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--- melange:papers:fall2021 [2021/09/23 08:07]
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+@InProceedings{10.1007/3-540-17179-7_30,
+  author       = {Rajopadhye, Sanjay V. and Purushothaman, S. and Fujimoto, Richard M.},
+  editor       = {Nori, Kesav V.},
+  title        = {On synthesizing systolic arrays from Recurrence Equations with Linear Dependencies},
+  booktitle    = {Foundations of Software Technology and Theoretical Computer Science},
+  year         = {1986},
+  publisher    = {Springer Berlin Heidelberg},
+  address      = {Berlin, Heidelberg},
+  pages        = {488--503},
+  abstract     = {We present a technique for synthesizing systolic architectures from Recurrence Equations. A class of such equations (Recurrence Equations with Linear Dependencies) is defined and the problem of mapping such equations onto a two dimensional architecture is studied. We show that such a mapping is provided by means of a linear allocation and timing function. An important result is that under such a mapping the dependencies remain linear. After obtaining a two-dimensional architecture by applying such a mapping, a systolic array can be derived if the communication can be spatially and temporally localized. We show that a simple test consisting of finding the zeroes of a matrix is sufficient to determine whether this localization can be achieved by pipelining and give a construction that generates the array when such a pipelining is possible. The technique is illustrated by automatically deriving a well known systolic array for factoring a band matrix into lower and upper triangular factors.},
+  isbn         = {978-3-540-47239-1},
+  loc          = {Foundations of Software Technology and Theoretical Computer Science},
+  number       = {},
+  doi          = {10.1007/3-540-17179-7_30},
+  url          = {https://link.springer.com/chapter/10.1007/3-540-17179-7_30}
+}

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