/*
* Copyright (c) 1999
* Silicon Graphics Computer Systems, Inc.
*
* Copyright (c) 1999
* Boris Fomitchev
*
* This material is provided "as is", with absolutely no warranty expressed
* or implied. Any use is at your own risk.
*
* Permission to use or copy this software for any purpose is hereby granted
* without fee, provided the above notices are retained on all copies.
* Permission to modify the code and to distribute modified code is granted,
* provided the above notices are retained, and a notice that the code was
* modified is included with the above copyright notice.
*
*/
#include "stlport_prefix.h"
#include <numeric>
#include <cmath>
#include <complex>
#if defined (_STLP_MSVC_LIB) && (_STLP_MSVC_LIB >= 1400)
// hypot is deprecated.
# if defined (_STLP_MSVC)
# pragma warning (disable : 4996)
# elif defined (__ICL)
# pragma warning (disable : 1478)
# endif
#endif
_STLP_BEGIN_NAMESPACE
// Complex division and square roots.
// Absolute value
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC float _STLP_CALL abs(const complex<float>& __z)
{ return ::hypot(__z._M_re, __z._M_im); }
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC double _STLP_CALL abs(const complex<double>& __z)
{ return ::hypot(__z._M_re, __z._M_im); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC long double _STLP_CALL abs(const complex<long double>& __z)
{ return ::hypot(__z._M_re, __z._M_im); }
#endif
// Phase
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC float _STLP_CALL arg(const complex<float>& __z)
{ return ::atan2(__z._M_im, __z._M_re); }
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC double _STLP_CALL arg(const complex<double>& __z)
{ return ::atan2(__z._M_im, __z._M_re); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC long double _STLP_CALL arg(const complex<long double>& __z)
{ return ::atan2(__z._M_im, __z._M_re); }
#endif
// Construct a complex number from polar representation
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC complex<float> _STLP_CALL polar(const float& __rho, const float& __phi)
{ return complex<float>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC complex<double> _STLP_CALL polar(const double& __rho, const double& __phi)
{ return complex<double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_TEMPLATE_NULL
_STLP_DECLSPEC complex<long double> _STLP_CALL polar(const long double& __rho, const long double& __phi)
{ return complex<long double>(__rho * ::cos(__phi), __rho * ::sin(__phi)); }
#endif
// Division
template <class _Tp>
static void _divT(const _Tp& __z1_r, const _Tp& __z1_i,
const _Tp& __z2_r, const _Tp& __z2_i,
_Tp& __res_r, _Tp& __res_i) {
_Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r;
_Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i;
if (__ar <= __ai) {
_Tp __ratio = __z2_r / __z2_i;
_Tp __denom = __z2_i * (1 + __ratio * __ratio);
__res_r = (__z1_r * __ratio + __z1_i) / __denom;
__res_i = (__z1_i * __ratio - __z1_r) / __denom;
}
else {
_Tp __ratio = __z2_i / __z2_r;
_Tp __denom = __z2_r * (1 + __ratio * __ratio);
__res_r = (__z1_r + __z1_i * __ratio) / __denom;
__res_i = (__z1_i - __z1_r * __ratio) / __denom;
}
}
template <class _Tp>
static void _divT(const _Tp& __z1_r,
const _Tp& __z2_r, const _Tp& __z2_i,
_Tp& __res_r, _Tp& __res_i) {
_Tp __ar = __z2_r >= 0 ? __z2_r : -__z2_r;
_Tp __ai = __z2_i >= 0 ? __z2_i : -__z2_i;
if (__ar <= __ai) {
_Tp __ratio = __z2_r / __z2_i;
_Tp __denom = __z2_i * (1 + __ratio * __ratio);
__res_r = (__z1_r * __ratio) / __denom;
__res_i = - __z1_r / __denom;
}
else {
_Tp __ratio = __z2_i / __z2_r;
_Tp __denom = __z2_r * (1 + __ratio * __ratio);
__res_r = __z1_r / __denom;
__res_i = - (__z1_r * __ratio) / __denom;
}
}
void _STLP_CALL
complex<float>::_div(const float& __z1_r, const float& __z1_i,
const float& __z2_r, const float& __z2_i,
float& __res_r, float& __res_i)
{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
void _STLP_CALL
complex<float>::_div(const float& __z1_r,
const float& __z2_r, const float& __z2_i,
float& __res_r, float& __res_i)
{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
void _STLP_CALL
complex<double>::_div(const double& __z1_r, const double& __z1_i,
const double& __z2_r, const double& __z2_i,
double& __res_r, double& __res_i)
{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
void _STLP_CALL
complex<double>::_div(const double& __z1_r,
const double& __z2_r, const double& __z2_i,
double& __res_r, double& __res_i)
{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
#if !defined (_STLP_NO_LONG_DOUBLE)
void _STLP_CALL
complex<long double>::_div(const long double& __z1_r, const long double& __z1_i,
const long double& __z2_r, const long double& __z2_i,
long double& __res_r, long double& __res_i)
{ _divT(__z1_r, __z1_i, __z2_r, __z2_i, __res_r, __res_i); }
void _STLP_CALL
complex<long double>::_div(const long double& __z1_r,
const long double& __z2_r, const long double& __z2_i,
long double& __res_r, long double& __res_i)
{ _divT(__z1_r, __z2_r, __z2_i, __res_r, __res_i); }
#endif
//----------------------------------------------------------------------
// Square root
template <class _Tp>
static complex<_Tp> sqrtT(const complex<_Tp>& z) {
