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 /*
  27  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  28  * Use is subject to license terms.
  29  */
  30 
  31 #include "libm.h"
  32 
  33 
  34 /*
  35  * float __k_cos(double x);
  36  * kernel (float) cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
  37  * Input x is in double and assumed to be bounded by ~pi/4 in magnitude.
  38  *
  39  * Method: Let z = x * x, then
  40  *      C(x) = (C0 + C1*z + C2*z*z) * (C3 + C4*z + z*z)
  41  * where
  42  *      C0 =   1.09349482127188401868272000389539985058873853699e-0003
  43  *      C1 =  -5.03324285989964979398034700054920226866107675091e-0004
  44  *      C2 =   2.43792880266971107750418061559602239831538067410e-0005
  45  *      C3 =   9.14499072605666582228127405245558035523741471271e+0002
  46  *      C4 =  -3.63151270591815439197122504991683846785293207730e+0001
  47  *
  48  * The remez error is bound by  |cos(x) - C(x)| < 2**(-34.2)
  49  *
  50  * Constants:
  51  * The hexadecimal values are the intended ones for the following constants.
  52  * The decimal values may be used, provided that the compiler will convert
  53  * from decimal to binary accurately enough to produce the hexadecimal values
  54  * shown.
  55  */
  56 
  57 static const double q[] = {
  58 /* C0 = */
  59         1.09349482127188401868272000389539985058873853699e-0003,
  60 /* C1 = */ -5.03324285989964979398034700054920226866107675091e-0004,
  61 /* C2 = */ 2.43792880266971107750418061559602239831538067410e-0005,
  62 /* C3 = */ 9.14499072605666582228127405245558035523741471271e+0002,
  63 /* C4 = */ -3.63151270591815439197122504991683846785293207730e+0001, };
  64 
  65 #define C0              q[0]
  66 #define C1              q[1]
  67 #define C2              q[2]
  68 #define C3              q[3]
  69 #define C4              q[4]
  70 
  71 float
  72 __k_cosf(double x)
  73 {
  74         float ft;
  75         double z;
  76         int hx;
  77 
  78         hx = ((int *)&x)[HIWORD];           /* hx = leading x  */
  79 
  80         if ((hx & ~0x80000000) < 0x3f100000) {   /* |x| < 2**-14 */
  81                 ft = (float)1;
  82 
  83                 if (((int)x) == 0)              /* raise inexact if x != 0 */
  84                         return (ft);
  85         }
  86 
  87         z = x * x;
  88         ft = (float)(((C0 + z * C1) + (z * z) * C2) * (C3 + z * (C4 + z)));
  89         return (ft);
  90 }