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