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Publication# Architectural improvements for field programmable counter arrays: enabling efficient synthesis of fast compressor trees on FPGAs

Paolo Ienne, Yusuf Leblebici, Philip Brisk, Alessandro Cevrero, Ajay Kumar Verma, Hadi Parandeh Afshar, Panagiotis Athanasopoulos

2008

Conference paper

2008

Conference paper

Abstract

The Field Programmable Counter Array (FPCA) was introduced to improve FPGA performance for arithmetic circuits. An FPCA is a reconfigurable IP core that can be integrated into an FPGA. To exploit the FPCA, a circuit is transformed by merging disparate addition and multiplication operations into large multi-input addition operations, which are synthesized as compressor trees on the FPCA; the remaining portion of the circuit is synthesized on the FPGA. This paper presents a series of architectural improvements to the FPCA that reduce routing delay, increase flexibility and component utilization, and simplify the integration process. Using an FPGA containing six FPCAs, we observed average and maximum speedups of 1.60x and 2.40x on a set of arithmetic benchmarks

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In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression. For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. Thus, the expression 1 + 2 × 3 is interpreted to have the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.

Multiplication

Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product. The multiplication of whole numbers may be thought of as repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the quantity of the other one, the multiplier; both numbers can be referred to as factors.

Multiplication table

In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. The oldest known multiplication tables were used by the Babylonians about 4000 years ago.

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