Commit | Line | Data |
---|---|---|
4acf9396 GCI |
1 | /* @(#)k_sin.c 5.1 93/09/24 */ |
2 | /* | |
3 | * ==================================================== | |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
5 | * | |
6 | * Developed at SunPro, a Sun Microsystems, Inc. business. | |
7 | * Permission to use, copy, modify, and distribute this | |
8 | * software is freely granted, provided that this notice | |
9 | * is preserved. | |
10 | * ==================================================== | |
11 | */ | |
12 | ||
13 | #ifndef lint | |
14 | static char rcsid[] = "$Id: k_sin.c,v 1.4 1994/03/03 17:04:24 jtc Exp $"; | |
15 | #endif | |
16 | ||
17 | /* __kernel_sin( x, y, iy) | |
18 | * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 | |
19 | * Input x is assumed to be bounded by ~pi/4 in magnitude. | |
20 | * Input y is the tail of x. | |
21 | * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). | |
22 | * | |
23 | * Algorithm | |
24 | * 1. Since sin(-x) = -sin(x), we need only to consider positive x. | |
25 | * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. | |
26 | * 3. sin(x) is approximated by a polynomial of degree 13 on | |
27 | * [0,pi/4] | |
28 | * 3 13 | |
29 | * sin(x) ~ x + S1*x + ... + S6*x | |
30 | * where | |
31 | * | |
32 | * |sin(x) 2 4 6 8 10 12 | -58 | |
33 | * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 | |
34 | * | x | | |
35 | * | |
36 | * 4. sin(x+y) = sin(x) + sin'(x')*y | |
37 | * ~ sin(x) + (1-x*x/2)*y | |
38 | * For better accuracy, let | |
39 | * 3 2 2 2 2 | |
40 | * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) | |
41 | * then 3 2 | |
42 | * sin(x) = x + (S1*x + (x *(r-y/2)+y)) | |
43 | */ | |
44 | ||
45 | #include "math.h" | |
46 | #include <machine/endian.h> | |
47 | ||
48 | #if BYTE_ORDER == LITTLE_ENDIAN | |
49 | #define n0 1 | |
50 | #else | |
51 | #define n0 0 | |
52 | #endif | |
53 | ||
54 | #ifdef __STDC__ | |
55 | static const double | |
56 | #else | |
57 | static double | |
58 | #endif | |
59 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ | |
60 | S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ | |
61 | S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ | |
62 | S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ | |
63 | S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ | |
64 | S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ | |
65 | S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ | |
66 | ||
67 | #ifdef __STDC__ | |
68 | double __kernel_sin(double x, double y, int iy) | |
69 | #else | |
70 | double __kernel_sin(x, y, iy) | |
71 | double x,y; int iy; /* iy=0 if y is zero */ | |
72 | #endif | |
73 | { | |
74 | double z,r,v; | |
75 | int ix; | |
76 | ix = (*(n0+(int*)&x))&0x7fffffff; /* high word of x */ | |
77 | if(ix<0x3e400000) /* |x| < 2**-27 */ | |
78 | {if((int)x==0) return x;} /* generate inexact */ | |
79 | z = x*x; | |
80 | v = z*x; | |
81 | r = S2+z*(S3+z*(S4+z*(S5+z*S6))); | |
82 | if(iy==0) return x+v*(S1+z*r); | |
83 | else return x-((z*(half*y-v*r)-y)-v*S1); | |
84 | } |