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 sinpil = __sinpil 31 32 /* long double sinpil(long double x), 33 * return long double precision sinl(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_synonyms.h" 74 #include "longdouble.h" 75 76 #include <sys/isa_defs.h> 77 78 #define I(q, m) ((int *) &(q))[m] 79 #define U(q, m) ((unsigned *) &(q))[m] 80 #if defined(__i386) || defined(__amd64) 81 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15))) 82 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0) 83 #define PREC 64 84 #define PRECM1 63 85 #define PRECM2 62 86 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L; 87 #else 88 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0) 89 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof(long double) / sizeof(int) - 1) 90 #define PREC 113 91 #define PRECM1 112 92 #define PRECM2 111 93 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L; 94 #endif 95 96 static const long double 97 zero = 0.0L, 98 quater = 0.25L, 99 one = 1.0L, 100 pi = 3.141592653589793238462643383279502884197e+0000L, 101 sqrth = 0.707106781186547524400844362104849039284835937688474, 102 tiny = 1.0e-100; 103 104 long double 105 sinpil(long double x) { 106 long double y, z, t; 107 int hx, n, k; 108 unsigned lx; 109 110 hx = LDBL_MOST_SIGNIF_I(x); 111 lx = LDBL_LEAST_SIGNIF_U(x); 112 k = ((hx & 0x7fff0000) >> 16) - 0x3fff; 113 if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */ 114 if (k >= 16384) 115 y = x - x; 116 else { 117 if (k >= PREC) 118 y = zero; 119 else if (k == PRECM1) 120 y = (lx & 1) == 0 ? zero: -zero; 121 else { /* k = Prec - 2 */ 122 y = (lx & 1) == 0 ? zero : one; 123 if ((lx & 2) != 0) 124 y = -y; 125 } 126 } 127 } 128 else if (k < -2) /* |x| < 0.25 */ 129 y = __k_sinl(pi * fabsl(x), zero); 130 else { 131 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */ 132 y = 4.0L * fabsl(x); 133 if (k < PRECM2) { 134 z = y + twoPRECM2; 135 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */ 136 t = z - twoPRECM2; 137 k = 0; 138 if (t == y) 139 k = 1; 140 else if (t > y) { 141 n -= 1; 142 t = quater + (y - t) * quater; 143 } 144 else 145 t = (y - t) * quater; 146 } 147 else { /* k = Prec-3 */ 148 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */ 149 k = 1; 150 } 151 if (k) { /* x = N/4 */ 152 if ((n & 1) != 0) 153 y = sqrth + tiny; 154 else 155 y = (n & 2) == 0 ? zero : one; 156 if ((n & 4) != 0) 157 y = -y; 158 } 159 else { 160 if ((n & 1) != 0) 161 t = quater - t; 162 if (((n + (n & 1)) & 2) == 0) 163 y = __k_sinl(pi * t, zero); 164 else 165 y = __k_cosl(pi * t, zero); 166 if ((n & 4) != 0) 167 y = -y; 168 } 169 } 170 return hx >= 0 ? y : -y; 171 } 172 #undef U 173 #undef LDBL_LEAST_SIGNIF_U 174 #undef I 175 #undef LDBL_MOST_SIGNIF_I 176