The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega, nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can...

This book describes the Splash 2 computing system as designed and built at the Supercomputing Research Center. This is a novel attached processor using Xilinx 4010 FPGAs as its processing elements and whose application programming language is VHDL. This is the first publication that details the complete Splash 2 project -- the hardware and software systems, the architecture and their implementations, and the design process by which the architecture evolved from an earlier version machine. This text allows you to understand why the machine has been engineered in the way it has. In addition to...

The first coherent exposition of the theory of binary quadratic forms was given by Gauss in the Disqnisitiones Arithmeticae. During the nine teenth century, as the theory of ideals and the rudiments of algebraic number theory were developed, it became clear that this theory of bi nary quadratic forms, so elementary and computationally explicit, was indeed just a special case of a much more elega, nt and abstract theory which, unfortunately, is not computationally explicit. In recent years the original theory has been laid aside. Gauss's proofs, which involved brute force computations that can...