1/* $OpenBSD: s_casin.c,v 1.8 2016/09/12 19:47:02 guenther Exp $ */ 2/* 3 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> 4 * 5 * Permission to use, copy, modify, and distribute this software for any 6 * purpose with or without fee is hereby granted, provided that the above 7 * copyright notice and this permission notice appear in all copies. 8 * 9 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES 10 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF 11 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR 12 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES 13 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN 14 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF 15 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 16 */ 17 18/* casin() 19 * 20 * Complex circular arc sine 21 * 22 * 23 * 24 * SYNOPSIS: 25 * 26 * double complex casin(); 27 * double complex z, w; 28 * 29 * w = casin (z); 30 * 31 * 32 * 33 * DESCRIPTION: 34 * 35 * Inverse complex sine: 36 * 37 * 2 38 * w = -i clog( iz + csqrt( 1 - z ) ). 39 * 40 * casin(z) = -i casinh(iz) 41 * 42 * ACCURACY: 43 * 44 * Relative error: 45 * arithmetic domain # trials peak rms 46 * DEC -10,+10 10100 2.1e-15 3.4e-16 47 * IEEE -10,+10 30000 2.2e-14 2.7e-15 48 * Larger relative error can be observed for z near zero. 49 * Also tested by csin(casin(z)) = z. 50 */ 51 52#include <complex.h> 53#include <float.h> 54#include <math.h> 55 56double complex 57casin(double complex z) 58{ 59 double complex w; 60 static double complex ca, ct, zz, z2; 61 double x, y; 62 63 x = creal (z); 64 y = cimag (z); 65 66#if 0 67 if (y == 0.0) { 68 if (fabs(x) > 1.0) { 69 w = M_PI_2 + 0.0 * I; 70 /*mtherr ("casin", DOMAIN);*/ 71 } 72 else { 73 w = asin (x) + 0.0 * I; 74 } 75 return (w); 76 } 77#endif 78 79 /* Power series expansion */ 80 /* 81 b = cabs(z); 82 if( b < 0.125 ) { 83 z2.r = (x - y) * (x + y); 84 z2.i = 2.0 * x * y; 85 86 cn = 1.0; 87 n = 1.0; 88 ca.r = x; 89 ca.i = y; 90 sum.r = x; 91 sum.i = y; 92 do { 93 ct.r = z2.r * ca.r - z2.i * ca.i; 94 ct.i = z2.r * ca.i + z2.i * ca.r; 95 ca.r = ct.r; 96 ca.i = ct.i; 97 98 cn *= n; 99 n += 1.0; 100 cn /= n; 101 n += 1.0; 102 b = cn/n; 103 104 ct.r *= b; 105 ct.i *= b; 106 sum.r += ct.r; 107 sum.i += ct.i; 108 b = fabs(ct.r) + fabs(ct.i); 109 } 110 while( b > MACHEP ); 111 w->r = sum.r; 112 w->i = sum.i; 113 return; 114 } 115 */ 116 117 ca = x + y * I; 118 ct = ca * I; 119 /* sqrt( 1 - z*z) */ 120 /* cmul( &ca, &ca, &zz ) */ 121 /*x * x - y * y */ 122 zz = (x - y) * (x + y) + (2.0 * x * y) * I; 123 124 zz = 1.0 - creal(zz) - cimag(zz) * I; 125 z2 = csqrt (zz); 126 127 zz = ct + z2; 128 zz = clog (zz); 129 /* multiply by 1/i = -i */ 130 w = zz * (-1.0 * I); 131 return (w); 132} 133DEF_STD(casin); 134LDBL_MAYBE_CLONE(casin); 135