base/math/s_tan.c

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/* @(#)s_tan.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.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: s_tan.c,v 1.7 1995/05/10 20:48:18 jtc Exp $";
#endif

/* 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 "math.h"
#include "mathP.h"

#ifdef __STDC__
    double tan(double x)
#else
    double tan(x)
    double x;
#endif
{
    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_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 */
    }
}

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