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/*
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* Copyright (c) 1999
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* Silicon Graphics Computer Systems, Inc.
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*
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* Copyright (c) 1999
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* Boris Fomitchev
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*
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* This material is provided "as is", with absolutely no warranty expressed
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* or implied. Any use is at your own risk.
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*
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* Permission to use or copy this software for any purpose is hereby granted
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* without fee, provided the above notices are retained on all copies.
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* Permission to modify the code and to distribute modified code is granted,
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* provided the above notices are retained, and a notice that the code was
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* modified is included with the above copyright notice.
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*
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*/
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#include "stlport_prefix.h"
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#include <numeric>
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#include <cmath>
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#include <complex>
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#if defined (_STLP_MSVC_LIB) && (_STLP_MSVC_LIB >= 1400)
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// hypot is deprecated.
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# if defined (_STLP_MSVC)
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# pragma warning (disable : 4996)
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# elif defined (__ICL)
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# pragma warning (disable : 1478)
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# endif
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#endif
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_STLP_BEGIN_NAMESPACE
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// Complex division and square roots.
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// Absolute value
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC float _STLP_CALL abs(const complex<float>& __z)
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{ return ::hypot(__z._M_re, __z._M_im); }
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC double _STLP_CALL abs(const complex<double>& __z)
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{ return ::hypot(__z._M_re, __z._M_im); }
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#if !defined (_STLP_NO_LONG_DOUBLE)
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC long double _STLP_CALL abs(const complex<long double>& __z)
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{ return ::hypot(__z._M_re, __z._M_im); }
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#endif
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// Phase
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC float _STLP_CALL arg(const complex<float>& __z)
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{ return ::atan2(__z._M_im, __z._M_re); }
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC double _STLP_CALL arg(const complex<double>& __z)
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{ return ::atan2(__z._M_im, __z._M_re); }
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#if !defined (_STLP_NO_LONG_DOUBLE)
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC long double _STLP_CALL arg(const complex<long double>& __z)
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{ return ::atan2(__z._M_im, __z._M_re); }
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#endif
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// Construct a complex number from polar representation
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC complex<float> _STLP_CALL polar(const float& __rho, const float& __phi)
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{ return complex<float>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC complex<double> _STLP_CALL polar(const double& __rho, const double& __phi)
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{ return complex<double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
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#if !defined (_STLP_NO_LONG_DOUBLE)
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_STLP_TEMPLATE_NULL
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_STLP_DECLSPEC complex<long double> _STLP_CALL polar(const long double& __rho, const long double& __phi)
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{ return complex<long double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
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#endif
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// Division
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template <class _Tp>
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static void _divT(const _Tp& __z1_r, const _Tp& __z1_i,
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const _Tp& __z2_r, const _Tp& __z2_i,
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_Tp& __res_r, _Tp& __res_i) {
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_Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r;
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_Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i;
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if (__ar <= __ai) {
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_Tp __ratio = __z2_r / __z2_i;
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_Tp __denom = __z2_i * (1 + __ratio * __ratio);
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__res_r = (__z1_r * __ratio + __z1_i) / __denom;
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__res_i = (__z1_i * __ratio - __z1_r) / __denom;
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}
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else {
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_Tp __ratio = __z2_i / __z2_r;
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_Tp __denom = __z2_r * (1 + __ratio * __ratio);
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__res_r = (__z1_r + __z1_i * __ratio) / __denom;
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__res_i = (__z1_i - __z1_r * __ratio) / __denom;
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}
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}
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template <class _Tp>
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static void _divT(const _Tp& __z1_r,
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const _Tp& __z2_r, const _Tp& __z2_i,
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_Tp& __res_r, _Tp& __res_i) {
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_Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r;
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_Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i;
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if (__ar <= __ai) {
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_Tp __ratio = __z2_r / __z2_i;
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_Tp __denom = __z2_i * (1 + __ratio * __ratio);
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__res_r = (__z1_r * __ratio) / __denom;
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__res_i = - __z1_r / __denom;
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}
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else {
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_Tp __ratio = __z2_i / __z2_r;
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_Tp __denom = __z2_r * (1 + __ratio * __ratio);
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__res_r = __z1_r / __denom;
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__res_i = - (__z1_r * __ratio) / __denom;
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}
