One-off error in the MIP solver?

[Hartmut Henkel]

Hi,

here seems to be some one-off error in gmpl/glpk (5.0, debian Linux):

param v := 131072;
param n := 20; # number of bits
set J  := 1..n; # set of all bits
var x{j in J}, binary;
var e, >= 0;
minimize slack: e;

s.t. cs1: sum{j in J} (2**(j - 1) * x[j]) - v <=  e;
s.t. cs2: sum{j in J} (2**(j - 1) * x[j]) - v >= -e;

solve;

printf "v: %d\nv: ", v;
for {j in J} printf "%d", x[n - j + 1];
printf "\n";
printf "v: %d\n", sum{j in J} (2**(j - 1) * x[j]);
printf "e: %d\n", e;

end;

Here it prints:

v: 131072
v: 0011111111111111111
v: 131071
e: 0

With v = 131071 or v = 131073 or v = 65536 it works fine. Also fine with
larger numbers like v = 888888. Same problem when solving the exported
.lp file, which looks ok., confirmed by another solver. Seems not to be
a general int limitation or printing issue. Do you have any idea what's
happening here?

Best Regards, Hartmut