Fast Constant Division Routines
IEEE Transactions on Computers
ICS '90 Proceedings of the 4th international conference on Supercomputing
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
Division Algorithms and Implementations
IEEE Transactions on Computers
Computer arithmetic: algorithms and hardware designs
Computer arithmetic: algorithms and hardware designs
A fast division technique for constant divisors
Communications of the ACM
Computer Arithmetic I (Tutorial)
Computer Arithmetic I (Tutorial)
Advanced Computer Arithmetic Design
Advanced Computer Arithmetic Design
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Efficient Initial Approximation and Fast Converging Methods for Division and Square Root
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
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Division is one of the basic operations of arithmetic algorithms, but the cost associated to its hardware implementation exceeds the reasonable limits for most dedicated architectures. This paper provides a systematic algorithm that (a) transforms the constant coefficient division into a constant coefficient multiplication, selectable under some given constraints, and (b) optimizes the resulting multiplier by analyzing the quantization noise inherent to the finite wordlength implementation process. Consequently, this algorithm achieves reduced-area, high-speed constant coefficient dividers that maintain the accuracy in the range of represented numbers. The theorems and presented results confirm that the proposed algorithm computes the most suitable fraction under a given set of noise constraints.