Design of a high-speed square root multiply and divide unit
IEEE Transactions on Computers
Division Algorithms and Implementations
IEEE Transactions on Computers
Computer arithmetic: algorithms and hardware designs
Computer arithmetic: algorithms and hardware designs
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Choices of Operand Truncation in the SRT Division Algorithm
IEEE Transactions on Computers
SRT Division Architectures and Implementations
ARITH '97 Proceedings of the 13th Symposium on Computer Arithmetic (ARITH '97)
Minimizing the complexity of SRT tables
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Digit-Recurrence Dividers with Reduced Logical Depth
IEEE Transactions on Computers
Decimal Division Algorithms: The Issue of Partial Remainders
Journal of Signal Processing Systems
Hi-index | 14.98 |
Digit-recurrence binary dividers are sped up via two complementary methods: keeping the partial remainder in redundant form and selecting the quotient digits in a radix higher than 2. Use of a redundant partial remainder replaces the standard addition in each cycle by a carry-free addition, thus making the cycles shorter. Deriving the quotient in high radix reduces the number of cycles (by a factor of about h for radix 2^h). To make the redundant partial remainder scheme work, quotient digits must be chosen from a redundant set, such as [-2, 2] in radix 4. The redundancy provides some tolerance to imprecision so that the quotient digits can be selected based on examining truncated versions of the partial remainder and divisor. No closed form formula for the required precision in the partial remainder and divisor, as a function of the quotient digit set and the range of the partial remainder, is known. In this paper, we establish tight upper bounds on the required precision for the partial remainder and divisor. The bounds are tight in the sense that each is only one bit over a well-known simple lower bound. We also discuss the implications of these bounds for the quotient digit selection process.