extended algorithm implementation in matlab

Question

i have found following pseudo-code for extended euclidean algorithm

i implemented following algorithm

    function [x1,y1,d1]=extend_eucledian(a,b)
            if b==0
                x1=1;
                y1=0;
                d1=a;
                return;
            end

            [x1,y1,d1]=extend_eucledian(b,mod(a,b));


 x1=y1;
y1=x1-floor(a/b)*y1;
d1=d1;

        end

when i run following this program, i got following result

[x1,y1,d1]=extend_eucledian(23,20)

x1 =

     0


y1 =

     0


d1 =

     1

i guess that [x1,y1,d1] are not changing their values during the iteration, for instance , i have tried following code

    function [x1,y1,d1]=extend_eucledian(a,b)
            if b==0
                x1=1;
                y1=0;
                d1=a;
                return;
            else
                 x1=y1;
y1=x1-floor(a/b)*y1;
d1=d1;
            end

            [x1,y1,d1]=extend_eucledian(b,mod(a,b));



        end

but i got

>> [x1,y1,d1]=extend_eucledian(23,20)
Undefined function or variable 'y1'.

Error in extend_eucledian (line 8)
                 x1=y1;

how can i fix this problem? where i am making mistake?

Answer 1

The problem can be solved by introducing intermediate working variables, that will store the result of the recursive call:

function [x,y,d]=extended_euclid(a,b)
    if b==0
        x=1;
        y=0;
        d=a;
        return;
    end
    [x1,y1,d1]=extended_euclid(b,mod(a,b));  

    x=y1;
    y=x1-floor(a/b)*y1;
    d=d1;

end 

This function works as expected:

>> [x, y, d] = extended_euclid(23,20)

x =    
     7

y =    
    -8

d =    
     1


>> [x, y, d] = extended_euclid(25,20)

x =    
     1    

y =    
    -1    

d =    
     5