Short Division of Long Integers

—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-floating-point division, arbitrary precision, GNU MP, GNU MPFR

• Type: Journal
• Year: 2011
• Where: ARITH
• Authors: David Harvey, Paul Zimmermann
• Keywords: Applied Computing, ARITH 2011, Gnu Mp, Multiple Precision, Precision Integers