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 cos = __cos 30 31 /* INDENT OFF */ 32 /* 33 * cos(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 /* Q1 = */ -0.5, 64 /* Q2 = */ 4.166666666500350703680945520860748617445e-0002, 65 /* Q3 = */ -1.388888596436972210694266290577848696006e-0003, 66 /* Q4 = */ 2.478563078858589473679519517892953492192e-0005, 67 /* PIO2_H = */ 1.570796326794896557999, 68 /* PIO2_L = */ 6.123233995736765886130e-17, 69 /* PIO2_L0 = */ 6.123233995727922165564e-17, 70 /* PIO2_L1 = */ 8.843720566135701120255e-29, 71 /* PI3O2_H = */ 4.712388980384689673997, 72 /* PI3O2_L = */ 1.836970198721029765839e-16, 73 /* PI3O2_L0 = */ 1.836970198720396133587e-16, 74 /* PI3O2_L1 = */ 6.336322524749201142226e-29, 75 /* PI5O2_H = */ 7.853981633974482789995, 76 /* PI5O2_L = */ 3.061616997868382943065e-16, 77 /* PI5O2_L0 = */ 3.061616997861941598865e-16, 78 /* PI5O2_L1 = */ 6.441344200433640781982e-28, 79 }; 80 /* INDENT ON */ 81 82 #define ONE sc[0] 83 #define PP1 sc[2] 84 #define PP2 sc[3] 85 #define P1 sc[4] 86 #define P2 sc[5] 87 #define P3 sc[6] 88 #define P4 sc[7] 89 #define QQ1 sc[8] 90 #define QQ2 sc[9] 91 #define Q1 sc[10] 92 #define Q2 sc[11] 93 #define Q3 sc[12] 94 #define Q4 sc[13] 95 #define PIO2_H sc[14] 96 #define PIO2_L sc[15] 97 #define PIO2_L0 sc[16] 98 #define PIO2_L1 sc[17] 99 #define PI3O2_H sc[18] 100 #define PI3O2_L sc[19] 101 #define PI3O2_L0 sc[20] 102 #define PI3O2_L1 sc[21] 103 #define PI5O2_H sc[22] 104 #define PI5O2_L sc[23] 105 #define PI5O2_L0 sc[24] 106 #define PI5O2_L1 sc[25] 107 108 extern const double _TBL_sincos[], _TBL_sincosx[]; 109 110 double 111 cos(double x) { 112 double z, y[2], w, s, v, p, q; 113 int i, j, n, hx, ix, lx; 114 115 hx = ((int *)&x)[HIWORD]; 116 lx = ((int *)&x)[LOWORD]; 117 ix = hx & ~0x80000000; 118 119 if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */ 120 if (ix < 0x3e400000) { /* |x| < 2**-27 */ 121 if ((int)x == 0) 122 return (ONE); 123 } 124 z = x * x; 125 if (ix < 0x3f800000) /* |x| < 0.008 */ 126 w = z * (QQ1 + z * QQ2); 127 else 128 w = z * ((Q1 + z * Q2) + (z * z) * (Q3 + z * Q4)); 129 return (ONE + w); 130 } 131 132 /* for 0.164062500 < x < M, */ 133 n = ix >> 20; 134 if (n < 0x402) { /* x < 8 */ 135 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n); 136 j = i - 10; 137 x = fabs(x); 138 v = x - _TBL_sincosx[j]; 139 if (((j - 81) ^ (j - 101)) < 0) { 140 /* near pi/2, cos(pi/2-x)=sin(x) */ 141 p = PIO2_H - x; 142 i = ix - 0x3ff921fb; 143 x = p + PIO2_L; 144 if ((i | ((lx - 0x54442D00) & 0xffffff00)) == 0) { 145 /* very close to pi/2 */ 146 x = p + PIO2_L0; 147 return (x + PIO2_L1); 148 } 149 z = x * x; 150 if (((ix - 0x3ff92000) >> 12) == 0) { 151 /* |pi/2-x|<2**-8 */ 152 w = PIO2_L + (z * x) * (PP1 + z * PP2); 153 } else { 154 w = PIO2_L + (z * x) * ((P1 + z * P2) + 155 (z * z) * (P3 + z * P4)); 156 } 157 return (p + w); 158 } 159 s = v * v; 160 if (((j - 282) ^ (j - 302)) < 0) { 161 /* near 3/2pi, cos(x-3/2pi)=sin(x) */ 162 p = x - PI3O2_H; 163 i = ix - 0x4012D97C; 164 x = p - PI3O2_L; 165 if ((i | ((lx - 0x7f332100) & 0xffffff00)) == 0) { 166 /* very close to 3/2pi */ 167 x = p - PI3O2_L0; 168 return (x - PI3O2_L1); 169 } 170 z = x * x; 171 if (((ix - 0x4012D800) >> 9) == 0) { 172 /* |x-3/2pi|<2**-8 */ 173 w = (z * x) * (PP1 + z * PP2) - PI3O2_L; 174 } else { 175 w = (z * x) * ((P1 + z * P2) + (z * z) 176 * (P3 + z * P4)) - PI3O2_L; 177 } 178 return (p + w); 179 } 180 if (((j - 483) ^ (j - 503)) < 0) { 181 /* near 5pi/2, cos(5pi/2-x)=sin(x) */ 182 p = PI5O2_H - x; 183 i = ix - 0x401F6A7A; 184 x = p + PI5O2_L; 185 if ((i | ((lx - 0x29553800) & 0xffffff00)) == 0) { 186 /* very close to pi/2 */ 187 x = p + PI5O2_L0; 188 return (x + PI5O2_L1); 189 } 190 z = x * x; 191 if (((ix - 0x401F6A7A) >> 7) == 0) { 192 /* |pi/2-x|<2**-8 */ 193 w = PI5O2_L + (z * x) * (PP1 + z * PP2); 194 } else { 195 w = PI5O2_L + (z * x) * ((P1 + z * P2) + 196 (z * z) * (P3 + z * P4)); 197 } 198 return (p + w); 199 } 200 j <<= 1; 201 w = _TBL_sincos[j]; 202 z = _TBL_sincos[j+1]; 203 p = v + (v * s) * (PP1 + s * PP2); 204 q = s * (QQ1 + s * QQ2); 205 return (z - (w * p - z * q)); 206 } 207 208 if (ix >= 0x7ff00000) /* cos(Inf or NaN) is NaN */ 209 return (x / x); 210 211 /* argument reduction needed */ 212 n = __rem_pio2(x, y); 213 switch (n & 3) { 214 case 0: 215 return (__k_cos(y[0], y[1])); 216 case 1: 217 return (-__k_sin(y[0], y[1])); 218 case 2: 219 return (-__k_cos(y[0], y[1])); 220 default: 221 return (__k_sin(y[0], y[1])); 222 } 223 } 224