1
2 /* @(#)k_sin.c 5.1 93/09/24 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 /* __kernel_sin( x, y, iy)
15 * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
16 * Input x is assumed to be bounded by ~pi/4 in magnitude.
17 * Input y is the tail of x.
18 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
19 *
20 * Algorithm
21 * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
22 * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
23 * 3. sin(x) is approximated by a polynomial of degree 13 on
24 * [0,pi/4]
25 * 3 13
26 * sin(x) ~ x + S1*x + ... + S6*x
27 * where
28 *
29 * |sin(x) 2 4 6 8 10 12 | -58
30 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
31 * | x |
32 *
33 * 4. sin(x+y) = sin(x) + sin'(x')*y
34 * ~ sin(x) + (1-x*x/2)*y
35 * For better accuracy, let
36 * 3 2 2 2 2
37 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
38 * then 3 2
39 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
40 */
41
42 #include "fdlibm.h"
43
44 #ifdef _NEED_FLOAT64
45
46 static const __float64
47 half = _F_64(5.00000000000000000000e-01), /* 0x3FE00000, 0x00000000 */
48 S1 = _F_64(-1.66666666666666324348e-01), /* 0xBFC55555, 0x55555549 */
49 S2 = _F_64(8.33333333332248946124e-03), /* 0x3F811111, 0x1110F8A6 */
50 S3 = _F_64(-1.98412698298579493134e-04), /* 0xBF2A01A0, 0x19C161D5 */
51 S4 = _F_64(2.75573137070700676789e-06), /* 0x3EC71DE3, 0x57B1FE7D */
52 S5 = _F_64(-2.50507602534068634195e-08), /* 0xBE5AE5E6, 0x8A2B9CEB */
53 S6 = _F_64(1.58969099521155010221e-10); /* 0x3DE5D93A, 0x5ACFD57C */
54
55 __float64
__kernel_sin(__float64 x,__float64 y,int iy)56 __kernel_sin(__float64 x, __float64 y, int iy)
57 {
58 __float64 z, r, v;
59 __int32_t ix;
60 GET_HIGH_WORD(ix, x);
61 ix &= 0x7fffffff; /* high word of x */
62 if (ix < 0x3e400000) /* |x| < 2**-27 */
63 return __math_inexact64(x); /* generate inexact */
64 z = x * x;
65 v = z * x;
66 r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
67 if (iy == 0)
68 return x + v * (S1 + z * r);
69 else
70 return x - ((z * (half * y - v * r) - y) - v * S1);
71 }
72
73 #endif /* _NEED_FLOAT64 */
74
