/[jscoverage]/trunk/js/src/fdlibm/k_cos.c
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Contents of /trunk/js/src/fdlibm/k_cos.c

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Wed Aug 1 13:51:53 2007 UTC (12 years, 11 months ago) by siliconforks
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Initial import.

1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
2 *
3 * ***** BEGIN LICENSE BLOCK *****
4 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
5 *
6 * The contents of this file are subject to the Mozilla Public License Version
7 * 1.1 (the "License"); you may not use this file except in compliance with
8 * the License. You may obtain a copy of the License at
9 * http://www.mozilla.org/MPL/
10 *
11 * Software distributed under the License is distributed on an "AS IS" basis,
12 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13 * for the specific language governing rights and limitations under the
14 * License.
15 *
16 * The Original Code is Mozilla Communicator client code, released
17 * March 31, 1998.
18 *
19 * The Initial Developer of the Original Code is
20 * Sun Microsystems, Inc.
21 * Portions created by the Initial Developer are Copyright (C) 1998
22 * the Initial Developer. All Rights Reserved.
23 *
24 * Contributor(s):
25 *
26 * Alternatively, the contents of this file may be used under the terms of
27 * either of the GNU General Public License Version 2 or later (the "GPL"),
28 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29 * in which case the provisions of the GPL or the LGPL are applicable instead
30 * of those above. If you wish to allow use of your version of this file only
31 * under the terms of either the GPL or the LGPL, and not to allow others to
32 * use your version of this file under the terms of the MPL, indicate your
33 * decision by deleting the provisions above and replace them with the notice
34 * and other provisions required by the GPL or the LGPL. If you do not delete
35 * the provisions above, a recipient may use your version of this file under
36 * the terms of any one of the MPL, the GPL or the LGPL.
37 *
38 * ***** END LICENSE BLOCK ***** */
39
40 /* @(#)k_cos.c 1.3 95/01/18 */
41 /*
42 * ====================================================
43 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
44 *
45 * Developed at SunSoft, a Sun Microsystems, Inc. business.
46 * Permission to use, copy, modify, and distribute this
47 * software is freely granted, provided that this notice
48 * is preserved.
49 * ====================================================
50 */
51
52 /*
53 * __kernel_cos( x, y )
54 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
55 * Input x is assumed to be bounded by ~pi/4 in magnitude.
56 * Input y is the tail of x.
57 *
58 * Algorithm
59 * 1. Since cos(-x) = cos(x), we need only to consider positive x.
60 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
61 * 3. cos(x) is approximated by a polynomial of degree 14 on
62 * [0,pi/4]
63 * 4 14
64 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
65 * where the remez error is
66 *
67 * | 2 4 6 8 10 12 14 | -58
68 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
69 * | |
70 *
71 * 4 6 8 10 12 14
72 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
73 * cos(x) = 1 - x*x/2 + r
74 * since cos(x+y) ~ cos(x) - sin(x)*y
75 * ~ cos(x) - x*y,
76 * a correction term is necessary in cos(x) and hence
77 * cos(x+y) = 1 - (x*x/2 - (r - x*y))
78 * For better accuracy when x > 0.3, let qx = |x|/4 with
79 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
80 * Then
81 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
82 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
83 * magnitude of the latter is at least a quarter of x*x/2,
84 * thus, reducing the rounding error in the subtraction.
85 */
86
87 #include "fdlibm.h"
88
89 #ifdef __STDC__
90 static const double
91 #else
92 static double
93 #endif
94 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
95 C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
96 C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
97 C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
98 C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
99 C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
100 C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
101
102 #ifdef __STDC__
103 double __kernel_cos(double x, double y)
104 #else
105 double __kernel_cos(x, y)
106 double x,y;
107 #endif
108 {
109 fd_twoints u;
110 double qx = 0;
111 double a,hz,z,r;
112 int ix;
113 u.d = x;
114 ix = __HI(u)&0x7fffffff; /* ix = |x|'s high word*/
115 if(ix<0x3e400000) { /* if x < 2**27 */
116 if(((int)x)==0) return one; /* generate inexact */
117 }
118 z = x*x;
119 r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
120 if(ix < 0x3FD33333) /* if |x| < 0.3 */
121 return one - (0.5*z - (z*r - x*y));
122 else {
123 if(ix > 0x3fe90000) { /* x > 0.78125 */
124 qx = 0.28125;
125 } else {
126 u.d = qx;
127 __HI(u) = ix-0x00200000; /* x/4 */
128 __LO(u) = 0;
129 qx = u.d;
130 }
131 hz = 0.5*z-qx;
132 a = one-qx;
133 return a - (hz - (z*r-x*y));
134 }
135 }

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