libm/upstream-freebsd/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:
 *	__kernel_sin		... sine function on [-pi/4,pi/4]
 *	__kernel_cos		... cose function on [-pi/4,pi/4]
 *	__ieee754_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 <float.h>

#include "math.h"
#define INLINE_REM_PIO2
#include "math_private.h"
#include "e_rem_pio2.c"

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) {
	    if(ix<0x3e500000)			/* |x| < 2**-26 */
	       {if((int)x==0) return x;}	/* generate inexact */
	    return __kernel_sin(x,z,0);
	}

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

    /* argument reduction needed */
	else {
	    n = __ieee754_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]);
	    }
	}
}

#if (LDBL_MANT_DIG == 53)
__weak_reference(sin, sinl);
#endif