25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER START
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * The contents of this file are subject to the terms of the
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Common Development and Distribution License (the "License").
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You may not use this file except in compliance with the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * See the License for the specific language governing permissions
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * and limitations under the License.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * CDDL HEADER END
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT OFF */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * long double __k_sincos( long double x, long double y, long double *c )
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * kernel sincosl function on [-pi/4, pi/4], pi/4 ~ 0.785398164
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Input x is assumed to be bounded by ~pi/4 in magnitude.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Input y is the tail of x.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * return sinl(x) with *c = cosl(x)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Table look up algorithm
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * see __k_sinl() and __k_cosl()
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "libm.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include <sys/isa_defs.h>
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern const long double _TBL_sinl_hi[], _TBL_sinl_lo[], _TBL_cosl_hi[],
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis _TBL_cosl_lo[];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const long double
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisone = 1.0,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |sin(x) - (x+pp1*x^3+...+pp5*x^11)| <= 2^-122.32 for |x|<1/64
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtispp1 = -1.666666666666666666666666666586782940810e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtispp2 = 8.333333333333333333333003723660929317540e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtispp3 = -1.984126984126984076045903483778337804470e-0004L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtispp4 = 2.755731922361906641319723106210900949413e-0006L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtispp5 = -2.505198398570947019093998469135012057673e-0008L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |(sin(x) - (x+p1*x^3+...+p8*x^17)|
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |------------------------------- | <= 2^-116.17 for |x|<0.1953125
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * | x |
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisp1 = -1.666666666666666666666666666666211262297e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisp2 = 8.333333333333333333333333301497876908541e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisp3 = -1.984126984126984126984041302881180621922e-0004L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisp4 = 2.755731922398589064100587351307269621093e-0006L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisp5 = -2.505210838544163129378906953765595393873e-0008L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisp6 = 1.605904383643244375050998243778534074273e-0010L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisp7 = -7.647162722800685516901456114270824622699e-0013L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisp8 = 2.810046428661902961725428841068844462603e-0015L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |cos(x) - (1+qq1*x^2+...+ qq5*x^10)| <= 2^-123.84 for |x|<=1/128
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisqq1 = -4.999999999999999999999999999999378373641e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisqq2 = 4.166666666666666666666665478399327703130e-0002L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisqq3 = -1.388888888888888888058211230618051613494e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisqq4 = 2.480158730156105377771585658905303111866e-0005L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisqq5 = -2.755728099762526325736488376695157008736e-0007L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * |cos(x) - (1+q1*x^2+...+ q8*x^16)| <= 2^-117.11 for |x|<= 0.15625
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisq1 = -4.999999999999999999999999999999756416975e-0001L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisq2 = 4.166666666666666666666666664006066577258e-0002L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisq3 = -1.388888888888888888888877700363937169637e-0003L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisq4 = 2.480158730158730158494468463031814083559e-0005L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisq5 = -2.755731922398586276322819250356005542871e-0007L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisq6 = 2.087675698767424261441959760729854017855e-0009L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisq7 = -1.147074481239662089072452129010790774761e-0011L,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisq8 = 4.777761647399651599730663422263531034782e-0014L;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT ON */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtislong double
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis__k_sincosl(long double x, long double y, long double *c) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis long double a1, a2, t, t1, t2, z, w;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis int *pt = (int *) &t, *px = (int *) &x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis int i, j, hx, ix;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = 1.0;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#if defined(__i386) || defined(__amd64)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis XTOI(px, hx);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis hx = px[0];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#endif
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ix = hx & 0x7fffffff;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (ix < 0x3ffc4000) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (ix < 0x3fc60000)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (((int) x) == 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = one;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } /* generate inexact */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z = x * x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (ix < 0x3ff80000) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = one + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 +
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z * qq5))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z * p6)))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = one + z * (q1 + z * (q2 + z * (q3 + z * (q4 + z *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (q5 + z * (q6 + z * (q7 + z * q8)))))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = z * (p1 + z * (p2 + z * (p3 + z * (p4 + z * (p5 +
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z * (p6 + z * (p7 + z * p8)))))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = y + x * t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (x + t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis j = (ix + 0x400) & 0x7ffff800;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis i = (j - 0x3ffc4000) >> 11;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#if defined(__i386) || defined(__amd64)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ITOX(j, pt);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis pt[0] = j;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#endif
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (hx > 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis x = y - (t - x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis x = (-y) - (t + x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis a1 = _TBL_sinl_hi[i];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z = x * x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t = z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis w = x * (one + z * (pp1 + z * (pp2 + z * (pp3 + z * (pp4 + z *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis pp5)))));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis a2 = _TBL_cosl_hi[i];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t2 = _TBL_cosl_lo[i] - (a1 * w - a2 * t);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = a2 + t2;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t1 = a2 * w + a1 * t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis t1 += _TBL_sinl_lo[i];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (hx < 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (-a1 - t1);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return (a1 + t1);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis}