1 /*
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunPro, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 /* __kernel_sin( x, y, iy)
13 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
14 * Input x is assumed to be bounded by ~pi/4 in magnitude.
15 * Input y is the tail of x.
16 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
17 *
18 * Algorithm
19 * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
20 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
21 * 3. sin(x) is approximated by a polynomial of degree 13 on
22 * [0,pi/4]
23 * 3 13
24 * sin(x) ~ x + S1*x + ... + S6*x
25 * where
26 *
27 * |sin(x) 2 4 6 8 10 12 | -58
28 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
29 * | x |
30 *
31 * 4. sin(x+y) = sin(x) + sin'(x')*y
32 * ~ sin(x) + (1-x*x/2)*y
33 * For better accuracy, let
34 * 3 2 2 2 2
35 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
36 * then 3 2
37 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
38 */
39
40 #include "math.h"
41 #include "math_private.h"
42
43 static const double
44 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
45 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
46 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
47 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
48 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
49 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
50 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
51
__kernel_sin(double x,double y,int iy)52 double __kernel_sin(double x, double y, int iy)
53 {
54 double z,r,v;
55 int32_t ix;
56 GET_HIGH_WORD(ix,x);
57 ix &= 0x7fffffff; /* high word of x */
58 if(ix<0x3e400000) /* |x| < 2**-27 */
59 {if((int)x==0) return x;} /* generate inexact */
60 z = x*x;
61 v = z*x;
62 r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
63 if(iy==0) return x+v*(S1+z*r);
64 else return x-((z*(half*y-v*r)-y)-v*S1);
65 }
66