Optimized Binary64 and Binary128 Arithmetic with GNU MPFR

Vincent Lefèvre 1 Paul Zimmermann 2
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est
Abstract : We describe 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. We also introduce a new faithful rounding mode, which enables even faster computations. Those optimizations will be available in version 4 of MPFR.
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Vincent Lefèvre, Paul Zimmermann. Optimized Binary64 and Binary128 Arithmetic with GNU MPFR. 24th IEEE Symposium on Computer Arithmetic (ARITH 24), Jul 2017, London, United Kingdom. pp.18-26, ⟨10.1109/ARITH.2017.28⟩. ⟨hal-01502326⟩

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