1*25c28e83SPiotr Jasiukajtis /* 2*25c28e83SPiotr Jasiukajtis * CDDL HEADER START 3*25c28e83SPiotr Jasiukajtis * 4*25c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the 5*25c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License"). 6*25c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License. 7*25c28e83SPiotr Jasiukajtis * 8*25c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9*25c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing. 10*25c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions 11*25c28e83SPiotr Jasiukajtis * and limitations under the License. 12*25c28e83SPiotr Jasiukajtis * 13*25c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each 14*25c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15*25c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the 16*25c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying 17*25c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner] 18*25c28e83SPiotr Jasiukajtis * 19*25c28e83SPiotr Jasiukajtis * CDDL HEADER END 20*25c28e83SPiotr Jasiukajtis */ 21*25c28e83SPiotr Jasiukajtis 22*25c28e83SPiotr Jasiukajtis /* 23*25c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24*25c28e83SPiotr Jasiukajtis */ 25*25c28e83SPiotr Jasiukajtis /* 26*25c28e83SPiotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27*25c28e83SPiotr Jasiukajtis * Use is subject to license terms. 28*25c28e83SPiotr Jasiukajtis */ 29*25c28e83SPiotr Jasiukajtis 30*25c28e83SPiotr Jasiukajtis /* 31*25c28e83SPiotr Jasiukajtis * long double __k_sincos(long double x, long double y, long double *c); 32*25c28e83SPiotr Jasiukajtis * kernel sincosl function on [-pi/4, pi/4], pi/4 ~ 0.785398164 33*25c28e83SPiotr Jasiukajtis * Input x is assumed to be bounded by ~pi/4 in magnitude. 34*25c28e83SPiotr Jasiukajtis * Input y is the tail of x. 35*25c28e83SPiotr Jasiukajtis * return sinl(x) with *c = cosl(x) 36*25c28e83SPiotr Jasiukajtis * 37*25c28e83SPiotr Jasiukajtis * Table look up algorithm 38*25c28e83SPiotr Jasiukajtis * see __k_sinl and __k_cosl 39*25c28e83SPiotr Jasiukajtis */ 40*25c28e83SPiotr Jasiukajtis 41*25c28e83SPiotr Jasiukajtis #include "libm.h" 42*25c28e83SPiotr Jasiukajtis 43*25c28e83SPiotr Jasiukajtis extern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], 44*25c28e83SPiotr Jasiukajtis _TBL_cosl_hi[], _TBL_cosl_lo[]; 45*25c28e83SPiotr Jasiukajtis static const long double 46*25c28e83SPiotr Jasiukajtis one = 1.0L, 47*25c28e83SPiotr Jasiukajtis /* 48*25c28e83SPiotr Jasiukajtis * 3 11 -122.32 49*25c28e83SPiotr Jasiukajtis * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64 50*25c28e83SPiotr Jasiukajtis */ 51*25c28e83SPiotr Jasiukajtis pp1 = -1.666666666666666666666666666586782940810e-0001L, 52*25c28e83SPiotr Jasiukajtis pp2 = +8.333333333333333333333003723660929317540e-0003L, 53*25c28e83SPiotr Jasiukajtis pp3 = -1.984126984126984076045903483778337804470e-0004L, 54*25c28e83SPiotr Jasiukajtis pp4 = +2.755731922361906641319723106210900949413e-0006L, 55*25c28e83SPiotr Jasiukajtis pp5 = -2.505198398570947019093998469135012057673e-0008L, 56*25c28e83SPiotr Jasiukajtis /* 57*25c28e83SPiotr Jasiukajtis * |(sin(x) - (x+p1*x^3+...+p8*x^17)| 58*25c28e83SPiotr Jasiukajtis * |------------------------------- | <= 2^-116.17 for |x|<0.1953125 59*25c28e83SPiotr Jasiukajtis * | x | 60*25c28e83SPiotr Jasiukajtis */ 61*25c28e83SPiotr Jasiukajtis p1 = -1.666666666666666666666666666666211262297e-0001L, 62*25c28e83SPiotr Jasiukajtis p2 = +8.333333333333333333333333301497876908541e-0003L, 63*25c28e83SPiotr Jasiukajtis p3 = -1.984126984126984126984041302881180621922e-0004L, 64*25c28e83SPiotr Jasiukajtis p4 = +2.755731922398589064100587351307269621093e-0006L, 65*25c28e83SPiotr Jasiukajtis p5 = -2.505210838544163129378906953765595393873e-0008L, 66*25c28e83SPiotr Jasiukajtis p6 = +1.605904383643244375050998243778534074273e-0010L, 67*25c28e83SPiotr Jasiukajtis p7 = -7.647162722800685516901456114270824622699e-0013L, 68*25c28e83SPiotr Jasiukajtis p8 = +2.810046428661902961725428841068844462603e-0015L, 69*25c28e83SPiotr Jasiukajtis /* 70*25c28e83SPiotr Jasiukajtis * 2 10 -123.84 71*25c28e83SPiotr Jasiukajtis * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128 72*25c28e83SPiotr Jasiukajtis */ 73*25c28e83SPiotr Jasiukajtis qq1 = -4.999999999999999999999999999999378373641e-0001L, 74*25c28e83SPiotr Jasiukajtis qq2 = +4.166666666666666666666665478399327703130e-0002L, 75*25c28e83SPiotr Jasiukajtis qq3 = -1.388888888888888888058211230618051613494e-0003L, 76*25c28e83SPiotr Jasiukajtis qq4 = +2.480158730156105377771585658905303111866e-0005L, 77*25c28e83SPiotr Jasiukajtis qq5 = -2.755728099762526325736488376695157008736e-0007L, 78*25c28e83SPiotr Jasiukajtis /* 79*25c28e83SPiotr Jasiukajtis * 2 16 -117.11 80*25c28e83SPiotr Jasiukajtis * |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625 81*25c28e83SPiotr Jasiukajtis */ 82*25c28e83SPiotr Jasiukajtis q1 = -4.999999999999999999999999999999756416975e-0001L, 83*25c28e83SPiotr Jasiukajtis q2 = +4.166666666666666666666666664006066577258e-0002L, 84*25c28e83SPiotr Jasiukajtis q3 = -1.388888888888888888888877700363937169637e-0003L, 85*25c28e83SPiotr Jasiukajtis q4 = +2.480158730158730158494468463031814083559e-0005L, 86*25c28e83SPiotr Jasiukajtis q5 = -2.755731922398586276322819250356005542871e-0007L, 87*25c28e83SPiotr Jasiukajtis q6 = +2.087675698767424261441959760729854017855e-0009L, 88*25c28e83SPiotr Jasiukajtis q7 = -1.147074481239662089072452129010790774761e-0011L, 89*25c28e83SPiotr Jasiukajtis q8 = +4.777761647399651599730663422263531034782e-0014L; 90*25c28e83SPiotr Jasiukajtis 91*25c28e83SPiotr Jasiukajtis #define i0 0 92*25c28e83SPiotr Jasiukajtis 93*25c28e83SPiotr Jasiukajtis long double 94*25c28e83SPiotr Jasiukajtis __k_sincosl(long double x, long double y, long double *c) { 95*25c28e83SPiotr Jasiukajtis long double a1, a2, t, t1, t2, z, w; 96*25c28e83SPiotr Jasiukajtis int *pt = (int *) &t, *px = (int *) &x; 97*25c28e83SPiotr Jasiukajtis int i, j, hx, ix; 98*25c28e83SPiotr Jasiukajtis 99*25c28e83SPiotr Jasiukajtis t = 1.0L; 100*25c28e83SPiotr Jasiukajtis hx = px[i0]; 101*25c28e83SPiotr Jasiukajtis ix = hx & 0x7fffffff; 102*25c28e83SPiotr Jasiukajtis if (ix < 0x3ffc4000) { 103*25c28e83SPiotr Jasiukajtis if (ix < 0x3fc60000) 104*25c28e83SPiotr Jasiukajtis if (((int) x) == 0) { 105*25c28e83SPiotr Jasiukajtis *c = one; 106*25c28e83SPiotr Jasiukajtis return (x); 107*25c28e83SPiotr Jasiukajtis } /* generate inexact */ 108*25c28e83SPiotr Jasiukajtis z = x * x; 109*25c28e83SPiotr Jasiukajtis 110*25c28e83SPiotr Jasiukajtis if (ix < 0x3ff80000) { 111*25c28e83SPiotr Jasiukajtis *c = one + z * (qq1 + z * (qq2 + z * (qq3 + 112*25c28e83SPiotr Jasiukajtis z * (qq4 + z * qq5)))); 113*25c28e83SPiotr Jasiukajtis t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + 114*25c28e83SPiotr Jasiukajtis z * (p5 + z * p6))))); 115*25c28e83SPiotr Jasiukajtis } else { 116*25c28e83SPiotr Jasiukajtis *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 + 117*25c28e83SPiotr Jasiukajtis z * (q5 + z * (q6 + z * (q7 + z * q8))))))); 118*25c28e83SPiotr Jasiukajtis t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 + 119*25c28e83SPiotr Jasiukajtis z * (p6 + z * (p7 + z * p8))))))); 120*25c28e83SPiotr Jasiukajtis } 121*25c28e83SPiotr Jasiukajtis 122*25c28e83SPiotr Jasiukajtis t = y + x * t; 123*25c28e83SPiotr Jasiukajtis return (x + t); 124*25c28e83SPiotr Jasiukajtis } 125*25c28e83SPiotr Jasiukajtis j = (ix + 0x400) & 0x7ffff800; 126*25c28e83SPiotr Jasiukajtis i = (j - 0x3ffc4000) >> 11; 127*25c28e83SPiotr Jasiukajtis pt[i0] = j; 128*25c28e83SPiotr Jasiukajtis if (hx > 0) 129*25c28e83SPiotr Jasiukajtis x = y - (t - x); 130*25c28e83SPiotr Jasiukajtis else 131*25c28e83SPiotr Jasiukajtis x = (-y) - (t + x); 132*25c28e83SPiotr Jasiukajtis a1 = _TBL_sinl_hi[i]; 133*25c28e83SPiotr Jasiukajtis z = x * x; 134*25c28e83SPiotr Jasiukajtis t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); 135*25c28e83SPiotr Jasiukajtis w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5))))); 136*25c28e83SPiotr Jasiukajtis a2 = _TBL_cosl_hi[i]; 137*25c28e83SPiotr Jasiukajtis t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t); 138*25c28e83SPiotr Jasiukajtis *c = a2 + t2; 139*25c28e83SPiotr Jasiukajtis t1 = a2 * w + a1 * t; 140*25c28e83SPiotr Jasiukajtis t1 += _TBL_sinl_lo[i]; 141*25c28e83SPiotr Jasiukajtis if (hx < 0) 142*25c28e83SPiotr Jasiukajtis return (-a1 - t1); 143*25c28e83SPiotr Jasiukajtis else 144*25c28e83SPiotr Jasiukajtis return (a1 + t1); 145*25c28e83SPiotr Jasiukajtis } 146