1 /* 2 * CDDL HEADER START 3 * 4 * The contents of this file are subject to the terms of the 5 * Common Development and Distribution License (the "License"). 6 * You may not use this file except in compliance with the License. 7 * 8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE 9 * or http://www.opensolaris.org/os/licensing. 10 * See the License for the specific language governing permissions 11 * and limitations under the License. 12 * 13 * When distributing Covered Code, include this CDDL HEADER in each 14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE. 15 * If applicable, add the following below this CDDL HEADER, with the 16 * fields enclosed by brackets "[]" replaced with your own identifying 17 * information: Portions Copyright [yyyy] [name of copyright owner] 18 * 19 * CDDL HEADER END 20 */ 21 22 /* 23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved. 24 */ 25 /* 26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved. 27 * Use is subject to license terms. 28 */ 29 30 #include "libm.h" 31 32 /* INDENT OFF */ 33 /* 34 * void __k_sincosf(double x, float *s, float *c); 35 * kernel (float) sincos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 36 * Input x is in double and assumed to be bounded by ~pi/4 in magnitude. 37 * 38 * Method: Let z = x * x, then 39 * S(x) = x(S0 + S1*z)(S2 + S3*z + z*z) 40 * C(x) = (C0 + C1*z + C2*z*z) * (C3 + C4*z + z*z) 41 * where 42 * S0 = 1.85735322054308378716204874632872525989806770558e-0003 43 * S1 = -1.95035094218403635082921458859320791358115801259e-0004 44 * S2 = 5.38400550766074785970952495168558701485841707252e+0002 45 * S3 = -3.31975110777873728964197739157371509422022905947e+0001 46 * C0 = 1.09349482127188401868272000389539985058873853699e-0003 47 * C1 = -5.03324285989964979398034700054920226866107675091e-0004 48 * C2 = 2.43792880266971107750418061559602239831538067410e-0005 49 * C3 = 9.14499072605666582228127405245558035523741471271e+0002 50 * C4 = -3.63151270591815439197122504991683846785293207730e+0001 51 * 52 * The remez error in S is bound by |(sin(x) - S(x))/x| < 2**(-28.2) 53 * The remez error in C is bound by |cos(x) - C(x)| < 2**(-34.2) 54 * 55 * Constants: 56 * The hexadecimal values are the intended ones for the following constants. 57 * The decimal values may be used, provided that the compiler will convert 58 * from decimal to binary accurately enough to produce the hexadecimal values 59 * shown. 60 */ 61 /* INDENT ON */ 62 63 static const double q[] = { 64 /* S0 = */ 1.85735322054308378716204874632872525989806770558e-0003, 65 /* S1 = */ -1.95035094218403635082921458859320791358115801259e-0004, 66 /* S2 = */ 5.38400550766074785970952495168558701485841707252e+0002, 67 /* S3 = */ -3.31975110777873728964197739157371509422022905947e+0001, 68 /* C0 = */ 1.09349482127188401868272000389539985058873853699e-0003, 69 /* C1 = */ -5.03324285989964979398034700054920226866107675091e-0004, 70 /* C2 = */ 2.43792880266971107750418061559602239831538067410e-0005, 71 /* C3 = */ 9.14499072605666582228127405245558035523741471271e+0002, 72 /* C4 = */ -3.63151270591815439197122504991683846785293207730e+0001, 73 }; 74 75 76 #define S0 q[0] 77 #define S1 q[1] 78 #define S2 q[2] 79 #define S3 q[3] 80 #define C0 q[4] 81 #define C1 q[5] 82 #define C2 q[6] 83 #define C3 q[7] 84 #define C4 q[8] 85 86 void 87 __k_sincosf(double x, float *s, float *c) { 88 double z; 89 int hx; 90 91 hx = ((int *) &x)[HIWORD]; /* hx = leading x */ 92 /* small argument */ 93 if ((hx & ~0x80000000) < 0x3f100000) { /* if |x| < 2**-14 */ 94 *s = (float) x; *c = (float) 1; 95 if ((int) x == 0) /* raise inexact if x != 0 */ 96 return; 97 } 98 z = x * x; 99 *s = (float) ((x * (S0 + z * S1)) * (S2 + z * (S3 + z))); 100 *c = (float) (((C0 + z * C1) + (z * z) * C2) * (C3 + z * (C4 + z))); 101 } 102