Titlebook: Application-Specific Arithmetic; Computing Just Right Florent de Dinechin,Martin Kumm Book 2024 The Editor(s) (if applicable) and The Autho

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Book 2024c arithmetic beyond the classic operators and the standard precisions. It targets silicon designers who have to do better with less in the post-Moore era, and FPGA developers who want to exploit the full possibilities of reconfigurable computing platforms.

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Computing Just Right: Accuracy Specification and Error Analysis,n application-specific way) which parameter values lead to best accurate design. This generic methodology is also shown to be well suited to the hierarchical design of complex computing cores assembled out of simpler ones and will be used throughout the book.

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designers who have to do better with less in the post-Moore era, and FPGA developers who want to exploit the full possibilities of reconfigurable computing platforms.978-3-031-42810-4978-3-031-42808-1

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Computing Just Right: Accuracy Specification and Error Analysis,roaches to the notion of rounding. It then states that for efficient application-specific arithmetic, operators should be accurate to their last bit. To reach this objective, it sketches a generic methodology: the error analysis of parametric designs, which can then be exploited to investigate (in a

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Fixed-Point Additionters of this book. The present chapter reviews the main techniques for adder construction, from simple but slow adders to larger and faster ones. Integer addition also received special attention in most FPGA architectures, and this chapter reviews in depth the specificities of addition in FPGAs.

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Sums of Weighted Bitsn one being that the associativity of the sum can be exploited at the bit level to build efficient architectures, called compressor trees, that perform such computations. This chapter defines a data structure, the bit heap, that captures sums of weighted bits. It then discusses the construction of a