...one of the most highly
regarded and expertly designed C++ library projects in the
world.

— Herb Sutter and Andrei
Alexandrescu, C++
Coding Standards

The following complex number algorithms are the inverses of trigonometric functions currently present in the C++ standard. Equivalents to these functions are part of the C99 standard, and will be part of the forthcoming Technical Report on C++ Standard Library Extensions.

Although there are deceptively simple formulae available for all of these functions, a naive implementation that used these formulae would fail catastrophically for some input values. The Boost versions of these functions have been implemented using the methodology described in "Implementing the Complex Arcsine and Arccosine Functions Using Exception Handling" by T. E. Hull Thomas F. Fairgrieve and Ping Tak Peter Tang, ACM Transactions on Mathematical Software, Vol. 23, No. 3, September 1997. This means that the functions are well defined over the entire complex number range, and produce accurate values even at the extremes of that range, where as a naive formula would cause overflow or underflow to occur during the calculation, even though the result is actually a representable value. The maximum theoretical relative error for all of these functions is less than 9.5E for every machine-representable point in the complex plane. Please refer to comments in the header files themselves and to the above mentioned paper for more information on the implementation methodology.

#include <boost/math/complex/asin.hpp>

template<class T> std::complex<T> asin(const std::complex<T>& z);

**Effects: ** returns the inverse sine of the
complex number z.

**Formula: **

#include <boost/math/complex/acos.hpp>

template<class T> std::complex<T> acos(const std::complex<T>& z);

**Effects: ** returns the inverse cosine of
the complex number z.

**Formula: **

#include <boost/math/complex/atan.hpp>

template<class T> std::complex<T> atan(const std::complex<T>& z);

**Effects: ** returns the inverse tangent of
the complex number z.

**Formula: **

#include <boost/math/complex/asinh.hpp>

template<class T> std::complex<T> asinh(const std::complex<T>& z);

**Effects: ** returns the inverse hyperbolic
sine of the complex number z.

**Formula: **

#include <boost/math/complex/acosh.hpp>

template<class T> std::complex<T> acosh(const std::complex<T>& z);

**Effects: ** returns the inverse hyperbolic
cosine of the complex number z.

**Formula: **

Copyright © 2001 -2002 Daryle Walker, 2001-2003 Hubert Holin, 2005 John Maddock |