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 * long double sinpil(long double x), 32 * return long double precision sinl(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 #define I(q, m) ((int *) &(q))[m] 75 #define U(q, m) ((unsigned *) &(q))[m] 76 #if defined(__LITTLE_ENDIAN) || defined(__x86) 77 #define LDBL_MOST_SIGNIF_I(ld) ((I(ld, 2) << 16) | (0xffff & (I(ld, 1) >> 15))) 78 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, 0) 79 #define PREC 64 80 #define PRECM1 63 81 #define PRECM2 62 82 static const long double twoPRECM2 = 9.223372036854775808000000000000000e+18L; 83 #else 84 #define LDBL_MOST_SIGNIF_I(ld) I(ld, 0) 85 #define LDBL_LEAST_SIGNIF_U(ld) U(ld, sizeof (long double) / sizeof (int) - 1) 86 #define PREC 113 87 #define PRECM1 112 88 #define PRECM2 111 89 static const long double twoPRECM2 = 5.192296858534827628530496329220096e+33L; 90 #endif 91 92 static const long double 93 zero = 0.0L, 94 quater = 0.25L, 95 one = 1.0L, 96 pi = 3.141592653589793238462643383279502884197e+0000L, 97 sqrth = 0.707106781186547524400844362104849039284835937688474, 98 tiny = 1.0e-100; 99 100 long double 101 sinpil(long double x) { 102 long double y, z, t; 103 int hx, n, k; 104 unsigned lx; 105 106 hx = LDBL_MOST_SIGNIF_I(x); 107 lx = LDBL_LEAST_SIGNIF_U(x); 108 k = ((hx & 0x7fff0000) >> 16) - 0x3fff; 109 if (k >= PRECM2) { /* |x| >= 2**(Prec-2) */ 110 if (k >= 16384) 111 y = x - x; 112 else { 113 if (k >= PREC) 114 y = zero; 115 else if (k == PRECM1) 116 y = (lx & 1) == 0 ? zero: -zero; 117 else { /* k = Prec - 2 */ 118 y = (lx & 1) == 0 ? zero : one; 119 if ((lx & 2) != 0) 120 y = -y; 121 } 122 } 123 } else if (k < -2) /* |x| < 0.25 */ 124 y = __k_sinl(pi * fabsl(x), zero); 125 else { 126 /* y = |4x|, z = floor(y), and n = (int)(z mod 8.0) */ 127 y = 4.0L * fabsl(x); 128 if (k < PRECM2) { 129 z = y + twoPRECM2; 130 n = LDBL_LEAST_SIGNIF_U(z) & 7; /* 3 LSb of z */ 131 t = z - twoPRECM2; 132 k = 0; 133 if (t == y) 134 k = 1; 135 else if (t > y) { 136 n -= 1; 137 t = quater + (y - t) * quater; 138 } else 139 t = (y - t) * quater; 140 } else { /* k = Prec-3 */ 141 n = LDBL_LEAST_SIGNIF_U(y) & 7; /* 3 LSb of z */ 142 k = 1; 143 } 144 if (k) { /* x = N/4 */ 145 if ((n & 1) != 0) 146 y = sqrth + tiny; 147 else 148 y = (n & 2) == 0 ? zero : one; 149 if ((n & 4) != 0) 150 y = -y; 151 } else { 152 if ((n & 1) != 0) 153 t = quater - t; 154 if (((n + (n & 1)) & 2) == 0) 155 y = __k_sinl(pi * t, zero); 156 else 157 y = __k_cosl(pi * t, zero); 158 if ((n & 4) != 0) 159 y = -y; 160 } 161 } 162 return (hx >= 0 ? y : -y); 163 } 164 #undef U 165 #undef LDBL_LEAST_SIGNIF_U 166 #undef I 167 #undef LDBL_MOST_SIGNIF_I 168