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| 25 | <div class="chapter" lang="en"> |
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| 26 | <div class="titlepage"><div> |
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| 27 | <div><h2 class="title"> |
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| 28 | <a name="boost_math"></a>Chapter 9. Boost.Math</h2></div> |
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| 29 | <div><div class="author"><h3 class="author"> |
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| 30 | <span class="firstname">Hubert</span> <span class="surname">Holin</span> |
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| 31 | </h3></div></div> |
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| 32 | <div><div class="author"><h3 class="author"> |
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| 33 | <span class="firstname">John</span> <span class="surname">Maddock</span> |
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| 34 | </h3></div></div> |
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| 35 | <div><div class="author"><h3 class="author"> |
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| 36 | <span class="firstname">Daryle</span> <span class="surname">Walker</span> |
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| 37 | </h3></div></div> |
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| 38 | <div><p class="copyright">Copyright © 2001 -2002 Daryle Walker, 2001-2003 Hubert Holin, 2005 |
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| 39 | John Maddock</p></div> |
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| 40 | <div><div class="legalnotice"> |
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| 41 | <a name="id1250634"></a><p> |
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| 42 | Distributed under the Boost Software License, Version 1.0. (See accompanying |
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| 43 | file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
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| 44 | </p> |
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| 45 | </div></div> |
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| 46 | </div></div> |
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| 47 | <div class="toc"> |
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| 48 | <p><b>Table of Contents</b></p> |
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| 49 | <dl> |
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| 50 | <dt><span class="section"><a href="boost_math.html#boost_math.overview">Overview</a></span></dt> |
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| 51 | <dt><span class="section"><a href="boost_math/gcd_lcm.html"> Greatest Common Divisor and Least Common Multiple</a></span></dt> |
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| 52 | <dd><dl> |
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| 53 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.introduction">Introduction</a></span></dt> |
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| 54 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.synopsis">Synopsis</a></span></dt> |
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| 55 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.gcd_function_object">GCD Function Object</a></span></dt> |
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| 56 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.lcm_function_object">LCM Function Object</a></span></dt> |
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| 57 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.run_time_gcd___lcm_determination">Run-time GCD & LCM Determination</a></span></dt> |
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| 58 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.compile_time_gcd_and_lcm_determination">Compile time GCD and LCM determination</a></span></dt> |
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| 59 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.header__boost_math_common_factor_hpp_">Header <boost/math/common_factor.hpp></a></span></dt> |
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| 60 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.demonstration_program">Demonstration Program</a></span></dt> |
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| 61 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.rationale">Rationale</a></span></dt> |
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| 62 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.history">History</a></span></dt> |
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| 63 | <dt><span class="section"><a href="boost_math/gcd_lcm.html#boost_math.gcd_lcm.credits">Credits</a></span></dt> |
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| 64 | </dl></dd> |
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| 65 | <dt><span class="section"><a href="boost_math/math_special_functions.html">Math Special Functions</a></span></dt> |
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| 66 | <dd><dl> |
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| 67 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.overview">Overview</a></span></dt> |
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| 68 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.header_files">Header Files</a></span></dt> |
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| 69 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.synopsis">Synopsis</a></span></dt> |
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| 70 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.acosh">acosh</a></span></dt> |
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| 71 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.asinh">asinh</a></span></dt> |
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| 72 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.atanh">atanh</a></span></dt> |
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| 73 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.expm1"> expm1</a></span></dt> |
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| 74 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.hypot"> hypot</a></span></dt> |
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| 75 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.log1p"> log1p</a></span></dt> |
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| 76 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.sinc_pi">sinc_pi</a></span></dt> |
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| 77 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.sinhc_pi">sinhc_pi</a></span></dt> |
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| 78 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.test_programs">Test Programs</a></span></dt> |
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| 79 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.acknowledgements">Acknowledgements</a></span></dt> |
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| 80 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.history">History</a></span></dt> |
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| 81 | <dt><span class="section"><a href="boost_math/math_special_functions.html#boost_math.math_special_functions.to_do">To Do</a></span></dt> |
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| 82 | </dl></dd> |
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| 83 | <dt><span class="section"><a href="boost_math/inverse_complex.html"> Complex Number Inverse Trigonometric Functions</a></span></dt> |
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| 84 | <dd><dl> |
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| 85 | <dt><span class="section"><a href="boost_math/inverse_complex.html#boost_math.inverse_complex.implementation_and_accuracy">Implementation and Accuracy</a></span></dt> |
