/* 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)) ); }