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 }