/* @(#)s_sin.c 5.1 93/09/24 */
/*
 * ====================================================
 * 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 <math.h>
#include "math_private.h"

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 = __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]);
            }
        }
}