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| 86 | <dt><span class="section"><a href="boost_math/inverse_complex.html#boost_math.inverse_complex.asin"> asin</a></span></dt> |
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| 87 | <dt><span class="section"><a href="boost_math/inverse_complex.html#boost_math.inverse_complex.acos"> acos</a></span></dt> |
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| 88 | <dt><span class="section"><a href="boost_math/inverse_complex.html#boost_math.inverse_complex.atan"> atan</a></span></dt> |
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| 89 | <dt><span class="section"><a href="boost_math/inverse_complex.html#boost_math.inverse_complex.asinh"> asinh</a></span></dt> |
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| 90 | <dt><span class="section"><a href="boost_math/inverse_complex.html#boost_math.inverse_complex.acosh"> acosh</a></span></dt> |
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| 91 | <dt><span class="section"><a href="boost_math/inverse_complex.html#boost_math.inverse_complex.atanh"> atanh</a></span></dt> |
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| 92 | <dt><span class="section"><a href="boost_math/inverse_complex.html#boost_math.inverse_complex.history">History</a></span></dt> |
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| 93 | </dl></dd> |
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| 94 | <dt><span class="section"><a href="boost_math/quaternions.html">Quaternions</a></span></dt> |
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| 95 | <dd><dl> |
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| 96 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.overview">Overview</a></span></dt> |
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| 97 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.header_file">Header File</a></span></dt> |
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| 98 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.synopsis">Synopsis</a></span></dt> |
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| 99 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.template_class_quaternion">Template Class quaternion</a></span></dt> |
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| 100 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.quaternion_specializations">Quaternion Specializations</a></span></dt> |
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| 101 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.quaternion_member_typedefs">Quaternion Member Typedefs</a></span></dt> |
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| 102 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.quaternion_member_functions">Quaternion Member Functions</a></span></dt> |
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| 103 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.quaternion_non_member_operators">Quaternion Non-Member Operators</a></span></dt> |
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| 104 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.quaternion_value_operations">Quaternion Value Operations</a></span></dt> |
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| 105 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.quaternion_creation_functions">Quaternion Creation Functions</a></span></dt> |
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| 106 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.quaternion_transcendentals">Quaternion Transcendentals</a></span></dt> |
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| 107 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.test_program">Test Program</a></span></dt> |
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| 108 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.acknowledgements">Acknowledgements</a></span></dt> |
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| 109 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.history">History</a></span></dt> |
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| 110 | <dt><span class="section"><a href="boost_math/quaternions.html#boost_math.quaternions.to_do">To Do</a></span></dt> |
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| 111 | </dl></dd> |
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| 112 | <dt><span class="section"><a href="boost_math/octonions.html">Octonions</a></span></dt> |
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| 113 | <dd><dl> |
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| 114 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.overview">Overview</a></span></dt> |
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| 115 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.header_file">Header File</a></span></dt> |
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| 116 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.synopsis">Synopsis</a></span></dt> |
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| 117 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.template_class_octonion">Template Class octonion</a></span></dt> |
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| 118 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.octonion_specializations">Octonion Specializations</a></span></dt> |
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| 119 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.octonion_member_typedefs">Octonion Member Typedefs</a></span></dt> |
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| 120 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.octonion_member_functions">Octonion Member Functions</a></span></dt> |
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| 121 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.octonion_non_member_operators">Octonion Non-Member Operators</a></span></dt> |
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| 122 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.octonion_value_operations">Octonion Value Operations</a></span></dt> |
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| 123 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.quaternion_creation_functions">Quaternion Creation Functions</a></span></dt> |
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| 124 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.octonions_transcendentals">Octonions Transcendentals</a></span></dt> |
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| 125 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.test_program">Test Program</a></span></dt> |
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| 126 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.acknowledgements">Acknowledgements</a></span></dt> |
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| 127 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.history">History</a></span></dt> |
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| 128 | <dt><span class="section"><a href="boost_math/octonions.html#boost_math.octonions.to_do">To Do</a></span></dt> |
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| 129 | </dl></dd> |
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| 130 | <dt><span class="section"><a href="boost_math/background_information_and_white_papers.html">Background Information and White Papers</a></span></dt> |
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| 131 | <dd><dl> |
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| 132 | <dt><span class="section"><a href="boost_math/background_information_and_white_papers.html#boost_math.background_information_and_white_papers.the_inverse_hyperbolic_functions">The Inverse Hyperbolic Functions</a></span></dt> |
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| 133 | <dt><span class="section"><a href="boost_math/background_information_and_white_papers.html#boost_math.background_information_and_white_papers.sinus_cardinal_and_hyperbolic_sinus_cardinal_functions">Sinus Cardinal and Hyperbolic Sinus Cardinal Functions</a></span></dt> |
