src/fdlibm/s_cos.c

/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
 *
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is Mozilla Communicator client code, released
 * March 31, 1998.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 1998
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either of the GNU General Public License Version 2 or later (the "GPL"),
 * or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */

/* @(#)s_cos.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* cos(x)
 * Return cosine function of x.
 *
 * kernel function:
 *      __kernel_sin            ... sine function on [-pi/4,pi/4]
 *      __kernel_cos            ... cosine function on [-pi/4,pi/4]
 *      __ieee754_rem_pio2      ... argument reduction routine
 *
 * Method.
 *      Let S,C and T denote the sin, cos and tan respectively on 
 *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 
 *      in [-pi/4 , +pi/4], and let n = k mod 4.
 *      We have
 *
 *          n        sin(x)      cos(x)        tan(x)
 *     ----------------------------------------------------------
 *          0          S           C             T
 *          1          C          -S            -1/T
 *          2         -S          -C             T
 *          3         -C           S            -1/T
 *     ----------------------------------------------------------
 *
 * Special cases:
 *      Let trig be any of sin, cos, or tan.
 *      trig(+-INF)  is NaN, with signals;
 *      trig(NaN)    is that NaN;
 *
 * Accuracy:
 *      TRIG(x) returns trig(x) nearly rounded 
 */

#include "fdlibm.h"

#ifdef __STDC__
        double fd_cos(double x)
#else
        double fd_cos(x)
        double x;
#endif
{
        fd_twoints u;
        double y[2],z=0.0;
        int n, ix;

    /* High word of x. */
        u.d = x;
        ix = __HI(u);

    /* |x| ~< pi/4 */
        ix &= 0x7fffffff;
        if(ix <= 0x3fe921fb) return __kernel_cos(x,z);

    /* cos(Inf or NaN) is NaN */
        else if (ix>=0x7ff00000) return x-x;

    /* argument reduction needed */
        else {
            n = __ieee754_rem_pio2(x,y);
            switch(n&3) {
                case 0: return  __kernel_cos(y[0],y[1]);
                case 1: return -__kernel_sin(y[0],y[1],1);
                case 2: return -__kernel_cos(y[0],y[1]);
                default:
                        return  __kernel_sin(y[0],y[1],1);
            }
        }
}
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	/* @(#)s_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	/* cos(x)
53	* Return cosine function of x.
54	*
55	* kernel function:
56	* __kernel_sin ... sine function on [-pi/4,pi/4]
57	* __kernel_cos ... cosine function on [-pi/4,pi/4]
58	* __ieee754_rem_pio2 ... argument reduction routine
59	*
60	* Method.
61	* Let S,C and T denote the sin, cos and tan respectively on
62	* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
63	* in [-pi/4 , +pi/4], and let n = k mod 4.
64	* We have
65	*
66	* n sin(x) cos(x) tan(x)
67	* ----------------------------------------------------------
68	* 0 S C T
69	* 1 C -S -1/T
70	* 2 -S -C T
71	* 3 -C S -1/T
72	* ----------------------------------------------------------
73	*
74	* Special cases:
75	* Let trig be any of sin, cos, or tan.
76	* trig(+-INF) is NaN, with signals;
77	* trig(NaN) is that NaN;
78	*
79	* Accuracy:
80	* TRIG(x) returns trig(x) nearly rounded
81	*/
82
83	#include "fdlibm.h"
84
85	#ifdef __STDC__
86	double fd_cos(double x)
87	#else
88	double fd_cos(x)
89	double x;
90	#endif
91	{
92	fd_twoints u;
93	double y[2],z=0.0;
94	int n, ix;
95
96	/* High word of x. */
97	u.d = x;
98	ix = __HI(u);
99
100	/* \|x\| ~< pi/4 */
101	ix &= 0x7fffffff;
102	if(ix <= 0x3fe921fb) return __kernel_cos(x,z);
103
104	/* cos(Inf or NaN) is NaN */
105	else if (ix>=0x7ff00000) return x-x;
106
107	/* argument reduction needed */
108	else {
109	n = __ieee754_rem_pio2(x,y);
110	switch(n&3) {
111	case 0: return __kernel_cos(y[0],y[1]);
112	case 1: return -__kernel_sin(y[0],y[1],1);
113	case 2: return -__kernel_cos(y[0],y[1]);
114	default:
115	return __kernel_sin(y[0],y[1],1);
116	}
117	}
118	}