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 * __k_sin( double x; double y ) 32 * kernel sin 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 * 36 * Accurate Table look-up algorithm by K.C. Ng, May, 1995. 37 * 38 * Algorithm: see __sincos.c 39 */ 40 41 #include "libm.h" 42 43 static const double sc[] = { 44 /* ONE = */ 1.0, 45 /* NONE = */ -1.0, 46 /* 47 * |sin(x) - (x+pp1*x^3+pp2*x^5)| <= 2^-58.79 for |x| < 0.008 48 */ 49 /* PP1 = */ -0.166666666666316558867252052378889521480627858683055567, 50 /* PP2 = */ .008333315652997472323564894248466758248475374977974017927, 51 /* 52 * |(sin(x) - (x+p1*x^3+...+p4*x^9)| 53 * |------------------------------ | <= 2^-57.63 for |x| < 0.1953125 54 * | x | 55 */ 56 /* P1 = */ -1.666666666666629669805215138920301589656e-0001, 57 /* P2 = */ 8.333333332390951295683993455280336376663e-0003, 58 /* P3 = */ -1.984126237997976692791551778230098403960e-0004, 59 /* P4 = */ 2.753403624854277237649987622848330351110e-0006, 60 /* 61 * |cos(x) - (1+qq1*x^2+qq2*x^4)| <= 2^-55.99 for |x| <= 0.008 (0x3f80624d) 62 */ 63 /* QQ1 = */ -0.4999999999975492381842911981948418542742729, 64 /* QQ2 = */ 0.041666542904352059294545209158357640398771740, 65 /* 66 * |cos(x) - (1+q1*x^2+...+q4*x^8)| <= 2^-55.86 for |x| <= 0.1640625 (10.5/64) 67 */ 68 /* Q1 = */ -0.5, 69 /* Q2 = */ 4.166666666500350703680945520860748617445e-0002, 70 /* Q3 = */ -1.388888596436972210694266290577848696006e-0003, 71 /* Q4 = */ 2.478563078858589473679519517892953492192e-0005, 72 }; 73 /* INDENT ON */ 74 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 Q1 sc[10] 86 #define Q2 sc[11] 87 #define Q3 sc[12] 88 #define Q4 sc[13] 89 90 extern const double _TBL_sincos[], _TBL_sincosx[]; 91 92 double 93 __k_sin(double x, double y) { 94 double z, w, s, v, p, q; 95 int i, j, n, hx, ix; 96 97 hx = ((int *)&x)[HIWORD]; 98 ix = hx & ~0x80000000; 99 100 if (ix <= 0x3fc50000) { /* |x| < 10.5/64 = 0.164062500 */ 101 if (ix < 0x3e400000) /* |x| < 2**-27 */ 102 if ((int)x == 0) 103 return (x + y); 104 z = x * x; 105 if (ix < 0x3f800000) /* |x| < 0.008 */ 106 p = (x * z) * (PP1 + z * PP2) + y; 107 else 108 p = (x * z) * ((P1 + z * P2) + (z * z) * (P3 + 109 z * P4)) + y; 110 return (x + p); 111 } else { /* 0.164062500 < |x| < ~pi/4 */ 112 n = ix >> 20; 113 i = (((ix >> 12) & 0xff) | 0x100) >> (0x401 - n); 114 j = i - 10; 115 if (hx < 0) 116 v = -y - (_TBL_sincosx[j] + x); 117 else 118 v = y - (_TBL_sincosx[j] - x); 119 s = v * v; 120 j <<= 1; 121 w = _TBL_sincos[j]; 122 z = _TBL_sincos[j+1]; 123 p = s * (PP1 + s * PP2); 124 q = s * (QQ1 + s * QQ2); 125 p = v + v * p; 126 s = w * q + z * p; 127 return ((hx >= 0)? w + s : -(w + s)); 128 } 129 } 130