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k_sin.c
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1 /* @(#)k_sin.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
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 }
GET_HIGH_WORD
#define GET_HIGH_WORD(i, d)
Definition: math_private.h:102
S3
static double S3
Definition: k_sin.c:57
x
EGLSurface EGLint x
Definition: eglext.h:293
int32_t
long int32_t
Definition: types.h:9
S1
static double S1
Definition: k_sin.c:55
S4
static double S4
Definition: k_sin.c:58
v
const GLdouble * v
Definition: glew.h:1377
S6
static double S6
Definition: k_sin.c:60
math_libm.h
y
EGLSurface EGLint EGLint y
Definition: eglext.h:293
attribute_hidden
double attribute_hidden
ix
int32_t ix
Definition: e_rem_pio2.c:100
half
static double half
Definition: k_sin.c:54
S5
static double S5
Definition: k_sin.c:59
r
GLdouble GLdouble GLdouble r
Definition: glew.h:1392
z
GLint GLint GLint GLint z
Definition: gl2ext.h:1214
iy
int iy
Definition: k_sin.c:69
__kernel_sin
double __kernel_sin(double, double, int) attribute_hidden
S2
static double S2
Definition: k_sin.c:56
math_private.h