Abstract. Nowadays, many embedded processors include in their architecture on-chip static memories, so called scratch-pad memories (SPM). Compared to cache, these memories do not require complex control logic, thus resulting in increased efficiency both in silicon area and energy consumption. Last years, many papers have proposed algorithms to allocate memory segments in SPM in order to enhance its usage. However, very few care about the SPM architecture itself, to make it more controllable, more power efficient and faster. This paper proposes architecture extensions to automatically load code into the SPM whilst it is fetched for execution to reduce the SPM updating delays, which motivates a very dynamic use of the SPM. We test our proposal in a derivation of the Simplescalar simulator, with typical embedded benchmarks. The results show improvements, on average, of 30.6% in energy saving and 7.6% in performance compared to a system with cache.
Given a subset D of the interval (0, 1), if a Borel set A ⊂ [0, 1) contains no pair of elements whose difference modulo 1 is in D, then how large can the Lebesgue measure of A be? This is the analogue in the circle group of a well-known problem of Motzkin, originally posed for sets of integers. We make a first treatment of this circle-group analogue, for finite sets D of missing differences, using techniques from ergodic theory, graph theory and the geometry of numbers. Our results include an exact solution when D has two elements at least one of which is irrational. When every element of D is rational, the problem is equivalent to estimating the independence ratio of a circulant graph. In the case of two rational elements, we give an estimate for this ratio in terms of the odd girth of the graph, which is asymptotically sharp and also recovers the classical solution of Cantor and Gordon to Motzkin's original problem for two missing differences.
The fractional and circular chromatic numbers are the two most studied non-integral refinements of the chromatic number of a graph. Starting from the definition of a coloring base of a graph, which originated in work related to ergodic theory, we formalize the notion of a gyrocoloring of a graph: the vertices are colored by translates of a single Borel set in the circle group, and neighbouring vertices receive disjoint translates. The corresponding gyrochromatic number of a graph always lies between the fractional chromatic number and the circular chromatic number. We investigate basic properties of gyrocolorings. In particular, we construct examples of graphs whose gyrochromatic number is strictly between the fractional chromatic number and the circular chromatic number. We also establish several equivalent definitions of the gyrochromatic number, including a version involving all finite abelian groups.
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