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/* origin: OpenBSD /usr/src/lib/libm/src/s_catanf.c */
/*
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/*
* Complex circular arc tangent
*
*
* SYNOPSIS:
*
* float complex catanf();
* float complex z, w;
*
* w = catanf( z );
*
*
* DESCRIPTION:
*
* If
* z = x + iy,
*
* then
* 1 ( 2x )
* Re w = - arctan(-----------) + k PI
* 2 ( 2 2)
* (1 - x - y )
*
* ( 2 2)
* 1 (x + (y+1) )
* Im w = - log(------------)
* 4 ( 2 2)
* (x + (y-1) )
*
* Where k is an arbitrary integer.
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -10,+10 30000 2.3e-6 5.2e-8
*/
#include "complex_impl.h"
float complex catanf(float complex z)
{
float complex w;
float a, t, x, x2, y;
x = crealf(z);
y = cimagf(z);
x2 = x * x;
a = 1.0f - x2 - (y * y);
t = 0.5f * atan2f(2.0f * x, a);
w = t;
t = y - 1.0f;
a = x2 + (t * t);
t = y + 1.0f;
a = (x2 + (t * t))/a;
w = CMPLXF(w, 0.25f * logf(a));
return w;
}
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