zenilib  0.5.3.0
k_sin.c
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1 /* @(#)k_sin.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_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp \$";
16 #endif
17
18 /* __kernel_sin( x, y, iy)
19  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
20  * Input x is assumed to be bounded by ~pi/4 in magnitude.
21  * Input y is the tail of x.
22  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
23  *
24  * Algorithm
25  * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
26  * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
27  * 3. sin(x) is approximated by a polynomial of degree 13 on
28  * [0,pi/4]
29  * 3 13
30  * sin(x) ~ x + S1*x + ... + S6*x
31  * where
32  *
33  * |sin(x) 2 4 6 8 10 12 | -58
34  * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
35  * | x |
36  *
37  * 4. sin(x+y) = sin(x) + sin'(x')*y
38  * ~ sin(x) + (1-x*x/2)*y
39  * For better accuracy, let
40  * 3 2 2 2 2
41  * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
42  * then 3 2
43  * sin(x) = x + (S1*x + (x *(r-y/2)+y))
44  */
45
46 #include "math_libm.h"
47 #include "math_private.h"
48
49 #ifdef __STDC__
50 static const double
51 #else
52 static double
53 #endif
54  half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
55  S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
56  S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
57  S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
58  S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
59  S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
60  S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
61
62 #ifdef __STDC__
63 double attribute_hidden
64 __kernel_sin(double x, double y, int iy)
65 #else
66 double attribute_hidden
67 __kernel_sin(x, y, iy)
68  double x, y;
69  int iy; /* iy=0 if y is zero */
70 #endif
71 {
72  double z, r, v;
73  int32_t ix;
74  GET_HIGH_WORD(ix, x);
75  ix &= 0x7fffffff; /* high word of x */
76  if (ix < 0x3e400000) { /* |x| < 2**-27 */
77  if ((int) x == 0)
78  return x;
79  } /* generate inexact */
80  z = x * x;
81  v = z * x;
82  r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
83  if (iy == 0)
84  return x + v * (S1 + z * r);
85  else
86  return x - ((z * (half * y - v * r) - y) - v * S1);
87 }
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:102
static double S3
Definition: k_sin.c:57
EGLSurface EGLint x
Definition: eglext.h:293
long int32_t
Definition: types.h:9
static double S1
Definition: k_sin.c:55
static double S4
Definition: k_sin.c:58
const GLdouble * v
Definition: glew.h:1377
static double S6
Definition: k_sin.c:60
EGLSurface EGLint EGLint y
Definition: eglext.h:293
double attribute_hidden
int32_t ix
Definition: e_rem_pio2.c:100
static double half
Definition: k_sin.c:54
static double S5
Definition: k_sin.c:59
GLdouble GLdouble GLdouble r
Definition: glew.h:1392
GLint GLint GLint GLint z
Definition: gl2ext.h:1214
int iy
Definition: k_sin.c:69
double __kernel_sin(double, double, int) attribute_hidden
static double S2
Definition: k_sin.c:56