zenilib  0.5.3.0
k_cos.c
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1 /* @(#)k_cos.c 5.1 93/09/24 */
2 /*
3  * ====================================================
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 #if defined(LIBM_SCCS) && !defined(lint)
14 static const char rcsid[] =
15  "\$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc 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_libm.h"
54 #include "math_private.h"
55
56 #ifdef __STDC__
57 static const double
58 #else
59 static double
60 #endif
61  one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
62  C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
63  C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
64  C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
65  C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
66  C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
67  C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
68
69 #ifdef __STDC__
70 double attribute_hidden
71 __kernel_cos(double x, double y)
72 #else
73 double attribute_hidden
74 __kernel_cos(x, y)
75  double x, y;
76 #endif
77 {
78  double a, hz, z, r, qx;
79  int32_t ix;
80  GET_HIGH_WORD(ix, x);
81  ix &= 0x7fffffff; /* ix = |x|'s high word */
82  if (ix < 0x3e400000) { /* if x < 2**27 */
83  if (((int) x) == 0)
84  return one; /* generate inexact */
85  }
86  z = x * x;
87  r = z * (C1 + z * (C2 + z * (C3 + z * (C4 + z * (C5 + z * C6)))));
88  if (ix < 0x3FD33333) /* if |x| < 0.3 */
89  return one - (0.5 * z - (z * r - x * y));
90  else {
91  if (ix > 0x3fe90000) { /* x > 0.78125 */
92  qx = 0.28125;
93  } else {
94  INSERT_WORDS(qx, ix - 0x00200000, 0); /* x/4 */
95  }
96  hz = 0.5 * z - qx;
97  a = one - qx;
98  return a - (hz - (z * r - x * y));
99  }
100 }
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:102
EGLSurface EGLint x
Definition: eglext.h:293
static double one
Definition: k_cos.c:61
GLboolean GLboolean GLboolean GLboolean a
Definition: glew.h:8736
long int32_t
Definition: types.h:9
static double C2
Definition: k_cos.c:63
static double C5
Definition: k_cos.c:66
double __kernel_cos(double, double) attribute_hidden
static double C4
Definition: k_cos.c:65
static double C3
Definition: k_cos.c:64
EGLSurface EGLint EGLint y
Definition: eglext.h:293
static double C6
Definition: k_cos.c:67
double attribute_hidden
int32_t ix
Definition: e_rem_pio2.c:100
static double C1
Definition: k_cos.c:62
GLdouble GLdouble GLdouble r
Definition: glew.h:1392
GLint GLint GLint GLint z
Definition: gl2ext.h:1214
INSERT_WORDS(z, ix0, ix1)