173 lines
3.5 KiB
C
173 lines
3.5 KiB
C
/* sinhl.c
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*
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* Hyperbolic sine, long double precision
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*
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*
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*
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* SYNOPSIS:
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*
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* long double x, y, sinhl();
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*
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* y = sinhl( x );
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*
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*
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*
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* DESCRIPTION:
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*
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* Returns hyperbolic sine of argument in the range MINLOGL to
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* MAXLOGL.
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*
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* The range is partitioned into two segments. If |x| <= 1, a
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* rational function of the form x + x**3 P(x)/Q(x) is employed.
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* Otherwise the calculation is sinh(x) = ( exp(x) - exp(-x) )/2.
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*
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* IEEE -2,2 10000 1.5e-19 3.9e-20
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* IEEE +-10000 30000 1.1e-19 2.8e-20
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*
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*/
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/*
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Cephes Math Library Release 2.7: January, 1998
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Copyright 1984, 1991, 1998 by Stephen L. Moshier
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*/
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/*
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Modified for mingw
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2002-07-22 Danny Smith <dannysmith@users.sourceforge.net>
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*/
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#ifdef __MINGW32__
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#include "cephes_mconf.h"
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#else
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#include "mconf.h"
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#endif
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#ifndef _SET_ERRNO
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#define _SET_ERRNO(x)
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#endif
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#ifdef UNK
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static long double P[] = {
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1.7550769032975377032681E-6L,
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4.1680702175874268714539E-4L,
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3.0993532520425419002409E-2L,
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9.9999999999999999998002E-1L,
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};
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static long double Q[] = {
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1.7453965448620151484660E-8L,
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-5.9116673682651952419571E-6L,
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1.0599252315677389339530E-3L,
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-1.1403880487744749056675E-1L,
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6.0000000000000000000200E0L,
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};
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#endif
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#ifdef IBMPC
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static const unsigned short P[] = {
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0xec6a,0xd942,0xfbb3,0xeb8f,0x3feb, XPD
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0x365e,0xb30a,0xe437,0xda86,0x3ff3, XPD
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0x8890,0x01f6,0x2612,0xfde6,0x3ff9, XPD
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0x0000,0x0000,0x0000,0x8000,0x3fff, XPD
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};
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static const unsigned short Q[] = {
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0x4edd,0x4c21,0xad09,0x95ed,0x3fe5, XPD
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0x4376,0x9b70,0xd605,0xc65c,0xbfed, XPD
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0xc8ad,0x5d21,0x3069,0x8aed,0x3ff5, XPD
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0x9c32,0x6374,0x2d4b,0xe98d,0xbffb, XPD
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0x0000,0x0000,0x0000,0xc000,0x4001, XPD
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};
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#endif
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#ifdef MIEEE
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static long P[] = {
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0x3feb0000,0xeb8ffbb3,0xd942ec6a,
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0x3ff30000,0xda86e437,0xb30a365e,
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0x3ff90000,0xfde62612,0x01f68890,
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0x3fff0000,0x80000000,0x00000000,
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};
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static long Q[] = {
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0x3fe50000,0x95edad09,0x4c214edd,
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0xbfed0000,0xc65cd605,0x9b704376,
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0x3ff50000,0x8aed3069,0x5d21c8ad,
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0xbffb0000,0xe98d2d4b,0x63749c32,
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0x40010000,0xc0000000,0x00000000,
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};
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#endif
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#ifndef __MINGW32__
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extern long double MAXNUML, MAXLOGL, MINLOGL, LOGE2L;
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#ifdef ANSIPROT
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extern long double fabsl ( long double );
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extern long double expl ( long double );
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extern long double polevll ( long double, void *, int );
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extern long double p1evll ( long double, void *, int );
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#else
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long double fabsl(), expl(), polevll(), p1evll();
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#endif
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#ifdef INFINITIES
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extern long double INFINITYL;
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#endif
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#ifdef NANS
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extern long double NANL;
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#endif
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#endif /* __MINGW32__ */
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long double sinhl(x)
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long double x;
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{
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long double a;
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#ifdef MINUSZERO
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if( x == 0.0 )
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return(x);
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#endif
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#ifdef NANS
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if (isnanl(x))
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{
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_SET_ERRNO(EDOM);
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}
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#endif
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a = fabsl(x);
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if( (x > (MAXLOGL + LOGE2L)) || (x > -(MINLOGL-LOGE2L) ) )
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{
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mtherr( "sinhl", DOMAIN );
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_SET_ERRNO(ERANGE);
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#ifdef INFINITIES
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if( x > 0.0L )
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return( INFINITYL );
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else
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return( -INFINITYL );
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#else
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if( x > 0.0L )
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return( MAXNUML );
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else
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return( -MAXNUML );
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#endif
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}
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if( a > 1.0L )
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{
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if( a >= (MAXLOGL - LOGE2L) )
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{
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a = expl(0.5L*a);
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a = (0.5L * a) * a;
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if( x < 0.0L )
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a = -a;
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return(a);
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}
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a = expl(a);
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a = 0.5L*a - (0.5L/a);
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if( x < 0.0L )
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a = -a;
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return(a);
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}
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a *= a;
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return( x + x * a * (polevll(a,P,3)/polevll(a,Q,4)) );
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}
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