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 /* INDENT OFF */ 30 /* 31 * double __k_sincos(double x, double y, double *c); 32 * kernel sincos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 33 * Input x is assumed to be bounded by ~pi/4 in magnitude. 34 * Input y is the tail of x. 35 * return sin(x) with *c = cos(x) 36 * 37 * Accurate Table look-up algorithm by K.C. Ng, May, 1995. 38 * 39 * 1. Reduce x to x>0 by sin(-x)=-sin(x),cos(-x)=cos(x). 40 * 2. For 0<= x < pi/4, let i = (64*x chopped)-10. Let d = x - a[i], where 41 * a[i] is a double that is close to (i+10.5)/64 and such that 42 * sin(a[i]) and cos(a[i]) is close to a double (with error less 43 * than 2**-8 ulp). Then 44 * cos(x) = cos(a[i]+d) = cos(a[i])cos(d) - sin(a[i])*sin(d) 45 * = TBL_cos_a[i]*(1+QQ1*d^2+QQ2*d^4) - 46 * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5) 47 * = TBL_cos_a[i] + (TBL_cos_a[i]*d^2*(QQ1+QQ2*d^2) - 48 * TBL_sin_a[i]*(d+PP1*d^3+PP2*d^5)) 49 * sin(x) = sin(a[i]+d) = sin(a[i])cos(d) + cos(a[i])*sin(d) 50 * = TBL_sin_a[i]*(1+QQ1*d^2+QQ2*d^4) + 51 * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5) 52 * = TBL_sin_a[i] + (TBL_sin_a[i]*d^2*(QQ1+QQ2*d^2) + 53 * TBL_cos_a[i]*(d+PP1*d^3+PP2*d^5)) 54 * 55 * For |y| less than 10.5/64 = 0.1640625, use 56 * sin(y) = y + y^3*(p1+y^2*(p2+y^2*(p3+y^2*p4))) 57 * cos(y) = 1 + y^2*(q1+y^2*(q2+y^2*(q3+y^2*q4))) 58 * 59 * For |y| less than 0.008, use 60 * sin(y) = y + y^3*(pp1+y^2*pp2) 61 * cos(y) = 1 + y^2*(qq1+y^2*qq2) 62 * 63 * Accuracy: 64 * TRIG(x) returns trig(x) nearly rounded (less than 1 ulp) 65 */ 66 67 #include "libm.h" 68 69 static const double sc[] = { 70 /* ONE = */ 1.0, 71 /* NONE = */ -1.0, 72 /* 73 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008 74 */ 75 /* PP1 = */ -0.166666666666316558867252052378889521480627858683055567, 76 /* PP2 = */ .008333315652997472323564894248466758248475374977974017927, 77 /* 78 * |(sin(x) - (x+p1*x^3+...+p4*x^9)| 79 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125 80 * | x | 81 */ 82 /* P1 = */ -1.666666666666629669805215138920301589656e-0001, 83 /* P2 = */ 8.333333332390951295683993455280336376663e-0003, 84 /* P3 = */ -1.984126237997976692791551778230098403960e-0004, 85 /* P4 = */ 2.753403624854277237649987622848330351110e-0006, 86 /* 87 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d) 88 */ 89 /* QQ1 = */ -0.4999999999975492381842911981948418542742729, 90 /* QQ2 = */ 0.041666542904352059294545209158357640398771740, 91 /* 92 * |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64) 93 */ 94 /* Q1 = */ -0.5, 95 /* Q2 = */ 4.166666666500350703680945520860748617445e-0002, 96 /* Q3 = */ -1.388888596436972210694266290577848696006e-0003, 97 /* Q4 = */ 2.478563078858589473679519517892953492192e-0005, 98 }; 99 /* INDENT ON */ 100 101 #define ONE sc[0] 102 #define NONE sc[1] 103 #define PP1 sc[2] 104 #define PP2 sc[3] 105 #define P1 sc[4] 106 #define P2 sc[5] 107 #define P3 sc[6] 108 #define P4 sc[7] 109 #define QQ1 sc[8] 110 #define QQ2 sc[9] 111 #define Q1 sc[10] 112 #define Q2 sc[11] 113 #define Q3 sc[12] 114 #define Q4 sc[13] 115 116 extern const double _TBL_sincos[], _TBL_sincosx[]; 117 118 double 119 __k_sincos(double x, double y, double *c) { 120 double z, w, s, v, p, q; 121 int i, j, n, hx, ix; 122 123 hx = ((int *)&x)[HIWORD]; 124 ix = hx & ~0x80000000; 125 126 if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */ 127 if (ix < 0x3e400000) { /* |x| < 2**-27 */ 128 if ((int)x == 0) 129 *c = ONE; 130 return (x + y); 131 } else { 132 z = x * x; 133 if (ix < 0x3f800000) { /* |x| < 0.008 */ 134 q = z * (QQ1 + z * QQ2); 135 p = (x * z) * (PP1 + z * PP2) + y; 136 } else { 137 q = z * ((Q1 + z * Q2) + (z * z) * (Q3 + 138 z * Q4)); 139 p = (x * z) * ((P1 + z * P2) + (z * z) * (P3 + 140 z * P4)) + y; 141 } 142 *c = ONE + q; 143 return (x + p); 144 } 145 } else { /* 0.164062500 < |x| < ~pi/4 */ 146 n = ix >> 20; 147 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n); 148 j = i - 10; 149 if (hx < 0) 150 v = -y - (_TBL_sincosx[j] + x); 151 else 152 v = y - (_TBL_sincosx[j] - x); 153 s = v * v; 154 j <<= 1; 155 w = _TBL_sincos[j]; 156 z = _TBL_sincos[j+1]; 157 p = s * (PP1 + s * PP2); 158 q = s * (QQ1 + s * QQ2); 159 p = v + v * p; 160 *c = z - (w * p - z * q); 161 s = w * q + z * p; 162 return ((hx >= 0)? w + s : -(w + s)); 163 } 164 } 165