1*25c28e83SPiotr Jasiukajtis /* 2*25c28e83SPiotr Jasiukajtis * CDDL HEADER START 3*25c28e83SPiotr Jasiukajtis * 4*25c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the 5*25c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License"). 6*25c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License. 7*25c28e83SPiotr Jasiukajtis * 8*25c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9*25c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing. 10*25c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions 11*25c28e83SPiotr Jasiukajtis * and limitations under the License. 12*25c28e83SPiotr Jasiukajtis * 13*25c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each 14*25c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15*25c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the 16*25c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying 17*25c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner] 18*25c28e83SPiotr Jasiukajtis * 19*25c28e83SPiotr Jasiukajtis * CDDL HEADER END 20*25c28e83SPiotr Jasiukajtis */ 21*25c28e83SPiotr Jasiukajtis /* 22*25c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 23*25c28e83SPiotr Jasiukajtis */ 24*25c28e83SPiotr Jasiukajtis /* 25*25c28e83SPiotr Jasiukajtis * Copyright 2005 Sun Microsystems, Inc. All rights reserved. 26*25c28e83SPiotr Jasiukajtis * Use is subject to license terms. 27*25c28e83SPiotr Jasiukajtis */ 28*25c28e83SPiotr Jasiukajtis 29*25c28e83SPiotr Jasiukajtis #pragma weak sincosf = __sincosf 30*25c28e83SPiotr Jasiukajtis 31*25c28e83SPiotr Jasiukajtis /* INDENT OFF */ 32*25c28e83SPiotr Jasiukajtis /* 33*25c28e83SPiotr Jasiukajtis * For |x| < pi/4, let z = x * x, and approximate sin(x) by 34*25c28e83SPiotr Jasiukajtis * 35*25c28e83SPiotr Jasiukajtis * S(x) = x(S0 + S1*z)(S2 + S3*z + z*z) 36*25c28e83SPiotr Jasiukajtis * where 37*25c28e83SPiotr Jasiukajtis * S0 = 1.85735322054308378716204874632872525989806770558e-0003, 38*25c28e83SPiotr Jasiukajtis * S1 = -1.95035094218403635082921458859320791358115801259e-0004, 39*25c28e83SPiotr Jasiukajtis * S2 = 5.38400550766074785970952495168558701485841707252e+0002, 40*25c28e83SPiotr Jasiukajtis * S3 = -3.31975110777873728964197739157371509422022905947e+0001, 41*25c28e83SPiotr Jasiukajtis * 42*25c28e83SPiotr Jasiukajtis * with error bounded by |(sin(x) - S(x))/x| < 2**(-28.2), and 43*25c28e83SPiotr Jasiukajtis * cos(x) by 44*25c28e83SPiotr Jasiukajtis * 45*25c28e83SPiotr Jasiukajtis * C(x) = (C0 + C1*z + C2*z*z) * (C3 + C4*z + z*z) 46*25c28e83SPiotr Jasiukajtis * where 47*25c28e83SPiotr Jasiukajtis * C0 = 1.09349482127188401868272000389539985058873853699e-0003 48*25c28e83SPiotr Jasiukajtis * C1 = -5.03324285989964979398034700054920226866107675091e-0004 49*25c28e83SPiotr Jasiukajtis * C2 = 2.43792880266971107750418061559602239831538067410e-0005 50*25c28e83SPiotr Jasiukajtis * C3 = 9.14499072605666582228127405245558035523741471271e+0002 51*25c28e83SPiotr Jasiukajtis * C4 = -3.63151270591815439197122504991683846785293207730e+0001 52*25c28e83SPiotr Jasiukajtis * 53*25c28e83SPiotr Jasiukajtis * with error bounded by |cos(x) - C(x)| < 2**(-34.2). 