137 lines
2.8 KiB
C
137 lines
2.8 KiB
C
/* $OpenBSD: s_casin.c,v 1.6 2013/07/03 04:46:36 espie Exp $ */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/* casin()
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*
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* Complex circular arc sine
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*
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*
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*
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* SYNOPSIS:
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*
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* double complex casin();
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* double complex z, w;
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*
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* w = casin (z);
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*
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*
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*
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* DESCRIPTION:
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*
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* Inverse complex sine:
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*
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* 2
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* w = -i clog( iz + csqrt( 1 - z ) ).
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*
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* casin(z) = -i casinh(iz)
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC -10,+10 10100 2.1e-15 3.4e-16
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* IEEE -10,+10 30000 2.2e-14 2.7e-15
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* Larger relative error can be observed for z near zero.
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* Also tested by csin(casin(z)) = z.
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*/
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#include <float.h>
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#include <openlibm_complex.h>
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#include <openlibm_math.h>
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#include "math_private.h"
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double complex
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casin(double complex z)
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{
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double complex w;
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static double complex ca, ct, zz, z2;
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double x, y;
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x = creal (z);
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y = cimag (z);
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if (y == 0.0) {
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if (fabs(x) > 1.0) {
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w = M_PI_2 + 0.0 * I;
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/*mtherr ("casin", DOMAIN);*/
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}
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else {
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w = asin (x) + 0.0 * I;
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}
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return (w);
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}
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/* Power series expansion */
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/*
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b = cabs(z);
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if( b < 0.125 ) {
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z2.r = (x - y) * (x + y);
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z2.i = 2.0 * x * y;
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cn = 1.0;
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n = 1.0;
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ca.r = x;
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ca.i = y;
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sum.r = x;
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sum.i = y;
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do {
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ct.r = z2.r * ca.r - z2.i * ca.i;
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ct.i = z2.r * ca.i + z2.i * ca.r;
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ca.r = ct.r;
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ca.i = ct.i;
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cn *= n;
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n += 1.0;
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cn /= n;
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n += 1.0;
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b = cn/n;
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ct.r *= b;
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ct.i *= b;
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sum.r += ct.r;
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sum.i += ct.i;
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b = fabs(ct.r) + fabs(ct.i);
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}
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while( b > MACHEP );
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w->r = sum.r;
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w->i = sum.i;
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return;
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}
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*/
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ca = x + y * I;
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ct = ca * I;
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/* sqrt( 1 - z*z) */
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/* cmul( &ca, &ca, &zz ) */
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/*x * x - y * y */
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zz = (x - y) * (x + y) + (2.0 * x * y) * I;
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zz = 1.0 - creal(zz) - cimag(zz) * I;
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z2 = csqrt (zz);
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zz = ct + z2;
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zz = clog (zz);
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/* multiply by 1/i = -i */
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w = zz * (-1.0 * I);
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return (w);
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}
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#if LDBL_MANT_DIG == DBL_MANT_DIG
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openlibm_strong_reference(casin, casinl);
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#endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
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