/*************************************************************************************************************
 The MIT License

 Copyright (C) 2006-2019 David Dubbeldam, Sofia Calero, Thijs Vlugt, Donald E. Ellis, and Randall Q. Snurr.

     D.Dubbeldam@uva.nl            http://www.uva.nl/profiel/d/u/d.dubbeldam/d.dubbeldam.html
     scaldia@upo.es                http://www.upo.es/raspa/
     t.j.h.vlugt@tudelft.nl        http://homepage.tudelft.nl/v9k6y
     don-ellis@northwestern.edu    http://dvworld.northwestern.edu/
     snurr@northwestern.edu        http://zeolites.cqe.northwestern.edu/

 Permission is hereby granted, free of charge, to any person
 obtaining a copy of this software and associated documentation
 files (the "Software"), to deal in the Software without
 restriction, including without limitation the rights to use,
 copy, modify, merge, publish, distribute, sublicense, and/or sell
 copies of the Software, and to permit persons to whom the
 Software is furnished to do so, subject to the following
 conditions:

 The above copyright notice and this permission notice shall be
 included in all copies or substantial portions of the Software.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
 EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
 OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
 HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
 OTHER DEALINGS IN THE SOFTWARE.
**************************************************************************************************************/

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "complex.h"

REAL Re(Complex a)
{
  return a.re;
}

REAL Im(Complex a)
{
  return a.im;
}

// creates a Complex number from the real and imaginary part
Complex MakeComplex(REAL re,REAL im)
{
  Complex c;
  c.re=re;
  c.im=im;
  return c;
}

// returns the Complex addition of Complex a and Complex b
Complex ComplexAdd(Complex a,Complex b)
{
  Complex c;

  c.re=a.re+b.re;
  c.im=a.im+b.im;
  return c;
}

// returns the Complex subtraction of Complex a and Complex b
Complex ComplexSubtraction(Complex a,Complex b)
{
  Complex c;
  c.re=a.re-b.re;
  c.im=a.im-b.im;
  return c;
}

// returns the Complex multiplication of Complex a and Complex b
Complex ComplexMultiplication(Complex a,Complex b)
{
  Complex c;
  c.re=a.re*b.re-a.im*b.im;
  c.im=a.im*b.re+a.re*b.im;
  return c;
}

// returns the Complex division of Complex a and Complex b (without under/overflow)
Complex ComplexDivision(Complex a,Complex b)
{
  Complex c;
  REAL r,den;
  if (fabs(b.re)>=fabs(b.im))
  {
    r=b.im/b.re;
    den=b.re+r*b.im;
    c.re=(a.re+r*a.im)/den;
    c.im=(a.im-r*a.re)/den;
  }
  else
  {
    r=b.re/b.im;
    den=b.im+r*b.re;
    c.re=(a.re*r+a.im)/den;
    c.im=(a.im*r-a.re)/den;
  }
  return c;
}

// returns the multiplication of real x with Complex a
Complex ComplexRealMuliplication(REAL x,Complex a)
{
  Complex c;
  c.re=x*a.re;
  c.im=x*a.im;
  return c;
}
// returns the conjugate of Complex z
Complex Conjugate(Complex z)
{
  Complex c;
  c.re=z.re;
  c.im=-z.im;
  return c;
}

// returns the absolute value of Complex z (without under/overflow)
REAL ComplexAbs(Complex z)
{
  REAL x,y,ans,temp;
  x=z.re>=0.0?z.re:-z.re;
  y=z.im>=0.0?z.im:-z.im;
  if(x==0.0) ans=y;
  else if(y==0.0) ans=x;
  else if(x>y)
  {
    temp=y/x;
    ans=x*sqrt(1.0+temp*temp);
  }
  else
  {
    temp=x/y;
    ans=y*sqrt(1.0+temp*temp);
  }
  return ans;
}

// returns the squareroot of Complex z (without under/overflow)
Complex ComplexSqrt(Complex z)
{
  Complex c;
  REAL x,y,w,r;
  if ((z.re==0.0)&&(z.im==0.0))
  {
    c.re=0.0;
    c.im=0.0;
    return c;
  }
  else
  {
    x=z.re>=0.0?z.re:-z.re;
    y=z.im>=0.0?z.im:-z.im;
    if (x >= y)
    {
      r=y/x;
      w=sqrt(x)*sqrt(0.5*(1.0+sqrt(1.0+r*r)));
    }
    else
    {
      r=x/y;
      w=sqrt(y)*sqrt(0.5*(r+sqrt(1.0+r*r)));
    }
    if (z.re>=0.0)
    {
      c.re=w;
      c.im=z.im/(2.0*w);
    }
    else
    {
      c.im=(z.im>=0.0)?w:-w;
      c.re=z.im/(2.0*c.im);
    }
    return c;
  }
}

Complex ComplexLog(Complex a)
{
  Complex c;

  c.re=log(sqrt(a.re*a.re+a.im*a.im));
  c.im=atan2(a.im,a.re);
  return c;
}