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