125c28e83SPiotr Jasiukajtis /* 225c28e83SPiotr Jasiukajtis * CDDL HEADER START 325c28e83SPiotr Jasiukajtis * 425c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the 525c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License"). 625c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License. 725c28e83SPiotr Jasiukajtis * 825c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 925c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing. 1025c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions 1125c28e83SPiotr Jasiukajtis * and limitations under the License. 1225c28e83SPiotr Jasiukajtis * 1325c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each 1425c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 1525c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the 1625c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying 1725c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner] 1825c28e83SPiotr Jasiukajtis * 1925c28e83SPiotr Jasiukajtis * CDDL HEADER END 2025c28e83SPiotr Jasiukajtis */ 2125c28e83SPiotr Jasiukajtis /* 2225c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 2325c28e83SPiotr Jasiukajtis */ 2425c28e83SPiotr Jasiukajtis /* 2525c28e83SPiotr Jasiukajtis * Copyright 2005 Sun Microsystems, Inc. All rights reserved. 2625c28e83SPiotr Jasiukajtis * Use is subject to license terms. 2725c28e83SPiotr Jasiukajtis */ 2825c28e83SPiotr Jasiukajtis 29*ddc0e0b5SRichard Lowe #pragma weak __sincosf = sincosf 3025c28e83SPiotr Jasiukajtis 3125c28e83SPiotr Jasiukajtis /* INDENT OFF */ 3225c28e83SPiotr Jasiukajtis /* 3325c28e83SPiotr Jasiukajtis * For |x| < pi/4, let z = x * x, and approximate sin(x) by 3425c28e83SPiotr Jasiukajtis * 3525c28e83SPiotr Jasiukajtis * S(x) = x(S0 + S1*z)(S2 + S3*z + z*z) 3625c28e83SPiotr Jasiukajtis * where 3725c28e83SPiotr Jasiukajtis * S0 = 1.85735322054308378716204874632872525989806770558e-0003, 3825c28e83SPiotr Jasiukajtis * S1 = -1.95035094218403635082921458859320791358115801259e-0004, 3925c28e83SPiotr Jasiukajtis * S2 = 5.38400550766074785970952495168558701485841707252e+0002, 4025c28e83SPiotr Jasiukajtis * S3 = -3.31975110777873728964197739157371509422022905947e+0001, 4125c28e83SPiotr Jasiukajtis * 4225c28e83SPiotr Jasiukajtis * with error bounded by |(sin(x) - S(x))/x| < 2**(-28.2), and 4325c28e83SPiotr Jasiukajtis * cos(x) by 4425c28e83SPiotr Jasiukajtis * 4525c28e83SPiotr Jasiukajtis * C(x) = (C0 + C1*z + C2*z*z) * (C3 + C4*z + z*z) 4625c28e83SPiotr Jasiukajtis * where 4725c28e83SPiotr Jasiukajtis * C0 = 1.09349482127188401868272000389539985058873853699e-0003 4825c28e83SPiotr Jasiukajtis * C1 = -5.03324285989964979398034700054920226866107675091e-0004 4925c28e83SPiotr Jasiukajtis * C2 = 2.43792880266971107750418061559602239831538067410e-0005 5025c28e83SPiotr Jasiukajtis * C3 = 9.14499072605666582228127405245558035523741471271e+0002 5125c28e83SPiotr Jasiukajtis * C4 = -3.63151270591815439197122504991683846785293207730e+0001 5225c28e83SPiotr Jasiukajtis * 5325c28e83SPiotr Jasiukajtis * with error bounded by |cos(x) - C(x)| < 2**(-34.2). 