e_sinh.c

/*
 *                               POK header
 * 
 * The following file is a part of the POK project. Any modification should
 * made according to the POK licence. You CANNOT use this file or a part of
 * this file is this part of a file for your own project
 *
 * For more information on the POK licence, please see our LICENCE FILE
 *
 * Please follow the coding guidelines described in doc/CODING_GUIDELINES
 *
 *                                      Copyright (c) 2007-2009 POK team 
 *
 * Created by julien on Fri Jan 30 14:41:34 2009 
 */

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

/* __ieee754_sinh(x)
 * Method :
 * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
 *      1. Replace x by |x| (sinh(-x) = -sinh(x)).
 *      2.
 *                                                  E + E/(E+1)
 *          0        <= x <= 22     :  sinh(x) := --------------, E=expm1(x)
 *                                                      2
 *
 *          22       <= x <= lnovft :  sinh(x) := exp(x)/2
 *          lnovft   <= x <= ln2ovft:  sinh(x) := exp(x/2)/2 * exp(x/2)
 *          ln2ovft  <  x           :  sinh(x) := x*shuge (overflow)
 *
 * Special cases:
 *      sinh(x) is |x| if x is +INF, -INF, or NaN.
 *      only sinh(0)=0 is exact for finite x.
 */

#ifdef POK_NEEDS_LIBMATH

#include <libm.h>
#include "math_private.h"

static const double one = 1.0, shuge = 1.0e307;

double
__ieee754_sinh(double x)
{
        double t,w,h;
        int32_t ix,jx;
        uint32_t lx;

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

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

        h = 0.5;
        if (jx<0) h = -h;
    /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
        if (ix < 0x40360000) {          /* |x|<22 */
            if (ix<0x3e300000)          /* |x|<2**-28 */
                if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */
            t = expm1(fabs(x));
            if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one));
            return h*(t+t/(t+one));
        }

    /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
        if (ix < 0x40862E42)  return h*__ieee754_exp(fabs(x));

    /* |x| in [log(maxdouble), overflowthresold] */
        GET_LOW_WORD(lx,x);
        if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(uint32_t)0x8fb9f87d))) {
            w = __ieee754_exp(0.5*fabs(x));
            t = h*w;
            return t*w;
        }

    /* |x| > overflowthresold, sinh(x) overflow */
        return x*shuge;
}
#endif