79 lines
2.1 KiB
C
79 lines
2.1 KiB
C
|
/* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
|
||
|
|
/*
|
||
|
|
* ====================================================
|
||
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
||
|
|
*
|
||
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
||
|
|
* Permission to use, copy, modify, and distribute this
|
||
|
|
* software is freely granted, provided that this notice
|
||
|
|
* is preserved.
|
||
|
|
* ====================================================
|
||
|
|
*/
|
||
|
|
/* sin(x)
|
||
|
|
* Return sine function of x.
|
||
|
|
*
|
||
|
|
* kernel function:
|
||
|
|
* __sin ... sine function on [-pi/4,pi/4]
|
||
|
|
* __cos ... cose function on [-pi/4,pi/4]
|
||
|
|
* __rem_pio2 ... argument reduction routine
|
||
|
|
*
|
||
|
|
* Method.
|
||
|
|
* Let S,C and T denote the sin, cos and tan respectively on
|
||
|
|
* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
|
||
|
|
* in [-pi/4 , +pi/4], and let n = k mod 4.
|
||
|
|
* We have
|
||
|
|
*
|
||
|
|
* n sin(x) cos(x) tan(x)
|
||
|
|
* ----------------------------------------------------------
|
||
|
|
* 0 S C T
|
||
|
|
* 1 C -S -1/T
|
||
|
|
* 2 -S -C T
|
||
|
|
* 3 -C S -1/T
|
||
|
|
* ----------------------------------------------------------
|
||
|
|
*
|
||
|
|
* Special cases:
|
||
|
|
* Let trig be any of sin, cos, or tan.
|
||
|
|
* trig(+-INF) is NaN, with signals;
|
||
|
|
* trig(NaN) is that NaN;
|
||
|
|
*
|
||
|
|
* Accuracy:
|
||
|
|
* TRIG(x) returns trig(x) nearly rounded
|
||
|
|
*/
|
||
|
|
|
||
|
|
#include "libm.h"
|
||
|
|
|
||
|
|
double sin(double x)
|
||
|
|
{
|
||
|
|
double y[2];
|
||
|
|
uint32_t ix;
|
||
|
|
unsigned n;
|
||
|
|
|
||
|
|
/* High word of x. */
|
||
|
|
GET_HIGH_WORD(ix, x);
|
||
|
|
ix &= 0x7fffffff;
|
||
|
|
|
||
|
|
/* |x| ~< pi/4 */
|
||
|
|
if (ix <= 0x3fe921fb) {
|
||
|
|
if (ix < 0x3e500000) { /* |x| < 2**-26 */
|
||
|
|
/* raise inexact if x != 0 and underflow if subnormal*/
|
||
|
|
FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
|
||
|
|
return x;
|
||
|
|
}
|
||
|
|
return __sin(x, 0.0, 0);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* sin(Inf or NaN) is NaN */
|
||
|
|
if (ix >= 0x7ff00000)
|
||
|
|
return x - x;
|
||
|
|
|
||
|
|
/* argument reduction needed */
|
||
|
|
n = __rem_pio2(x, y);
|
||
|
|
switch (n&3) {
|
||
|
|
case 0: return __sin(y[0], y[1], 1);
|
||
|
|
case 1: return __cos(y[0], y[1]);
|
||
|
|
case 2: return -__sin(y[0], y[1], 1);
|
||
|
|
default:
|
||
|
|
return -__cos(y[0], y[1]);
|
||
|
|
}
|
||
|
|
}
|