/* * CDDL HEADER START * * The contents of this file are subject to the terms of the * Common Development and Distribution License (the "License"). * You may not use this file except in compliance with the License. * * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE * or http://www.opensolaris.org/os/licensing. * See the License for the specific language governing permissions * and limitations under the License. * * When distributing Covered Code, include this CDDL HEADER in each * file and include the License file at usr/src/OPENSOLARIS.LICENSE. * If applicable, add the following below this CDDL HEADER, with the * fields enclosed by brackets "[]" replaced with your own identifying * information: Portions Copyright [yyyy] [name of copyright owner] * * CDDL HEADER END */ /* * Copyright 2011 Nexenta Systems, Inc. All rights reserved. */ /* * Copyright 2006 Sun Microsystems, Inc. All rights reserved. * Use is subject to license terms. */ /* * __k_cosl(long double x, long double y) * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 * Input x is assumed to be bounded by ~pi/4 in magnitude. * Input y is the tail of x. * * Table look up algorithm * 1. by cos(-x) = cos(x), we may replace x by |x| * 2. if x < 25/128 = [0x3ffc4000, 0] = 0.15625 , then * if x < 2^-57 (hx < 0x3fc60000 0), return 1.0 with inexact if x != 0 * z = x*x; * if x <= 1/128 = 2**-7 = 0.0078125 * cos(x)=1.0+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))) * else * cos(x)=1.0+z*(q1+ ... z*q8) * 3. else * ht = (hx + 0x400)&0x7ffff800 (round x to a break point t) * lt = 0 * i = (hy-0x3ffc4000)>>11; (i<=64) * x' = (x - t)+y (|x'| ~<= 2^-7 * By * cos(t+x') * = cos(t)cos(x')-sin(t)sin(x') * = cos(t)(1+z*(qq1+z*qq2))-[sin(t)]*x*(1+z*(pp1+z*pp2)) * = cos(t) + [cos(t)]*(z*(qq1+z*qq2))- * [sin(t)]*x*(1+z*(pp1+z*pp2)) * * Thus, * let a= _TBL_cos_hi[i], b = _TBL_cos_lo[i], c= _TBL_sin_hi[i], * x = (x-t)+y * z = x*x; * cos(t+x) = a+(b+ (-c*x*(1+z*(pp1+z*pp2))+a*(z*(qq1+z*qq2))) */ #include "libm.h" extern const long double _TBL_cosl_hi[], _TBL_cosl_lo[], _TBL_sinl_hi[]; static const long double one = 1.0L, /* * 3 11 -122.32 * |sin(x) - (x+pp1*x +...+ pp5*x )| <= 2 for |x|<1/64 */ pp1 = -1.666666666666666666666666666586782940810e-0001L, pp2 = +8.333333333333333333333003723660929317540e-0003L, pp3 = -1.984126984126984076045903483778337804470e-0004L, pp4 = +2.755731922361906641319723106210900949413e-0006L, pp5 = -2.505198398570947019093998469135012057673e-0008L, /* * 2 16 -117.11 * |cos(x) - (1+q1*x + ... + q8*x )| <= 2 for |x|<= 0.15625 */ q1 = -4.999999999999999999999999999999756416975e-0001L, q2 = +4.166666666666666666666666664006066577258e-0002L, q3 = -1.388888888888888888888877700363937169637e-0003L, q4 = +2.480158730158730158494468463031814083559e-0005L, q5 = -2.755731922398586276322819250356005542871e-0007L, q6 = +2.087675698767424261441959760729854017855e-0009L, q7 = -1.147074481239662089072452129010790774761e-0011L, q8 = +4.777761647399651599730663422263531034782e-0014L, /* * 2 10 -123.84 * |cos(x) - (1+qq1*x +...+ qq5*x )| <= 2 for |x|<=1/128 */ qq1 = -4.999999999999999999999999999999378373641e-0001L, qq2 = +4.166666666666666666666665478399327703130e-0002L, qq3 = -1.388888888888888888058211230618051613494e-0003L, qq4 = +2.480158730156105377771585658905303111866e-0005L, qq5 = -2.755728099762526325736488376695157008736e-0007L; #define i0 0 long double __k_cosl(long double x, long double y) { long double a, t, z, w; int *pt = (int *) &t, *px = (int *) &x; int i, j, hx, ix; t = 1.0L; hx = px[i0]; ix = hx & 0x7fffffff; if (ix < 0x3ffc4000) { if (ix < 0x3fc60000) if ((i = (int) x) == 0) return (one); /* generate inexact */ z = x * x; if (ix < 0x3ff80000) /* 0.0078125 */ return one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); else return one + z * (q1 + z * (q2 + z * (q3 + z * (q4 + z * (q5 + z * (q6 + z * (q7 + z * q8))))))); } j = (ix + 0x400) & 0x7ffff800; i = (j - 0x3ffc4000) >> 11; pt[i0] = j; if (hx > 0) x = y - (t - x); else x = (-y) - (t + x); a = _TBL_cosl_hi[i]; z = x * x; t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z * pp5))))); t = _TBL_cosl_lo[i] - (_TBL_sinl_hi[i] * w - a * t); return (a + t); }