Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : SINHL.C

/* sinhl.c
*
* Hyperbolic sine, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, sinhl();
*
* y = sinhl( x );
*
*
*
* DESCRIPTION:
*
* Returns hyperbolic sine of argument in the range MINLOGL to
* MAXLOGL.
*
* The range is partitioned into two segments. If |x| <= 1, a
* rational function of the form x + x**3 P(x)/Q(x) is employed.
* Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -2,2 10000 1.5e-19 3.9e-20
* IEEE +-10000 30000 1.1e-19 2.8e-20
*
*/

/*
Cephes Math Library Release 2.2: January, 1991
Copyright 1984, 1991 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

#include "mconf.h"

#ifdef UNK
static long double P[] = {
1.7550769032975377032681E-6L,
4.1680702175874268714539E-4L,
3.0993532520425419002409E-2L,
9.9999999999999999998002E-1L,
};
static long double Q[] = {
1.7453965448620151484660E-8L,
-5.9116673682651952419571E-6L,
1.0599252315677389339530E-3L,
-1.1403880487744749056675E-1L,
6.0000000000000000000200E0L,
};
#endif

#ifdef IBMPC
static short P[] = {
0xec6a,0xd942,0xfbb3,0xeb8f,0x3feb,
0x365e,0xb30a,0xe437,0xda86,0x3ff3,
0x8890,0x01f6,0x2612,0xfde6,0x3ff9,
0x0000,0x0000,0x0000,0x8000,0x3fff,
};
static short Q[] = {
0x4edd,0x4c21,0xad09,0x95ed,0x3fe5,
0x4376,0x9b70,0xd605,0xc65c,0xbfed,
0xc8ad,0x5d21,0x3069,0x8aed,0x3ff5,
0x9c32,0x6374,0x2d4b,0xe98d,0xbffb,
0x0000,0x0000,0x0000,0xc000,0x4001,
};
#endif

#ifdef MIEEE
static long P[] = {
0x3feb0000,0xeb8ffbb3,0xd942ec6a,
0x3ff30000,0xda86e437,0xb30a365e,
0x3ff90000,0xfde62612,0x01f68890,
0x3fff0000,0x80000000,0x00000000,
};
static long Q[] = {
0x3fe50000,0x95edad09,0x4c214edd,
0xbfed0000,0xc65cd605,0x9b704376,
0x3ff50000,0x8aed3069,0x5d21c8ad,
0xbffb0000,0xe98d2d4b,0x63749c32,
0x40010000,0xc0000000,0x00000000,
};
#endif

extern long double MAXNUML, MAXLOGL;

long double sinhl(x)
long double x;
{
long double a;
long double fabsl(), expl(), polevll(), p1evll();

a = fabsl(x);
if( a > MAXLOGL )
{
mtherr( "sinhl", DOMAIN );
if( x > 0 )
return( MAXNUML );
else
return( -MAXNUML );
}
if( a > 1.0L )
{
a = expl(a);
a = 0.5L*a - (0.5L/a);
if( x < 0 )
a = -a;
return(a);
}

a *= a;
return( x + x * a * (polevll(a,P,3)/polevll(a,Q,4)) );
}