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