/*

 * 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;

  }

}

_STLP_DECLSPEC 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); }

_STLP_DECLSPEC 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); }

_STLP_DECLSPEC 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); }

_STLP_DECLSPEC 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)

_STLP_DECLSPEC 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); }

_STLP_DECLSPEC 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;

}

_STLP_DECLSPEC complex<float> _STLP_CALL

sqrt(const complex<float>& z) { return sqrtT(z); }

_STLP_DECLSPEC complex<double>  _STLP_CALL

sqrt(const complex<double>& z) { return sqrtT(z); }

#if !defined (_STLP_NO_LONG_DOUBLE)

_STLP_DECLSPEC 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