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
56static const double
57one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
58C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
59C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
60C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
61C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
62C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
63C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
64
65double
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