﻿ continued-fraction expansion of a real number
```/*CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C                                                                             C
C  CONTINUED FRACTION EXPANSION OF A REAL NUMBER                              C
C  06/10/07 (DKC)							      C
C                                                                             C
C  This C program approximates given real numbers with rational numbers using C
C  the continued fraction algorithm.					      C
C                                                                             C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC*/
#include <stdio.h>
#include <math.h>
void main() {
double X,Y,B,MAX;
unsigned int I,J;
unsigned int A[21],H[21],K[21];
//
printf(" CONTINUED FRACTION EXPANSION OF A REAL NUMBER \n");
MAX=65536.0;
MAX=MAX*32768.0-1.0;
//
// REAL NUMBER
//
X=0.372965733829521;
printf(" X=%f \n",X);
//
// COMPUTE THE PARTIAL QUOTIENTS
//
I=1;
A[1]=(unsigned int)X;
if((X<0.0)&&(X!=(double)A[1])) A[1]=A[1]-1;
B=X-(double)A[1];
if(B<=0.0) goto L300;
X=1.0/B;
for (I=2; I<=20; I++) {
if(X>MAX) goto L250;
A[I]=(unsigned int)X;
B=X-(double)A[I];
if(B<=0.0) goto L300;
X=1.0/B;
}
I=21;
L250: I=I-1;
//
// COMPUTE THE CONVERGENTS
//
L300: J=I;
H[1]=A[1];
K[1]=1;
Y=(double)H[1];
Y=Y/(double)K[1];
I=1;
printf(" I=%d, H[I]=%d, K[I]=%d, Y=%f \n",I,H[I],K[I],Y);
if(J==1) goto L500;
//
H[2]=A[2]*H[1]+1;
K[2]=A[2]*K[1];
Y=(double)H[2];
Y=Y/(double)K[2];
I=2;
printf(" I=%d, H[I]=%d, K[I]=%d, Y=%f \n",I,H[I],K[I],Y);
if(J==2) goto L500;
//
for (I=3; I<=J; I++) {
H[I]=A[I]*H[I-1]+H[I-2];
K[I]=A[I]*K[I-1]+K[I-2];
Y=(double)H[I];
Y=Y/(double)K[I];
printf(" I=%d, H[I]=%d, K[I]=%d, Y=%f \n",I,H[I],K[I],Y);
}
L500: return;
}
```