157 lines
3.0 KiB
C
157 lines
3.0 KiB
C
/* atanh.c
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*
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* Inverse 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, atanh();
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*
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* y = atanh( 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 inverse hyperbolic tangent of argument in the range
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* MINLOG to MAXLOG.
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*
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* If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is
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* employed. Otherwise,
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* atanh(x) = 0.5 * log( (1+x)/(1-x) ).
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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 -1,1 50000 2.4e-17 6.4e-18
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* IEEE -1,1 30000 1.9e-16 5.2e-17
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*
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*/
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/* atanh.c */
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/*
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Cephes Math Library Release 2.8: June, 2000
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Copyright (C) 1987, 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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const static double P[] = {
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-8.54074331929669305196E-1,
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1.20426861384072379242E1,
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-4.61252884198732692637E1,
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6.54566728676544377376E1,
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-3.09092539379866942570E1
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};
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const static double Q[] = {
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/* 1.00000000000000000000E0,*/
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-1.95638849376911654834E1,
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1.08938092147140262656E2,
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-2.49839401325893582852E2,
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2.52006675691344555838E2,
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-9.27277618139601130017E1
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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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0140132,0122235,0105775,0130300,
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0041100,0127327,0124407,0034722,
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0141470,0100113,0115607,0130535,
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0041602,0164721,0003257,0013673,
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0141367,0043046,0166673,0045750
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};
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static unsigned short Q[] = {
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/*0040200,0000000,0000000,0000000,*/
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0141234,0101326,0015460,0134564,
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0041731,0160115,0116451,0032045,
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0142171,0153343,0000532,0167226,
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0042174,0000665,0077604,0000310,
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0141671,0072235,0031114,0074377
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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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0xb618,0xb17f,0x5493,0xbfeb,
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0xe73a,0xf520,0x15da,0x4028,
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0xf62c,0x7370,0x1009,0xc047,
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0xe2f7,0x20d5,0x5d3a,0x4050,
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0x697d,0xddb7,0xe8c4,0xc03e
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};
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static unsigned short Q[] = {
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/*0x0000,0x0000,0x0000,0x3ff0,*/
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0x172f,0xc366,0x905a,0xc033,
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0x2685,0xb3a5,0x3c09,0x405b,
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0x5dd3,0x602b,0x3adc,0xc06f,
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0x8019,0xaff0,0x8036,0x406f,
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0x8f20,0xa649,0x2e93,0xc057
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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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0xbfeb,0x5493,0xb17f,0xb618,
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0x4028,0x15da,0xf520,0xe73a,
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0xc047,0x1009,0x7370,0xf62c,
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0x4050,0x5d3a,0x20d5,0xe2f7,
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0xc03e,0xe8c4,0xddb7,0x697d
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};
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static unsigned short Q[] = {
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0xc033,0x905a,0xc366,0x172f,
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0x405b,0x3c09,0xb3a5,0x2685,
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0xc06f,0x3adc,0x602b,0x5dd3,
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0x406f,0x8036,0xaff0,0x8019,
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0xc057,0x2e93,0xa649,0x8f20
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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 log ( double x );
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extern double polevl ( double x, void *P, int N );
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extern double p1evl ( double x, void *P, int N );
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#else
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double fabs(), log(), polevl(), p1evl();
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#endif
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extern double INFINITY, NAN;
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double atanh(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 >= 1.0 )
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{
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if( x == 1.0 )
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return( INFINITY );
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if( x == -1.0 )
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return( -INFINITY );
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mtherr( "atanh", DOMAIN );
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return( NAN );
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}
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if( z < 1.0e-7 )
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return(x);
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if( z < 0.5 )
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{
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z = x * x;
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s = x + x * z * (polevl(z, P, 4) / p1evl(z, Q, 5));
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return(s);
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}
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return( 0.5 * log((1.0+x)/(1.0-x)) );
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}
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