Quelle e_acosh.cpp Sprache: unbekannt

/* @(#)e_acosh.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_acosh(x)
* Method :
* Based on
* acosh(x) = log [ x + sqrt(x*x-1) ]
* we have
* acosh(x) := log(x)+ln2, if x is large; else
* acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
*
* Special cases:
* acosh(x) is NaN with signal if x<1.
* acosh(NaN) is NaN without signal.
*/

#include <cmath>
#include <float.h>

#include "math_private.h"

static const double
one = 1.0,
ln2 = 6.93147180559945286227e-01;  /* 0x3FE62E42, 0xFEFA39EF */

double
__ieee754_acosh(double x)
{
double t;
int32_t hx;
u_int32_t lx;
EXTRACT_WORDS(hx,lx,x);
if(hx<0x3ff00000) {  /* x < 1 */
     return (x-x)/(x-x);
} else if(hx >=0x41b00000) { /* x > 2**28 */
     if(hx >=0x7ff00000) { /* x is inf of NaN */
         return x+x;
     } else
  return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */
} else if(((hx-0x3ff00000)|lx)==0) {
     return 0.0;   /* acosh(1) = 0 */
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
     t=x*x;
     return __ieee754_log(2.0*x-one/(x+std::sqrt(t-one)));
} else {   /* 1<x<2 */
     t = x-one;
     return log1p(t+std::sqrt(2.0*t+t*t));
}
}

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Quelle e_acosh.cpp Sprache: unbekannt

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