133 lines
2.6 KiB
C
133 lines
2.6 KiB
C
/* $OpenBSD: s_casinf.c,v 1.3 2011/07/20 19:28:33 martynas Exp $ */
|
|
/*
|
|
* 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.
|
|
*/
|
|
|
|
/* casinf()
|
|
*
|
|
* Complex circular arc sine
|
|
*
|
|
*
|
|
*
|
|
* SYNOPSIS:
|
|
*
|
|
* void casinf();
|
|
* cmplxf z, w;
|
|
*
|
|
* casinf( &z, &w );
|
|
*
|
|
*
|
|
*
|
|
* DESCRIPTION:
|
|
*
|
|
* Inverse complex sine:
|
|
*
|
|
* 2
|
|
* w = -i clog( iz + csqrt( 1 - z ) ).
|
|
*
|
|
*
|
|
* ACCURACY:
|
|
*
|
|
* Relative error:
|
|
* arithmetic domain # trials peak rms
|
|
* IEEE -10,+10 30000 1.1e-5 1.5e-6
|
|
* Larger relative error can be observed for z near zero.
|
|
*
|
|
*/
|
|
|
|
#include <openlibm_complex.h>
|
|
#include <openlibm_math.h>
|
|
|
|
float complex
|
|
casinf(float complex z)
|
|
{
|
|
float complex w;
|
|
float x, y;
|
|
static float complex ca, ct, zz, z2;
|
|
/*
|
|
float cn, n;
|
|
static float a, b, s, t, u, v, y2;
|
|
static cmplxf sum;
|
|
*/
|
|
|
|
x = crealf(z);
|
|
y = cimagf(z);
|
|
|
|
if(y == 0.0f) {
|
|
if(fabsf(x) > 1.0f) {
|
|
w = (float)M_PI_2 + 0.0f * I;
|
|
/*mtherr( "casinf", DOMAIN );*/
|
|
}
|
|
else {
|
|
w = asinf (x) + 0.0f * I;
|
|
}
|
|
return (w);
|
|
}
|
|
|
|
/* Power series expansion */
|
|
/*
|
|
b = cabsf(z);
|
|
if(b < 0.125) {
|
|
z2.r = (x - y) * (x + y);
|
|
z2.i = 2.0 * x * y;
|
|
|
|
cn = 1.0;
|
|
n = 1.0;
|
|
ca.r = x;
|
|
ca.i = y;
|
|
sum.r = x;
|
|
sum.i = y;
|
|
do {
|
|
ct.r = z2.r * ca.r - z2.i * ca.i;
|
|
ct.i = z2.r * ca.i + z2.i * ca.r;
|
|
ca.r = ct.r;
|
|
ca.i = ct.i;
|
|
|
|
cn *= n;
|
|
n += 1.0;
|
|
cn /= n;
|
|
n += 1.0;
|
|
b = cn/n;
|
|
|
|
ct.r *= b;
|
|
ct.i *= b;
|
|
sum.r += ct.r;
|
|
sum.i += ct.i;
|
|
b = fabsf(ct.r) + fabsf(ct.i);
|
|
}
|
|
while(b > MACHEPF);
|
|
w->r = sum.r;
|
|
w->i = sum.i;
|
|
return;
|
|
}
|
|
*/
|
|
|
|
|
|
ca = x + y * I;
|
|
ct = ca * I; /* iz */
|
|
/* sqrt( 1 - z*z) */
|
|
/* cmul( &ca, &ca, &zz ) */
|
|
/*x * x - y * y */
|
|
zz = (x - y) * (x + y) + (2.0f * x * y) * I;
|
|
zz = 1.0f - crealf(zz) - cimagf(zz) * I;
|
|
z2 = csqrtf (zz);
|
|
|
|
zz = ct + z2;
|
|
zz = clogf (zz);
|
|
/* multiply by 1/i = -i */
|
|
w = zz * (-1.0f * I);
|
|
return (w);
|
|
}
|