1 /* $OpenBSD: s_casin.c,v 1.6 2013/07/03 04:46:36 espie 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 56 double complex 57 casin(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 (y == 0.0) { 67 if (fabs(x) > 1.0) { 68 w = M_PI_2 + 0.0 * I; 69 /*mtherr ("casin", DOMAIN);*/ 70 } 71 else { 72 w = asin (x) + 0.0 * I; 73 } 74 return (w); 75 } 76 77 /* Power series expansion */ 78 /* 79 b = cabs(z); 80 if( b < 0.125 ) { 81 z2.r = (x - y) * (x + y); 82 z2.i = 2.0 * x * y; 83 84 cn = 1.0; 85 n = 1.0; 86 ca.r = x; 87 ca.i = y; 88 sum.r = x; 89 sum.i = y; 90 do { 91 ct.r = z2.r * ca.r - z2.i * ca.i; 92 ct.i = z2.r * ca.i + z2.i * ca.r; 93 ca.r = ct.r; 94 ca.i = ct.i; 95 96 cn *= n; 97 n += 1.0; 98 cn /= n; 99 n += 1.0; 100 b = cn/n; 101 102 ct.r *= b; 103 ct.i *= b; 104 sum.r += ct.r; 105 sum.i += ct.i; 106 b = fabs(ct.r) + fabs(ct.i); 107 } 108 while( b > MACHEP ); 109 w->r = sum.r; 110 w->i = sum.i; 111 return; 112 } 113 */ 114 115 ca = x + y * I; 116 ct = ca * I; 117 /* sqrt( 1 - z*z) */ 118 /* cmul( &ca, &ca, &zz ) */ 119 /*x * x - y * y */ 120 zz = (x - y) * (x + y) + (2.0 * x * y) * I; 121 122 zz = 1.0 - creal(zz) - cimag(zz) * I; 123 z2 = csqrt (zz); 124 125 zz = ct + z2; 126 zz = clog (zz); 127 /* multiply by 1/i = -i */ 128 w = zz * (-1.0 * I); 129 return (w); 130 } 131 132 #if LDBL_MANT_DIG == DBL_MANT_DIG 133 __strong_alias(casinl, casin); 134 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */ 135