4 citations · 10 across the 5 of their papers we have counts for
5 papers
On the maximum relative error when computing x^n in floating-point arithmetic
Stef Graillat, Vincent Lefèvre, Jean-Michel Muller
In this paper, we improve the usual relative error bound for the computation of x^n through iterated multiplications by x in binary floating-point arithmetic. The obtained error bo…
Radix Conversion for IEEE754-2008 Mixed Radix Floating-Point Arithmetic
O. Kupriianova, Ch. Lauter, J. -M. Muller
Conversion between binary and decimal floating-point representations is ubiquitous. Floating-point radix conversion means converting both the exponent and the mantissa. We develop…
Floating-Point Arithmetic on Round-to-Nearest Representations
Peter Kornerup, Jean-Michel Muller, Adrien Panhaleux
Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper w…
Computing Integer Powers in Floating-Point Arithmetic
Peter Kornerup, Vincent Lefèvre, Jean-Michel Muller
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We sh…
Finding the "truncated" polynomial that is closest to a function
Nicolas Brisebarre, Jean-Michel Muller
When implementing regular enough functions (e.g., elementary or special functions) on a computing system, we frequently use polynomial approximations. In most cases, the polynomial…