Autran.cin

Autran.cin is C++ implementation of function AuTra; it is Abelfunction of the elementary Trappmann function \(\mathrm{tra} = z\mapsto z+\exp(z)\)

It is "new" implementation as substitute of the representation through the Tania function. It is not optimized, but it allows to generate the complex maps in real time.

call: autran(z)

Primary approximation: autran0(z)

The evaluation is described in the Applied Mathematical Sciences , 2013
and in book «Superfunctions», 2020
and also in its Russian version «Суперфункции», 2014.

Code

z_type autran0(z_type z) {z_type e=exp(z); z_type s; int n,M;
DB c[20]={-0.166666666666666667, 0.062500000000000, -0.0351851851851851852, 0.0208333333333333333,
-0.00976190476190476190, 0.000356867283950617284, 0.00577884857646762409, -0.0054935515873015873,
-0.00258505283582444076, 0.0121986400462962963, -0.00649411105018518438, -0.0264514796679871911,
 0.0478515524404502325, 0.0537587298747943833, -0.270736261932081259, -0.00655211866410402040,
 1.62788126261366988, -1.60768769009409886, -10.8381871746651334, 24.7850929105834429};
//M=14;
M=9;
s=c[M];
for(n=M-1;n>=0;n--) { s*=e; s+=c[n];}
                         return z/2.-1./e +e*s + 1.1259817765745026;}

z_type autran(z_type z) 
{ int n; z_type s=z; DB y; 
   DO(n,400){ y=fabs(Im(s)); 
              if( y<3. && y < 1.5*(-2.5-Re(s)) ) return autran0(s)+(0.+n);
              s=arctran(s);
            }
//   printf("autran: z=%9.6f %9.7f s=%9.6f %9.6f \n",Re(z),Im(z),Re(s),Im(s) );
// getchar(); 
return autran0(z);
}

References

Keywords

«Abelfunction», «AuTra», «C++», «Entire Function with Logarithmic Asimptotic», «Iterate», «Numerical implementation», «Superfunctions», «Trappmann function»,