Lower bounds for integer greatest common divisor computations

An Ω(log log n) lower bound is proved on the depth of any computation tree with operations {+, -, /, mod, ⩽} that computes the greatest common divisor (GCD) of all pairs of n-bit integers. A novel technique for handling the truncation operation is implicit in the proof. Also proved is a Θ(n) bound on the depth of any algebraic computation trees with operations {+, -, *, /, ⩽} (where "/" stands for exact division) that solve many simple problems, e.g. testing if an n-bit integer is odd or computing the GCD of two n-bit integers