SDL  2.0
k_cos.c
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1 /*
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunPro, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 /*
13  * __kernel_cos( x, y )
14  * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
15  * Input x is assumed to be bounded by ~pi/4 in magnitude.
16  * Input y is the tail of x.
17  *
18  * Algorithm
19  * 1. Since cos(-x) = cos(x), we need only to consider positive x.
20  * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
21  * 3. cos(x) is approximated by a polynomial of degree 14 on
22  * [0,pi/4]
23  * 4 14
24  * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
25  * where the remez error is
26  *
27  * | 2 4 6 8 10 12 14 | -58
28  * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2
29  * | |
30  *
31  * 4 6 8 10 12 14
32  * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then
33  * cos(x) = 1 - x*x/2 + r
34  * since cos(x+y) ~ cos(x) - sin(x)*y
35  * ~ cos(x) - x*y,
36  * a correction term is necessary in cos(x) and hence
37  * cos(x+y) = 1 - (x*x/2 - (r - x*y))
38  * For better accuracy when x > 0.3, let qx = |x|/4 with
39  * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
40  * Then
41  * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
42  * Note that 1-qx and (x*x/2-qx) is EXACT here, and the
43  * magnitude of the latter is at least a quarter of x*x/2,
44  * thus, reducing the rounding error in the subtraction.
45  */
46 
47 #include "math_libm.h"
48 #include "math_private.h"
49 
50 static const double
51 one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
52 C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
53 C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
54 C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
55 C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
56 C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
57 C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
58 
59 double attribute_hidden __kernel_cos(double x, double y)
60 {
61  double a,hz,z,r,qx;
62  int32_t ix;
63  GET_HIGH_WORD(ix,x);
64  ix &= 0x7fffffff; /* ix = |x|'s high word*/
65  if(ix<0x3e400000) { /* if x < 2**27 */
66  if(((int)x)==0) return one; /* generate inexact */
67  }
68  z = x*x;
69  r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
70  if(ix < 0x3FD33333) /* if |x| < 0.3 */
71  return one - (0.5*z - (z*r - x*y));
72  else {
73  if(ix > 0x3fe90000) { /* x > 0.78125 */
74  qx = 0.28125;
75  } else {
76  INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */
77  }
78  hz = 0.5*z-qx;
79  a = one-qx;
80  return a - (hz - (z*r-x*y));
81  }
82 }
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:108
GLdouble GLdouble GLdouble r
Definition: SDL_opengl.h:2079
GLdouble GLdouble z
static const double C5
Definition: k_cos.c:56
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1574
signed int int32_t
static const double C1
Definition: k_cos.c:52
#define attribute_hidden
Definition: math_private.h:25
static const double C2
Definition: k_cos.c:53
static const double C4
Definition: k_cos.c:55
static const double C6
Definition: k_cos.c:57
#define INSERT_WORDS(d, ix0, ix1)
Definition: math_private.h:126
static const double C3
Definition: k_cos.c:54
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1574
static const double one
Definition: k_cos.c:51
GLboolean GLboolean GLboolean GLboolean a
double attribute_hidden __kernel_cos(double x, double y)
Definition: k_cos.c:59