Fast Multiplication Without Carry-Propagate Addition
IEEE Transactions on Computers
IEEE Transactions on Computers
Higher Radix Square Root with Prescaling
IEEE Transactions on Computers - Special issue on computer arithmetic
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Implementing complex elementary functions using exception handling
ACM Transactions on Mathematical Software (TOMS)
Fast high-precision computation of complex square roots
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Algorithm 786: multiple-precision complex arithmetic and functions
ACM Transactions on Mathematical Software (TOMS)
Very High Radix Square Root with Prescaling and Rounding and a Combined Division/Square Root Unit
IEEE Transactions on Computers
Approximating Elementary Functions with Symmetric Bipartite Tables
IEEE Transactions on Computers
Division and Square Root: Digit-Recurrence Algorithms and Implementations
Division and Square Root: Digit-Recurrence Algorithms and Implementations
On computing givens rotations reliably and efficiently
ACM Transactions on Mathematical Software (TOMS)
Faithful Bipartite ROM Reciprocal Tables
ARITH '95 Proceedings of the 12th Symposium on Computer Arithmetic
Some Improvements on Multipartite Table Methods
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
Complex number on-line arithmetic for reconfigurable hardware: algorithms, implementations, and applications
Complex Square Root with Operand Prescaling
ASAP '04 Proceedings of the Application-Specific Systems, Architectures and Processors, 15th IEEE International Conference
An Efficient Method for Evaluating Complex Polynomials
Journal of Signal Processing Systems
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We propose a radix-r digit-recurrence algorithm for complex square-root. The operand is prescaled to allow the selection of square-root digits by rounding of the residual. This leads to a simple hardware implementation of digit selection. Moreover, the use of digit recurrence approach allows correct rounding of the result if needed. The algorithm, compatible with the complex division presented in Ercegovac and Muller ("Complex Division with Prescaling of the Operands," in Proc. Application-Specific Systems, Architectures, and Processors (ASAP'03), The Hague, The Netherlands, June 24---26, 2003), and its design are described. We also give rough estimates of its latency and cost with respect to implementation based on standard floating-point instructions as used in software routines for complex square root.