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