New mathematical insights and rigorous results are often gained through extensive
experimentation using numerical examples or graphical images and analyzing them. Today …

IEEE 64-bit floating-point arithmetic is sufficient for most scientific applications, but a rapidly
growing body of scientific computing applications requires a higher level of numeric precision…

A new set of benchmarks has been developed for the performance evaluation of highly
parallel supercomputers. These benchmarks consist of five ‘parallel kernel” benchmarks and …

This article describes the design rationale, a C implementation, and conformance testing of
a subset of the new Standard for the BLAS (Basic Linear Algebra Subroutines): Extended …

This paper describes the “fractional Fourier transform,” which admits computation by an
algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the …

Conventional algorithms for computing large one-dimensional fast Fourier transforms (FFTs),
even those algorithms recently developed for vector and parallel computers, are largely …

Given the variety of numerical errors that can occur, floating-point programs are difficult to
write, test and debug. One common practice employed by developers without an advanced …

Over the past two decades, computational methods have radically changed the ability of
researchers from all areas of scholarship to process and analyze data and to simulate complex …

… Piotr Luszczek, David Bailey, Jack Dongarra, Jeremy Kepner, Robert Lucas, Rolf
Rabenseifner, Daisuke Takahashi … (H L … 1 E (A H P C R C …

A quad-double number is an unevaluated sum of four IEEE double precision numbers,
capable of representing at least 212 bits of significand. We present the algorithms for various …