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}
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_STLP_DECLSPEC void _STLP_CALL
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complex<float>::_div(const float& __z1_r, const float& __z1_i,
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const float& __z2_r, const float& __z2_i,
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float& __res_r, float& __res_i)
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{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
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_STLP_DECLSPEC void _STLP_CALL
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complex<float>::_div(const float& __z1_r,
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const float& __z2_r, const float& __z2_i,
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float& __res_r, float& __res_i)
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{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
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_STLP_DECLSPEC void _STLP_CALL
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complex<double>::_div(const double& __z1_r, const double& __z1_i,
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const double& __z2_r, const double& __z2_i,
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double& __res_r, double& __res_i)
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{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
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_STLP_DECLSPEC void _STLP_CALL
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complex<double>::_div(const double& __z1_r,
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const double& __z2_r, const double& __z2_i,
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double& __res_r, double& __res_i)
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{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
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#if !defined (_STLP_NO_LONG_DOUBLE)
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_STLP_DECLSPEC void _STLP_CALL
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complex<long double>::_div(const long double& __z1_r, const long double& __z1_i,
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const long double& __z2_r, const long double& __z2_i,
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long double& __res_r, long double& __res_i)
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{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
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_STLP_DECLSPEC void _STLP_CALL
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complex<long double>::_div(const long double& __z1_r,
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const long double& __z2_r, const long double& __z2_i,
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long double& __res_r, long double& __res_i)
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{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
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#endif
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//----------------------------------------------------------------------
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// Square root
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template <class _Tp>
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static complex<_Tp> sqrtT(const complex<_Tp>& z) {
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_Tp re = z._M_re;
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_Tp im = z._M_im;
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_Tp mag = ::hypot(re, im);
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complex<_Tp> result;
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if (mag == 0.f) {
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result._M_re = result._M_im = 0.f;
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} else if (re > 0.f) {
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result._M_re = ::sqrt(0.5f * (mag + re));
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result._M_im = im/result._M_re/2.f;
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} else {
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result._M_im = ::sqrt(0.5f * (mag - re));
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if (im < 0.f)
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result._M_im = - result._M_im;
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result._M_re = im/result._M_im/2.f;
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}
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return result;
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}
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_STLP_DECLSPEC complex<float> _STLP_CALL
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sqrt(const complex<float>& z) { return sqrtT(z); }
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_STLP_DECLSPEC complex<double> _STLP_CALL
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sqrt(const complex<double>& z) { return sqrtT(z); }
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#if !defined (_STLP_NO_LONG_DOUBLE)
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_STLP_DECLSPEC complex<long double> _STLP_CALL
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sqrt(const complex<long double>& z) { return sqrtT(z); }
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#endif
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// exp, log, pow for complex<float>, complex<double>, and complex<long double>
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//----------------------------------------------------------------------
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// exp
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template <class _Tp>
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static complex<_Tp> expT(const complex<_Tp>& z) {
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_Tp expx = ::exp(z._M_re);
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return complex<_Tp>(expx * ::cos(z._M_im),
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expx * ::sin(z._M_im));
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}
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_STLP_DECLSPEC complex<float> _STLP_CALL exp(const complex<float>& z)
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{ return expT(z); }
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_STLP_DECLSPEC complex<double> _STLP_CALL exp(const complex<double>& z)
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{ return expT(z); }
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#if !defined (_STLP_NO_LONG_DOUBLE)
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_STLP_DECLSPEC complex<long double> _STLP_CALL exp(const complex<long double>& z)
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{ return expT(z); }
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#endif
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//----------------------------------------------------------------------
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// log10
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template <class _Tp>
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static complex<_Tp> log10T(const complex<_Tp>& z, const _Tp& ln10_inv) {
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complex<_Tp> r;
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r._M_im = ::atan2(z._M_im, z._M_re) * ln10_inv;
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r._M_re = ::log10(::hypot(z._M_re, z._M_im));
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return r;
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}
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static const float LN10_INVF = 1.f / ::log(10.f);
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_STLP_DECLSPEC complex<float> _STLP_CALL log10(const complex<float>& z)
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{ return log10T(z, LN10_INVF); }
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static const double LN10_INV = 1. / ::log10(10.);
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_STLP_DECLSPEC complex<double> _STLP_CALL log10(const complex<double>& z)
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{ return log10T(z, LN10_INV); }
