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/* acoshl.c
*
* Inverse hyperbolic cosine, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, acoshl();
*
* y = acoshl( x );
*
*
*
* DESCRIPTION:
*
* Returns inverse hyperbolic cosine of argument.
*
* If 1 <= x < 1.5, a rational approximation
*
* sqrt(2z) * 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
* IEEE 1,3 30000 2.0e-19 3.9e-20
*
*
* ERROR MESSAGES:
*
* message condition value returned
* acoshl domain |x| < 1 0.0
*
*/
/* acosh.c */
/*
Cephes Math Library Release 2.7: May, 1998
Copyright 1984, 1991, 1998 by Stephen L. Moshier
*/
/* acosh(1+x) = sqrt(2x) * R(x), interval 0 < x < 0.5 */
#include <math.h>
#ifdef UNK
static long double P[] = {
2.9071989653343333587238E-5L,
3.2906030801088967279449E-3L,
6.3034445964862182128388E-2L,
4.1587081802731351459504E-1L,
1.0989714347599256302467E0L,
9.9999999999999999999715E-1L,
};
static long double Q[] = {
1.0443462486787584738322E-4L,
6.0085845375571145826908E-3L,
8.7750439986662958343370E-2L,
4.9564621536841869854584E-1L,
1.1823047680932589605190E0L,
1.0000000000000000000028E0L,
};
#endif
#ifdef IBMPC
static unsigned short P[] = {
0x4536,0x4dba,0x9f55,0xf3df,0x3fef, XPD
0x23a5,0xf9aa,0x289c,0xd7a7,0x3ff6, XPD
0x7e8b,0x8645,0x341f,0x8118,0x3ffb, XPD
0x0fd5,0x937f,0x0515,0xd4ed,0x3ffd, XPD
0x2364,0xc41b,0x1891,0x8cab,0x3fff, XPD
0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
};
static short Q[] = {
0x1e7c,0x4f16,0xe98c,0xdb03,0x3ff1, XPD
0xc319,0xc272,0xa90a,0xc4e3,0x3ff7, XPD
0x2f83,0x9e5e,0x80af,0xb3b6,0x3ffb, XPD
0xe1e0,0xc97c,0x573a,0xfdc5,0x3ffd, XPD
0xcdf2,0x6ec5,0xc33c,0x9755,0x3fff, XPD
0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
};
#endif
#ifdef MIEEE
static long P[] = {
0x3fef0000,0xf3df9f55,0x4dba4536,
0x3ff60000,0xd7a7289c,0xf9aa23a5,
0x3ffb0000,0x8118341f,0x86457e8b,
0x3ffd0000,0xd4ed0515,0x937f0fd5,
0x3fff0000,0x8cab1891,0xc41b2364,
0x3fff0000,0x80000000,0x00000000,
};
static long Q[] = {
0x3ff10000,0xdb03e98c,0x4f161e7c,
0x3ff70000,0xc4e3a90a,0xc272c319,
0x3ffb0000,0xb3b680af,0x9e5e2f83,
0x3ffd0000,0xfdc5573a,0xc97ce1e0,
0x3fff0000,0x9755c33c,0x6ec5cdf2,
0x3fff0000,0x80000000,0x00000000,
};
#endif
extern long double LOGE2L;
#ifdef INFINITIES
extern long double INFINITYL;
#endif
#ifdef NANS
extern long double NANL;
#endif
#ifdef ANSIPROT
extern long double logl ( long double );
extern long double sqrtl ( long double );
extern long double polevll ( long double, void *, int );
extern int isnanl ( long double );
#else
long double logl(), sqrtl(), polevll(), isnanl();
#endif
long double acoshl(x)
long double x;
{
long double a, z;
#ifdef NANS
if( isnanl(x) )
return(x);
#endif
if( x < 1.0L )
{
mtherr( "acoshl", DOMAIN );
#ifdef NANS
return(NANL);
#else
return(0.0L);
#endif
}
if( x > 1.0e10 )
{
#ifdef INFINITIES
if( x == INFINITYL )
return( INFINITYL );
#endif
return( logl(x) + LOGE2L );
}
z = x - 1.0L;
if( z < 0.5L )
{
a = sqrtl(2.0L*z) * (polevll(z, P, 5) / polevll(z, Q, 5) );
return( a );
}
a = sqrtl( z*(x+1.0L) );
return( logl(x + a) );
}
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