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/* @(#)e_acosh.c 5.1 93/09/24 */
/*
FUNCTION
<<acosh>>, <<acoshf>>---inverse hyperbolic cosine
INDEX
acosh
INDEX
acoshf
ANSI_SYNOPSIS
#include <math.h>
double acosh(double <[x]>);
float acoshf(float <[x]>);
TRAD_SYNOPSIS
#include <math.h>
double acosh(<[x]>)
double <[x]>;
float acoshf(<[x]>)
float <[x]>;
DESCRIPTION
<<acosh>> calculates the inverse hyperbolic cosine of <[x]>.
<<acosh>> is defined as
@ifinfo
. log(<[x]> + sqrt(<[x]>*<[x]>-1))
@end ifinfo
@tex
$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$
@end tex
<[x]> must be a number greater than or equal to 1.
<<acoshf>> is identical, other than taking and returning floats.
RETURNS
<<acosh>> and <<acoshf>> return the calculated value. If <[x]>
less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>.
You can change the error-handling behavior with the non-ANSI
<<matherr>> function.
PORTABILITY
Neither <<acosh>> nor <<acoshf>> are ANSI C. They are not recommended
for portable programs.
QUICKREF ANSI SVID POSIX RENTRANT
acos n,n,n,m
acosf n,n,n,m
MATHREF
acosh, NAN, arg,DOMAIN,EDOM
acosh, < 1.0, NAN,DOMAIN,EDOM
acosh, >=1.0, acosh(arg),,,
MATHREF
acoshf, NAN, arg,DOMAIN,EDOM
acoshf, < 1.0, NAN,DOMAIN,EDOM
acoshf, >=1.0, acosh(arg),,,
*/
/*
* ====================================================
* 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.
* ====================================================
*
*/
/* 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 "fdlibm.h"
#ifndef _DOUBLE_IS_32BITS
#ifdef __STDC__
static const double
#else
static double
#endif
one = 1.0,
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
#ifdef __STDC__
double acosh(double x)
#else
double acosh(x)
double x;
#endif
{
double t;
__int32_t hx;
__uint32_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 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 log(2.0*x-one/(x+sqrt(t-one)));
} else { /* 1<x<2 */
t = x-one;
return log1p(t+sqrt(2.0*t+t*t));
}
}
#endif /* defined(_DOUBLE_IS_32BITS) */
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