Large integer multiplication is becoming a major challenge for FPGA-based acceleration of
many cryptographic applications. Existing techniques for decomposing and optimizing large …

Achieving speed and accuracy for math library functions like exp, sin, and log is difficult. This
is because low-level implementation languages like C do not help math library developers …

In recent years, researchers have proposed a number of automated tools to identify and
improve floating-point rounding error in mathematical expressions. However, users struggle …

Precision tuning or customized precision number representations is emerging, in these
recent years, as one of the most promising techniques that make it possible to save the …

Equality saturation, originally developed in the late 1970s for use in automated theorem
provers, has been recently advanced to perform scalable rule-based rewriting for …

Standard implementations of functions like sin and exp optimize for accuracy, not speed,
because they are intended for general-purpose use. But just like many applications tolerate …

New low-precision accelerators, vector instruction sets, and library functions make
maximizing accuracy and performance of numerical code increasingly challenging. Two …

In this article, we apply a new methodology for precision tuning to the N-body problem. Our
technique, implemented in a tool named POP, makes it possible to optimize the numerical …

We introduce a floating-point (FP) error optimization approach called Arfa that partitions the
domain D of an FP expression fe into regimes and rewrites fe in each regime where fe …

Many floating-point formats are available, providing all different levels of precision. By
mixing several of these formats in the same program, it is possible to achieve good …