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casin.c

/**
 * This file has no copyright assigned and is placed in the Public Domain.
 * This file is part of the w64 mingw-runtime package.
 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
 */
/*
   casin.c
   Contributed by Danny Smith
   2003-10-20
*/

#include <math.h>
#include <complex.h>

/* casin (Z ) = -I * clog(I * Z + csqrt (1.0 - Z * Z))) */

double complex casin (double complex Z)
{
  double complex Res;
  double x, y;

  x = __real__ Z;
  y = __imag__ Z;

  if (y == 0.0)
    {
      __real__ Res = asin (x);
      __imag__ Res = 0.0;
    }
  else  /* -I * clog(I * Z + csqrt(1.0 - Z * Z))) */
    {
      double complex ZZ;
                                 
      /* Z * Z = ((x - y) * (x + y)) + (2.0 * x * y) * I */
      /* calculate 1 - Z * Z */
      __real__ ZZ = 1.0 - (x - y) * (x + y);
      __imag__ ZZ = -2.0 * x * y;
      ZZ = csqrt (ZZ);


      /* add  I * Z  to ZZ */

      __real__ ZZ -= y;
      __imag__ ZZ += x;

      ZZ = clog (ZZ);

      /* mult by -I */
      __real__ Res = __imag__ ZZ;
      __imag__ Res = - __real__ ZZ;  
    }
  return (Res);
}

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