Multiple Constant Multiplication Optimizations for Field Programmable Gate Arrays

1. Front Matter

   Pages I-XXXIII

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2. Introduction

   • Martin Kumm

   Pages 1-7

3. Background

   • Martin Kumm

   Pages 9-35

4. The Pipelined Multiple Constant Multiplication Problem

   1. Front Matter

      Pages 37-37

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   2. Optimal Pipelining of Precomputed Adder Graphs

      • Martin Kumm

      Pages 39-51

   3. The Reduced Pipelined Adder Graph Algorithm

      • Martin Kumm

      Pages 53-85

   4. Optimally Solving MCM Related Problems Using Integer Linear Programming

      • Martin Kumm

      Pages 87-111

   5. A Heuristic for the Constant Matrix Multiplication Problem

      • Martin Kumm

      Pages 113-124

5. FPGA Specific MCM Optimizations

   1. Front Matter

      Pages 125-125

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   2. Combining Adder Graphs with LUT-Based Constant Multipliers

      • Martin Kumm

      Pages 127-137

   3. Optimization of Hybrid Adder Graphs Containing Embedded Multipliers

      • Martin Kumm

      Pages 139-152

   4. Floating Point Multiple Constant Multiplication

      • Martin Kumm

      Pages 153-162

   5. Optimization of Adder Graphs with Ternary (3-Input) Adders

      • Martin Kumm

      Pages 163-175

   6. Conclusion and Future Work

      • Martin Kumm

      Pages 177-179

6. Back Matter

   Pages 181-206

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This work covers field programmable gate array (FPGA)-specific optimizations of circuits computing the multiplication of a variable by several constants, commonly denoted as multiple constant multiplication (MCM). These optimizations focus on low resource usage but high performance. They comprise the use of fast carry-chains in adder-based constant multiplications including ternary (3-input) adders as well as the integration of look-up table-based constant multipliers and embedded multipliers to get the optimal mapping to modern FPGAs. The proposed methods can be used for the efficient implementation of digital filters, discrete transforms and many other circuits in the domain of digital signal processing, communication and image processing.

• Digital Arithmetic
• Digital Filter
• Discrete Optimization
• The Pipelined Multiple Constant Multiplication Problem
• Hybrid Adder Graphs Containing Embedded Multipliers

• Universität Kassel, Kassel, Germany

  Martin Kumm

Martin Kumm is working as a postdoctoral researcher at the University of Kassel. His current research interests are digital arithmetic, digital signal processing and discrete optimization, all in the context of field programmable gate arrays. 

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