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 #pragma weak sincospil = __sincospil 31 32 /* 33 * void sincospil(long double x, long double *s, long double *c) 34 * *s = sinl(pi*x); *c = cosl(pi*x); 35 * 36 * Algorithm, 10/17/2002, K.C. Ng 37 * ------------------------------ 38 * Let y = |4x|, z = floor(y), and n = (int)(z mod 8.0) (displayed in binary). 39 * 1. If y == z, then x is a multiple of pi/4. Return the following values: 40 * --------------------------------------------------- 41 * n x mod 2 sin(x*pi) cos(x*pi) tan(x*pi) 42 * --------------------------------------------------- 43 * 000 0.00 +0 ___ +1 ___ +0 44 * 001 0.25 +\/0.5 +\/0.5 +1 45 * 010 0.50 +1 ___ +0 ___ +inf 46 * 011 0.75 +\/0.5 -\/0.5 -1 47 * 100 1.00 -0 ___ -1 ___ +0 48 * 101 1.25 -\/0.5 -\/0.5 +1 49 * 110 1.50 -1 ___ -0 ___ +inf 50 * 111 1.75 -\/0.5 +\/0.5 -1 51 * --------------------------------------------------- 52 * 2. Otherwise, 53 * --------------------------------------------------- 54 * n t sin(x*pi) cos(x*pi) tan(x*pi) 55 * --------------------------------------------------- 56 * 000 (y-z)/4 sinpi(t) cospi(t) tanpi(t) 57 * 001 (z+1-y)/4 cospi(t) sinpi(t) 1/tanpi(t) 58 * 010 (y-z)/4 cospi(t) -sinpi(t) -1/tanpi(t) 59 * 011 (z+1-y)/4 sinpi(t) -cospi(t) -tanpi(t) 60 * 100 (y-z)/4 -sinpi(t) -cospi(t) tanpi(t) 61 * 101 (z+1-y)/4 -cospi(t) -sinpi(t) 1/tanpi(t) 62 * 110 (y-z)/4 -cospi(t) sinpi(t) -1/tanpi(t) 63 * 111 (z+1-y)/4 -sinpi(t) cospi(t) -tanpi(t) 64 * --------------------------------------------------- 65 * 66 * NOTE. This program compute sinpi/cospi(t<0.25) by __k_sin/cos(pi*t, 0.0). 67 * This will return a result with error slightly more than one ulp (but less 68 * than 2 ulp). If one wants accurate result, one may break up pi*t in 69 * high (tpi_h) and low (tpi_l) parts and call __k_sin/cos(tip_h, tip_lo) 70 * instead. 71 */ 72 73 #include "libm.h" 74 #include "libm_synonyms.h" 75 #include "longdouble.h" 76 77 #include <sys/isa_defs.h> 78 79 #define I(q, m) ((int *) &(q))[m] 80 #define U(q, m) ((unsigned *) &(q))[m] 81 #if defined(__i386) || defined(__amd64) 82 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15))) 83 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0) 84 #define PREC 64 85 #define PRECM1 63 86 #define PRECM2 62 87 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L; 88 #else 89 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0) 90 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1) 91 #define PREC 113 92 #define PRECM1 112 93 #define PRECM2 111 94 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L; 95 #endif 96 97 static const long double 98 zero = 0.0L, 99 quater = 0.25L, 100 one = 1.0L, 101 pi = 3.141592653589793238462643383279502884197e+0000L, 102 sqrth = 0.707106781186547524400844362104849039284835937688474, 103 tiny = 1.0e-100; 104 105 void 106 sincospil(long double x, long double *s, long double *c) { 107 long double y, z, t; 108 int hx, n, k; 109 unsigned lx; 110 111 hx = LDBL_MOST_SIGNIF_I(x); 112 lx = LDBL_LEAST_SIGNIF_U(x); 113 k = ((hx & 0x7fff0000) >> 16) - 0x3fff; 114 if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */ 115 if (k >= 16384) { 116 *s = *c = x - x; 117 } 118 else { 119 if (k >= PREC) { 120 *s = zero; 121 *c = one; 122 } 123 else if (k == PRECM1) { 124 if ((lx & 1) == 0) { 125 *s = zero; 126 *c = one; 127 } 128 else { 129 *s = -zero; 130 *c = -one; 131 } 132 } 133 else { /* k = Prec - 2 */ 134 if ((lx & 1) == 0) { 135 *s = zero; 136 *c = one; 137 } 138 else { 139 *s = one; 140 *c = zero; 141 } 142 if ((lx & 2) != 0) { 143 *s = -*s; 144 *c = -*c; 145 } 146 } 147 } 148 } 149 else if (k < -2) /* |x| < 0.25 */ 150 *s = __k_sincosl(pi * fabsl(x), zero, c); 151 else { 152 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */ 153 y = 4.0L * fabsl(x); 154 if (k < PRECM2) { 155 z = y + twoPRECM2; 156 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */ 157 t = z - twoPRECM2; 158 k = 0; 159 if (t == y) 160 k = 1; 161 else if (t > y) { 162 n -= 1; 163 t = quater + (y - t) * quater; 164 } 165 else 166 t = (y - t) * quater; 167 } 168 else { /* k = Prec-3 */ 169 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */ 170 k = 1; 171 } 172 if (k) { /* x = N/4 */ 173 if ((n & 1) != 0) 174 *s = *c = sqrth + tiny; 175 else 176 if ((n & 2) == 0) { 177 *s = zero; 178 *c = one; 179 } 180 else { 181 *s = one; 182 *c = zero; 183 } 184 if ((n & 4) != 0) 185 *s = -*s; 186 if (((n + 1) & 4) != 0) 187 *c = -*c; 188 } 189 else { 190 if ((n & 1) != 0) 191 t = quater - t; 192 if (((n + (n & 1)) & 2) == 0) 193 *s = __k_sincosl(pi * t, zero, c); 194 else 195 *c = __k_sincosl(pi * t, zero, s); 196 if ((n & 4) != 0) 197 *s = -*s; 198 if (((n + 2) & 4) != 0) 199 *c = -*c; 200 } 201 } 202 if (hx < 0) 203 *s = -*s; 204 } 205 #undef U 206 #undef LDBL_LEAST_SIGNIF_U 207 #undef I 208 #undef LDBL_MOST_SIGNIF_I 209