Three-dimensional optical architecture and data-parallel algorithms for massively parallel computing

Abstract

The parallel nature of optics and free-space propagation, together with its freedom from communication interference, makes it ideal for designing massively paralle l computers. Our architecture is highly amenable to optical implementations and aims at data-parallel applications. �Pt ics, due to its inherent p arallelism and no ninterfering communications, is under serious consideration for de signs of massively parallel processing systems of the future. To contribute to this un dertaking, designers at the University of Arizona's Department of Electrical and Computing Engi neering explored a three-dimensional oplical computing architecture under a grant from the US National Science Foundation. 11lis model-a single-instruction, multiple-data system, or SIMD-e xploits spatial parallelism and processes 2D binary images as fundamental computational entities bas ed on symbolic substi tution logic. A better alternative than electronic mesh computers, this system effectively imple ments highly structured data-parallel algorithms, such as signal and image processing. partial dif terential equations. multidimensional numerical second) and input dat a rates appr oaching 1 Gbyte/s. A common factor of these applications is a high degree of data parallelism in which simple arith metic and logic operations must simultaneously take place across all data points. 1 Computing these applications with high-throughput rates requires massively parallel processing; however, traditional electronic technology faces major limitations in achieving massive parallelism. A key feature of this type of processing is the l arge amount of communication required among the processing elements (PEs). While the design of high-perfor mance PEs has pr ogressed significantly, the progress in designing high-perfoffilancc intercon nection networks has not been satisfactory. The major bottlenecks in today's massively parallel processing systems include the limited communi cation bandwidth and the lack of cost-effective means of achieving parallel I/O.'"

A parallel optical implementation of arithmetic operations

“…Optical symbolic substitution was used to implement addition [19,20] and multiplication [21,23]. Probably the most notable work in the literature is Louri's [22,24]: He presented a parallel optical processor capable of performing various arithmetic operations. In his model, the bits of the operands are stored in separate planes and using a technique called perfect shuffle, the corresponding bits of the operands are placed next to each other to perform logical operations using symbolic substitution.…”

“…But in this model, it is impossible to carry out useful operations like finding the minimum, calculating the sum or the average, or in general merging the results of independent branches. To make these operations possible, we add a new bit array operation called BITFOLD() to the processor (similar to Louri's horizontal and vertical shift functions [24]). Given the bit array B x and integer k, after the operation B y 'BitFoldðB x ,kÞ, the i-th bit of B y is the ð2 k þ iÞ-th bit of B x .…”

“…We combine bit arrays to form large arrays of numbers (Section 3.1) and implement arithmetic operations on these number arrays using processor's bit array operations (Section 3.3). The encoding of numbers and their operations are largely based on the processor presented by Louri in his three-dimensional optical architecture [24].…”

“…In fact, the studies for using optics for computing began more than five decades ago [1]. Especially in years 1980-1995, a large number of researchers invested in optical computing and presented several techniques to use optics in parallel processing, such as optical shadow casting [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], optical symbolic substitution [18][19][20][21][22][23][24], and optical vector-matrix multiplication [1,[25][26][27][28][29][30][31]. After this golden age of optical computing, it experienced a slowdown near the end of the last millennium.…”

Optical content-addressable parallel processor: architecture, algorithms, and design concepts

“…Optics advantages have been cited on numerous occasions [3,4,5,6]. These include inherent parallelism, high spatial and temporal bandwldths, and non-interfering communications.…”