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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
49static const double\r
50half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */\r
51S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */\r
52S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */\r
53S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */\r
54S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */\r
55S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */\r
56S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */\r
57\r
58double\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