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/* $OpenBSD: s_casin.c,v 1.8 2016/09/12 19:47:02 guenther 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 <complex.h> |
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#include <float.h> |
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#include <math.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 0 |
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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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#endif |
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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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DEF_STD(casin); |
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LDBL_MAYBE_CLONE(casin); |