Stochastic rounding (SR) randomly maps a real number x to one of the two nearest values in
a finite precision number system. The probability of choosing either of these two numbers is …

Bfloat16 (" BF16") is a new floating-point format tailored specifically for high-performance
processing of Neural Networks and will be supported by major CPU and GPU architectures …

Gappa is a tool designed to formally verify the correctness of numerical software and
hardware. It uses interval arithmetic and forward error analysis to bound mathematical …

On modern multi-core, many-core, and heterogeneous architectures, floating-point
computations, especially reductions, may become non-deterministic and, therefore, non …

Stone masons were building bridges—and using mathematics—long before 1773, when
Coulomb published his groundbreaking mathematical analysis of some fundamental …

Floating-point arithmetic is known to be tricky: roundings, formats, exceptional values. The
IEEE-754 standard was a push towards straightening the field and made formal reasoning …

Mainstream math libraries for floating point (FP) do not produce correctly rounded results for
all inputs. In contrast, CR-LIBM and RLIBM provide correctly rounded implementations for a …

We present FloatX (Float eXtended), a C++ framework to investigate the effect of leveraging
customized floating-point formats in numerical applications. FloatX formats are based on …

In this paper, a new family of formats to deal with real number for applications requiring
round to nearest is proposed. They are based on shifting the set of exactly represented …

Reconfigurable architectures are becoming mainstream: Amazon, Microsoft and IBM are
supporting such architectures in their data centres. The computationally intensive nature of …