107 lines
2.6 KiB
C++
107 lines
2.6 KiB
C++
# ifndef CPPAD_CORE_ERF_HPP
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# define CPPAD_CORE_ERF_HPP
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/* --------------------------------------------------------------------------
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CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell
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CppAD is distributed under multiple licenses. This distribution is under
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the terms of the
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Eclipse Public License Version 1.0.
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A copy of this license is included in the COPYING file of this distribution.
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Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
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-------------------------------------------------------------------------- */
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/*
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-------------------------------------------------------------------------------
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$begin erf$$
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$spell
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erf
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const
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Vec
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std
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cmath
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CppAD
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Vedder
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$$
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$section The Error Function$$
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$head Syntax$$
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$icode%y% = erf(%x%)%$$
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$head Description$$
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Returns the value of the error function which is defined by
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$latex \[
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{\rm erf} (x) = \frac{2}{ \sqrt{\pi} } \int_0^x \exp( - t * t ) \; {\bf d} t
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\] $$
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$head x, y$$
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See the $cref/possible types/unary_standard_math/Possible Types/$$
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for a unary standard math function.
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$head CPPAD_USE_CPLUSPLUS_2011$$
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$subhead true$$
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If this preprocessor symbol is true ($code 1$$),
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and $icode x$$ is an AD type,
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this is an $cref/atomic operation/glossary/Operation/Atomic/$$.
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$subhead false$$
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If this preprocessor symbol is false ($code 0$$),
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CppAD uses a fast approximation (few numerical operations)
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with relative error bound $latex 4 \times 10^{-4}$$; see
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Vedder, J.D.,
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$icode Simple approximations for the error function and its inverse$$,
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American Journal of Physics,
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v 55,
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n 8,
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1987,
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p 762-3.
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$head Example$$
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$children%
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example/general/erf.cpp
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%$$
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The file
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$cref erf.cpp$$
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contains an example and test of this function.
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It returns true if it succeeds and false otherwise.
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$end
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-------------------------------------------------------------------------------
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*/
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# include <cppad/configure.hpp>
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# if ! CPPAD_USE_CPLUSPLUS_2011
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// BEGIN CppAD namespace
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namespace CppAD {
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template <class Type>
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Type erf_template(const Type &x)
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{ using CppAD::exp;
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const Type a = static_cast<Type>(993./880.);
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const Type b = static_cast<Type>(89./880.);
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return tanh( (a + b * x * x) * x );
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}
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inline float erf(const float &x)
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{ return erf_template(x); }
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inline double erf(const double &x)
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{ return erf_template(x); }
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template <class Base>
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inline AD<Base> erf(const AD<Base> &x)
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{ return erf_template(x); }
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template <class Base>
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inline AD<Base> erf(const VecAD_reference<Base> &x)
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{ return erf_template( x.ADBase() ); }
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} // END CppAD namespace
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# endif // CPPAD_USE_CPLUSPLUS_2011
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# endif // CPPAD_ERF_INCLUDED
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