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 * __k_cosl(long double x, long double y) 32 * kernel cos 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 cos(-x) = cos(x), we may replace x by |x| 38 * 2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then 39 * if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x != 0 40 * z = x*x; 41 * if x <= 1/128 = 2**-7 = 0.0078125 42 * cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))) 43 * else 44 * cos(x)=1.0+z*(q1+ ... z*q8) 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 * cos(t+x') 52 * = cos(t)cos(x')-sin(t)sin(x') 53 * = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2)) 54 * = cos(t) + [cos(t)]*(z*(qq1+z*qq2))- 55 * [sin(t)]*x*(1+z*(pp1+z*pp2)) 56 * 57 * Thus, 58 * let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i], 59 * x = (x-t)+y 60 * z = x*x; 61 * cos(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_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_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 * 2 16 -117.11 80 * |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625 81 */ 82 q1 = -4.999999999999999999999999999999756416975e-0001L, 83 q2 = +4.166666666666666666666666664006066577258e-0002L, 84 q3 = -1.388888888888888888888877700363937169637e-0003L, 85 q4 = +2.480158730158730158494468463031814083559e-0005L, 86 q5 = -2.755731922398586276322819250356005542871e-0007L, 87 q6 = +2.087675698767424261441959760729854017855e-0009L, 88 q7 = -1.147074481239662089072452129010790774761e-0011L, 89 q8 = +4.777761647399651599730663422263531034782e-0014L, 90 /* 91 * 2 10 -123.84 92 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128 93 */ 94 qq1 = -4.999999999999999999999999999999378373641e-0001L, 95 qq2 = +4.166666666666666666666665478399327703130e-0002L, 96 qq3 = -1.388888888888888888058211230618051613494e-0003L, 97 qq4 = +2.480158730156105377771585658905303111866e-0005L, 98 qq5 = -2.755728099762526325736488376695157008736e-0007L; 99 100 #define i0 0 101 102 long double 103 __k_cosl(long double x, long double y) { 104 long double a, t, z, w; 105 int *pt = (int *) &t, *px = (int *) &x; 106 int i, j, hx, ix; 107 108 t = 1.0L; 109 hx = px[i0]; 110 ix = hx & 0x7fffffff; 111 if (ix < 0x3ffc4000) { 112 if (ix < 0x3fc60000) 113 if ((i = (int) x) == 0) 114 return (one); /* generate inexact */ 115 z = x * x; 116 117 if (ix < 0x3ff80000) /* 0.0078125 */ 118 return one + z * (qq1 + z * (qq2 + z * (qq3 + 119 z * (qq4 + z * qq5)))); 120 else 121 return one + z * (q1 + z * (q2 + z * (q3 + 122 z * (q4 + z * (q5 + z * (q6 + z * (q7 + 123 z * q8))))))); 124 } 125 j = (ix + 0x400) & 0x7ffff800; 126 i = (j - 0x3ffc4000) >> 11; 127 pt[i0] = j; 128 if (hx > 0) 129 x = y - (t - x); 130 else 131 x = (-y) - (t + x); 132 a = _TBL_cosl_hi[i]; 133 z = x * x; 134 t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); 135 w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5))))); 136 t = _TBL_cosl_lo[i] - (_TBL_sinl_hi[i] * w - a * t); 137 return (a + t); 138 } 139