| 1 |
207 |
jeremybenn |
|
| 2 |
|
|
/* @(#)k_sin.c 5.1 93/09/24 */
|
| 3 |
|
|
/*
|
| 4 |
|
|
* ====================================================
|
| 5 |
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
| 6 |
|
|
*
|
| 7 |
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
| 8 |
|
|
* Permission to use, copy, modify, and distribute this
|
| 9 |
|
|
* software is freely granted, provided that this notice
|
| 10 |
|
|
* is preserved.
|
| 11 |
|
|
* ====================================================
|
| 12 |
|
|
*/
|
| 13 |
|
|
|
| 14 |
|
|
/* __kernel_sin( x, y, iy)
|
| 15 |
|
|
* kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
|
| 16 |
|
|
* Input x is assumed to be bounded by ~pi/4 in magnitude.
|
| 17 |
|
|
* Input y is the tail of x.
|
| 18 |
|
|
* Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
|
| 19 |
|
|
*
|
| 20 |
|
|
* Algorithm
|
| 21 |
|
|
* 1. Since sin(-x) = -sin(x), we need only to consider positive x.
|
| 22 |
|
|
* 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
|
| 23 |
|
|
* 3. sin(x) is approximated by a polynomial of degree 13 on
|
| 24 |
|
|
* [0,pi/4]
|
| 25 |
|
|
* 3 13
|
| 26 |
|
|
* sin(x) ~ x + S1*x + ... + S6*x
|
| 27 |
|
|
* where
|
| 28 |
|
|
*
|
| 29 |
|
|
* |sin(x) 2 4 6 8 10 12 | -58
|
| 30 |
|
|
* |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
|
| 31 |
|
|
* | x |
|
| 32 |
|
|
*
|
| 33 |
|
|
* 4. sin(x+y) = sin(x) + sin'(x')*y
|
| 34 |
|
|
* ~ sin(x) + (1-x*x/2)*y
|
| 35 |
|
|
* For better accuracy, let
|
| 36 |
|
|
* 3 2 2 2 2
|
| 37 |
|
|
* r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
|
| 38 |
|
|
* then 3 2
|
| 39 |
|
|
* sin(x) = x + (S1*x + (x *(r-y/2)+y))
|
| 40 |
|
|
*/
|
| 41 |
|
|
|
| 42 |
|
|
#include "fdlibm.h"
|
| 43 |
|
|
|
| 44 |
|
|
#ifndef _DOUBLE_IS_32BITS
|
| 45 |
|
|
|
| 46 |
|
|
#ifdef __STDC__
|
| 47 |
|
|
static const double
|
| 48 |
|
|
#else
|
| 49 |
|
|
static double
|
| 50 |
|
|
#endif
|
| 51 |
|
|
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
| 52 |
|
|
S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
|
| 53 |
|
|
S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
|
| 54 |
|
|
S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
|
| 55 |
|
|
S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
|
| 56 |
|
|
S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
|
| 57 |
|
|
S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
|
| 58 |
|
|
|
| 59 |
|
|
#ifdef __STDC__
|
| 60 |
|
|
double __kernel_sin(double x, double y, int iy)
|
| 61 |
|
|
#else
|
| 62 |
|
|
double __kernel_sin(x, y, iy)
|
| 63 |
|
|
double x,y; int iy; /* iy=0 if y is zero */
|
| 64 |
|
|
#endif
|
| 65 |
|
|
{
|
| 66 |
|
|
double z,r,v;
|
| 67 |
|
|
__int32_t ix;
|
| 68 |
|
|
GET_HIGH_WORD(ix,x);
|
| 69 |
|
|
ix &= 0x7fffffff; /* high word of x */
|
| 70 |
|
|
if(ix<0x3e400000) /* |x| < 2**-27 */
|
| 71 |
|
|
{if((int)x==0) return x;} /* generate inexact */
|
| 72 |
|
|
z = x*x;
|
| 73 |
|
|
v = z*x;
|
| 74 |
|
|
r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
|
| 75 |
|
|
if(iy==0) return x+v*(S1+z*r);
|
| 76 |
|
|
else return x-((z*(half*y-v*r)-y)-v*S1);
|
| 77 |
|
|
}
|
| 78 |
|
|
|
| 79 |
|
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
