Computation of elementary functions on the IBM RISC System/6000 processor
IBM Journal of Research and Development
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Measuring the Accuracy of ROM Reciprocal Tables
IEEE Transactions on Computers
Faithful Bipartite ROM Reciprocal Tables
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Number-Theoretic Test Generation for Directed Rounding
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
On Infinitely Precise Rounding for Division, Square Root, Reciprocal and Square Root Reciprocal
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
High-Speed Inverse Square Roots
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Floating Point Division and Square Root Algorithms and Implementation in the AMD-K7 Microprocessor
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Correctness Proofs Outline for Newton-Raphson Based Floating-Point Divide and Square Root Algorithms
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
High-Speed Double-Precision Computation of Reciprocal, Division, Square Root and Inverse Square Root
IEEE Transactions on Computers
Mesh Algorithms for Multiplication and Division
HiPC '01 Proceedings of the 8th International Conference on High Performance Computing
Real-Time Systems
A goldschmidt division method with faster than quadratic convergence
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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The aim of this paper is to accelerate division, square root, and square root reciprocal computations when the Goldschmidt method is used on a pipelined multiplier. This is done by replacing the last iteration by the addition of a correcting term that can be looked up during the early iterations. We describe several variants of the Goldschmidt algorithm, assuming 4-cycle pipelined multiplier, and discuss obtained number of cycles and error achieved. Extensions to other than 4-cycle multipliers are given. If we call $G_m$ the Goldschmidt algorithm with $m$ iterations, our variants allow us to reach an accuracy that is between that of $G_3$ and that of $G_4$, with a number of cycle equal to that of $G_3$.