Buffer Placement and Sizing for High-Performance Dataflow Circuits

Commercial high-level synthesis tools typically produce statically scheduled circuits. Yet, effective C-to-circuit conversion of arbitrary software applications calls for dataflow circuits, as they can handle efficiently variable latencies (e.g., caches), unpredictable memory dependencies, and irregular control flow. Dataflow circuits exhibit an unconventional property: registers (usually referred to as “buffers”) can be placed anywhere in the circuit without changing its semantics, in strong contrast to what happens in traditional datapaths. Yet, although functionally irrelevant, this placement has a significant impact on the circuit’s timing and throughput. In this work, we show how to strategically place buffers into a dataflow circuit to optimize its performance. Our approach extracts a set of choice-free critical loops from arbitrary dataflow circuits and relies on the theory of marked graphs to optimize the buffer placement and sizing. Our performance optimization model supports important high-level synthesis features such as pipelined computational units, units with variable latency and throughput, and if-conversion. We demonstrate the performance benefits of our approach on a set of dataflow circuits obtained from imperative code.

Generalizations of a Conway algebra for oriented surface-links via marked graph diagrams

In 1987, Przytyski and Traczyk introduced an algebraic structure, called a Conway algebra, and constructed an invariant of oriented links, which is a generalization of the HOMFLY-PT polynomial invariant. In 2018, Kim generalized a Conway algebra, which is an algebraic structure with two skein relations, which is called a generalized Conway algebra. In 2017, Joung, Kamada, Kawauchi and Lee constructed a polynomial invariant of oriented surface-links by using marked graph diagrams. In this paper, we will introduce generalizations [Formula: see text] and [Formula: see text] of a Conway algebra and a generalized Conway algebra, which are called a marked Conway algebra and a generalized marked Conway algebra, respectively. We will construct invariants valued in [Formula: see text] and [Formula: see text] for oriented marked graphs and oriented surface-links by applying binary operations to classical crossings and marked vertices via marked graph diagrams. The polynomial invariant of oriented surface-links is obtained from the invariant valued in the marked Conway algebra with additional conditions.