1 /* $OpenBSD: s_casin.c,v 1.2 2011/07/08 19:25:31 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 /* LINTLIBRARY */ 19 20 /* casin() 21 * 22 * Complex circular arc sine 23 * 24 * 25 * 26 * SYNOPSIS: 27 * 28 * double complex casin(); 29 * double complex z, w; 30 * 31 * w = casin (z); 32 * 33 * 34 * 35 * DESCRIPTION: 36 * 37 * Inverse complex sine: 38 * 39 * 2 40 * w = -i clog( iz + csqrt( 1 - z ) ). 41 * 42 * casin(z) = -i casinh(iz) 43 * 44 * ACCURACY: 45 * 46 * Relative error: 47 * arithmetic domain # trials peak rms 48 * DEC -10,+10 10100 2.1e-15 3.4e-16 49 * IEEE -10,+10 30000 2.2e-14 2.7e-15 50 * Larger relative error can be observed for z near zero. 51 * Also tested by csin(casin(z)) = z. 52 */ 53 54 #include <sys/cdefs.h> 55 #include <complex.h> 56 #include <float.h> 57 #include <math.h> 58 59 double complex 60 casin(double complex z) 61 { 62 double complex w; 63 static double complex ca, ct, zz, z2; 64 double x, y; 65 66 x = creal (z); 67 y = cimag (z); 68 69 if (y == 0.0) { 70 if (fabs(x) > 1.0) { 71 w = M_PI_2 + 0.0 * I; 72 /*mtherr ("casin", DOMAIN);*/ 73 } 74 else { 75 w = asin (x) + 0.0 * I; 76 } 77 return (w); 78 } 79 80 /* Power series expansion */ 81 /* 82 b = cabs(z); 83 if( b < 0.125 ) { 84 z2.r = (x - y) * (x + y); 85 z2.i = 2.0 * x * y; 86 87 cn = 1.0; 88 n = 1.0; 89 ca.r = x; 90 ca.i = y; 91 sum.r = x; 92 sum.i = y; 93 do { 94 ct.r = z2.r * ca.r - z2.i * ca.i; 95 ct.i = z2.r * ca.i + z2.i * ca.r; 96 ca.r = ct.r; 97 ca.i = ct.i; 98 99 cn *= n; 100 n += 1.0; 101 cn /= n; 102 n += 1.0; 103 b = cn/n; 104 105 ct.r *= b; 106 ct.i *= b; 107 sum.r += ct.r; 108 sum.i += ct.i; 109 b = fabs(ct.r) + fabs(ct.i); 110 } 111 while( b > MACHEP ); 112 w->r = sum.r; 113 w->i = sum.i; 114 return; 115 } 116 */ 117 118 ca = x + y * I; 119 ct = ca * I; 120 /* sqrt( 1 - z*z) */ 121 /* cmul( &ca, &ca, &zz ) */ 122 /*x * x - y * y */ 123 zz = (x - y) * (x + y) + (2.0 * x * y) * I; 124 125 zz = 1.0 - creal(zz) - cimag(zz) * I; 126 z2 = csqrt (zz); 127 128 zz = ct + z2; 129 zz = clog (zz); 130 /* multiply by 1/i = -i */ 131 w = zz * (-1.0 * I); 132 return (w); 133 } 134 135 #if LDBL_MANT_DIG == 53 136 #ifdef lint 137 /* PROTOLIB1 */ 138 long double complex casinl(long double complex); 139 #else /* lint */ 140 __weak_alias(casinl, casin); 141 #endif /* lint */ 142 #endif /* LDBL_MANT_DIG == 53 */ 143