Section: New Results

Optimized Binary64 and Binary128 Arithmetic with GNU MPFR

Participant : Paul Zimmermann.

Together with Vincent Lefèvre (ARIC team, Inria Rhône-Alpes), Paul Zimmermann wrote an article “Optimized Binary64 and Binary128 Arithmetic with GNU MPFR”, and presented it at the 24th IEEE Symposium on Computer Arithmetic [9]. This article describes algorithms used to optimize the GNU MPFR library when the operands fit into one or two words. On modern processors, a correctly rounded addition of two quadruple precision numbers is now performed in 22 cycles, a subtraction in 24 cycles, a multiplication in 32 cycles, a division in 64 cycles, and a square root in 69 cycles. It also introduces a new faithful rounding mode, which enables even faster computations. These optimizations will be available in version 4 of MPFR.