High-Radix Division and Square-Root with Speculation

The speed of high-radix digit-recurrence dividers and square-root units is mainly determined by the complexity of the result-digit selection. We present a scheme in which a simpler function speculates the result digit, and, when this speculation is incorrect, a rollback or a partial advance is performed. This results in operations with a shorter cycle time and a variable number of cycles. The scheme can be used in separate division and square-root units, or in a combined one. Several designs were realized and compared in terms of execution time and area. The fastest unit considered is a radix-512 divider with a partial advance of six bits. >

[1]  M. Ercegovac,et al.  Division and Square Root: Digit-Recurrence Algorithms and Implementations , 1994 .

[2]  Tomás Lang,et al.  Fast Multiplication Without Carry-Propagate Addition , 1990, IEEE Trans. Computers.

[3]  Robert K. Brayton,et al.  MIS: A Multiple-Level Logic Optimization System , 1987, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[4]  Luigi Ciminiera,et al.  On the efficient implementation of higher radix square root algorithms , 1989, Proceedings of 9th Symposium on Computer Arithmetic.

[5]  Damiel E. Atkins.  Higher-Radix Division Using Estimates of the Divisor and Partial Remainders , 1968, IEEE Transactions on Computers.

[6]  T. E. Williams,et al.  A 160 ns 54 bit CMOS division implementation using self-timing and symmetrically overlapped SRT stages , 1991, [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic.

[7]  Jan Fandrianto.  Algorithm for high speed shared radix 4 division and radix 4 square-root , 1987, 1987 IEEE 8th Symposium on Computer Arithmetic (ARITH).

[8]  George S. Taylor.  Radix 16 SRT dividers with overlapped quotient selection stages: A 225 nanosecond double precision divider for the S-1 Mark IIB , 1985, 1985 IEEE 7th Symposium on Computer Arithmetic (ARITH).

[9]  Jordi Cortadella,et al.  Division with speculation of quotient digits , 1993, Proceedings of IEEE 11th Symposium on Computer Arithmetic.

[10]  Tomás Lang,et al.  Higher Radix Square Root with Prescaling , 1992, IEEE Trans. Computers.

[11]  Tomás Lang,et al.  On-the-Fly Conversion of Redundant into Conventional Representations , 1987, IEEE Transactions on Computers.

[12]  Luigi Ciminiera,et al.  Higher Radix Square Rooting , 1990, IEEE Trans. Computers.