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 "longdouble.h" 75 76 #define I(q, m) ((int *) &(q))[m] 77 #define U(q, m) ((unsigned *) &(q))[m] 78 #if defined(__LITTLE_ENDIAN) || defined(__x86) 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 } else { 115 if (k >= PREC) { 116 *s = zero; 117 *c = one; 118 } else if (k == PRECM1) { 119 if ((lx & 1) == 0) { 120 *s = zero; 121 *c = one; 122 } else { 123 *s = -zero; 124 *c = -one; 125 } 126 } else { /* k = Prec - 2 */ 127 if ((lx & 1) == 0) { 128 *s = zero; 129 *c = one; 130 } else { 131 *s = one; 132 *c = zero; 133 } 134 if ((lx & 2) != 0) { 135 *s = -*s; 136 *c = -*c; 137 } 138 } 139 } 140 } else if (k < -2) /* |x| < 0.25 */ 141 *s = __k_sincosl(pi * fabsl(x), zero, c); 142 else { 143 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */ 144 y = 4.0L * fabsl(x); 145 if (k < PRECM2) { 146 z = y + twoPRECM2; 147 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */ 148 t = z - twoPRECM2; 149 k = 0; 150 if (t == y) 151 k = 1; 152 else if (t > y) { 153 n -= 1; 154 t = quater + (y - t) * quater; 155 } else 156 t = (y - t) * quater; 157 } else { /* k = Prec-3 */ 158 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */ 159 k = 1; 160 } 161 if (k) { /* x = N/4 */ 162 if ((n & 1) != 0) 163 *s = *c = sqrth + tiny; 164 else 165 if ((n & 2) == 0) { 166 *s = zero; 167 *c = one; 168 } else { 169 *s = one; 170 *c = zero; 171 } 172 if ((n & 4) != 0) 173 *s = -*s; 174 if (((n + 1) & 4) != 0) 175 *c = -*c; 176 } else { 177 if ((n & 1) != 0) 178 t = quater - t; 179 if (((n + (n & 1)) & 2) == 0) 180 *s = __k_sincosl(pi * t, zero, c); 181 else 182 *c = __k_sincosl(pi * t, zero, s); 183 if ((n & 4) != 0) 184 *s = -*s; 185 if (((n + 2) & 4) != 0) 186 *c = -*c; 187 } 188 } 189 if (hx < 0) 190 *s = -*s; 191 } 192 #undef U 193 #undef LDBL_LEAST_SIGNIF_U 194 #undef I 195 #undef LDBL_MOST_SIGNIF_I 196