1/*
2 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26/*
27 * __kernel_cos( x, y )
28 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
29 * Input x is assumed to be bounded by ~pi/4 in magnitude.
30 * Input y is the tail of x.
31 *
32 * Algorithm
33 * 1. Since cos(-x) = cos(x), we need only to consider positive x.
34 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
35 * 3. cos(x) is approximated by a polynomial of degree 14 on
36 * [0,pi/4]
37 * 4 14
38 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
39 * where the remez error is
40 *
41 * | 2 4 6 8 10 12 14 | -58
42 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
43 * | |
44 *
45 * 4 6 8 10 12 14
46 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
47 * cos(x) = 1 - x*x/2 + r
48 * since cos(x+y) ~ cos(x) - sin(x)*y
49 * ~ cos(x) - x*y,
50 * a correction term is necessary in cos(x) and hence
51 * cos(x+y) = 1 - (x*x/2 - (r - x*y))
52 * For better accuracy when x > 0.3, let qx = |x|/4 with
53 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
54 * Then
55 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
56 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
57 * magnitude of the latter is at least a quarter of x*x/2,
58 * thus, reducing the rounding error in the subtraction.
59 */
60
61#include "fdlibm.h"
62
63#ifdef __STDC__
64static const double
65#else
66static double
67#endif
68one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
69C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
70C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
71C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
72C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
73C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
74C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
75
76#ifdef __STDC__
77 double __kernel_cos(double x, double y)
78#else
79 double __kernel_cos(x, y)
80 double x,y;
81#endif
82{
83 double a,hz,z,r,qx;
84 int ix;
85 ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/
86 if(ix<0x3e400000) { /* if x < 2**27 */
87 if(((int)x)==0) return one; /* generate inexact */
88 }
89 z = x*x;
90 r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
91 if(ix < 0x3FD33333) /* if |x| < 0.3 */
92 return one - (0.5*z - (z*r - x*y));
93 else {
94 if(ix > 0x3fe90000) { /* x > 0.78125 */
95 qx = 0.28125;
96 } else {
97 __HI(qx) = ix-0x00200000; /* x/4 */
98 __LO(qx) = 0;
99 }
100 hz = 0.5*z-qx;
101 a = one-qx;
102 return a - (hz - (z*r-x*y));
103 }
104}
105