e_cosh.c

/*
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 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
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/* __ieee754_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) := huge*huge (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 __STDC__
static const double one = 1.0, half=0.5, huge = 1.0e300;
#else
static double one = 1.0, half=0.5, huge = 1.0e300;
#endif

#ifdef __STDC__
        double __ieee754_cosh(double x)
#else
        double __ieee754_cosh(x)
        double x;
#endif
{
        double t,w;
        int ix;
        unsigned lx;

    /* High word of |x|. */
        ix = __HI(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(fabs(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 = __ieee754_exp(fabs(x));
                return half*t+half/t;
        }

    /* |x| in [22, log(maxdouble)] return half*exp(|x|) */
        if (ix < 0x40862E42)  return half*__ieee754_exp(fabs(x));

    /* |x| in [log(maxdouble), overflowthresold] */
        lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
        if (ix<0x408633CE ||
              ((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
            w = __ieee754_exp(half*fabs(x));
            t = half*w;
            return t*w;
        }

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