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.
 * ====================================================
 */

/* 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 <sys/cdefs.h>
#include <float.h>
#include <math.h>

#include "math_private.h"

double
tan(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_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 */
    }
}

#if LDBL_MANT_DIG == 53
#ifdef __weak_alias
__weak_alias(tanl, tan);
#endif /* __weak_alias */
#endif /* LDBL_MANT_DIG == 53 */