/* atanh.c * * Inverse hyperbolic tangent * * * * SYNOPSIS: * * double x, y, atanh(); * * y = atanh( x ); * * * * DESCRIPTION: * * Returns inverse hyperbolic tangent of argument in the range * MINLOG to MAXLOG. * * If |x| < 0.5, the rational form x + x**3 P(x)/Q(x) is * employed. Otherwise, * atanh(x) = 0.5 * log( (1+x)/(1-x) ). * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * DEC -1,1 50000 2.4e-17 6.4e-18 * IEEE -1,1 30000 1.9e-16 5.2e-17 * */ /* atanh.c */ /* Cephes Math Library Release 2.8: June, 2000 Copyright (C) 1987, 1995, 2000 by Stephen L. Moshier */ #include #ifdef UNK static double P[] = { -8.54074331929669305196E-1, 1.20426861384072379242E1, -4.61252884198732692637E1, 6.54566728676544377376E1, -3.09092539379866942570E1 }; static double Q[] = { /* 1.00000000000000000000E0,*/ -1.95638849376911654834E1, 1.08938092147140262656E2, -2.49839401325893582852E2, 2.52006675691344555838E2, -9.27277618139601130017E1 }; #endif #ifdef DEC static unsigned short P[] = { 0140132,0122235,0105775,0130300, 0041100,0127327,0124407,0034722, 0141470,0100113,0115607,0130535, 0041602,0164721,0003257,0013673, 0141367,0043046,0166673,0045750 }; static unsigned short Q[] = { /*0040200,0000000,0000000,0000000,*/ 0141234,0101326,0015460,0134564, 0041731,0160115,0116451,0032045, 0142171,0153343,0000532,0167226, 0042174,0000665,0077604,0000310, 0141671,0072235,0031114,0074377 }; #endif #ifdef IBMPC static unsigned short P[] = { 0xb618,0xb17f,0x5493,0xbfeb, 0xe73a,0xf520,0x15da,0x4028, 0xf62c,0x7370,0x1009,0xc047, 0xe2f7,0x20d5,0x5d3a,0x4050, 0x697d,0xddb7,0xe8c4,0xc03e }; static unsigned short Q[] = { /*0x0000,0x0000,0x0000,0x3ff0,*/ 0x172f,0xc366,0x905a,0xc033, 0x2685,0xb3a5,0x3c09,0x405b, 0x5dd3,0x602b,0x3adc,0xc06f, 0x8019,0xaff0,0x8036,0x406f, 0x8f20,0xa649,0x2e93,0xc057 }; #endif #ifdef MIEEE static unsigned short P[] = { 0xbfeb,0x5493,0xb17f,0xb618, 0x4028,0x15da,0xf520,0xe73a, 0xc047,0x1009,0x7370,0xf62c, 0x4050,0x5d3a,0x20d5,0xe2f7, 0xc03e,0xe8c4,0xddb7,0x697d }; static unsigned short Q[] = { 0xc033,0x905a,0xc366,0x172f, 0x405b,0x3c09,0xb3a5,0x2685, 0xc06f,0x3adc,0x602b,0x5dd3, 0x406f,0x8036,0xaff0,0x8019, 0xc057,0x2e93,0xa649,0x8f20 }; #endif #ifdef ANSIPROT extern double fabs ( double ); extern double log ( double x ); extern double polevl ( double x, void *P, int N ); extern double p1evl ( double x, void *P, int N ); #else double fabs(), log(), polevl(), p1evl(); #endif extern double INFINITY, NAN; double atanh(x) double x; { double s, z; #ifdef MINUSZERO if( x == 0.0 ) return(x); #endif z = fabs(x); if( z >= 1.0 ) { if( x == 1.0 ) return( INFINITY ); if( x == -1.0 ) return( -INFINITY ); mtherr( "atanh", DOMAIN ); return( NAN ); } if( z < 1.0e-7 ) return(x); if( z < 0.5 ) { z = x * x; s = x + x * z * (polevl(z, P, 4) / p1evl(z, Q, 5)); return(s); } return( 0.5 * log((1.0+x)/(1.0-x)) ); }