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2aa62f2b | 1 | /* @(#)k_cos.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_cos.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");\r | |
16 | #endif\r | |
17 | \r | |
18 | /*\r | |
19 | * __kernel_cos( x, y )\r | |
20 | * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164\r | |
21 | * Input x is assumed to be bounded by ~pi/4 in magnitude.\r | |
22 | * Input y is the tail of x.\r | |
23 | *\r | |
24 | * Algorithm\r | |
25 | * 1. Since cos(-x) = cos(x), we need only to consider positive x.\r | |
26 | * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.\r | |
27 | * 3. cos(x) is approximated by a polynomial of degree 14 on\r | |
28 | * [0,pi/4]\r | |
29 | * 4 14\r | |
30 | * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x\r | |
31 | * where the remez error is\r | |
32 | *\r | |
33 | * | 2 4 6 8 10 12 14 | -58\r | |
34 | * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2\r | |
35 | * | |\r | |
36 | *\r | |
37 | * 4 6 8 10 12 14\r | |
38 | * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then\r | |
39 | * cos(x) = 1 - x*x/2 + r\r | |
40 | * since cos(x+y) ~ cos(x) - sin(x)*y\r | |
41 | * ~ cos(x) - x*y,\r | |
42 | * a correction term is necessary in cos(x) and hence\r | |
43 | * cos(x+y) = 1 - (x*x/2 - (r - x*y))\r | |
44 | * For better accuracy when x > 0.3, let qx = |x|/4 with\r | |
45 | * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.\r | |
46 | * Then\r | |
47 | * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).\r | |
48 | * Note that 1-qx and (x*x/2-qx) is EXACT here, and the\r | |
49 | * magnitude of the latter is at least a quarter of x*x/2,\r | |
50 | * thus, reducing the rounding error in the subtraction.\r | |
51 | */\r | |
52 | \r | |
53 | #include "math.h"\r | |
54 | #include "math_private.h"\r | |
55 | \r | |
56 | static const double\r | |
57 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */\r | |
58 | C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */\r | |
59 | C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */\r | |
60 | C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */\r | |
61 | C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */\r | |
62 | C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */\r | |
63 | C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */\r | |
64 | \r | |
65 | double\r | |
66 | __kernel_cos(double x, double y)\r | |
67 | {\r | |
68 | double a,hz,z,r,qx;\r | |
69 | int32_t ix;\r | |
70 | GET_HIGH_WORD(ix,x);\r | |
71 | ix &= 0x7fffffff; /* ix = |x|'s high word*/\r | |
72 | if(ix<0x3e400000) { /* if x < 2**27 */\r | |
73 | if(((int)x)==0) return one; /* generate inexact */\r | |
74 | }\r | |
75 | z = x*x;\r | |
76 | r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));\r | |
77 | if(ix < 0x3FD33333) /* if |x| < 0.3 */\r | |
78 | return one - (0.5*z - (z*r - x*y));\r | |
79 | else {\r | |
80 | if(ix > 0x3fe90000) { /* x > 0.78125 */\r | |
81 | qx = 0.28125;\r | |
82 | } else {\r | |
83 | INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */\r | |
84 | }\r | |
85 | hz = 0.5*z-qx;\r | |
86 | a = one-qx;\r | |
87 | return a - (hz - (z*r-x*y));\r | |
88 | }\r | |
89 | }\r |