s_tan.c

/* @(#)s_tan.c 1.3 95/01/18 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

/* tan(x)
 * Return tangent function of x.
 *
 * kernel function:
 *      __kernel_tan            ... tangent 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 "fdlibm.h"

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

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

    /* |x| ~< pi/4 */
        ix &= 0x7fffffff;
        if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);

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

    /* argument reduction needed */
        else {
            n = __ieee754_rem_pio2(x,y);
            return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /*   1 -- n even
                                                        -1 -- n odd */
        }
}