src/fdlibm/k_sin.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 ***** */

/* @(#)k_sin.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.
 * ====================================================
 */

/* __kernel_sin( x, y, iy)
 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
 * Input x is assumed to be bounded by ~pi/4 in magnitude.
 * Input y is the tail of x.
 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). 
 *
 * Algorithm
 *      1. Since sin(-x) = -sin(x), we need only to consider positive x. 
 *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
 *      3. sin(x) is approximated by a polynomial of degree 13 on
 *         [0,pi/4]
 *                               3            13
 *              sin(x) ~ x + S1*x + ... + S6*x
 *         where
 *      
 *      |sin(x)         2     4     6     8     10     12  |     -58
 *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
 *      |  x                                               | 
 * 
 *      4. sin(x+y) = sin(x) + sin'(x')*y
 *                  ~ sin(x) + (1-x*x/2)*y
 *         For better accuracy, let 
 *                   3      2      2      2      2
 *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
 *         then                   3    2
 *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
 */

#include "fdlibm.h"

#ifdef __STDC__
static const double 
#else
static double 
#endif
half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */

#ifdef __STDC__
        double __kernel_sin(double x, double y, int iy)
#else
        double __kernel_sin(x, y, iy)
        double x,y; int iy;             /* iy=0 if y is zero */
#endif
{
        fd_twoints u;
        double z,r,v;
        int ix;
        u.d = x;
        ix = __HI(u)&0x7fffffff;        /* high word of x */
        if(ix<0x3e400000)                       /* |x| < 2**-27 */
           {if((int)x==0) return x;}            /* generate inexact */
        z       =  x*x;
        v       =  z*x;
        r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
        if(iy==0) return x+v*(S1+z*r);
        else      return x-((z*(half*y-v*r)-y)-v*S1);
}
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_sin.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	/* __kernel_sin( x, y, iy)
53	* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
54	* Input x is assumed to be bounded by ~pi/4 in magnitude.
55	* Input y is the tail of x.
56	* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
57	*
58	* Algorithm
59	* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
60	* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
61	* 3. sin(x) is approximated by a polynomial of degree 13 on
62	* [0,pi/4]
63	* 3 13
64	* sin(x) ~ x + S1x + ... + S6x
65	* where
66	*
67	* \|sin(x) 2 4 6 8 10 12 \| -58
68	* \|----- - (1+S1x +S2x +S3x +S4x +S5x +S6x )\| <= 2
69	* \| x \|
70	*
71	* 4. sin(x+y) = sin(x) + sin'(x')*y
72	* ~ sin(x) + (1-xx/2)y
73	* For better accuracy, let
74	* 3 2 2 2 2
75	* r = x (S2+x (S3+x (S4+x (S5+x *S6))))
76	* then 3 2
77	* sin(x) = x + (S1x + (x (r-y/2)+y))
78	*/
79
80	#include "fdlibm.h"
81
82	#ifdef __STDC__
83	static const double
84	#else
85	static double
86	#endif
87	half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
88	S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
89	S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
90	S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
91	S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
92	S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
93	S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
94
95	#ifdef __STDC__
96	double __kernel_sin(double x, double y, int iy)
97	#else
98	double __kernel_sin(x, y, iy)
99	double x,y; int iy; /* iy=0 if y is zero */
100	#endif
101	{
102	fd_twoints u;
103	double z,r,v;
104	int ix;
105	u.d = x;
106	ix = __HI(u)&0x7fffffff; /* high word of x */
107	if(ix<0x3e400000) /* \|x\| < 2*-27 /
108	{if((int)x==0) return x;} /* generate inexact */
109	z = x*x;
110	v = z*x;
111	r = S2+z(S3+z(S4+z(S5+zS6)));
112	if(iy==0) return x+v(S1+zr);
113	else return x-((z(halfy-vr)-y)-vS1);
114	}