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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 23 */ 24 /* 25 * Copyright 2005 Sun Microsystems, Inc. All rights reserved. 26 * Use is subject to license terms. 27 */ 28 29 #pragma weak __sin = sin 30 31 /* INDENT OFF */ 32 /* 33 * sin(x) 34 * Accurate Table look-up algorithm by K.C. Ng, May, 1995. 35 * 36 * Algorithm: see sincos.c 37 */ 38 39 #include "libm.h" 40 41 static const double sc[] = { 42 /* ONE = */ 1.0, 43 /* NONE = */ -1.0, 44 /* 45 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008 46 */ 47 /* PP1 = */ -0.166666666666316558867252052378889521480627858683055567, 48 /* PP2 = */ .008333315652997472323564894248466758248475374977974017927, 49 /* 50 * |(sin(x) - (x+p1*x^3+...+p4*x^9)| 51 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125 52 * | x | 53 */ 54 /* P1 = */ -1.666666666666629669805215138920301589656e-0001, 55 /* P2 = */ 8.333333332390951295683993455280336376663e-0003, 56 /* P3 = */ -1.984126237997976692791551778230098403960e-0004, 57 /* P4 = */ 2.753403624854277237649987622848330351110e-0006, 58 /* 59 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d) 60 */ 61 /* QQ1 = */ -0.4999999999975492381842911981948418542742729, 62 /* QQ2 = */ 0.041666542904352059294545209158357640398771740, 63 /* PI_H = */ 3.1415926535897931159979634685, 64 /* PI_L = */ 1.22464679914735317722606593227425e-16, 65 /* PI_L0 = */ 1.22464679914558443311283879205095e-16, 66 /* PI_L1 = */ 1.768744113227140223300005233735517376e-28, 67 /* PI2_H = */ 6.2831853071795862319959269370, 68 /* PI2_L = */ 2.44929359829470635445213186454850e-16, 69 /* PI2_L0 = */ 2.44929359829116886622567758410190e-16, 70 /* PI2_L1 = */ 3.537488226454280446600010467471034752e-28, 71 }; 72 /* INDENT ON */ 73 74 #define ONEA sc 75 #define ONE sc[0] 76 #define NONE sc[1] 77 #define PP1 sc[2] 78 #define PP2 sc[3] 79 #define P1 sc[4] 80 #define P2 sc[5] 81 #define P3 sc[6] 82 #define P4 sc[7] 83 #define QQ1 sc[8] 84 #define QQ2 sc[9] 85 #define PI_H sc[10] 86 #define PI_L sc[11] 87 #define PI_L0 sc[12] 88 #define PI_L1 sc[13] 89 #define PI2_H sc[14] 90 #define PI2_L sc[15] 91 #define PI2_L0 sc[16] 92 #define PI2_L1 sc[17] 93 94 extern const double _TBL_sincos[], _TBL_sincosx[]; 95 96 double 97 sin(double x) { 98 double z, y[2], w, s, v, p, q; 99 int i, j, n, hx, ix, lx; 100 101 hx = ((int *)&x)[HIWORD]; 102 lx = ((int *)&x)[LOWORD]; 103 ix = hx & ~0x80000000; 104 105 if (ix <= 0x3fc50000) { /* |x| < .1640625 */ 106 if (ix < 0x3e400000) /* |x| < 2**-27 */ 107 if ((int)x == 0) 108 return (x); 109 z = x * x; 110 if (ix < 0x3f800000) /* |x| < 2**-8 */ 111 w = (z * x) * (PP1 + z * PP2); 112 else 113 w = (x * z) * ((P1 + z * P2) + (z * z) * (P3 + z * P4)); 114 return (x + w); 115 } 116 117 /* for .1640625 < x < M, */ 118 n = ix >> 20; 119 if (n < 0x402) { /* x < 8 */ 120 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n); 121 j = i - 10; 122 x = fabs(x); 123 v = x - _TBL_sincosx[j]; 124 if (((j - 181) ^ (j - 201)) < 0) { 125 /* near pi, sin(x) = sin(pi-x) */ 126 p = PI_H - x; 127 i = ix - 0x400921fb; 128 x = p + PI_L; 129 if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) { 130 /* very close to pi */ 131 x = p + PI_L0; 132 return ((hx >= 0)? x + PI_L1 : -(x + PI_L1)); 133 } 134 z = x * x; 135 if (((ix - 0x40092000) >> 11) == 0) { 136 /* |pi-x|<2**-8 */ 137 w = PI_L + (z * x) * (PP1 + z * PP2); 138 } else { 139 w = PI_L + (z * x) * ((P1 + z * P2) + 140 (z * z) * (P3 + z * P4)); 141 } 142 return ((hx >= 0)? p + w : -p - w); 143 } 144 s = v * v; 145 if (((j - 382) ^ (j - 402)) < 0) { 146 /* near 2pi, sin(x) = sin(x-2pi) */ 147 p = x - PI2_H; 148 i = ix - 0x401921fb; 149 x = p - PI2_L; 150 if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) { 151 /* very close to 2pi */ 152 x = p - PI2_L0; 153 return ((hx >= 0)? x - PI2_L1 : -(x - PI2_L1)); 154 } 155 z = x * x; 156 if (((ix - 0x40192000) >> 10) == 0) { 157 /* |x-2pi|<2**-8 */ 158 w = (z * x) * (PP1 + z * PP2) - PI2_L; 159 } else { 160 w = (z * x) * ((P1 + z * P2) + 161 (z * z) * (P3 + z * P4)) - PI2_L; 162 } 163 return ((hx >= 0)? p + w : -p - w); 164 } 165 j <<= 1; 166 w = _TBL_sincos[j+1]; 167 z = _TBL_sincos[j]; 168 p = v + (v * s) * (PP1 + s * PP2); 169 q = s * (QQ1 + s * QQ2); 170 v = w * p + z * q; 171 return ((hx >= 0)? z + v : -z - v); 172 } 173 174 if (ix >= 0x7ff00000) /* sin(Inf or NaN) is NaN */ 175 return (x / x); 176 177 /* argument reduction needed */ 178 n = __rem_pio2(x, y); 179 switch (n & 3) { 180 case 0: 181 return (__k_sin(y[0], y[1])); 182 case 1: 183 return (__k_cos(y[0], y[1])); 184 case 2: 185 return (-__k_sin(y[0], y[1])); 186 default: 187 return (-__k_cos(y[0], y[1])); 188 } 189 } 190