e_sinh.c

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

/* 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.
 */

#include "math.h"
#include "math_private.h"

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

double
sinh(double x)
{   
    double t,w,h;
    int32_t ix,jx;
    u_int32_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*exp(fabs(x));

    /* |x| in [log(maxdouble), overflowthresold] */
    GET_LOW_WORD(lx,x);
    if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) {
        w = exp(0.5*fabs(x));
        t = h*w;
        return t*w;
    }

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