142 lines
2.5 KiB
C
142 lines
2.5 KiB
C
/* tanh.c
|
||
*
|
||
* Hyperbolic tangent
|
||
*
|
||
*
|
||
*
|
||
* SYNOPSIS:
|
||
*
|
||
* double x, y, tanh();
|
||
*
|
||
* y = tanh( x );
|
||
*
|
||
*
|
||
*
|
||
* DESCRIPTION:
|
||
*
|
||
* Returns hyperbolic tangent of argument in the range MINLOG to
|
||
* MAXLOG.
|
||
*
|
||
* 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
|
||
* DEC -2,2 50000 3.3e-17 6.4e-18
|
||
* IEEE -2,2 30000 2.5e-16 5.8e-17
|
||
*
|
||
*/
|
||
|
||
/*
|
||
Cephes Math Library Release 2.8: June, 2000
|
||
Copyright 1984, 1995, 2000 by Stephen L. Moshier
|
||
*/
|
||
|
||
#include "mconf.h"
|
||
|
||
#ifdef UNK
|
||
const static double P[] = {
|
||
-9.64399179425052238628E-1,
|
||
-9.92877231001918586564E1,
|
||
-1.61468768441708447952E3
|
||
};
|
||
const static double Q[] = {
|
||
/* 1.00000000000000000000E0,*/
|
||
1.12811678491632931402E2,
|
||
2.23548839060100448583E3,
|
||
4.84406305325125486048E3
|
||
};
|
||
#endif
|
||
#ifdef DEC
|
||
static unsigned short P[] = {
|
||
0140166,0161335,0053753,0075126,
|
||
0141706,0111520,0070463,0040552,
|
||
0142711,0153001,0101300,0025430
|
||
};
|
||
static unsigned short Q[] = {
|
||
/*0040200,0000000,0000000,0000000,*/
|
||
0041741,0117624,0051300,0156060,
|
||
0043013,0133720,0071251,0127717,
|
||
0043227,0060201,0021020,0020136
|
||
};
|
||
#endif
|
||
|
||
#ifdef IBMPC
|
||
static unsigned short P[] = {
|
||
0x6f4b,0xaafd,0xdc5b,0xbfee,
|
||
0x682d,0x0e26,0xd26a,0xc058,
|
||
0x0563,0x3058,0x3ac0,0xc099
|
||
};
|
||
static unsigned short Q[] = {
|
||
/*0x0000,0x0000,0x0000,0x3ff0,*/
|
||
0x1b86,0x8a58,0x33f2,0x405c,
|
||
0x35fa,0x0e55,0x76fa,0x40a1,
|
||
0x040c,0x2442,0xec10,0x40b2
|
||
};
|
||
#endif
|
||
|
||
#ifdef MIEEE
|
||
static unsigned short P[] = {
|
||
0xbfee,0xdc5b,0xaafd,0x6f4b,
|
||
0xc058,0xd26a,0x0e26,0x682d,
|
||
0xc099,0x3ac0,0x3058,0x0563
|
||
};
|
||
static unsigned short Q[] = {
|
||
0x405c,0x33f2,0x8a58,0x1b86,
|
||
0x40a1,0x76fa,0x0e55,0x35fa,
|
||
0x40b2,0xec10,0x2442,0x040c
|
||
};
|
||
#endif
|
||
|
||
#ifdef ANSIPROT
|
||
extern double fabs ( double );
|
||
extern double exp ( double );
|
||
extern double polevl ( double, void *, int );
|
||
extern double p1evl ( double, void *, int );
|
||
#else
|
||
double fabs(), exp(), polevl(), p1evl();
|
||
#endif
|
||
extern double MAXLOG;
|
||
|
||
double tanh(x)
|
||
double x;
|
||
{
|
||
double s, z;
|
||
|
||
#ifdef MINUSZERO
|
||
if( x == 0.0 )
|
||
return(x);
|
||
#endif
|
||
z = fabs(x);
|
||
if( z > 0.5 * MAXLOG )
|
||
{
|
||
if( x > 0 )
|
||
return( 1.0 );
|
||
else
|
||
return( -1.0 );
|
||
}
|
||
if( z >= 0.625 )
|
||
{
|
||
s = exp(2.0*z);
|
||
z = 1.0 - 2.0/(s + 1.0);
|
||
if( x < 0 )
|
||
z = -z;
|
||
}
|
||
else
|
||
{
|
||
if( x == 0.0 )
|
||
return(x);
|
||
s = x * x;
|
||
z = polevl( s, P, 2 )/p1evl(s, Q, 3);
|
||
z = x * s * z;
|
||
z = x + z;
|
||
}
|
||
return( z );
|
||
}
|