File:Esqrt2ite12mapT80.jpg

// Files [[ado.cin]] and [[conto.cin]] should be loaded to the working directory in order to compile the [[C++]] code below.

 #include <math.h>
 #include <stdio.h>
 #include <stdlib.h>
 #define DB double
 #define DO(x,y) for(x=0;x<y;x++)
 using namespace std;
 #include <complex>
 typedef complex<double> z_type;
 #define Re(x) x.real()
 #define Im(x) x.imag()
 #include "conto.cin"

 z_type f45E(z_type z){int n; z_type e,s;
 DB coeu[21]={1.,
 0.44858743119526122890, .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, 0.2e-8};
        e=exp(.32663425997828098238*(z-1.11520724513161));
        s=coeu[20]; for(n=19;n>=0;n--) { s*=e; s+=coeu[n]; }
 // s=coeu[19]; for(n=18;n>=0;n--) { s*=e; s+=coeu[n]; }
        return 4.+s*e;}

 z_type F45E(z_type z){ DB b=sqrt(2.);
                        if(Re(z)<-1.) return f45E(z);
                        return exp(F45E(z-1.)*log(b));
                }

 z_type f45L(z_type z){ int n; z_type e,s;
 DB Uco[21]={1,
 -.44858743119526122890, .21208912005491969757,
 -.10218436750697167872, 0.49698683037371830337e-1,
 -0.2430759032611955221e-1, 0.11933088396510860210e-1,
 -0.587369764200886206e-2, 0.289686728710575713e-2,
 -0.1430908106079253664e-2, 0.7076637148565759223e-3,
 -0.3503296158729878e-3, 0.17357560046634138e-3,
 -0.86061011929162626e-4, 0.426959089012891e-4,
 -0.2119302906819844809e-4, 0.1052442259960e-4,
 -0.52285174354086e-5, 0.259844999161e-5,
 -0.129178211214818578e-5, 0.4e-6 };
        z-=4.;
        s=Uco[19]; for(n=18; n>=0; n--){ s*=z; s+=Uco[n]; }
 // s=Uco[20]; for(n=19; n>=0; n--){ s*=z; s+=Uco[n]; }
 // return log(s*z)/.32663425997828098238 +1.1152091357215375;
        return log(s*z)/.32663425997828098238 +1.11520724513161;
  }

 z_type F45L(z_type z){ DB b=sqrt(2.);
                        if(abs(z-4.)>.4) return F45L(log(z)/log(b))+1. ;
                         return f45L(z);
                }
 // #include"sqrt2f45E.cin"

int main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
 int M=801,M1=M+1;
 int N=405,N1=N+1;
 DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
 char v[M1*N1]; // v is working array
 FILE *o;o=fopen("esqrt2ite12map.eps","w"); ado(o,202,202);
 fprintf(o,"101 101 translate\n 10 10 scale\n");
 DO(m,M1) X[m]=-10.+.025*(m-.5);
 //DO(n,N1) Y[n]=-10.+.04*(n-.5);
 // DO(n,200) Y[n]=sinh(3.*(n-200.5)/200.);
// DO(n,200) Y[n]=-10.+.05*(n-.5);
// Y[200]=-.0001;
// Y[201]= .0001;
for(n=0;n<N1;n++) Y[n]=.25*sinh(4.33*(n-202.5)/200.);
// for(n=202;n<N1;n++) Y[n]=-10.+.05*(n-2);
 for(m=-10;m<11;m++) {M(m,-10)L(m,10)}
 for(n=-10;n<11;n++) {M( -10,n)L(10,n)}
 fprintf(o,"1 setlinejoin 2 setlinecap\n");
 fprintf(o," .006 W 0 0 0 RGB S\n");
 // z_type tm,tp,F[M1*N1];
 DO(m,M1)DO(n,N1){ g[m*N1+n]=9999;
                        f[m*N1+n]=9999;}
 DO(m,M1){x=X[m];
 DO(n,N1){y=Y[n]; z=z_type(x,y);
                c=F45L(z); c=F45E(1./2.+c);
                p=Re(c);
                q=Im(c);
                if(p>-25. && p<25. && q>-25. && q<25.
 // && fabs(p)>1.e-14
 // && fabs(q)>1.e-14
                ) { g[m*N1+n]=p; f[m*N1+n]=q;}
        }}
 p=.4; q=.3;
 for(m=-10;m<10;m++)for(n=2 ;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".014 W 0 .7 0 RGB S\n");
 for(m=0;m<11;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q,q); fprintf(o,".014 W 1 0 0 RGB S\n");
 for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q,q); fprintf(o,".014 W 0 0 1 RGB S\n");
 for(m= 1;m<25;m++) conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p);fprintf(o,".03 W .8 0 0 RGB S\n");
 for(m= 1;m<25;m++) conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p);fprintf(o,".03 W 0 0 .8 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0. ),-2*p,2*p); fprintf(o,".03 W .5 0 .5 RGB S\n");
 for(m=-24;m<25;m++)conto(o,g,w,v,X,Y,M,N,(0.+m),-p,p);fprintf(o,".03 W 0 0 0 RGB S\n");

 // #include "plofu.cin"
  M(-10,0)L(2,0)fprintf(o,"0 setlinecap .036 W 1 1 1 RGB S\n");
 for(n=0;n<27;n++){ M(2-.5*(n+.2),0) L(2-.5*(n+.4),0) } fprintf(o,".06 W 1 .5 0 RGB S\n");
 for(n=0;n<27;n++){ M(2-.5*(n+.7),0) L(2-.5*(n+.9),0) } fprintf(o,".06 W 0 .5 1 RGB S\n");
 fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
        system("epstopdf esqrt2ite12map.eps");
        system( "open esqrt2ite12map.pdf"); //for macintosh
 }

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