Application-Specific Arithmetic

Florent de Dinechin is a professor at INSA-Lyon, France. His research interests include computer architecture and compilation, hardware and software computer arithmetic, FPGA arithmetic and FPGA computing at large, floating-point, formal proof for arithmetic algorithms, elementary function evaluation, and digital signal processing. He authored more than 100 international peer-reviewed publications and was the general chair of the International Symposium on Computer Arithmetic in 2022. Martin Kumm is a professor at Fulda University of Applied Sciences, Germany. His research focus is arithmetic circuits and their optimization, design automation, machine learning, and digital signal processing, all with particular emphasis on reconfigurable systems. He is the author or coauthor of more than 60 peer-reviewed publications.Together they develop the open-source FloPoCo arithmetic core generator, a project launched in 2008 which received the community award of the International Conference on Field Programmable Logic and Application in 2017.

• Chapter 1 Introduction.- Chapter 2 Number Formats.- Chapter 3 Computing Just Right: Accuracy Specification and Error Analysis.- Chapter 4 Field Programmable Gate Arrays.- Part 1 Revisiting Classic Arithmetic.- Chapter 5 Fixed-Point Addition.- Chapter 6 Fixed-Point Comparison.- Chapter 7 Sums of Weighted Bits.- Chapter 8 Fixed-Point Multiplication.- Chapter 9 Fixed-Point Division.- Chapter 10 Shifters and Leading Bit Counters.- Chapter 11 Basic Floating-Point Operators.- Part 2 Operator Specialization.- Chapter 12 Multiplication by Constants.- Chapter 13 Division by Constants.- Chapter 14 Fixed-Point Squares, Cubes, and Other Integer Powers.- Chapter 15 Specialization and Fusion of Floating-Point Operators.- Part 3 Generic Methods for Fixed-Point Function Approximation.- Chapter 16 Generalities on Fixed-Point Function Approximation.- Chapter 17 Function Evaluation Using Tables and Additions.- Chapter 18 Polynomial-Based Architectures for Function Evaluation.- Chapter 19 Digit Recurrence for Algebraic Functions.- Part 4 Example Composite Operators.- Chapter 20 Fixed-Point Sine and Cosine.- Chapter 21 Floating-Point Accumulation and Sum-of-Products.- Chapter 22 Floating-Point Exponential.- Part 5 Application Domains.- Chapter 23 Arithmetic in The Design of Linear Time-Invariant Filters.- Chapter 24 Arithmetic for Deep Learning.- Part 6 Appendix.- Chapter 25 Appendix A Custom Arithmetic Datapath Design with FloPoCo.- Chapter 26 Appendix B Optimization Using Integer Linear Programming.