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/* tanhl.c
*
* Hyperbolic tangent, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, tanhl();
*
* y = tanhl( x );
*
*
*
* DESCRIPTION:
*
* Returns hyperbolic tangent of argument in the range MINLOGL to
* MAXLOGL.
*
* A rational function is used for |x| < 0.625. The form
* x + x**3 P(x)/Q(x) of Cody _& Waite is employed.
* Otherwise,
* tanh(x) = sinh(x)/cosh(x) = 1 - 2/(exp(2x) + 1).
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -2,2 30000 1.3e-19 2.4e-20
*
*/
/*
Cephes Math Library Release 2.7: May, 1998
Copyright 1984, 1987, 1989, 1998 by Stephen L. Moshier
*/
#include <math.h>
#ifdef UNK
static long double P[] = {
-6.8473739392677100872869E-5L,
-9.5658283111794641589011E-1L,
-8.4053568599672284488465E1L,
-1.3080425704712825945553E3L,
};
static long double Q[] = {
/* 1.0000000000000000000000E0L,*/
9.6259501838840336946872E1L,
1.8218117903645559060232E3L,
3.9241277114138477845780E3L,
};
#endif
#ifdef IBMPC
static short P[] = {
0xd2a4,0x1b0c,0x8f15,0x8f99,0xbff1, XPD
0x5959,0x9111,0x9cc7,0xf4e2,0xbffe, XPD
0xb576,0xef5e,0x6d57,0xa81b,0xc005, XPD
0xe3be,0xbfbd,0x5cbc,0xa381,0xc009, XPD
};
static short Q[] = {
/*0x0000,0x0000,0x0000,0x8000,0x3fff,*/
0x687f,0xce24,0xdd6c,0xc084,0x4005, XPD
0x3793,0xc95f,0xfa2f,0xe3b9,0x4009, XPD
0xd5a2,0x1f9c,0x0b1b,0xf542,0x400a, XPD
};
#endif
#ifdef MIEEE
static long P[] = {
0xbff10000,0x8f998f15,0x1b0cd2a4,
0xbffe0000,0xf4e29cc7,0x91115959,
0xc0050000,0xa81b6d57,0xef5eb576,
0xc0090000,0xa3815cbc,0xbfbde3be,
};
static long Q[] = {
/*0x3fff0000,0x80000000,0x00000000,*/
0x40050000,0xc084dd6c,0xce24687f,
0x40090000,0xe3b9fa2f,0xc95f3793,
0x400a0000,0xf5420b1b,0x1f9cd5a2,
};
#endif
extern long double MAXLOGL;
#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
long double tanhl(x)
long double x;
{
long double s, z;
#ifdef MINUSZERO
if( x == 0.0L )
return(x);
#endif
z = fabsl(x);
if( z > 0.5L * MAXLOGL )
{
if( x > 0 )
return( 1.0L );
else
return( -1.0L );
}
if( z >= 0.625L )
{
s = expl(2.0*z);
z = 1.0L - 2.0/(s + 1.0L);
if( x < 0 )
z = -z;
}
else
{
s = x * x;
z = polevll( s, P, 3 )/p1evll(s, Q, 3);
z = x * s * z;
z = x + z;
}
return( z );
}
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