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c The index space with indexes interchanged.
stand density index space (Fig. 4).
d The index space flipped horizontally.
e Code example with two array references having an identical index space.
b The index space of the array reference A[ i][j].
Suppose that in the d-th dimension, we have S d discrete elements to be mapped from the index space.
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During the third step redundancy is introduced by deriving three equivalent algorithms with disjoint index spaces.
First, redundancies are introduced at the computational level by deriving three equivalent algorithms but with disjoint index spaces.
Finally, we perform mapping of the accommodated index spaces into fault-tolerant systolic array using valid transformation matrix.
Second, we perform the accommodation of index spaces to the projection direction to obtain hexagonal SA with optimal number of processing elements (PE) for a given problem size.
To obtain the parameters ŝ d and t ^ d, we normalize both feature and index spaces to (0, 1) and shift every normalized index i d by 1 2 S d to the right to fit the respective c i d d, such that c i d d int S d - 1 ( max ) d - int 0 ( min ) d = 2 i d + 1 2 S d. (7).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com