1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 /* INDENT OFF */ 31 /* 32 * void sincospi(double x, double *s, double *c) 33 * *s = sin(pi*x); *c = cos(pi*x); 34 * 35 * Algorithm, 10/17/2002, K.C. Ng 36 * ------------------------------ 37 * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary). 38 * 1. If y == z, then x is a multiple of pi/4. Return the following values: 39 * --------------------------------------------------- 40 * n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi) 41 * --------------------------------------------------- 42 * 000 0.00 +0 ___ +1 ___ +0 43 * 001 0.25 +\/0.5 +\/0.5 +1 44 * 010 0.50 +1 ___ +0 ___ +inf 45 * 011 0.75 +\/0.5 -\/0.5 -1 46 * 100 1.00 -0 ___ -1 ___ +0 47 * 101 1.25 -\/0.5 -\/0.5 +1 48 * 110 1.50 -1 ___ -0 ___ +inf 49 * 111 1.75 -\/0.5 +\/0.5 -1 50 * --------------------------------------------------- 51 * 2. Otherwise, 52 * --------------------------------------------------- 53 * n t sin(x*pi) cos(x*pi) tan(x*pi) 54 * --------------------------------------------------- 55 * 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t) 56 * 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t) 57 * 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t) 58 * 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t) 59 * 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t) 60 * 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t) 61 * 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t) 62 * 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t) 63 * --------------------------------------------------- 64 * 65 * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0). 66 * This will return a result with error slightly more than one ulp (but less 67 * than 2 ulp). If one wants accurate result, one may break up pi*t in 68 * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo) 69 * instead. 70 */ 71 72 #include "libm.h" 73 #include "libm_protos.h" 74 #include "libm_macros.h" 75 #include <math.h> 76 #if defined(__SUNPRO_C) 77 #include <sunmath.h> 78 #endif 79 80 static const double 81 pi = 3.14159265358979323846, /* 400921FB,54442D18 */ 82 sqrth_h = 0.70710678118654757273731092936941422522068023681640625, 83 sqrth_l = -4.8336466567264565185935844299127932213411660131004e-17; 84 /* INDENT ON */ 85 86 void 87 sincospi(double x, double *s, double *c) { 88 double y, z, t; 89 int n, ix, k; 90 int hx = ((int *) &x)[HIWORD]; 91 unsigned h, lx = ((unsigned *) &x)[LOWORD]; 92 93 ix = hx & ~0x80000000; 94 n = (ix >> 20) - 0x3ff; 95 if (n >= 51) { /* |x| >= 2**51 */ 96 if (n >= 1024) 97 #if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN) 98 *s = *c = ix >= 0x7ff80000 ? x : x - x; 99 /* assumes sparc-like QNaN */ 100 #else 101 *s = *c = x - x; 102 #endif 103 else { 104 if (n >= 53) { 105 *s = 0.0; 106 *c = 1.0; 107 } 108 else if (n == 52) { 109 if ((lx & 1) == 0) { 110 *s = 0.0; 111 *c = 1.0; 112 } 113 else { 114 *s = -0.0; 115 *c = -1.0; 116 } 117 } 118 else { /* n == 51 */ 119 if ((lx & 1) == 0) { 120 *s = 0.0; 121 *c = 1.0; 122 } 123 else { 124 *s = 1.0; 125 *c = 0.0; 126 } 127 if ((lx & 2) != 0) { 128 *s = -*s; 129 *c = -*c; 130 } 131 } 132 } 133 } 134 else if (n < -2) /* |x| < 0.25 */ 135 *s = __k_sincos(pi * fabs(x), 0.0, c); 136 else { 137 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */ 138 if (ix < 0x41C00000) { /* |x| < 2**29 */ 139 y = 4.0 * fabs(x); 140 n = (int) y; /* exact */ 141 z = (double) n; 142 k = z == y; 143 t = (y - z) * 0.25; 144 } 145 else { /* 2**29 <= |x| < 2**51 */ 146 y = fabs(x); 147 k = 50 - n; 148 n = lx >> k; 149 h = n << k; 150 ((unsigned *) &z)[LOWORD] = h; 151 ((int *) &z)[HIWORD] = ix; 152 k = h == lx; 153 t = y - z; 154 } 155 if (k) { /* x = N/4 */ 156 if ((n & 1) != 0) 157 *s = *c = sqrth_h + sqrth_l; 158 else 159 if ((n & 2) == 0) { 160 *s = 0.0; 161 *c = 1.0; 162 } 163 else { 164 *s = 1.0; 165 *c = 0.0; 166 } 167 y = (n & 2) == 0 ? 0.0 : 1.0; 168 if ((n & 4) != 0) 169 *s = -*s; 170 if (((n + 1) & 4) != 0) 171 *c = -*c; 172 } 173 else { 174 if ((n & 1) != 0) 175 t = 0.25 - t; 176 if (((n + (n & 1)) & 2) == 0) 177 *s = __k_sincos(pi * t, 0.0, c); 178 else 179 *c = __k_sincos(pi * t, 0.0, s); 180 if ((n & 4) != 0) 181 *s = -*s; 182 if (((n + 2) & 4) != 0) 183 *c = -*c; 184 } 185 } 186 if (hx < 0) 187 *s = -*s; 188 } 189