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 /* INDENT OFF */ 31 /* 32 * long double __k_sincos( long double x, long double y, long double *c ) 33 * kernel sincosl function on [-pi/4, pi/4], pi/4 ~ 0.785398164 34 * Input x is assumed to be bounded by ~pi/4 in magnitude. 35 * Input y is the tail of x. 36 * return sinl(x) with *c = cosl(x) 37 * 38 * Table look up algorithm 39 * see __k_sinl() and __k_cosl() 40 */ 41 42 #include "libm.h" 43 44 #include <sys/isa_defs.h> 45 46 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[], 47 _TBL_cosl_lo[]; 48 static const long double 49 one = 1.0, 50 /* 51 * |sin(x) - (x+pp1*x^3+...+pp5*x^11)| <= 2^-122.32 for |x|<1/64 52 */ 53 pp1 = -1.666666666666666666666666666586782940810e-0001L, 54 pp2 = 8.333333333333333333333003723660929317540e-0003L, 55 pp3 = -1.984126984126984076045903483778337804470e-0004L, 56 pp4 = 2.755731922361906641319723106210900949413e-0006L, 57 pp5 = -2.505198398570947019093998469135012057673e-0008L, 58 /* 59 * |(sin(x) - (x+p1*x^3+...+p8*x^17)| 60 * |------------------------------- | <= 2^-116.17 for |x|<0.1953125 61 * | x | 62 */ 63 p1 = -1.666666666666666666666666666666211262297e-0001L, 64 p2 = 8.333333333333333333333333301497876908541e-0003L, 65 p3 = -1.984126984126984126984041302881180621922e-0004L, 66 p4 = 2.755731922398589064100587351307269621093e-0006L, 67 p5 = -2.505210838544163129378906953765595393873e-0008L, 68 p6 = 1.605904383643244375050998243778534074273e-0010L, 69 p7 = -7.647162722800685516901456114270824622699e-0013L, 70 p8 = 2.810046428661902961725428841068844462603e-0015L, 71 /* 72 * 73 * |cos(x) - (1+qq1*x^2+...+ qq5*x^10)| <= 2^-123.84 for |x|<=1/128 74 */ 75 qq1 = -4.999999999999999999999999999999378373641e-0001L, 76 qq2 = 4.166666666666666666666665478399327703130e-0002L, 77 qq3 = -1.388888888888888888058211230618051613494e-0003L, 78 qq4 = 2.480158730156105377771585658905303111866e-0005L, 79 qq5 = -2.755728099762526325736488376695157008736e-0007L, 80 /* 81 * 82 * |cos(x) - (1+q1*x^2+...+ q8*x^16)| <= 2^-117.11 for |x|<= 0.15625 83 */ 84 q1 = -4.999999999999999999999999999999756416975e-0001L, 85 q2 = 4.166666666666666666666666664006066577258e-0002L, 86 q3 = -1.388888888888888888888877700363937169637e-0003L, 87 q4 = 2.480158730158730158494468463031814083559e-0005L, 88 q5 = -2.755731922398586276322819250356005542871e-0007L, 89 q6 = 2.087675698767424261441959760729854017855e-0009L, 90 q7 = -1.147074481239662089072452129010790774761e-0011L, 91 q8 = 4.777761647399651599730663422263531034782e-0014L; 92 /* INDENT ON */ 93 long double 94 __k_sincosl(long double x, long double y, long double *c) { 95 long double a1, a2, t, t1, t2, z, w; 96 int *pt = (int *) &t, *px = (int *) &x; 97 int i, j, hx, ix; 98 99 t = 1.0; 100 #if defined(__i386) || defined(__amd64) 101 XTOI(px, hx); 102 #else 103 hx = px[0]; 104 #endif 105 ix = hx & 0x7fffffff; 106 if (ix < 0x3ffc4000) { 107 if (ix < 0x3fc60000) 108 if (((int) x) == 0) { 109 *c = one; 110 return (x); 111 } /* generate inexact */ 112 z = x * x; 113 114 if (ix < 0x3ff80000) { 115 *c = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + 116 z * qq5)))); 117 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 + 118 z * p6))))); 119 } else { 120 *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 + z * 121 (q5 + z * (q6 + z * (q7 + z * q8))))))); 122 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 + 123 z * (p6 + z * (p7 + z * p8))))))); 124 } 125 126 t = y + x * t; 127 return (x + t); 128 } 129 j = (ix + 0x400) & 0x7ffff800; 130 i = (j - 0x3ffc4000) >> 11; 131 #if defined(__i386) || defined(__amd64) 132 ITOX(j, pt); 133 #else 134 pt[0] = j; 135 #endif 136 if (hx > 0) 137 x = y - (t - x); 138 else 139 x = (-y) - (t + x); 140 a1 = _TBL_sinl_hi[i]; 141 z = x * x; 142 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); 143 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * 144 pp5))))); 145 a2 = _TBL_cosl_hi[i]; 146 t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t); 147 *c = a2 + t2; 148 t1 = a2 * w + a1 * t; 149 t1 += _TBL_sinl_lo[i]; 150 if (hx < 0) 151 return (-a1 - t1); 152 else 153 return (a1 + t1); 154 } 155