Conference PaperPDF Available

A massively parallel RNS architecture

Authors:

Abstract

Parallelism on the algorithmic, architectural, and arithmetic levels is exploited in the design of a residue number system (RNS) based architecture. The architecture is based on modulo processors. Each modulo processor is implemented by a two-dimensional systolic array composed of very simple cells. The decoding state is implemented using a two-dimensional array. The decoding bottleneck is eliminated. The whole architecture is pipelined, which leads to a high throughput rate. High speed algorithms for modulo addition, modulo multiplication, and RNS decoding are presented
A preview of the PDF is not available
... The CRT gives a straight forward way in converting a RNS number {x 1 , . . . , x N } to its positional representation X and this has given rise to its application in almost all of the operations in residue arithmetic, including scaling, comparison [11,30], etc. It was actually the fact that the CRT showed up firstly around 1500 years ago [16] which was then followed by the arising of number theoretical properties as well as residue arithmetic [28]. ...
Article
Modular multiplication can be performed in the residue number system (RNS) using a type of Montgomery reduction. This paper presents an alternative in which RNS modular multiplication are performed by using the core function. All of the intermediate calculations use short wordlength operations within the RNS. This work contributes to the long wordlength modular multiplication operation \(Z = A \times B \mod M\), the basis of many DSPs and public-key cryptosystems.
Article
Genetic algorithms are a group of stochastic search algorithms with a broad field of application. Although highly successful in many fields, genetic algorithms in general suffer from long execution times. In this article we describe parallel models for genetic algorithms in general and the massively parallel Diffusion Model in particular, in order to speedup the execution.Implemented in hardware, the Diffusion Model constitutes an efficient, flexible, scalable and mobile machine learning system. This fine-grained system consists of a large number of processing nodes that evolve a large number of small, overlapping subpopulations. Every processing node has an embedded CPU that executes a linear machine code representation at a rate of up to 20,000 generations per second.Besides being efficient, implemented in hardware this model is highly portable and applicable to mobile, on-line applications. The architecture is also scalable so that larger problems can be addressed with a system with more processing nodes. Finally, the use of linear machine code as genetic programming representation and VHDL as hardware description language, makes the system highly flexible and easy to adapt to different applications.Through a series of experiments we determine the settings of the most important parameters of the Diffusion Model. We also demonstrate the effectiveness and flexibility of the architecture on a set of regression problems, a classification application and a time series forecasting application.
Chapter
Full-text available
Herbivores, decomposers, and fire are three alternative consumers of primary production in grasslands, each with different requirements for and effects on carbon (C) and nitrogen (N). Differences between plant species in their tissue C and N chemistry can determine which of these three consumer pathways the bulk of primary production will follow in a particular system. This stoichiometric approach is applied to native humid grasslands and their dominant tall-grass species.
Article
Full-text available
Ecosystem engineers are organisms that directly or indirectly modulate the availability of resources to other species, by causing physical state changes in biotic or abiotic materials. In so doing they modify, maintain and create habitats. Autogenic engineers (e.g. corals, or trees) change the environment via their own physical structures (i.e. their living and dead tissues). Allogenic engineers (e.g. woodpeckers, beavers) change the environment by transforming living or non-living materials from one physical state to another, via mechanical or other means. The direct provision of resources to other species, in the form of living or dead tissues is not engineering. Organisms act as engineers when they modulate the supply of a resource or resources other than themselves. We recognise and define five types of engineering and provide examples. Humans are allogenic engineers par excellence, and also mimic the behaviour of autogenic engineers, for example by constructing glasshouses. We explore related concepts including the notions of extended phenotypes and keystone species. Some (but not all) products of ecosystem engineering are extended phenotypes. Many (perhaps most) impacts of keystone species include not only trophic effects, but also engineers and engineering. Engineers differ in their impacts. The biggest effects are attributable to species with large per capita impacts, living at high densities, over large areas for a long time, giving rise to structures that persist for millennia and that modulate many resource flows (e.g. mima mounds created by fossorial rodents). The ephemeral nests constructed by small, passerine birds lie at the opposite end of this continuum. We provide a tentative research agenda for an exploration of the phenomenon of organisms as ecosystem engineers, and suggest that all habitats on earth support, and are influenced by, ecosystem engineers.
