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 /* __kernel_sin( x, y, iy)
27  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
28  * Input x is assumed to be bounded by ~pi/4 in magnitude.
29  * Input y is the tail of x.
30  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
31  *
32  * Algorithm
33  *      1. Since sin(-x) = -sin(x), we need only to consider positive x.
34  *      2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
35  *      3. sin(x) is approximated by a polynomial of degree 13 on
36  *         [0,pi/4]
37  *                               3            13
38  *              sin(x) ~ x + S1*x + ... + S6*x
39  *         where
40  *
41  *      |sin(x)         2     4     6     8     10     12  |     -58
42  *      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
43  *      |  x                                               |
44  *
45  *      4. sin(x+y) = sin(x) + sin'(x')*y
46  *                  ~ sin(x) + (1-x*x/2)*y
47  *         For better accuracy, let
48  *                   3      2      2      2      2
49  *              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
50  *         then                   3    2
51  *              sin(x) = x + (S1*x + (x *(r-y/2)+y))
52  */
53 
54 #include "fdlibm.h"
55 
56 #ifdef __STDC__
57 static const double
58 #else
59 static double
60 #endif
61 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
62 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
63 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
64 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
65 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
66 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
67 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
68 
69 #ifdef __STDC__
__kernel_sin(double x,double y,int iy)70         double __kernel_sin(double x, double y, int iy)
71 #else
72         double __kernel_sin(x, y, iy)
73         double x,y; int iy;             /* iy=0 if y is zero */
74 #endif
75 {
76         double z,r,v;
77         int ix;
78         ix = __HI(x)&0x7fffffff;        /* high word of x */
79         if(ix<0x3e400000)                       /* |x| < 2**-27 */
80            {if((int)x==0) return x;}            /* generate inexact */
81         z       =  x*x;
82         v       =  z*x;
83         r       =  S2+z*(S3+z*(S4+z*(S5+z*S6)));
84         if(iy==0) return x+v*(S1+z*r);
85         else      return x-((z*(half*y-v*r)-y)-v*S1);
86 }
87