5425c28e83SPiotr Jasiukajtis */ 5525c28e83SPiotr Jasiukajtis /* INDENT ON */ 5625c28e83SPiotr Jasiukajtis 5725c28e83SPiotr Jasiukajtis #include "libm.h" 5825c28e83SPiotr Jasiukajtis 5925c28e83SPiotr Jasiukajtis extern const int _TBL_ipio2_inf[]; 6025c28e83SPiotr Jasiukajtis extern int __rem_pio2m(double *, double *, int, int, int, const int *); 6125c28e83SPiotr Jasiukajtis #if defined(__i386) && !defined(__amd64) 6225c28e83SPiotr Jasiukajtis extern int __swapRP(int); 6325c28e83SPiotr Jasiukajtis #endif 6425c28e83SPiotr Jasiukajtis 6525c28e83SPiotr Jasiukajtis static const double C[] = { 6625c28e83SPiotr Jasiukajtis 1.85735322054308378716204874632872525989806770558e-0003, 6725c28e83SPiotr Jasiukajtis -1.95035094218403635082921458859320791358115801259e-0004, 6825c28e83SPiotr Jasiukajtis 5.38400550766074785970952495168558701485841707252e+0002, 6925c28e83SPiotr Jasiukajtis -3.31975110777873728964197739157371509422022905947e+0001, 7025c28e83SPiotr Jasiukajtis 1.09349482127188401868272000389539985058873853699e-0003, 7125c28e83SPiotr Jasiukajtis -5.03324285989964979398034700054920226866107675091e-0004, 7225c28e83SPiotr Jasiukajtis 2.43792880266971107750418061559602239831538067410e-0005, 7325c28e83SPiotr Jasiukajtis 9.14499072605666582228127405245558035523741471271e+0002, 7425c28e83SPiotr Jasiukajtis -3.63151270591815439197122504991683846785293207730e+0001, 7525c28e83SPiotr Jasiukajtis 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */ 7625c28e83SPiotr Jasiukajtis 0.5, 7725c28e83SPiotr Jasiukajtis 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */ 7825c28e83SPiotr Jasiukajtis 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */ 7925c28e83SPiotr Jasiukajtis }; 8025c28e83SPiotr Jasiukajtis 8125c28e83SPiotr Jasiukajtis #define S0 C[0] 8225c28e83SPiotr Jasiukajtis #define S1 C[1] 8325c28e83SPiotr Jasiukajtis #define S2 C[2] 8425c28e83SPiotr Jasiukajtis #define S3 C[3] 8525c28e83SPiotr Jasiukajtis #define C0 C[4] 8625c28e83SPiotr Jasiukajtis #define C1 C[5] 8725c28e83SPiotr Jasiukajtis #define C2 C[6] 8825c28e83SPiotr Jasiukajtis #define C3 C[7] 8925c28e83SPiotr Jasiukajtis #define C4 C[8] 9025c28e83SPiotr Jasiukajtis #define invpio2 C[9] 9125c28e83SPiotr Jasiukajtis #define half C[10] 9225c28e83SPiotr Jasiukajtis #define pio2_1 C[11] 9325c28e83SPiotr Jasiukajtis #define pio2_t C[12] 9425c28e83SPiotr Jasiukajtis 9525c28e83SPiotr Jasiukajtis void 9625c28e83SPiotr Jasiukajtis sincosf(float x, float *s, float *c) 9725c28e83SPiotr Jasiukajtis { 9825c28e83SPiotr Jasiukajtis double y, z, w; 9925c28e83SPiotr Jasiukajtis float f, g; 10025c28e83SPiotr Jasiukajtis int n, ix, hx, hy; 10125c28e83SPiotr Jasiukajtis volatile int i; 10225c28e83SPiotr Jasiukajtis 10325c28e83SPiotr Jasiukajtis hx = *((int *)&x); 10425c28e83SPiotr Jasiukajtis ix = hx & 0x7fffffff; 10525c28e83SPiotr Jasiukajtis 10625c28e83SPiotr Jasiukajtis y = (double)x; 10725c28e83SPiotr Jasiukajtis 10825c28e83SPiotr Jasiukajtis if (ix <= 0x4016cbe4) { /* |x| < 3*pi/4 */ 10925c28e83SPiotr Jasiukajtis if (ix <= 0x3f490fdb) { /* |x| < pi/4 */ 11025c28e83SPiotr Jasiukajtis if (ix <= 0x39800000) { /* |x| <= 2**-12 */ 11125c28e83SPiotr Jasiukajtis i = (int)y; 11225c28e83SPiotr Jasiukajtis #ifdef lint 11325c28e83SPiotr Jasiukajtis i = i; 11425c28e83SPiotr Jasiukajtis #endif 11525c28e83SPiotr Jasiukajtis *s = x; 11625c28e83SPiotr Jasiukajtis *c = 1.0f; 11725c28e83SPiotr Jasiukajtis return; 11825c28e83SPiotr Jasiukajtis } 11925c28e83SPiotr Jasiukajtis z = y * y; 12025c28e83SPiotr Jasiukajtis *s = (float)((y * (S0 + z * S1)) * 12125c28e83SPiotr Jasiukajtis (S2 + z * (S3 + z))); 12225c28e83SPiotr Jasiukajtis *c = (float)(((C0 + z * C1) + (z * z) * C2) * 12325c28e83SPiotr Jasiukajtis (C3 + z * (C4 + z))); 12425c28e83SPiotr Jasiukajtis } else if (hx > 0) { 12525c28e83SPiotr Jasiukajtis y = (y - pio2_1) - pio2_t; 12625c28e83SPiotr Jasiukajtis z = y * y; 12725c28e83SPiotr Jasiukajtis *s = (float)(((C0 + z * C1) + (z * z) * C2) * 12825c28e83SPiotr Jasiukajtis (C3 + z * (C4 + z))); 12925c28e83SPiotr Jasiukajtis *c = (float)-((y * (S0 + z * S1)) * 13025c28e83SPiotr Jasiukajtis (S2 + z * (S3 + z))); 13125c28e83SPiotr Jasiukajtis } else { 13225c28e83SPiotr Jasiukajtis y = (y + pio2_1) + pio2_t; 13325c28e83SPiotr Jasiukajtis z = y * y; 13425c28e83SPiotr Jasiukajtis *s = (float)-(((C0 + z * C1) + (z * z) * C2) * 13525c28e83SPiotr Jasiukajtis (C3 + z * (C4 + z))); 13625c28e83SPiotr Jasiukajtis *c = (float)((y * (S0 + z * S1)) * 13725c28e83SPiotr Jasiukajtis (S2 + z * (S3 + z))); 13825c28e83SPiotr Jasiukajtis } 13925c28e83SPiotr Jasiukajtis return; 14025c28e83SPiotr Jasiukajtis } else if (ix <= 0x49c90fdb) { /* |x| < 2^19*pi */ 14125c28e83SPiotr Jasiukajtis #if defined(__i386) && !defined(__amd64) 14225c28e83SPiotr Jasiukajtis int rp; 14325c28e83SPiotr Jasiukajtis 14425c28e83SPiotr Jasiukajtis rp = __swapRP(fp_extended); 14525c28e83SPiotr Jasiukajtis #endif 14625c28e83SPiotr Jasiukajtis w = y * invpio2; 14725c28e83SPiotr Jasiukajtis if (hx < 0) 14825c28e83SPiotr Jasiukajtis n = (int)(w - half); 14925c28e83SPiotr Jasiukajtis else 15025c28e83SPiotr Jasiukajtis n = (int)(w + half); 15125c28e83SPiotr Jasiukajtis y = (y - n * pio2_1) - n * pio2_t; 15225c28e83SPiotr Jasiukajtis #if defined(__i386) && !defined(__amd64) 15325c28e83SPiotr Jasiukajtis if (rp != fp_extended) 15425c28e83SPiotr Jasiukajtis (void) __swapRP(rp); 15525c28e83SPiotr Jasiukajtis #endif 15625c28e83SPiotr Jasiukajtis } else { 15725c28e83SPiotr Jasiukajtis if (ix >= 0x7f800000) { 15825c28e83SPiotr Jasiukajtis *s = *c = x / x; 15925c28e83SPiotr Jasiukajtis return; 16025c28e83SPiotr Jasiukajtis } 16125c28e83SPiotr Jasiukajtis hy = ((int *)&y)[HIWORD]; 16225c28e83SPiotr Jasiukajtis n = ((hy >> 20) & 0x7ff) - 1046; 16325c28e83SPiotr Jasiukajtis ((int *)&w)[HIWORD] = (hy & 0xfffff) | 0x41600000; 16425c28e83SPiotr Jasiukajtis ((int *)&w)[LOWORD] = ((int *)&y)[LOWORD]; 16525c28e83SPiotr Jasiukajtis n = __rem_pio2m(&w, &y, n, 1, 0, _TBL_ipio2_inf); 16625c28e83SPiotr Jasiukajtis if (hy < 0) { 16725c28e83SPiotr Jasiukajtis y = -y; 16825c28e83SPiotr Jasiukajtis n = -n; 16925c28e83SPiotr Jasiukajtis } 17025c28e83SPiotr Jasiukajtis } 17125c28e83SPiotr Jasiukajtis 17225c28e83SPiotr Jasiukajtis z = y * y; 17325c28e83SPiotr Jasiukajtis f = (float)((y * (S0 + z * S1)) * (S2 + z * (S3 + z))); 17425c28e83SPiotr Jasiukajtis g = (float)(((C0 + z * C1) + (z * z) * C2) * 17525c28e83SPiotr Jasiukajtis (C3 + z * (C4 + z))); 17625c28e83SPiotr Jasiukajtis if (n & 2) { 17725c28e83SPiotr Jasiukajtis f = -f; 17825c28e83SPiotr Jasiukajtis g = -g; 17925c28e83SPiotr Jasiukajtis } 18025c28e83SPiotr Jasiukajtis if (n & 1) { 18125c28e83SPiotr Jasiukajtis *s = g; 18225c28e83SPiotr Jasiukajtis *c = -f; 18325c28e83SPiotr Jasiukajtis } else { 18425c28e83SPiotr Jasiukajtis *s = f; 18525c28e83SPiotr Jasiukajtis *c = g; 18625c28e83SPiotr Jasiukajtis } 18725c28e83SPiotr Jasiukajtis } 188