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 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Copyright 2005 Sun Microsystems, Inc. All rights reserved.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * Use is subject to license terms.
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
ddc0e0b53c661f6e439e3b7072b3ef353eadb4afRichard Lowe#pragma weak __sincosf = sincosf
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT OFF */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/*
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * For |x| < pi/4, let z = x * x, and approximate sin(x) by
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * S(x) = x(S0 + S1*z)(S2 + S3*z + z*z)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * where
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * S0 = 1.85735322054308378716204874632872525989806770558e-0003,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * S1 = -1.95035094218403635082921458859320791358115801259e-0004,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * S2 = 5.38400550766074785970952495168558701485841707252e+0002,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * S3 = -3.31975110777873728964197739157371509422022905947e+0001,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * with error bounded by |(sin(x) - S(x))/x| < 2**(-28.2), and
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * cos(x) by
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * C(x) = (C0 + C1*z + C2*z*z) * (C3 + C4*z + z*z)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * where
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * C0 = 1.09349482127188401868272000389539985058873853699e-0003
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * C1 = -5.03324285989964979398034700054920226866107675091e-0004
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * C2 = 2.43792880266971107750418061559602239831538067410e-0005
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * C3 = 9.14499072605666582228127405245558035523741471271e+0002
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * C4 = -3.63151270591815439197122504991683846785293207730e+0001
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis * with error bounded by |cos(x) - C(x)| < 2**(-34.2).
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis/* INDENT ON */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#include "libm.h"
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern const int _TBL_ipio2_inf[];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern int __rem_pio2m(double *, double *, int, int, int, const int *);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#if defined(__i386) && !defined(__amd64)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisextern int __swapRP(int);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#endif
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisstatic const double C[] = {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 1.85735322054308378716204874632872525989806770558e-0003,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis -1.95035094218403635082921458859320791358115801259e-0004,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 5.38400550766074785970952495168558701485841707252e+0002,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis -3.31975110777873728964197739157371509422022905947e+0001,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 1.09349482127188401868272000389539985058873853699e-0003,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis -5.03324285989964979398034700054920226866107675091e-0004,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 2.43792880266971107750418061559602239831538067410e-0005,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 9.14499072605666582228127405245558035523741471271e+0002,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis -3.63151270591815439197122504991683846785293207730e+0001,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 0.5,
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis};
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define S0 C[0]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define S1 C[1]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define S2 C[2]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define S3 C[3]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define C0 C[4]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define C1 C[5]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define C2 C[6]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define C3 C[7]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define C4 C[8]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define invpio2 C[9]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define half C[10]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define pio2_1 C[11]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#define pio2_t C[12]
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtisvoid
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtissincosf(float x, float *s, float *c)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis{
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis double y, z, w;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis float f, g;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis int n, ix, hx, hy;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis volatile int i;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis hx = *((int *)&x);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ix = hx & 0x7fffffff;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis y = (double)x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (ix <= 0x4016cbe4) { /* |x| < 3*pi/4 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (ix <= 0x3f490fdb) { /* |x| < pi/4 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (ix <= 0x39800000) { /* |x| <= 2**-12 */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis i = (int)y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#ifdef lint
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis i = i;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#endif
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *s = x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = 1.0f;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z = y * y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *s = (float)((y * (S0 + z * S1)) *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (S2 + z * (S3 + z)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = (float)(((C0 + z * C1) + (z * z) * C2) *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (C3 + z * (C4 + z)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } else if (hx > 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis y = (y - pio2_1) - pio2_t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z = y * y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *s = (float)(((C0 + z * C1) + (z * z) * C2) *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (C3 + z * (C4 + z)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = (float)-((y * (S0 + z * S1)) *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (S2 + z * (S3 + z)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis y = (y + pio2_1) + pio2_t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z = y * y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *s = (float)-(((C0 + z * C1) + (z * z) * C2) *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (C3 + z * (C4 + z)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = (float)((y * (S0 + z * S1)) *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (S2 + z * (S3 + z)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } else if (ix <= 0x49c90fdb) { /* |x| < 2^19*pi */
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#if defined(__i386) && !defined(__amd64)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis int rp;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis rp = __swapRP(fp_extended);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#endif
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis w = y * invpio2;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (hx < 0)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis n = (int)(w - half);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis else
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis n = (int)(w + half);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis y = (y - n * pio2_1) - n * pio2_t;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#if defined(__i386) && !defined(__amd64)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (rp != fp_extended)
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (void) __swapRP(rp);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis#endif
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (ix >= 0x7f800000) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *s = *c = x / x;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis return;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis hy = ((int *)&y)[HIWORD];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis n = ((hy >> 20) & 0x7ff) - 1046;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ((int *)&w)[HIWORD] = (hy & 0xfffff) | 0x41600000;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis ((int *)&w)[LOWORD] = ((int *)&y)[LOWORD];
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis n = __rem_pio2m(&w, &y, n, 1, 0, _TBL_ipio2_inf);
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (hy < 0) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis y = -y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis n = -n;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis z = y * y;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis f = (float)((y * (S0 + z * S1)) * (S2 + z * (S3 + z)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis g = (float)(((C0 + z * C1) + (z * z) * C2) *
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis (C3 + z * (C4 + z)));
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (n & 2) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis f = -f;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis g = -g;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis if (n & 1) {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *s = g;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = -f;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis } else {
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *s = f;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis *c = g;
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis }
25c28e83beb90e7c80452a7c818c5e6f73a07dc8Piotr Jasiukajtis}