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/* acosh.c
*
* Inverse hyperbolic cosine
*
*
*
* SYNOPSIS:
*
* double x, y, acosh();
*
* y = acosh( x );
*
*
*
* DESCRIPTION:
*
* Returns inverse hyperbolic cosine of argument.
*
* If 1 <= x < 1.5, a rational approximation
*
* sqrt(z) * P(z)/Q(z)
*
* where z = x-1, is used. Otherwise,
*
* acosh(x) = log( x + sqrt( (x-1)(x+1) ).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* DEC 1,3 30000 4.2e-17 1.1e-17
* IEEE 1,3 30000 4.6e-16 8.7e-17
*
*
* ERROR MESSAGES:
*
* message condition value returned
* acosh domain |x| < 1 NAN
*
*/
/* acosh.c */
/*
Cephes Math Library Release 2.3: March, 1995
Copyright 1984, 1995 by Stephen L. Moshier
*/
/* acosh(z) = sqrt(x) * R(x), z = x + 1, interval 0 < x < 0.5 */
#include "mconf.h"
static double P[] = {
1.18801130533544501356E2,
3.94726656571334401102E3,
3.43989375926195455866E4,
1.08102874834699867335E5,
1.10855947270161294369E5
};
static double Q[] = {
/* 1.00000000000000000000E0,*/
1.86145380837903397292E2,
4.15352677227719831579E3,
2.97683430363289370382E4,
8.29725251988426222434E4,
7.83869920495893927727E4
};
#ifndef ANSIPROT
double log(), sqrt(), polevl(), p1evl();
#endif
extern double LOGE2;
double acosh(x)
double x;
{
double a, z;
if( x < 1.0 )
{
mtherr( "acosh", DOMAIN );
return(quiet_nan());
}
if( x > 1.0e8 )
{
if( !finite(x) )
return(x);
return( log(x) + LOGE2 );
}
z = x - 1.0;
if( z < 0.5 )
{
a = sqrt(z) * (polevl(z, P, 4) / p1evl(z, Q, 5) );
return( a );
}
a = sqrt( z*(x+1.0) );
return( log(x + a) );
}
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