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/* 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 2.7: January, 1998
Copyright 1984, 1991, 1998 by Stephen L. Moshier
*/
#include <math.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, XPD
0x365e,0xb30a,0xe437,0xda86,0x3ff3, XPD
0x8890,0x01f6,0x2612,0xfde6,0x3ff9, XPD
0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
};
static short Q[] = {
0x4edd,0x4c21,0xad09,0x95ed,0x3fe5, XPD
0x4376,0x9b70,0xd605,0xc65c,0xbfed, XPD
0xc8ad,0x5d21,0x3069,0x8aed,0x3ff5, XPD
0x9c32,0x6374,0x2d4b,0xe98d,0xbffb, XPD
0x0000,0x0000,0x0000,0xc000,0x4001, XPD
};
#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, MINLOGL, LOGE2L;
#ifdef ANSIPROT
extern long double fabsl ( long double );
extern long double expl ( long double );
extern long double polevll ( long double, void *, int );
extern long double p1evll ( long double, void *, int );
#else
long double fabsl(), expl(), polevll(), p1evll();
#endif
#ifdef INFINITIES
extern long double INFINITYL;
#endif
#ifdef NANS
extern long double NANL;
#endif
long double sinhl(x)
long double x;
{
long double a;
#ifdef MINUSZERO
if( x == 0.0 )
return(x);
#endif
a = fabsl(x);
if( (x > (MAXLOGL + LOGE2L)) || (x > -(MINLOGL-LOGE2L) ) )
{
mtherr( "sinhl", DOMAIN );
#ifdef INFINITIES
if( x > 0.0L )
return( INFINITYL );
else
return( -INFINITYL );
#else
if( x > 0.0L )
return( MAXNUML );
else
return( -MAXNUML );
#endif
}
if( a > 1.0L )
{
if( a >= (MAXLOGL - LOGE2L) )
{
a = expl(0.5L*a);
a = (0.5L * a) * a;
if( x < 0.0L )
a = -a;
return(a);
}
a = expl(a);
a = 0.5L*a - (0.5L/a);
if( x < 0.0L )
a = -a;
return(a);
}
a *= a;
return( x + x * a * (polevll(a,P,3)/polevll(a,Q,4)) );
}
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