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 /* 31 * long double __k_sinl(long double x, long 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 * Table look up algorithm 37 * 1. by sin(-x) = -sin(x), need only to consider positive x 38 * 2. if x < 25/128 = [0x3ffc9000,0,0,0] = 0.1953125 , then 39 * if x < 2^-57 (hx < 0x3fc60000,0,0,0), return x (inexact if x != 0) 40 * z = x*x; 41 * if x <= 1/64 = 2**-6 42 * sin(x) = x + (y+(x*z)*(p1 + z*p2)) 43 * else 44 * sin(x) = x + (y+(x*z)*(p1 + z*(p2 + z*(p3 + z*p4)))) 45 * 3. else 46 * ht = (hx + 0x400)&0x7ffff800 (round x to a break point t) 47 * lt = 0 48 * i = (hy-0x3ffc4000)>>11; (i<=64) 49 * x' = (x - t)+y (|x'| ~<= 2^-7 50 * By 51 * sin(t+x') 52 * = sin(t)cos(x')+cos(t)sin(x') 53 * = sin(t)(1+z*(qq1+z*qq2))+[cos(t)]*x*(1+z*(pp1+z*pp2)) 54 * = sin(t) + [sin(t)]*(z*(qq1+z*qq2))+ 55 * [cos(t)]*x*(1+z*(pp1+z*pp2)) 56 * 57 * Thus, 58 * let a= _TBL_sin_hi[i], b = _TBL_sin_lo[i], c= _TBL_cos_hi[i], 59 * x = (x-t)+y 60 * z = x*x; 61 * sin(t+x) = a+(b+ ((c*x)*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2))) 62 */ 63 64 #include "libm.h" 65 66 extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[]; 67 static const long double 68 one = 1.0L, 69 /* 70 * 3 11 -122.32 71 * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64 72 */ 73 pp1 = -1.666666666666666666666666666586782940810e-0001L, 74 pp2 = +8.333333333333333333333003723660929317540e-0003L, 75 pp3 = -1.984126984126984076045903483778337804470e-0004L, 76 pp4 = +2.755731922361906641319723106210900949413e-0006L, 77 pp5 = -2.505198398570947019093998469135012057673e-0008L, 78 /* 79 * |(sin(x) - (x+p1*x^3+...+p8*x^17)| 80 * |------------------------------- | <= 2^-116.17 for |x|<0.1953125 81 * | x | 82 */ 83 p1 = -1.666666666666666666666666666666211262297e-0001L, 84 p2 = +8.333333333333333333333333301497876908541e-0003L, 85 p3 = -1.984126984126984126984041302881180621922e-0004L, 86 p4 = +2.755731922398589064100587351307269621093e-0006L, 87 p5 = -2.505210838544163129378906953765595393873e-0008L, 88 p6 = +1.605904383643244375050998243778534074273e-0010L, 89 p7 = -7.647162722800685516901456114270824622699e-0013L, 90 p8 = +2.810046428661902961725428841068844462603e-0015L, 91 /* 92 * 2 10 -123.84 93 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128 94 */ 95 qq1 = -4.999999999999999999999999999999378373641e-0001L, 96 qq2 = +4.166666666666666666666665478399327703130e-0002L, 97 qq3 = -1.388888888888888888058211230618051613494e-0003L, 98 qq4 = +2.480158730156105377771585658905303111866e-0005L, 99 qq5 = -2.755728099762526325736488376695157008736e-0007L; 100 101 #define i0 0 102 103 long double 104 __k_sinl(long double x, long double y) { 105 long double a, t, z, w; 106 int *pt = (int *) &t, *px = (int *) &x; 107 int i, j, hx, ix; 108 109 t = 1.0L; 110 hx = px[i0]; 111 ix = hx & 0x7fffffff; 112 if (ix < 0x3ffc9000) { 113 *(3 - i0 + (int *) &t) = -1; /* one-ulp */ 114 *(2 + (int *) &t) = -1; /* one-ulp */ 115 *(1 + (int *) &t) = -1; /* one-ulp */ 116 *(i0 + (int *) &t) -= 1; /* one-ulp */ 117 if (ix < 0x3fc60000) 118 if (((int) (x * t)) < 1) 119 return (x); /* inexact and underflow */ 120 z = x * x; 121 t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 + 122 z * (p6 + z * (p7 + z * p8))))))); 123 t = y + x * t; 124 return (x + t); 125 } 126 j = (ix + 0x400) & 0x7ffff800; 127 i = (j - 0x3ffc4000) >> 11; 128 pt[i0] = j; 129 if (hx > 0) 130 x = y - (t - x); 131 else 132 x = (-y) - (t + x); 133 a = _TBL_sinl_hi[i]; 134 z = x * x; 135 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); 136 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5))))); 137 t = _TBL_cosl_hi[i] * w + a * t; 138 t += _TBL_sinl_lo[i]; 139 if (hx < 0) 140 return (-a - t); 141 else 142 return (a + t); 143 } 144