Correctly Rounded Arbitrary-Precision Floating-Point Summation

Vincent Lefèvre (1)

1 ARIC - Arithmetic and Computing

We present a fast algorithm together with its low-level implementation of correctly rounded arbitrary-precision floating-point summation. The arithmetic is the one used by the GNU MPFR library: radix 2; no subnormals; each variable (each input and the output) has its own precision. We also give a worst-case complexity of this algorithm and describe how the implementation is tested.

Mots clés: arbitrary precision; correct rounding; multiple precision; summation; floating point

Domaines: Arithmétique des ordinateurs

Vincent Lefèvre. Correctly Rounded Arbitrary-Precision Floating-Point Summation. IEEE Transactions on Computers, 2017, 66 (12), pp.14. ⟨10.1109/TC.2017.2690632⟩. ⟨hal-01394289v2⟩