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By analogy with the regular pumping of blood by the heart, a systolic array is an arrangement of processors in an array (often rectangular) where data flows synchronously across the array between neighbours, usually with different data flowing in different directions.
Each processor at each step takes in data from one or more neighbours (e.g. North and West), processes it and, in the next step, outputs results in the opposite direction (South and East).
An example of a systolic algorithm might be matrix multiplication. One matrix is fed in a row at a time from the top of the array and is passed down the array, the other matrix is fed in a column at a time from the left hand side of the array and passes from left to right. Dummy values are then passed in until each processor has seen one whole row and one whole column. At this point, the result of the multiplication is stored in the array and can now be output a row or a column at a time, flowing down or across the array.
See also: SISAL.
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