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/* catanl.c */
/*
Contributed by Danny Smith
2005-01-04
FIXME: This needs some serious numerical analysis.
*/
#include <math.h>
#include <complex.h>
#include <errno.h>
/* catan (z) = -I/2 * clog ((I + z) / (I - z)) */
#ifndef _M_PI_2L
#define _M_PI_2L 1.5707963267948966192313L
#endif
long double complex
catanl (long double complex Z)
{
long double complex Res;
long double complex Tmp;
long double x = __real__ Z;
long double y = __imag__ Z;
if ( x == 0.0L && (1.0L - fabsl (y)) == 0.0L)
{
errno = ERANGE;
__real__ Res = HUGE_VALL;
__imag__ Res = HUGE_VALL;
}
else if (isinf (hypotl (x, y)))
{
__real__ Res = (x > 0 ? _M_PI_2L : -_M_PI_2L);
__imag__ Res = 0.0L;
}
else
{
__real__ Tmp = - x;
__imag__ Tmp = 1.0L - y;
__real__ Res = x;
__imag__ Res = y + 1.0L;
Tmp = clogl (Res/Tmp);
__real__ Res = - 0.5L * __imag__ Tmp;
__imag__ Res = 0.5L * __real__ Tmp;
}
return Res;
}
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