T>&, const charT*);

- template<class A, class T>
- bool operator >= (const mp_int<A,T>&, const wchar_t*);
+ template<class A, class T, typename charT>
+ bool operator >= (const mp_int<A,T>&, const charT*);

* [*Effects:] Converts the string argument to an `mp_int` object and compares it
to the object on the left side of the expression.
@@ -1282,23 +1213,23 @@
 * `std::invalid_argument` if the string contains an invalid character.

- template<class A, class T>
- bool operator == (const wchar_t*, const mp_int<A,T>&);
+ template<class A, class T, typename charT>
+ bool operator == (const charT*, const mp_int<A,T>&);

- template<class A, class T>
- bool operator != (const wchar_t*, const mp_int<A,T>&);
+ template<class A, class T, typename charT>
+ bool operator != (const charT*, const mp_int<A,T>&);

- template<class A, class T>
- bool operator < (const wchar_t*, const mp_int<A,T>&);
+ template<class A, class T, typename charT>
+ bool operator < (const charT*, const mp_int<A,T>&);

- template<class A, class T>
- bool operator > (const wchar_t*, const mp_int<A,T>&);
+ template<class A, class T, typename charT>
+ bool operator > (const charT*, const mp_int<A,T>&);

- template<class A, class T>
- bool operator <= (const wchar_t*, const mp_int<A,T>&);
+ template<class A, class T, typename charT>
+ bool operator <= (const charT*, const mp_int<A,T>&);

- template<class A, class T>
- bool operator >= (const wchar_t*, const mp_int<A,T>&);
+ template<class A, class T, typename charT>
+ bool operator >= (const charT*, const mp_int<A,T>&);

* [*Effects:] Converts the string argument to an `mp_int` object and compares it
to the object on the right side of the expression.
@@ -1402,6 +1333,9 @@
 template<class A, class T>
 mp_int<A,T> pow(const mp_int<A,T>& x, typename mp_int<A,T>::digit_type n);

+ template<class A, class T>
+ mp_int<A,T> pow(const mp_int<A,T>& x, const mp_int<A,T>& n);
+
* [*Returns:] The `n`th power of `x`.
* [*Throws: ] `std::bad_alloc`.

@@ -1428,6 +1362,9 @@
 template<class A, class T>
 mp_int<A,T> nth_root(const mp_int<A,T>& x, typename mp_int<A,T>::digit_type n);

+ template<class A, class T>
+ mp_int<A,T> nth_root(const mp_int<A,T>& x, const mp_int<A,T>& n);
+
* [*Returns:] The `n`th root of `x`.
* [*Complexity:] O(log(N)).
* [*Throws:]

Modified: sandbox/mp_math/libs/mp_math/doc/primality_tests_reference.qbk
==============================================================================
--- sandbox/mp_math/libs/mp_math/doc/primality_tests_reference.qbk (original)
+++ sandbox/mp_math/libs/mp_math/doc/primality_tests_reference.qbk 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -1,4 +1,4 @@
-[/ Copyright Kevin Sopp 2008.
+[/ Copyright Kevin Sopp 2008 - 2009.
 / Distributed under the Boost Software License, Version 1.0.
 / (See accompanying file LICENSE_1_0.txt or copy at
 / http://www.boost.org/LICENSE_1_0.txt)]
@@ -118,7 +118,7 @@
 template<class Engine, class A, class T>
 bool operator()(Engine& e, const mp_int<A,T>& p) const;

-* [*Requires:] `p` is odd.
+* [*Requires: ] `p` is odd.
* [*Effects:] Returns true if `p` is probably prime. Returns false if `p`
is definitely composite.

Modified: sandbox/mp_math/libs/mp_math/test/integral_ops.cpp
==============================================================================
--- sandbox/mp_math/libs/mp_math/test/integral_ops.cpp (original)
+++ sandbox/mp_math/libs/mp_math/test/integral_ops.cpp 2009-01-16 18:53:21 EST (Fri, 16 Jan 2009)
@@ -146,6 +146,13 @@
BOOST_CHECK_EQUAL(z, "123495198423");
}

+BOOST_AUTO_TEST_CASE_TEMPLATE(subtract_signed_integral4, mp_int_type, mp_int_types)
+{
+ const mp_int_type x("1");
+ const mp_int_type z = x - 2;
+ BOOST_CHECK_EQUAL(z, "-1");
+}
+
BOOST_AUTO_TEST_CASE_TEMPLATE(subtract_unsigned_char1, mp_int_type, mp_int_types)
{
const unsigned char y = 14;

Next message: baraclese_at_[hidden]: "[Boost-commit] svn:boost r50648 - in sandbox/mp_math/libs/mp_math/doc: . html html/mp_int"
Previous message: fmhess_at_[hidden]: "[Boost-commit] svn:boost r50646 - sandbox/thread_safe_signals/trunk/libs/signals2/doc"

Date view	Thread view	Subject view	Author view

Boost-Commit list run by bdawes at acm.org, david.abrahams at rcn.com, gregod at cs.rpi.edu, cpdaniel at pacbell.net, john at johnmaddock.co.uk