# Factorial/Code/LogFactorialZ

< Factorial‎ | Code
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//

```// Generator of figure http://en.citizendium.org/wiki/Image:LogFactorialZ.jpg
// plot of LogFactorial(z) in the complex z-plane.
// In order to complie this program, files
//ContourPlot/code/ado.cin (function that makes header of the eps file) and
//ContourPlot/code/conto.cin (function which draws a level) should be loaded.
//
// Copyleft 2009 by Dmitrii Kouznetsov
// Please, indicate the source and modifications (if any) at the use.
```
```#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
#include <complex.h>
#define z_type complex<double>
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
```
```DB expaunoc[31]= {1.,
0.5772156649015329,    -0.6558780715202537,	 -0.04200263503409518,    0.16653861138229112,
-0.04219773455554465,   -0.009621971527877027,   0.0072189432466631676, -0.0011651675918590183,
-0.0002152416741149077,  0.00012805028238804805,-0.00002013485478102872,-1.2504934818746705e-6,
1.1330272320364543e-6, -2.0563384228733383e-7,  6.1160952968819515e-9,  5.00200766282674e-9,
-1.1812748557105124e-9,  1.0434320074637071e-10, 7.782441358017422e-12, -3.696820627396846e-12,
5.10702591327572e-13,  -2.0650148258027912e-14,-6.217248937900877e-15,  7.771561172376096e-16,
-9.992007221626409e-16, -3.3306690738754696e-16, 5.551115123125783e-16, -1.1102230246251565e-16,
1.3322676295501878e-15, 9.992007221626409e-16 };
z_type expauno(z_type z) {int n,m; DB x,y; z_type s; s=expaunoc[24];
x=Re(z);if(x<-.9) return expauno(z+1.)-log(z+1.);
if(x>.5) return expauno(z-1.)+log(z);
y=Im(z); if(fabs(y)>.7)return expauno(z/2.)+expauno(z/2.-.5)+z*log(2.)-log(sqrt(M_PI));
for(n=23; n>=0; n--) { s*=z;s+=expaunoc[n]; }
return -log(s); }
```
```z_type fracti(z_type z){ z_type s; int n;  DB a[17]=
{0.0833333333333333333, 0.0333333333333333333,  .252380952380952381, .525606469002695418,
1.01152306812684171,   1.51747364915328740,   2.26948897420495996, 3.00991738325939817,
4.02688719234390123,   5.00276808075403005,   6.28391137081578218, 7.49591912238403393,
9.04066023436772670,  10.4893036545094823,   12.2971936103862059, 13.9828769539924302, 16.0535514167049355
};
/* a[0]=1./12.; a[1]=1./30.; a[2]=53./210.; a[3]=195./371.; a[4]=22999./22737.; a[5]=29944523./19773142.;
a[6]=109535241009./48264275462.;  a[7]=29404527905795295658./9769214287853155785.;
a[8]=455377030420113432210116914702./113084128923675014537885725485.;
a[9]=26370812569397719001931992945645578779849./5271244267917980801966553649147604697542.;
a[10]=152537496709054809881638897472985990866753853122697839./24274291553105128438297398108902195365373879212227726.;
a[11]= too long... */
//s=a[16]/(z+19./(z+25./(z+40.)));
s=a[16]/(z+19./(z+25./(z)));
for(n=15;n>=0;n--) s=a[n]/(z+s);
return  s + log(2.*M_PI)/2. - z + (z+.5)*log(z);
}
```
```z_type lofac(z_type z){DB x,y,r;
x=Re(z); y=Im(z);
if(fabs(y)>5 ) return fracti(z);
if(x>0 && (x-3)*(x-3.)+y*y >25) return fracti(z);
return expauno(z);
}
```
```#include "conto.cin"

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d, cu,cd;
int M=421,M1=M+1;
int N=361,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
fprintf(o,"91 71 translate\n 10 10 scale\n");
DO(m,M1) X[m]=-8.2+.04*(m-.5);
DO(n,N1) Y[n]=-7. +.04*(n-.5);
for(m=-8;m<9;m++) {	if(m==0){M(m,-6.2)L(m,6.2)} else	{M(m,-6)L(m,6)}			}
for(n=-6;n<7;n++) {	M(  -8,n)L(8,n)}
fprintf(o,".006 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; //	printf("%2.0fd\n",0.);
DO(n,N1){y=Y[n]; 	z=z_type(x,y);
c=lofac(z);
//c= 	fracti(z);
//d=	expauno(z);
// d= 	exp(fracti(z))*(z+1.)	;
//p=abs(c-d)/(abs(c)+abs(d));   p=-log(p)/log(10.);
p=Re(c);q=Im(c);
if(p>-999 && p<999 && fabs(p)> 1.e-9 && fabs(p-1.)>1.e-9) 	g[m*N1+n]=p;
if(q>-999 && q<999 && fabs(q)> 1.e-9) 				f[m*N1+n]=q;
}}
p=2;q=1;
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-4.+.1*n),-q, q); fprintf(o,".006 W 0 1 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-3.+.1*n),-q, q); fprintf(o,".006 W 0 1 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-2.+.1*n),-q, q); fprintf(o,".006 W 0 1 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, (-1.+.1*n),-q, q); fprintf(o,".006 W 0 1 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 0.+.1*n),-q, q); fprintf(o,".006 W 0 1 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 1.+.1*n),-q, q); fprintf(o,".006 W 0 1 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 2.+.1*n),-q, q); fprintf(o,".006 W 0 1 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N, ( 3.+.1*n),-q, q); fprintf(o,".006 W 0 1 0 RGB S\n");
