Optimal Size Integer Division Circuits

Division is a fundamental problem for arithmetic and algebraic computation. This paper describes Boolean circuits of bounded fan-in for integer division  nding reciprocals that have size OMn and depth Olognloglogn, where Mn is the size complexity of Ologn depth integer multiplication circuits. Currently, Mn is known to be Onlognloglogn, but any improvement in this bound that preserves circuit depth will be re ected by a similar improvement in the size complexity of our division algorithm. Previously, no one has been able to derive a division circuit with size Onlogc n for any c, and simultaneous depth less than log2 n. The circuit families described in this paper are logspace uniform; that is, they can be constructed by a deterministic Turing machine in space Ologn. The results match the best-known depth bounds for logspace uniform circuits, and are optimal in size. The general method of high-order iterative formulas is of independent interest as a way of efcien...

• Type: Conference
• Year: 1989
• Where: STOC
• Authors: John H. Reif, Stephen R. Tate
• Keywords: Algorithms, Circuit Depth, Depth Integer Multiplication, Size Complexity, STOC 1989