Quelle e_cosh.cpp Sprache: C

/* @(#)e_cosh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

//#include <sys/cdefs.h>
//__FBSDID("$FreeBSD$");

/* __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 <float.h>

#include "math_private.h"

static const double one = 1.0, half=0.5, huge = 1.0e300;

double
__ieee754_cosh(double x)
{
double t,w;
int32_t ix;

    /* 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(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] */
if (ix<=0x408633CE)
     return __ldexp_exp(fabs(x), -1);

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

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