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

/* cosh(x)
 * Method :
 * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
 *	1. Replace x by |x| (cosh(x) = cosh(-x)).
 *	2.
 *		                                        [ exp(x) - 1 ]^2
 *	    0        <= x <= ln2/2  :  cosh(x) := 1 + -------------------
 *			       			           2*exp(x)
 *
 *		                                  exp(x) +  1/exp(x)
 *	    ln2/2    <= x <= 22     :  cosh(x) := -------------------
 *			       			          2
 *	    22       <= x <= lnovft :  cosh(x) := exp(x)/2
 *	    lnovft   <= x <= ln2ovft:  cosh(x) := exp(x/2)/2 * exp(x/2)
 *	    ln2ovft  <  x	    :  cosh(x) := overflow
 *
 * Special cases:
 *	cosh(x) is |x| if x is +INF, -INF, or NaN.
 *	only cosh(0)=1 is exact for finite x.
 */

#include "fdlibm.h"

#ifdef _NEED_FLOAT64

static const __float64 one = _F_64(1.0), half = _F_64(0.5);

__float64
cosh64(__float64 x)
{
    __float64 t, w;
    __int32_t ix;
    __uint32_t lx;

    x = fabs64(x);

    /* High word of |x|. */
    GET_HIGH_WORD(ix, x);
    ix &= 0x7fffffff;

    /* x is INF or NaN */
    if (ix >= 0x7ff00000)
        return x + x;

    /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
    if (ix < 0x3fd62e43) {
        t = expm1(x);
        w = one + t;
        if (ix < 0x3c800000)
            return w; /* cosh(tiny) = 1 */
        return one + (t * t) / (w + w);
    }

    /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
    if (ix < 0x40360000) {
        t = exp(x);
        return half * t + half / t;
    }

    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
    if (ix < 0x40862E42)
        return half * exp(x);

    /* |x| in [log(maxdouble), overflowthresold] */
    GET_LOW_WORD(lx, x);
    if (ix < 0x408633CE || (ix == 0x408633ce && lx <= (__uint32_t)0x8fb9f87d)) {
        w = exp(half * x);
        t = half * w;
        return t * w;
    }

    /* |x| > overflowthresold, cosh(x) overflow */
    return __math_oflow(0);
}

_MATH_ALIAS_d_d(cosh)

#endif /* _NEED_FLOAT64 */
