1 /* @(#)k_cos.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 #include <LibConfig.h>
13 #include <sys/EfiCdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: k_cos.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");
16 #endif
17
18 /*
19 * __kernel_cos( x, y )
20 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
21 * Input x is assumed to be bounded by ~pi/4 in magnitude.
22 * Input y is the tail of x.
23 *
24 * Algorithm
25 * 1. Since cos(-x) = cos(x), we need only to consider positive x.
26 * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
27 * 3. cos(x) is approximated by a polynomial of degree 14 on
28 * [0,pi/4]
29 * 4 14
30 * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
31 * where the remez error is
32 *
33 * | 2 4 6 8 10 12 14 | -58
34 * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
35 * | |
36 *
37 * 4 6 8 10 12 14
38 * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
39 * cos(x) = 1 - x*x/2 + r
40 * since cos(x+y) ~ cos(x) - sin(x)*y
41 * ~ cos(x) - x*y,
42 * a correction term is necessary in cos(x) and hence
43 * cos(x+y) = 1 - (x*x/2 - (r - x*y))
44 * For better accuracy when x > 0.3, let qx = |x|/4 with
45 * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
46 * Then
47 * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
48 * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
49 * magnitude of the latter is at least a quarter of x*x/2,
50 * thus, reducing the rounding error in the subtraction.
51 */
52
53 #include "math.h"
54 #include "math_private.h"
55
56 static const double
57 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
58 C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
59 C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
60 C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
61 C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
62 C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
63 C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
64
65 double
__kernel_cos(double x,double y)66 __kernel_cos(double x, double y)
67 {
68 double a,hz,z,r,qx;
69 int32_t ix;
70 GET_HIGH_WORD(ix,x);
71 ix &= 0x7fffffff; /* ix = |x|'s high word*/
72 if(ix<0x3e400000) { /* if x < 2**27 */
73 if(((int)x)==0) return one; /* generate inexact */
74 }
75 z = x*x;
76 r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
77 if(ix < 0x3FD33333) /* if |x| < 0.3 */
78 return one - (0.5*z - (z*r - x*y));
79 else {
80 if(ix > 0x3fe90000) { /* x > 0.78125 */
81 qx = 0.28125;
82 } else {
83 INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
84 }
85 hz = 0.5*z-qx;
86 a = one-qx;
87 return a - (hz - (z*r-x*y));
88 }
89 }
90