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- [def __effects [*Effects: ]]
- [def __formula [*Formula: ]]
- [def __exm1 '''<code>e<superscript>x</superscript> - 1</code>''']
- [def __ex '''<code>e<superscript>x</superscript></code>''']
- [def __te '''2ε''']
- [mathpart inverse_complex..Complex Number Functions]
- 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
- are part of the [tr1].
- [section:complex_implementation Implementation and Accuracy]
- 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 9.5[epsilon] 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.
- [endsect]
- [section:asin asin]
- [h4 Header:]
- #include <boost/math/complex/asin.hpp>
- [h4 Synopsis:]
- template<class T>
- std::complex<T> asin(const std::complex<T>& z);
- __effects returns the inverse sine of the complex number z.
- __formula [$../images/asin.png]
- [endsect]
- [section:acos acos]
- [h4 Header:]
- #include <boost/math/complex/acos.hpp>
- [h4 Synopsis:]
- template<class T>
- std::complex<T> acos(const std::complex<T>& z);
- __effects returns the inverse cosine of the complex number z.
- __formula [$../images/acos.png]
- [endsect]
- [section:atan atan]
- [h4 Header:]
- #include <boost/math/complex/atan.hpp>
- [h4 Synopsis:]
- template<class T>
- std::complex<T> atan(const std::complex<T>& z);
- __effects returns the inverse tangent of the complex number z.
- __formula [$../images/atan.png]
- [endsect]
- [section:asinh asinh]
- [h4 Header:]
- #include <boost/math/complex/asinh.hpp>
- [h4 Synopsis:]
- template<class T>
- std::complex<T> asinh(const std::complex<T>& z);
- __effects returns the inverse hyperbolic sine of the complex number z.
- __formula [$../images/asinh.png]
- [endsect]
- [section:acosh acosh]
- [h4 Header:]
- #include <boost/math/complex/acosh.hpp>
- [h4 Synopsis:]
- template<class T>
- std::complex<T> acosh(const std::complex<T>& z);
- __effects returns the inverse hyperbolic cosine of the complex number z.
- __formula [$../images/acosh.png]
- [endsect]
- [section:atanh atanh]
- [h4 Header:]
- #include <boost/math/complex/atanh.hpp>
- [h4 Synopsis:]
- template<class T>
- std::complex<T> atanh(const std::complex<T>& z);
- __effects returns the inverse hyperbolic tangent of the complex number z.
- __formula [$../images/atanh.png]
- [endsect]
- [section:complex_history History]
- * 2005/12/17: Added support for platforms with no meaningful numeric_limits<>::infinity().
- * 2005/12/01: Initial version, added as part of the TR1 library.
- [endsect]
- [endmathpart]
- [/
- Copyright 2008, 2009 John Maddock and Paul A. Bristow.
- 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).
- ]
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