SDL  2.0
k_sin.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 /* __kernel_sin( x, y, iy)
13  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
14  * Input x is assumed to be bounded by ~pi/4 in magnitude.
15  * Input y is the tail of x.
16  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
17  *
18  * Algorithm
19  * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
20  * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
21  * 3. sin(x) is approximated by a polynomial of degree 13 on
22  * [0,pi/4]
23  * 3 13
24  * sin(x) ~ x + S1*x + ... + S6*x
25  * where
26  *
27  * |sin(x) 2 4 6 8 10 12 | -58
28  * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
29  * | x |
30  *
31  * 4. sin(x+y) = sin(x) + sin'(x')*y
32  * ~ sin(x) + (1-x*x/2)*y
33  * For better accuracy, let
34  * 3 2 2 2 2
35  * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
36  * then 3 2
37  * sin(x) = x + (S1*x + (x *(r-y/2)+y))
38  */
39 
40 #include "math_libm.h"
41 #include "math_private.h"
42 
43 static const double
44 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
45 S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
46 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
47 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
48 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
49 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
50 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
51 
52 double attribute_hidden __kernel_sin(double x, double y, int iy)
53 {
54  double z,r,v;
55  int32_t ix;
56  GET_HIGH_WORD(ix,x);
57  ix &= 0x7fffffff; /* high word of x */
58  if(ix<0x3e400000) /* |x| < 2**-27 */
59  {if((int)x==0) return x;} /* generate inexact */
60  z = x*x;
61  v = z*x;
62  r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
63  if(iy==0) return x+v*(S1+z*r);
64  else return x-((z*(half*y-v*r)-y)-v*S1);
65 }
#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 S3
Definition: k_sin.c:47
const GLdouble * v
Definition: SDL_opengl.h:2064
GLint GLint GLint GLint GLint x
Definition: SDL_opengl.h:1574
signed int int32_t
#define attribute_hidden
Definition: math_private.h:25
static const double S6
Definition: k_sin.c:50
static const double S4
Definition: k_sin.c:48
static const double half
Definition: k_sin.c:44
GLint GLint GLint GLint GLint GLint y
Definition: SDL_opengl.h:1574
double attribute_hidden __kernel_sin(double x, double y, int iy)
Definition: k_sin.c:52
static const double S2
Definition: k_sin.c:46
static const double S1
Definition: k_sin.c:45
static const double S5
Definition: k_sin.c:49