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2aa62f2b | 1 | /* @(#)k_sin.c 5.1 93/09/24 */\r |
2 | /*\r | |
3 | * ====================================================\r | |
4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\r | |
5 | *\r | |
6 | * Developed at SunPro, a Sun Microsystems, Inc. business.\r | |
7 | * Permission to use, copy, modify, and distribute this\r | |
8 | * software is freely granted, provided that this notice\r | |
9 | * is preserved.\r | |
10 | * ====================================================\r | |
11 | */\r | |
12 | #include <LibConfig.h>\r | |
13 | #include <sys/EfiCdefs.h>\r | |
14 | #if defined(LIBM_SCCS) && !defined(lint)\r | |
15 | __RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");\r | |
16 | #endif\r | |
17 | \r | |
18 | /* __kernel_sin( x, y, iy)\r | |
19 | * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854\r | |
20 | * Input x is assumed to be bounded by ~pi/4 in magnitude.\r | |
21 | * Input y is the tail of x.\r | |
22 | * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).\r | |
23 | *\r | |
24 | * Algorithm\r | |
25 | * 1. Since sin(-x) = -sin(x), we need only to consider positive x.\r | |
26 | * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.\r | |
27 | * 3. sin(x) is approximated by a polynomial of degree 13 on\r | |
28 | * [0,pi/4]\r | |
29 | * 3 13\r | |
30 | * sin(x) ~ x + S1*x + ... + S6*x\r | |
31 | * where\r | |
32 | *\r | |
33 | * |sin(x) 2 4 6 8 10 12 | -58\r | |
34 | * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2\r | |
35 | * | x |\r | |
36 | *\r | |
37 | * 4. sin(x+y) = sin(x) + sin'(x')*y\r | |
38 | * ~ sin(x) + (1-x*x/2)*y\r | |
39 | * For better accuracy, let\r | |
40 | * 3 2 2 2 2\r | |
41 | * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))\r | |
42 | * then 3 2\r | |
43 | * sin(x) = x + (S1*x + (x *(r-y/2)+y))\r | |
44 | */\r | |
45 | \r | |
46 | #include "math.h"\r | |
47 | #include "math_private.h"\r | |
48 | \r | |
49 | static const double\r | |
50 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */\r | |
51 | S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */\r | |
52 | S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */\r | |
53 | S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */\r | |
54 | S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */\r | |
55 | S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */\r | |
56 | S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */\r | |
57 | \r | |
58 | double\r | |
59 | __kernel_sin(double x, double y, int iy)\r | |
60 | {\r | |
61 | double z,r,v;\r | |
62 | int32_t ix;\r | |
63 | GET_HIGH_WORD(ix,x);\r | |
64 | ix &= 0x7fffffff; /* high word of x */\r | |
65 | if(ix<0x3e400000) /* |x| < 2**-27 */\r | |
66 | {if((int)x==0) return x;} /* generate inexact */\r | |
67 | z = x*x;\r | |
68 | v = z*x;\r | |
69 | r = S2+z*(S3+z*(S4+z*(S5+z*S6)));\r | |
70 | if(iy==0) return x+v*(S1+z*r);\r | |
71 | else return x-((z*(half*y-v*r)-y)-v*S1);\r | |
72 | }\r |