Title :
Short Division of Long Integers
Author :
Harvey, David ; Zimmermann, Paul
Author_Institution :
Courant Inst. of Math. Sci., New York Univ., New York, NY, USA
Abstract :
We consider the problem of short division - i.e., approximate quotient - of multiple-precision integers. We present ready-to-implement algorithms that yield an approximation of the quotient, with tight and rigorous error bounds. We exhibit speedups of up to 30% with respect to GMP division with remainder, and up to 10% with respect to GMP short division, with room for further improvements. This work enables one to implement fast correctly rounded division routines in multiple-precision software tools.
Keywords :
approximation theory; floating point arithmetic; software tools; GMP division; approximation; error bounds; floating-point division; multiple-precision integers; multiple-precision software tools; ready-to-implement algorithms; short division; Algorithm design and analysis; Approximation algorithms; Approximation methods; Context; Error analysis; Libraries; Tuning; GNU MP; GNU MPFR; arbitrary precision; floating-point division;
Conference_Titel :
Computer Arithmetic (ARITH), 2011 20th IEEE Symposium on
Conference_Location :
Tubingen
Print_ISBN :
978-1-4244-9457-6
DOI :
10.1109/ARITH.2011.11
