|
|
/* @(#)e_acosh.c 5.1 93/09/24 */
|
/* @(#)e_acosh.c 5.1 93/09/24 */
|
|
|
/*
|
/*
|
FUNCTION
|
FUNCTION
|
<<acosh>>, <<acoshf>>---inverse hyperbolic cosine
|
<<acosh>>, <<acoshf>>---inverse hyperbolic cosine
|
|
|
INDEX
|
INDEX
|
acosh
|
acosh
|
INDEX
|
INDEX
|
acoshf
|
acoshf
|
|
|
ANSI_SYNOPSIS
|
ANSI_SYNOPSIS
|
#include <math.h>
|
#include <math.h>
|
double acosh(double <[x]>);
|
double acosh(double <[x]>);
|
float acoshf(float <[x]>);
|
float acoshf(float <[x]>);
|
|
|
TRAD_SYNOPSIS
|
TRAD_SYNOPSIS
|
#include <math.h>
|
#include <math.h>
|
double acosh(<[x]>)
|
double acosh(<[x]>)
|
double <[x]>;
|
double <[x]>;
|
|
|
float acoshf(<[x]>)
|
float acoshf(<[x]>)
|
float <[x]>;
|
float <[x]>;
|
|
|
DESCRIPTION
|
DESCRIPTION
|
<<acosh>> calculates the inverse hyperbolic cosine of <[x]>.
|
<<acosh>> calculates the inverse hyperbolic cosine of <[x]>.
|
<<acosh>> is defined as
|
<<acosh>> is defined as
|
@ifnottex
|
@ifnottex
|
. log(<[x]> + sqrt(<[x]>*<[x]>-1))
|
. log(<[x]> + sqrt(<[x]>*<[x]>-1))
|
@end ifnottex
|
@end ifnottex
|
@tex
|
@tex
|
$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$
|
$$ln\Bigl(x + \sqrt{x^2-1}\Bigr)$$
|
@end tex
|
@end tex
|
|
|
<[x]> must be a number greater than or equal to 1.
|
<[x]> must be a number greater than or equal to 1.
|
|
|
<<acoshf>> is identical, other than taking and returning floats.
|
<<acoshf>> is identical, other than taking and returning floats.
|
|
|
RETURNS
|
RETURNS
|
<<acosh>> and <<acoshf>> return the calculated value. If <[x]>
|
<<acosh>> and <<acoshf>> return the calculated value. If <[x]>
|
less than 1, the return value is NaN and <<errno>> is set to <<EDOM>>.
|
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
|
You can change the error-handling behavior with the non-ANSI
|
<<matherr>> function.
|
<<matherr>> function.
|
|
|
PORTABILITY
|
PORTABILITY
|
Neither <<acosh>> nor <<acoshf>> are ANSI C. They are not recommended
|
Neither <<acosh>> nor <<acoshf>> are ANSI C. They are not recommended
|
for portable programs.
|
for portable programs.
|
|
|
|
|
QUICKREF ANSI SVID POSIX RENTRANT
|
QUICKREF ANSI SVID POSIX RENTRANT
|
acos n,n,n,m
|
acos n,n,n,m
|
acosf n,n,n,m
|
acosf n,n,n,m
|
|
|
MATHREF
|
MATHREF
|
acosh, NAN, arg,DOMAIN,EDOM
|
acosh, NAN, arg,DOMAIN,EDOM
|
acosh, < 1.0, NAN,DOMAIN,EDOM
|
acosh, < 1.0, NAN,DOMAIN,EDOM
|
acosh, >=1.0, acosh(arg),,,
|
acosh, >=1.0, acosh(arg),,,
|
|
|
MATHREF
|
MATHREF
|
acoshf, NAN, arg,DOMAIN,EDOM
|
acoshf, NAN, arg,DOMAIN,EDOM
|
acoshf, < 1.0, NAN,DOMAIN,EDOM
|
acoshf, < 1.0, NAN,DOMAIN,EDOM
|
acoshf, >=1.0, acosh(arg),,,
|
acoshf, >=1.0, acosh(arg),,,
|
|
|
*/
|
*/
|
|
|
/*
|
/*
|
* ====================================================
|
* ====================================================
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
*
|
*
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
* Permission to use, copy, modify, and distribute this
|
* Permission to use, copy, modify, and distribute this
|
* software is freely granted, provided that this notice
|
* software is freely granted, provided that this notice
|
* is preserved.
