On-the-fly conversion of redundant into conventional representations
IEEE Transactions on Computers
Fast Multiplication Without Carry-Propagate Addition
IEEE Transactions on Computers
An accurate elementary mathematical library for the IEEE floating point standard
ACM Transactions on Mathematical Software (TOMS)
Sigmoid Generators for Neural Computing Using Piecewise Approximations
IEEE Transactions on Computers
Elementary functions: algorithms and implementation
Elementary functions: algorithms and implementation
Powering by a Table Look-Up and a Multiplication with Operand Modification
IEEE Transactions on Computers
Approximating Elementary Functions with Symmetric Bipartite Tables
IEEE Transactions on Computers
IEEE Transactions on Computers - Special issue on computer arithmetic
Computer Approximations
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Division and Square Root: Digit-Recurrence Algorithms and Implementations
On-the-Fly Rounding (Computing Arithmetic)
IEEE Transactions on Computers
BKM: A New Hardware Algorithm for Complex Elementary Functions
IEEE Transactions on Computers
High-Speed Double-Precision Computation of Reciprocal, Division, Square Root and Inverse Square Root
IEEE Transactions on Computers
High-Radix Logarithm with Selection by Rounding
ASAP '02 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
Reviewing 4-to-2 Adders for Multi-Operand Addition
ASAP '02 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
Very-High Radix CORDIC Vectoring with Scalings and Selection by Rounding
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
High-Radix Iterative Algorithm for Powering Computation
ARITH '03 Proceedings of the 16th IEEE Symposium on Computer Arithmetic (ARITH-16'03)
ICCD '98 Proceedings of the International Conference on Computer Design
Faithful Powering Computation Using Table Look-Up and a Fused Accumulation Tree
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics)
Software Manual for the Elementary Functions (Prentice-Hall series in computational mathematics)
A Digit-by-Digit Algorithm for mth Root Extraction
IEEE Transactions on Computers
Multi-Gb/s LDPC code design and implementation
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A study of decimal left shifters for binary numbers
Information and Computation
Floating-Point Exponentiation Units for Reconfigurable Computing
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
| Hi-index | 14.98 |
An architecture for the computation of logarithm, exponential, and powering operations is presented in this paper, based on a high-radix composite algorithm for the computation of the powering function (X^{Y}). The algorithm consists of a sequence of overlapped operations: 1) digit-recurrence logarithm, 2) left-to-right carry-free (LRCF) multiplication, and 3) online exponential. A redundant number system is used and the selection in 1) and 3) is done by rounding except from the first iteration, when selection by table look-up is necessary to guarantee the convergence of the recurrences. A sequential implementation of the algorithm, with a control unit which allows the independent computation of logarithm and exponential, is proposed and the execution times and hardware requirements are estimated for single and double-precision floating-point computations. These estimates are obtained for radices from r=8 to r=1,024, according to an approximate model for the delay and area of the main logic blocks and help determining the radix values which lead to the most efficient implementations: r=32 and r=128.