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#if !defined (_STLP_NO_LONG_DOUBLE)
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static const long double LN10_INVL = 1.l / ::log(10.l);
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_STLP_DECLSPEC complex<long double> _STLP_CALL log10(const complex<long double>& z)
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{ return log10T(z, LN10_INVL); }
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#endif
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//----------------------------------------------------------------------
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// log
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template <class _Tp>
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static complex<_Tp> logT(const complex<_Tp>& z) {
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complex<_Tp> r;
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r._M_im = ::atan2(z._M_im, z._M_re);
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r._M_re = ::log(::hypot(z._M_re, z._M_im));
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return r;
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}
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_STLP_DECLSPEC complex<float> _STLP_CALL log(const complex<float>& z)
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{ return logT(z); }
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_STLP_DECLSPEC complex<double> _STLP_CALL log(const complex<double>& z)
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{ return logT(z); }
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#ifndef _STLP_NO_LONG_DOUBLE
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_STLP_DECLSPEC complex<long double> _STLP_CALL log(const complex<long double>& z)
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{ return logT(z); }
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# endif
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//----------------------------------------------------------------------
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// pow
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template <class _Tp>
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static complex<_Tp> powT(const _Tp& a, const complex<_Tp>& b) {
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_Tp logr = ::log(a);
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_Tp x = ::exp(logr * b._M_re);
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_Tp y = logr * b._M_im;
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return complex<_Tp>(x * ::cos(y), x * ::sin(y));
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}
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template <class _Tp>
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static complex<_Tp> powT(const complex<_Tp>& z_in, int n) {
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complex<_Tp> z = z_in;
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z = _STLP_PRIV __power(z, (n < 0 ? -n : n), multiplies< complex<_Tp> >());
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if (n < 0)
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return _Tp(1.0) / z;
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else
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return z;
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}
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template <class _Tp>
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static complex<_Tp> powT(const complex<_Tp>& a, const _Tp& b) {
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_Tp logr = ::log(::hypot(a._M_re,a._M_im));
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_Tp logi = ::atan2(a._M_im, a._M_re);
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_Tp x = ::exp(logr * b);
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_Tp y = logi * b;
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return complex<_Tp>(x * ::cos(y), x * ::sin(y));
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}
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template <class _Tp>
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static complex<_Tp> powT(const complex<_Tp>& a, const complex<_Tp>& b) {
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_Tp logr = ::log(::hypot(a._M_re,a._M_im));
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_Tp logi = ::atan2(a._M_im, a._M_re);
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_Tp x = ::exp(logr * b._M_re - logi * b._M_im);
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_Tp y = logr * b._M_im + logi * b._M_re;
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301 |
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302 |
return complex<_Tp>(x * ::cos(y), x * ::sin(y));
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303 |
}
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|
305 |
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const float& a, const complex<float>& b)
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|
306 |
{ return powT(a, b); }
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307 |
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|
308 |
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& z_in, int n)
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|
309 |
{ return powT(z_in, n); }
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310 |
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311 |
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const float& b)
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|
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|
312 |
{ return powT(a, b); }
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|
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|
313 |
|
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|
314 |
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const complex<float>& b)
|
|
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|
315 |
{ return powT(a, b); }
|
|
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|
316 |
|
|
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|
317 |
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const double& a, const complex<double>& b)
|
|
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|
318 |
{ return powT(a, b); }
|
|
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|
319 |
|
|
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|
320 |
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& z_in, int n)
|
|
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|
321 |
{ return powT(z_in, n); }
|
|
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|
322 |
|
|
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|
323 |
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const double& b)
|
|
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|
324 |
{ return powT(a, b); }
|
|
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|
325 |
|
|
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|
326 |
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const complex<double>& b)
|
|
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|
327 |
{ return powT(a, b); }
|
|
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|
328 |
|
|
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|
329 |
#if !defined (_STLP_NO_LONG_DOUBLE)
|
|
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|
330 |
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const long double& a,
|
|
sl@0
|
331 |
const complex<long double>& b)
|
|
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|
332 |
{ return powT(a, b); }
|
|
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|
333 |
|
|
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|
334 |
|
|
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|
335 |
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& z_in, int n)
|
|
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|
336 |
{ return powT(z_in, n); }
|
|
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|
337 |
|
|
sl@0
|
338 |
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a,
|
|
sl@0
|
339 |
const long double& b)
|
|
sl@0
|
340 |
{ return powT(a, b); }
|
|
sl@0
|
341 |
|
|
sl@0
|
342 |
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a,
|
|
sl@0
|
343 |
const complex<long double>& b)
|
|
sl@0
|
344 |
{ return powT(a, b); }
|
|
sl@0
|
345 |
#endif
|
|
sl@0
|
346 |
|
|
sl@0
|
347 |
_STLP_END_NAMESPACE
|