Title :
A rounding method with improved error tolerance for division by convergence
Author :
Kong, Inwook ; Swartzlander, Earl E., Jr.
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Texas at Austin, Austin, TX
Abstract :
A new rounding method for division by convergence is presented. It allows twice the error tolerance of current methods, so it allows the multiplier of a 3-iteration Goldschmidt divider to be implemented using only 3 extra bits. The new rounding method applies special truncation methods at the final iteration step, and it requires a minor modification in rounding constants of the multiplier. It has been verified using a SystemC model of the Goldschmidt divider supporting variable precision. The verification consists of two parts: the maximum error of approximate quotients and the rounding result correctness. The maximum error of approximate quotients is checked by analysis and via simulation. The final rounding results are checked with both random double precision floating-point significants and exhaustive 17-bit precision test vectors.
Keywords :
floating point arithmetic; iterative methods; roundoff errors; vectors; 17-bit precision test vectors; 3-iteration Goldschmidt divider; SystemC model; approximate quotients maximum error; division by convergence; error tolerance; random double precision floating-point significands; rounding method; rounding result correctness; truncation methods; Analytical models; Circuits; Computer architecture; Computer errors; Convergence; Degradation; Error correction; Frequency; Pipelines; Testing;
Conference_Titel :
Signals, Systems and Computers, 2008 42nd Asilomar Conference on
Conference_Location :
Pacific Grove, CA
Print_ISBN :
978-1-4244-2940-0
Electronic_ISBN :
1058-6393
DOI :
10.1109/ACSSC.2008.5074740
