#WHILE
#MAXREG 5
#IMPORT AddSub

def GCDWhile     
out: o0
in: i0, i1
aux: a0, a1, a2, a3
do

o0 := 0;                     // Initialize with 0
o0 := IfLet(i0,i1)();        // Now x0 is nonzero unless either n = 0 or m = 0 

a0 := i0;
a1 := i1;

while o0 do

        a2 := Sub(a0,a1)();       // Trunkated sum n - m
        a3 := Sub(a1,a0)();       // Trunkated sum m - n
        o0 := Add(a2,a3)();       // o0 = 0 iff n = m

        a0 := IfLet(a2,a2)();     // Try to update n 
        a1 := IfLet(a3,a3)()      // Try to update m

end;

o0 := IfLet(a0,a1)()          // Update x0 with x1=x2 unless one of them is 0 

enddef

def GCDLoop
out: o0
in: i0, i1
aux: a0, a1, a2, a3
do

o0 := Add(i1,i0)();                // This is to estimate the number of iterations
                                   // The algorithm would not need more than n+m steps

a3 := 0;                           // Cheching if n = 0 or m = 0
a2:= IfLet(i0,i1)();
a3:= IfLet(a2,o0)();
o0:=a3;                            // This would be o0 calculated previosly unless n = 0 or m = 0

a0 := i0;
a1 := i1;

loop o0 do

        a2 := Sub(a0,a1)();       // Trunkated sum n - m
        a3 := Sub(a1,a0)();       // Trunkated sum m - n

        a0 := IfLet(a2,a2)();     // Try to update n 
        a1 := IfLet(a3,a3)()      // Try to update m

end;

o0 := IfLet(a0,a1)()      // Update x0 with a0=a1 unless one of them is 0 

enddef

x0:= GCDLoop(x1,x2)(x3,x4,x5,x6)