A Goldschmidt Division Method With Faster Than Quadratic Convergence

A new method to implement faster than quadratic convergence for Goldschmidt division using simple logic circuits is presented. While the approximate quotient converges quadratically in conventional Goldschmidt division, the new method achieves nearly cubic convergence. Although division with cubic c...

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Bibliographic Details
Published in:IEEE transactions on very large scale integration (VLSI) systems 2011-04, Vol.19 (4), p.696-700
Main Authors: Inwook Kong, Swartzlander, E E
Format: Article
Language:English
Subjects:
Applied sciences
Approximation
Arithmetic
Circuit properties
Complexity
Computer simulation
Convergence
Cubic convergence
Degradation
Delay
Design. Technologies. Operation analysis. Testing
Digital circuits
Division
division by convergence
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Function approximation
Goldschmidt division
Hardware design languages
higher order convergence
Integrated circuits
Logic
Logic circuits
Mathematical models
Pipelines
Read only memory
redundant binary Booth recoding
Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices
Testing
Very large scale integration
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Summary:A new method to implement faster than quadratic convergence for Goldschmidt division using simple logic circuits is presented. While the approximate quotient converges quadratically in conventional Goldschmidt division, the new method achieves nearly cubic convergence. Although division with cubic convergence has been regarded as impractical due to its complexity, the proposed method reduces the logic complexity and the delay by using an approximate squarer with a simple logic implementation and a redundant binary Booth recoder. It is especially effective in a system that already has a radix-8 multiplier. As a result, the effective area for the reciprocal table can be reduced by 25.4%. The proposed method has been verified by SystemC and Verilog models. The final results are confirmed by simulation with both random double precision numbers and an exhaustive suite of 17-bit test vectors.
ISSN:1063-8210
1557-9999
DOI:10.1109/TVLSI.2009.2036926