54*25c28e83SPiotr Jasiukajtis */ 55*25c28e83SPiotr Jasiukajtis /* INDENT ON */ 56*25c28e83SPiotr Jasiukajtis 57*25c28e83SPiotr Jasiukajtis #include "libm.h" 58*25c28e83SPiotr Jasiukajtis 59*25c28e83SPiotr Jasiukajtis extern const int _TBL_ipio2_inf[]; 60*25c28e83SPiotr Jasiukajtis extern int __rem_pio2m(double *, double *, int, int, int, const int *); 61*25c28e83SPiotr Jasiukajtis #if defined(__i386) && !defined(__amd64) 62*25c28e83SPiotr Jasiukajtis extern int __swapRP(int); 63*25c28e83SPiotr Jasiukajtis #endif 64*25c28e83SPiotr Jasiukajtis 65*25c28e83SPiotr Jasiukajtis static const double C[] = { 66*25c28e83SPiotr Jasiukajtis 1.85735322054308378716204874632872525989806770558e-0003, 67*25c28e83SPiotr Jasiukajtis -1.95035094218403635082921458859320791358115801259e-0004, 68*25c28e83SPiotr Jasiukajtis 5.38400550766074785970952495168558701485841707252e+0002, 69*25c28e83SPiotr Jasiukajtis -3.31975110777873728964197739157371509422022905947e+0001, 70*25c28e83SPiotr Jasiukajtis 1.09349482127188401868272000389539985058873853699e-0003, 71*25c28e83SPiotr Jasiukajtis -5.03324285989964979398034700054920226866107675091e-0004, 72*25c28e83SPiotr Jasiukajtis 2.43792880266971107750418061559602239831538067410e-0005, 73*25c28e83SPiotr Jasiukajtis 9.14499072605666582228127405245558035523741471271e+0002, 74*25c28e83SPiotr Jasiukajtis -3.63151270591815439197122504991683846785293207730e+0001, 75*25c28e83SPiotr Jasiukajtis 0.636619772367581343075535, /* 2^ -1 * 1.45F306DC9C883 */ 76*25c28e83SPiotr Jasiukajtis 0.5, 77*25c28e83SPiotr Jasiukajtis 1.570796326734125614166, /* 2^ 0 * 1.921FB54400000 */ 78*25c28e83SPiotr Jasiukajtis 6.077100506506192601475e-11, /* 2^-34 * 1.0B4611A626331 */ 79*25c28e83SPiotr Jasiukajtis }; 80*25c28e83SPiotr Jasiukajtis 81*25c28e83SPiotr Jasiukajtis #define S0 C[0] 82*25c28e83SPiotr Jasiukajtis #define S1 C[1] 83*25c28e83SPiotr Jasiukajtis #define S2 C[2] 84*25c28e83SPiotr Jasiukajtis #define S3 C[3] 85*25c28e83SPiotr Jasiukajtis #define C0 C[4] 86*25c28e83SPiotr Jasiukajtis #define C1 C[5] 87*25c28e83SPiotr Jasiukajtis #define C2 C[6] 88*25c28e83SPiotr Jasiukajtis #define C3 C[7] 89*25c28e83SPiotr Jasiukajtis #define C4 C[8] 90*25c28e83SPiotr Jasiukajtis #define invpio2 C[9] 91*25c28e83SPiotr Jasiukajtis #define half C[10] 92*25c28e83SPiotr Jasiukajtis #define pio2_1 C[11] 93*25c28e83SPiotr Jasiukajtis #define pio2_t C[12] 94*25c28e83SPiotr Jasiukajtis 95*25c28e83SPiotr Jasiukajtis void 96*25c28e83SPiotr Jasiukajtis sincosf(float x, float *s, float *c) 97*25c28e83SPiotr Jasiukajtis { 98*25c28e83SPiotr Jasiukajtis double y, z, w; 99*25c28e83SPiotr Jasiukajtis float f, g; 100*25c28e83SPiotr Jasiukajtis int n, ix, hx, hy; 101*25c28e83SPiotr Jasiukajtis volatile int i; 102*25c28e83SPiotr Jasiukajtis 103*25c28e83SPiotr Jasiukajtis hx = *((int *)&x); 104*25c28e83SPiotr Jasiukajtis ix = hx & 0x7fffffff; 105*25c28e83SPiotr Jasiukajtis 106*25c28e83SPiotr Jasiukajtis y = (double)x; 107*25c28e83SPiotr Jasiukajtis 108*25c28e83SPiotr Jasiukajtis if (ix <= 0x4016cbe4) { /* |x| < 3*pi/4 */ 109*25c28e83SPiotr Jasiukajtis if (ix <= 0x3f490fdb) { /* |x| < pi/4 */ 110*25c28e83SPiotr Jasiukajtis if (ix <= 0x39800000) { /* |x| <= 2**-12 */ 111*25c28e83SPiotr Jasiukajtis i = (int)y; 112*25c28e83SPiotr Jasiukajtis #ifdef lint 113*25c28e83SPiotr Jasiukajtis i = i; 114*25c28e83SPiotr Jasiukajtis #endif 115*25c28e83SPiotr Jasiukajtis *s = x; 116*25c28e83SPiotr Jasiukajtis *c = 1.0f; 117*25c28e83SPiotr Jasiukajtis return; 118*25c28e83SPiotr Jasiukajtis } 119*25c28e83SPiotr Jasiukajtis z = y * y; 120*25c28e83SPiotr Jasiukajtis *s = (float)((y * (S0 + z * S1)) * 121*25c28e83SPiotr Jasiukajtis (S2 + z * (S3 + z))); 122*25c28e83SPiotr Jasiukajtis *c = (float)(((C0 + z * C1) + (z * z) * C2) * 123*25c28e83SPiotr Jasiukajtis (C3 + z * (C4 + z))); 124*25c28e83SPiotr Jasiukajtis } else if (hx > 0) { 125*25c28e83SPiotr Jasiukajtis y = (y - pio2_1) - pio2_t; 126*25c28e83SPiotr Jasiukajtis z = y * y; 127*25c28e83SPiotr Jasiukajtis *s = (float)(((C0 + z * C1) + (z * z) * C2) * 128*25c28e83SPiotr Jasiukajtis (C3 + z * (C4 + z))); 129*25c28e83SPiotr Jasiukajtis *c = (float)-((y * (S0 + z * S1)) * 130*25c28e83SPiotr Jasiukajtis (S2 + z * (S3 + z))); 131*25c28e83SPiotr Jasiukajtis } else { 132*25c28e83SPiotr Jasiukajtis y = (y + pio2_1) + pio2_t; 133*25c28e83SPiotr Jasiukajtis z = y * y; 134*25c28e83SPiotr Jasiukajtis *s = (float)-(((C0 + z * C1) + (z * z) * C2) * 135*25c28e83SPiotr Jasiukajtis (C3 + z * (C4 + z))); 136*25c28e83SPiotr Jasiukajtis *c = (float)((y * (S0 + z * S1)) * 137*25c28e83SPiotr Jasiukajtis (S2 + z * (S3 + z))); 138*25c28e83SPiotr Jasiukajtis } 139*25c28e83SPiotr Jasiukajtis return; 140*25c28e83SPiotr Jasiukajtis } else if (ix <= 0x49c90fdb) { /* |x| < 2^19*pi */ 141*25c28e83SPiotr Jasiukajtis #if defined(__i386) && !defined(__amd64) 142*25c28e83SPiotr Jasiukajtis int rp; 143*25c28e83SPiotr Jasiukajtis 144*25c28e83SPiotr Jasiukajtis rp = __swapRP(fp_extended); 145*25c28e83SPiotr Jasiukajtis #endif 146*25c28e83SPiotr Jasiukajtis w = y * invpio2; 147*25c28e83SPiotr Jasiukajtis if (hx < 0) 148*25c28e83SPiotr Jasiukajtis n = (int)(w - half); 149*25c28e83SPiotr Jasiukajtis else 150*25c28e83SPiotr Jasiukajtis n = (int)(w + half); 151*25c28e83SPiotr Jasiukajtis y = (y - n * pio2_1) - n * pio2_t; 152*25c28e83SPiotr Jasiukajtis #if defined(__i386) && !defined(__amd64) 153*25c28e83SPiotr Jasiukajtis if (rp != fp_extended) 154*25c28e83SPiotr Jasiukajtis (void) __swapRP(rp); 155*25c28e83SPiotr Jasiukajtis #endif 156*25c28e83SPiotr Jasiukajtis } else { 157*25c28e83SPiotr Jasiukajtis if (ix >= 0x7f800000) { 158*25c28e83SPiotr Jasiukajtis *s = *c = x / x; 159*25c28e83SPiotr Jasiukajtis return; 160*25c28e83SPiotr Jasiukajtis } 161*25c28e83SPiotr Jasiukajtis hy = ((int *)&y)[HIWORD]; 162*25c28e83SPiotr Jasiukajtis n = ((hy >> 20) & 0x7ff) - 1046; 163*25c28e83SPiotr Jasiukajtis ((int *)&w)[HIWORD] = (hy & 0xfffff) | 0x41600000; 164*25c28e83SPiotr Jasiukajtis ((int *)&w)[LOWORD] = ((int *)&y)[LOWORD]; 165*25c28e83SPiotr Jasiukajtis n = __rem_pio2m(&w, &y, n, 1, 0, _TBL_ipio2_inf); 166*25c28e83SPiotr Jasiukajtis if (hy < 0) { 167*25c28e83SPiotr Jasiukajtis y = -y; 168*25c28e83SPiotr Jasiukajtis n = -n; 169*25c28e83SPiotr Jasiukajtis } 170*25c28e83SPiotr Jasiukajtis } 171*25c28e83SPiotr Jasiukajtis 172*25c28e83SPiotr Jasiukajtis z = y * y; 173*25c28e83SPiotr Jasiukajtis f = (float)((y * (S0 + z * S1)) * (S2 + z * (S3 + z))); 174*25c28e83SPiotr Jasiukajtis g = (float)(((C0 + z * C1) + (z * z) * C2) * 175*25c28e83SPiotr Jasiukajtis (C3 + z * (C4 + z))); 176*25c28e83SPiotr Jasiukajtis if (n & 2) { 177*25c28e83SPiotr Jasiukajtis f = -f; 178*25c28e83SPiotr Jasiukajtis g = -g; 179*25c28e83SPiotr Jasiukajtis } 180*25c28e83SPiotr Jasiukajtis if (n & 1) { 181*25c28e83SPiotr Jasiukajtis *s = g; 182*25c28e83SPiotr Jasiukajtis *c = -f; 183*25c28e83SPiotr Jasiukajtis } else { 184*25c28e83SPiotr Jasiukajtis *s = f; 185*25c28e83SPiotr Jasiukajtis *c = g; 186*25c28e83SPiotr Jasiukajtis } 187*25c28e83SPiotr Jasiukajtis } 188