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We describe APE-100, a SIMD, modular parallel processor architecture for large scale scientific computation. The largest configuration that will be implemented in the present design will deliver a peak speed of 100 Gflops. This performance is, for instance, required for high precision computations in Quantum Chromo Dynamics, for which APE-100 is very well suited.

This paper presents the realization of binary and floating-point comparators on FPGA. The implementation is done by exploiting the primitive instantiation of FPGA resources which has enabled a significant improvement in resource utilization in terms of Look-Up Table (LUT) usage and overall combinational path delay when compared to the conventional inference approach. The comparator architectures are implemented using Vivado 2020.1 and ISE Design Suite 14.7 environment on multiple Xilinx FPGA platforms and are compared with the existing designs. The results indicate an improvement of 33.33% and 45.45% in LUT utilization, 14.41% and 30.73% in delay for 32-bit and 64-bit binary comparators respectively, compared to the existing architectures. The proposed floating-point comparator requires 88.57% and 285.29% lesser LUTs for single precision and double precision representation respectively, compared to the existing design.

I trace the main steps of the first fifty-five years of my career as an applied mathematician, pausing from time to time to describe problems that arose in asymptotics and numerical analysis and had far-reaching effects on this career.

Lecture delivered at Asymptotics and Applied Analysis, Conference in Honor of Frank W. J. Olver's 75th Birthday, January 10–14, 2000, San Diego State University, San Diego, California.

Editors' Note: Frank W. J. Olver died on April 23, 2013. The following text was typed by his son, Peter J. Olver, from handwritten notes found among his papers. At times the writing is unpolished, including incomplete sentences, but the editors have decided to leave it essentially the way it was written. However, for clarity, some abbreviations have been written out in full. A couple of handwritten words could not be deciphered, and a guess for what was intended is enclosed in brackets: […]. Endnotes have been made into footnotes within the body of the article. References were mostly not included in the handwritten text, but rather listed in order at the end. Citations to references have been included at the appropriate point in the text.

Explicit algebraic expressions are derived for the roots of a cubic equation having one real and two complex roots. As opposed to traditional methods for direct (that is, non-iterative) solution, evaluation of the expressions is unconditionally numerically stable. A floating-point error analysis of the computations is given, which shows that the computed roots have extremely small relative errors. The computations are proved to be backward stable, that is, the computed roots are exact for a closely neighbouring cubic equation. Applications and uncertainty propagation are also considered.

We describe APE-100, a SIMD, modular and fine-grained parallel processor architecture for large scale scientific computations. The largest configuration that will be implemented in the present design delivers a peak speed of 100 Gflops. This performance is, for instance, required for high precision computations in Quantum Chromo Dynamics, for which APE-100 is very well suited.