Sqrt2f43e.cin

// Sqrt2f43e.cin is routine for evaluation of superexponent to base \(\sqrt{2}\) that approach 4 at \(-\infty\) and has value 3 at zero.

z_type f43E(z_type z){int n; z_type e,s; DB coeud[23];
DB coeu[23]={ -1.,
 0.44858743119526122890, -0.19037224679780675668,
 0.77829576536968278770e-1, -0.30935860305707997953e-1,
 0.12022125769065893274e-1, -0.45849888965617461424e-2,
 0.17207423310577291102e-2, -0.63681090387985537364e-3,
 0.23276960030302567773e-3, -0.84145511838119915857e-4,
 0.30115646493706434120e-4, -0.10680745813035087964e-4,
 0.37565713615564248453e-5, -0.13111367785052622794e-5,
 0.45437916254218158081e-6, -0.15642984632975371803e-6,
 0.53523276400816416929e-7, -0.18207786280204973113e-7,
 0.61604764947389226744e-8,
         -0.207e-8, 0.70e-9, -0.23e-9
};
        e=exp(.32663425997828098238*(z+1.90057764535874));
        s=coeu[22]; for(n=21;n>=0;n--) { s*=e; s+=coeu[n]; }
        return 4.+s*e; }

z_type F43E(z_type z){ if(Re(z)> -4.8) return exp(log(sqrt(2))*F43E(z-1.));
                        if(abs(z)>1.e-16 ) return f43E(z);
                        return 3.;
                        }

//