Article
Focuses on individual plants and their immediate requirements for competitive success, especially in semiarid and arid environments.-from Author
Article
Field data came from Wind Cave National Park, South Dakota. Laboratory estimates of net nitrogen mineralization were highest in soils from the more altered areas of prairie dog colonies (Cynomys ludovicianus) and lowest in adjacent, lightly grazed, uncolonized grassland. The ratio of CO2:net N mineralized, an index of immobilization, was highest in the uncolonized grassland, lowest in the altered core areas. Soil moisture was an important modifier of in situ field estimates of net N mineralization. Root biomass, an important C source for decomposers in perennial grasslands, was lowest in the altered core area and highest in adjacent uncolonized grassland. Decreased N immobilization and increased net N mineralization in laboratory incubations likely resulted from decreased root C inputs in grazer areas, which limited C availability to decomposers. -from Authors
Article
1. This comment refutes the conclusion of Snaydon (1991) that replacement designs are fundamentally flawed and that additive designs should be used in preference. 2. Similarities and differences between additive and replacement designs are clarified, using de Wit's (1960) definitions of coefficients for competitive ability and resource complementarity. 3. Additive and replacement designs share similar problems. In both cases, the values of competition coefficients depend on the experimenter's choice of absolute and relative densities of the pure stands, and vary with the shape of the yield - density response curves. They also share similar statistical difficulties. 4. The two approaches serve complementary purposes. Additive designs are appropriate for quantifying inter-component competition regardless of intra-component competition. Replacement designs are appropriate for questions based on the similarity of competing taxa and the relationship of inter- to intra-component competition.
Article
The ecological trends in the vegetation of the calden (Prosopis caldenia Burk.) forest of central Argentina have generally been explained with a model that assumed a unique equilibrium state or "climax." This model does not adequately explain the ecological changes that occur in the understory of the calden forest. Recently, models that present different stable states of vegetation have been suggested. These vegetation states do not change unless relatively drastic management or climatic actions occur. Observations of vegetation changes, grazing regimes, and other aspects of management permitted the development of a basic scheme to explain changes in the herbaceous layer in the calden forest, based on the state and transition model. Five stable states and 9 transitions are proposed to account for current herbaceous associations and their origins. This model seems to more accurately explain transitions between the different vegetation states in the area, some of which could not be readily explained by the "climax" model.
Article
Absfrad -A O(l) algorithm for large modulo addition for residue number system (RNS) based archictectures is proposed. The addition is done in a fixed number of stages which does not depend on the size of the modulus. The proposed modulo adder is much faster than the previous adders and more area efficient. The implementation of the adder is modular and is based on simple cells which leads to efficient VLSI realization. I. INTRODUC~ION Recently, the residue member system (RNS) is receiving in-creased attention due to its ability to support high-speed concur-rent arithmetic [ 11. Applications such as fast Fourier transform, digital filtering, and image processing utilize the high-speed RNS arithmetic operations; addition and multiplication, do not require the difficult RNS operations such as division and magni-tude comparison. The technological advantages offered by VLSI have added a new dimension in the implementation of RNS-based architectures [2]. Several high-speed VLSI special pur-pose digital signal processors have been successfully imple-mented [31-[51. Modulo addition represents the computational kernel for RNS-based architectures. Subtraction is performed by adders using the additive inverse property [6]. Multiplication can be transformed into addition by several techniques [7]. Also, mod-ulo addition is the basic element in the conversion from RNS to binary using the Chinese remainder theorem (CRT) [6]. Banerji [8] analyzed modulo addition in MSI technology. A VLSI analy-sis of modulo addition has been reported in [9]-[11]. In general, lookup tables and PLAs have been the main logical modules used when the data granularity is the word. It has been found that such structure is only efficient for small size moduli. For medium size and large moduli, bit-level structures are more efficient, where the data granularity is the bit [12]. In this paper, we present a modulo adder for medium size and large moduli. It is based on using a two-dimensional array of very simple cells (full adders). The modulo addition is per-formed in a fixed time delay independent of the size of the moduli. 11. RESIDUE NUMBER SYSTEM (RNS)