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Chapter9.Boost.Math

Hubert Holin

John Maddock

Daryle Walker

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)

Table of Contents

Overview
Greatest Common Divisor and Least Common Multiple
Introduction
Synopsis
GCD Function Object
LCM Function Object
Run-time GCD & LCM Determination
Compile time GCD and LCM determination
Header <boost/math/common_factor.hpp>
Demonstration Program
Rationale
History
Credits
Math Special Functions
Overview
Header Files
Synopsis
acosh
asinh
atanh
expm1
hypot
log1p
sinc_pi
sinhc_pi
Test Programs
Acknowledgements
History
To Do
Complex Number Inverse Trigonometric Functions
Implementation and Accuracy
asin
acos
atan
asinh
acosh
atanh
History
Quaternions
Overview
Header File
Synopsis
Template Class quaternion
Quaternion Specializations
Quaternion Member Typedefs
Quaternion Member Functions
Quaternion Non-Member Operators
Quaternion Value Operations
Quaternion Creation Functions
Quaternion Transcendentals
Test Program
Acknowledgements
History
To Do
Octonions
Overview
Header File
Synopsis
Template Class octonion
Octonion Specializations
Octonion Member Typedefs
Octonion Member Functions
Octonion Non-Member Operators
Octonion Value Operations
Quaternion Creation Functions
Octonions Transcendentals
Test Program
Acknowledgements
History
To Do
Background Information and White Papers
The Inverse Hyperbolic Functions
Sinus Cardinal and Hyperbolic Sinus Cardinal Functions
The Quaternionic Exponential

Overview

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The Greatest Common Divisor and Least Common Multiple library provides run-time and compile-time evaluation of the greatest common divisor (GCD) or least common multiple (LCM) of two integers.

The Special Functions library currently provides eight templated special functions, in namespace boost. Two of these (sinc_pi and sinhc_pi) are needed by our implementation of quaternions and octonions. The functions acosh, asinh and atanh are entirely classical, the function sinc_pi sees heavy use in signal processing tasks, and the function sinhc_pi is an ad'hoc function whose naming is modelled on sinc_pi and hyperbolic functions. The functions log1p, expm1 and hypot are all part of the C99 standard but not yet C++. Two of these (log1p and hypot) were needed for the complex number inverse trigonometric functions.

The Complex Number Inverse Trigonometric Functions are the inverses of trigonometric functions currently present in the C++ standard. Equivalents to these functions are part of the C99 standard, and they will be part of the forthcoming Technical Report on C++ Standard Library Extensions.

Quaternions are a relative of complex numbers often used to parameterise rotations in three dimentional space.

Octonions, like quaternions, are a relative of complex numbers. Octonions see some use in theoretical physics.

Last revised: May 09, 2007 at 17:20:56 GMT


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