1 /* $OpenBSD: s_casin.c,v 1.1 2008/09/07 20:36:09 martynas 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 <math.h> 54 55 double complex 56 casin(double complex z) 57 { 58 double complex w; 59 static double complex ca, ct, zz, z2; 60 double x, y; 61 62 x = creal (z); 63 y = cimag (z); 64 65 if (y == 0.0) { 66 if (fabs(x) > 1.0) { 67 w = M_PI_2 + 0.0 * I; 68 /*mtherr ("casin", DOMAIN);*/ 69 } 70 else { 71 w = asin (x) + 0.0 * I; 72 } 73 return (w); 74 } 75 76 /* Power series expansion */ 77 /* 78 b = cabs(z); 79 if( b < 0.125 ) { 80 z2.r = (x - y) * (x + y); 81 z2.i = 2.0 * x * y; 82 83 cn = 1.0; 84 n = 1.0; 85 ca.r = x; 86 ca.i = y; 87 sum.r = x; 88 sum.i = y; 89 do { 90 ct.r = z2.r * ca.r - z2.i * ca.i; 91 ct.i = z2.r * ca.i + z2.i * ca.r; 92 ca.r = ct.r; 93 ca.i = ct.i; 94 95 cn *= n; 96 n += 1.0; 97 cn /= n; 98 n += 1.0; 99 b = cn/n; 100 101 ct.r *= b; 102 ct.i *= b; 103 sum.r += ct.r; 104 sum.i += ct.i; 105 b = fabs(ct.r) + fabs(ct.i); 106 } 107 while( b > MACHEP ); 108 w->r = sum.r; 109 w->i = sum.i; 110 return; 111 } 112 */ 113 114 ca = x + y * I; 115 ct = ca * I; 116 /* sqrt( 1 - z*z) */ 117 /* cmul( &ca, &ca, &zz ) */ 118 /*x * x - y * y */ 119 zz = (x - y) * (x + y) + (2.0 * x * y) * I; 120 121 zz = 1.0 - creal(zz) - cimag(zz) * I; 122 z2 = csqrt (zz); 123 124 zz = ct + z2; 125 zz = clog (zz); 126 /* multiply by 1/i = -i */ 127 w = zz * (-1.0 * I); 128 return (w); 129 } 130