Mod Builtin Constraints

[JulianGCalderon]

Right now, modulo builtin constraints are not always fulfilled.

• Given a sub mod gate (for example: x3 = x2 - x1), then it must always be true that x3 + x1 - x2 = 0 or p.

Take, for example, x2 = p + 1 and x1 = 1. Our current implementation will calculate x3 = 0 as a result of the operation (x2 - x1) % p. The expected output is p, as it's the minimum value that meets the constraint (p + 1 - (p + 1) = 0). (the other possible value is 2p.

See starkware-libs/cairo-lang#196 and cairo-lang implementation as reference.

[JulianGCalderon]

Although I haven't verified it, we may have similar bugs in the mul mod builtin implementation.