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| 134 | <dt><span class="section"><a href="boost_math/background_information_and_white_papers.html#boost_math.background_information_and_white_papers.the_quaternionic_exponential">The Quaternionic Exponential</a></span></dt> |
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| 135 | </dl></dd> |
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| 136 | </dl> |
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| 137 | </div> |
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| 138 | <div class="section" lang="en"> |
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| 139 | <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
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| 140 | <a name="boost_math.overview"></a>Overview</h2></div></div></div> |
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| 141 | <p> |
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| 142 | This documentation is <a href="http://boost-consulting.com/vault/index.php?action=downloadfile&filename=boost_math-1.34.pdf&directory=PDF%20Documentation&" target="_top">also |
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| 143 | available in printer-friendly PDF format</a>. |
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| 144 | </p> |
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| 145 | <p> |
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| 146 | The <a href="boost_math/gcd_lcm.html" title=" Greatest Common Divisor and Least Common Multiple">Greatest Common Divisor and Least Common |
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| 147 | Multiple library</a> provides run-time and compile-time evaluation of the |
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| 148 | greatest common divisor (GCD) or least common multiple (LCM) of two integers. |
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| 149 | </p> |
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| 150 | <p> |
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| 151 | The <a href="boost_math/math_special_functions.html" title="Math Special Functions">Special Functions library</a> |
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| 152 | currently provides eight templated special functions, in namespace boost. Two |
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| 153 | of these (<a href="boost_math/math_special_functions.html#boost_math.math_special_functions.sinc_pi" title="sinc_pi">sinc_pi</a> |
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| 154 | and <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.sinhc_pi" title="sinhc_pi">sinhc_pi</a>) |
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| 155 | are needed by our implementation of quaternions and octonions. The functions |
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| 156 | <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.acosh" title="acosh">acosh</a>, <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.asinh" title="asinh">asinh</a> and <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.atanh" title="atanh">atanh</a> |
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| 157 | are entirely classical, the function <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.sinc_pi" title="sinc_pi">sinc_pi</a> |
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| 158 | sees heavy use in signal processing tasks, and the function <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.sinhc_pi" title="sinhc_pi">sinhc_pi</a> |
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| 159 | is an ad'hoc function whose naming is modelled on <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.sinc_pi" title="sinc_pi">sinc_pi</a> |
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| 160 | and hyperbolic functions. The functions <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.log1p" title=" log1p">log1p</a>, |
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| 161 | <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.expm1" title=" expm1">expm1</a> and <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.hypot" title=" hypot">hypot</a> are all part |
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| 162 | of the C99 standard but not yet C++. Two of these (<a href="boost_math/math_special_functions.html#boost_math.math_special_functions.log1p" title=" log1p">log1p</a> |
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| 163 | and <a href="boost_math/math_special_functions.html#boost_math.math_special_functions.hypot" title=" hypot">hypot</a>) were |
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| 164 | needed for the <a href="boost_math/inverse_complex.html" title=" Complex Number Inverse Trigonometric Functions">complex number inverse |
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| 165 | trigonometric functions</a>. |
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| 166 | </p> |
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| 167 | <p> |
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| 168 | The <a href="boost_math/inverse_complex.html" title=" Complex Number Inverse Trigonometric Functions">Complex Number Inverse Trigonometric |
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| 169 | Functions</a> are the inverses of trigonometric functions currently present |
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| 170 | in the C++ standard. Equivalents to these functions are part of the C99 standard, |
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| 171 | and they will be part of the forthcoming Technical Report on C++ Standard Library |
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| 172 | Extensions. |
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| 173 | </p> |
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| 174 | <p> |
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| 175 | <a href="boost_math/quaternions.html" title="Quaternions">Quaternions</a> are a relative of |
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| 176 | complex numbers often used to parameterise rotations in three dimentional space. |
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| 177 | </p> |
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| 178 | <p> |
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| 179 | <a href="boost_math/octonions.html" title="Octonions">Octonions</a>, like <a href="boost_math/quaternions.html" title="Quaternions">quaternions</a>, |
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| 180 | are a relative of complex numbers. <a href="boost_math/octonions.html" title="Octonions">Octonions</a> |
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| 181 | see some use in theoretical physics. |
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| 182 | </p> |
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| 183 | </div> |
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| 184 | </div> |
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| 185 | <table width="100%"><tr> |
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| 186 | <td align="left"><small><p>Last revised: May 09, 2007 at 17:20:56 GMT</p></small></td> |
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| 187 | <td align="right"><small></small></td> |
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| 188 | </tr></table> |
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| 189 | <hr> |
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| 190 | <div class="spirit-nav"> |
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| 191 | <a accesskey="p" href="apa.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="libraries.html"><img src="images/up.png" alt="Up"></a><a accesskey="h" href="index.html"><img src="images/home.png" alt="Home"></a><a accesskey="n" href="boost_math/gcd_lcm.html"><img src="images/next.png" alt="Next"></a> |
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| 192 | </div> |
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