Affiliation:
1. Department of Computer Science, ETH Zurich, Zurich, Switzerland
2. Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY
Abstract
Sorting is a fundamental problem in computer science and has been studied extensively. Thus, a large variety of sorting methods exist for both software and hardware implementations. For the latter, there is a trade-off between the throughput achieved and the cost (i.e., the logic and storage invested to sort
n
elements). Two popular solutions are bitonic sorting networks with
O
(
n
log
2
n
) logic and storage, which sort
n
elements per cycle, and linear sorters with
O
(
n
) logic and storage, which sort
n
elements per
n
cycles. In this article, we present new hardware structures that we call
streaming sorting networks
, which we derive through a mathematical formalism that we introduce, and an accompanying domain-specific hardware generator that translates our formal mathematical description into synthesizable RTL Verilog. With the new networks, we achieve novel and improved cost-performance trade-offs. For example, assuming that
n
is a two-power and
w
is any divisor of
n
, one class of these networks can sort in
n
/;
w
cycles with
O
(
w
log
2
n
) logic and
O
(
n
log
2
n
) storage; the other class that we present sorts in
n
log
2
n
/;
w
cycles with
O
(
w
) logic and
O
(
n
) storage. We carefully analyze the performance of these networks and their cost at three levels of abstraction: (1) asymptotically, (2) exactly in terms of the number of basic elements needed, and (3) in terms of the resources required by the actual circuit when mapped to a field-programmable gate array. The accompanying hardware generator allows us to explore the entire design space, identify the Pareto-optimal solutions, and show superior cost-performance trade-offs compared to prior work.
Publisher
Association for Computing Machinery (ACM)
Subject
Electrical and Electronic Engineering,Computer Graphics and Computer-Aided Design,Computer Science Applications
Cited by
28 articles.
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