# sin_freeBSD.c   [plain text]

/* @(#)s_sin.c 5.1 93/09/24 */
/*
* ====================================================
*
* 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.
* ====================================================
*/

#ifndef lint
static char rcsid[] = "\$FreeBSD: src/lib/msun/src/s_sin.c,v 1.9 2003/07/23 04:53:47 peter Exp \$";
#endif

/* sin(x)
* Return sine function of x.
*
* kernel function:
*	__kernel_sin		... sine function on [-pi/4,pi/4]
*	__kernel_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 "math.h"
#include "math_private.h"

int32_t rem_pio2(double x, double *y);

double
sin(double x)
{
double y[2],z=0.0;
int32_t n, ix;

/* High word of x. */
GET_HIGH_WORD(ix,x);

/* |x| ~< pi/4 */
ix &= 0x7fffffff;
if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0);

/* sin(Inf or NaN) is NaN */
else if (ix>=0x7ff00000) return x-x;

/* argument reduction needed */
else {
n = rem_pio2(x,y);
switch(n&3) {
case 0: return  __kernel_sin(y[0],y[1],1);
case 1: return  __kernel_cos(y[0],y[1]);
case 2: return -__kernel_sin(y[0],y[1],1);
default:
return -__kernel_cos(y[0],y[1]);
}
}
}