|
* is preserved.
|
* ====================================================
|
* ====================================================
|
*
|
*
|
*/
|
*/
|
|
|
/* acosh(x)
|
/* acosh(x)
|
* Method :
|
* Method :
|
* Based on
|
* Based on
|
* acosh(x) = log [ x + sqrt(x*x-1) ]
|
* acosh(x) = log [ x + sqrt(x*x-1) ]
|
* we have
|
* we have
|
* acosh(x) := log(x)+ln2, if x is large; else
|
* 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) := 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.
|
* acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1.
|
*
|
*
|
* Special cases:
|
* Special cases:
|
* acosh(x) is NaN with signal if x<1.
|
* acosh(x) is NaN with signal if x<1.
|
* acosh(NaN) is NaN without signal.
|
* acosh(NaN) is NaN without signal.
|
*/
|
*/
|
|
|
#include "fdlibm.h"
|
#include "fdlibm.h"
|
|
|
#ifndef _DOUBLE_IS_32BITS
|
#ifndef _DOUBLE_IS_32BITS
|
|
|
#ifdef __STDC__
|
#ifdef __STDC__
|
static const double
|
static const double
|
#else
|
#else
|
static double
|
static double
|
#endif
|
#endif
|
one = 1.0,
|
one = 1.0,
|
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
|
ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
|
|
|
#ifdef __STDC__
|
#ifdef __STDC__
|
double acosh(double x)
|
double acosh(double x)
|
#else
|
#else
|
double acosh(x)
|
double acosh(x)
|
double x;
|
double x;
|
#endif
|
#endif
|
{
|
{
|
double t;
|
double t;
|
__int32_t hx;
|
__int32_t hx;
|
__uint32_t lx;
|
__uint32_t lx;
|
EXTRACT_WORDS(hx,lx,x);
|
EXTRACT_WORDS(hx,lx,x);
|
if(hx<0x3ff00000) { /* x < 1 */
|
if(hx<0x3ff00000) { /* x < 1 */
|
return (x-x)/(x-x);
|
return (x-x)/(x-x);
|
} else if(hx >=0x41b00000) { /* x > 2**28 */
|
} else if(hx >=0x41b00000) { /* x > 2**28 */
|
if(hx >=0x7ff00000) { /* x is inf of NaN */
|
if(hx >=0x7ff00000) { /* x is inf of NaN */
|
return x+x;
|
return x+x;
|
} else
|
} else
|
return log(x)+ln2; /* acosh(huge)=log(2x) */
|
return log(x)+ln2; /* acosh(huge)=log(2x) */
|
} else if(((hx-0x3ff00000)|lx)==0) {
|
} else if(((hx-0x3ff00000)|lx)==0) {
|
return 0.0; /* acosh(1) = 0 */
|
return 0.0; /* acosh(1) = 0 */
|
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
|
} else if (hx > 0x40000000) { /* 2**28 > x > 2 */
|
t=x*x;
|
t=x*x;
|
return log(2.0*x-one/(x+sqrt(t-one)));
|
return log(2.0*x-one/(x+sqrt(t-one)));
|
} else { /* 1<x<2 */
|
} else { /* 1<x<2 */
|
t = x-one;
|
t = x-one;
|
return log1p(t+sqrt(2.0*t+t*t));
|
return log1p(t+sqrt(2.0*t+t*t));
|
}
|
}
|
}
|
}
|
|
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|
|
|