//
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-4.+.1*n),-q, q); fprintf(o,".006 W 1 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-3.+.1*n),-q, q); fprintf(o,".006 W 1 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-2.+.1*n),-q, q); fprintf(o,".006 W 1 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (-1.+.1*n),-q, q); fprintf(o,".006 W 1 0 0 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 0.+.1*n),-q, q); fprintf(o,".006 W 0 0 1 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 1.+.1*n),-q, q); fprintf(o,".006 W 0 0 1 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 2.+.1*n),-q, q); fprintf(o,".006 W 0 0 1 RGB S\n");
for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, ( 3.+.1*n),-q, q); fprintf(o,".006 W 0 0 1 RGB S\n");
//
conto(o,f,w,v,X,Y,M,N, (-24.     ),-4*p,4*p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-20.     ),-4*p,4*p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-16.     ),-4*p,4*p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-12.     ),-4*p,4*p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-8.     ),-4*p,4*p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-7.     ),-p,p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-6.     ),-p,p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-5.     ),-p,p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-4.     ),-p,p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-3.     ),-p,p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-2.     ),-p,p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (-1.     ),-p,p); fprintf(o,".020 W 1 0 0 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 0.  ),-8*p,8*p); fprintf(o,".020 W 1 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 1.     ),-p,p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 2.     ),-p,p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 3.     ),-p,p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 4.     ),-p,p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 5.     ),-p,p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 6.     ),-p,p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 7.     ),-p,p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, ( 8.     ),-4*p,4*p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (12.     ),-4*p,4*p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (16.     ),-4*p,4*p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (20.     ),-4*p,4*p); fprintf(o,".020 W 0 0 1 RGB S\n");
conto(o,f,w,v,X,Y,M,N, (24.     ),-4*p,4*p); fprintf(o,".020 W 0 0 1 RGB S\n");
//
conto(o,g,w,v,X,Y,M,N, (-24.    ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-20.    ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-16.    ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-12.    ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-8.     ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-7.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-6.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-5.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-4.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-3.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-2.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (-1.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 0. ),-8*p,8*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 1.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 2.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 3.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 4.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 5.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 6.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 7.     ),-p,p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, ( 8.     ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (12.     ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (16.     ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (20.     ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
conto(o,g,w,v,X,Y,M,N, (24.     ),-4*p,4*p); fprintf(o,".020 W 0 0 0 RGB S\n");
// #include"plofu.cin"
M(-1,0)L(-8.2,0)
fprintf(o,"0 0 0 RGB 0.05 W [.07 .12] .1 setdash S\n"); fclose(o);
fprintf(o,"showpage\n\%\%\%Trailer"); fclose(o);
//system( "ggv LogFactorialZ.eps"); // for linux
system("open LogFactorialZ.eps"); //for macintosh
system("ps2pdf LogFactorialZ.eps");
getchar(); system("killall Preview");//for macintosh
}
```

// End of generator of figure http://en.citizendium.org/wiki/Image:LogFactorialZ.jpg