_Tp re = z._M_re;
_Tp im = z._M_im;
_Tp mag = ::hypot(re, im);
complex<_Tp> result;
if (mag == 0.f) {
result._M_re = result._M_im = 0.f;
} else if (re > 0.f) {
result._M_re = ::sqrt(0.5f * (mag + re));
result._M_im = im/result._M_re/2.f;
} else {
result._M_im = ::sqrt(0.5f * (mag - re));
if (im < 0.f)
result._M_im = - result._M_im;
result._M_re = im/result._M_im/2.f;
}
return result;
}
complex<float> _STLP_CALL
sqrt(const complex<float>& z) { return sqrtT(z); }
complex<double> _STLP_CALL
sqrt(const complex<double>& z) { return sqrtT(z); }
#if !defined (_STLP_NO_LONG_DOUBLE)
complex<long double> _STLP_CALL
sqrt(const complex<long double>& z) { return sqrtT(z); }
#endif
// exp, log, pow for complex<float>, complex<double>, and complex<long double>
//----------------------------------------------------------------------
// exp
template <class _Tp>
static complex<_Tp> expT(const complex<_Tp>& z) {
_Tp expx = ::exp(z._M_re);
return complex<_Tp>(expx * ::cos(z._M_im),
expx * ::sin(z._M_im));
}
_STLP_DECLSPEC complex<float> _STLP_CALL exp(const complex<float>& z)
{ return expT(z); }
_STLP_DECLSPEC complex<double> _STLP_CALL exp(const complex<double>& z)
{ return expT(z); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_DECLSPEC complex<long double> _STLP_CALL exp(const complex<long double>& z)
{ return expT(z); }
#endif
//----------------------------------------------------------------------
// log10
template <class _Tp>
static complex<_Tp> log10T(const complex<_Tp>& z, const _Tp& ln10_inv) {
complex<_Tp> r;
r._M_im = ::atan2(z._M_im, z._M_re) * ln10_inv;
r._M_re = ::log10(::hypot(z._M_re, z._M_im));
return r;
}
static const float LN10_INVF = 1.f / ::log(10.f);
_STLP_DECLSPEC complex<float> _STLP_CALL log10(const complex<float>& z)
{ return log10T(z, LN10_INVF); }
static const double LN10_INV = 1. / ::log10(10.);
_STLP_DECLSPEC complex<double> _STLP_CALL log10(const complex<double>& z)
{ return log10T(z, LN10_INV); }
#if !defined (_STLP_NO_LONG_DOUBLE)
static const long double LN10_INVL = 1.l / ::log(10.l);
_STLP_DECLSPEC complex<long double> _STLP_CALL log10(const complex<long double>& z)
{ return log10T(z, LN10_INVL); }
#endif
//----------------------------------------------------------------------
// log
template <class _Tp>
static complex<_Tp> logT(const complex<_Tp>& z) {
complex<_Tp> r;
r._M_im = ::atan2(z._M_im, z._M_re);
r._M_re = ::log(::hypot(z._M_re, z._M_im));
return r;
}
_STLP_DECLSPEC complex<float> _STLP_CALL log(const complex<float>& z)
{ return logT(z); }
_STLP_DECLSPEC complex<double> _STLP_CALL log(const complex<double>& z)
{ return logT(z); }
#ifndef _STLP_NO_LONG_DOUBLE
_STLP_DECLSPEC complex<long double> _STLP_CALL log(const complex<long double>& z)
{ return logT(z); }
# endif
//----------------------------------------------------------------------
// pow
template <class _Tp>
static complex<_Tp> powT(const _Tp& a, const complex<_Tp>& b) {
_Tp logr = ::log(a);
_Tp x = ::exp(logr * b._M_re);
_Tp y = logr * b._M_im;
return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}
template <class _Tp>
static complex<_Tp> powT(const complex<_Tp>& z_in, int n) {
complex<_Tp> z = z_in;
z = _STLP_PRIV __power(z, (n < 0 ? -n : n), multiplies< complex<_Tp> >());
if (n < 0)
return _Tp(1.0) / z;
else
return z;
}
template <class _Tp>
static complex<_Tp> powT(const complex<_Tp>& a, const _Tp& b) {
_Tp logr = ::log(::hypot(a._M_re,a._M_im));
_Tp logi = ::atan2(a._M_im, a._M_re);
_Tp x = ::exp(logr * b);
_Tp y = logi * b;
return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}
template <class _Tp>
static complex<_Tp> powT(const complex<_Tp>& a, const complex<_Tp>& b) {
_Tp logr = ::log(::hypot(a._M_re,a._M_im));
_Tp logi = ::atan2(a._M_im, a._M_re);
_Tp x = ::exp(logr * b._M_re - logi * b._M_im);
_Tp y = logr * b._M_im + logi * b._M_re;
return complex<_Tp>(x * ::cos(y), x * ::sin(y));
}
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const float& a, const complex<float>& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& z_in, int n)
{ return powT(z_in, n); }
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const float& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<float> _STLP_CALL pow(const complex<float>& a, const complex<float>& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const double& a, const complex<double>& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& z_in, int n)
{ return powT(z_in, n); }
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const double& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<double> _STLP_CALL pow(const complex<double>& a, const complex<double>& b)
{ return powT(a, b); }
#if !defined (_STLP_NO_LONG_DOUBLE)
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const long double& a,
const complex<long double>& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& z_in, int n)
{ return powT(z_in, n); }
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a,
const long double& b)
{ return powT(a, b); }
_STLP_DECLSPEC complex<long double> _STLP_CALL pow(const complex<long double>& a,
const complex<long double>& b)
{ return powT(a, b); }
#endif
_STLP_END_NAMESPACE