On the Time Scheduling Problem of Uniform Recurrence Equations Wei-Yang Lin and Tai-Lin Chin ECE 734 VLSI Array Structures for Digital Signal Processing

Uniform Recurrence Equation URE Definition: where Ex: matrix multiplication AB=C

Linear Schedule: Xp

Uniform Schedule: Xp+c i

Affine Schedule: X i p+c i Execution Time: Linear schedule: 2N-1. Affine: N

Scheduling Vector X The scheduling vector X can be obtained by solving a linear programming problem. Example: Linear Schedule Duality XD  1

Multi-dimensional Schedule Multi-dimensional Uniform Schedule Multi-dimensional Affine Schedule

Case Study EX: A complex loop

Solution

Execution sequence

Conclusion Linear schedule Uniform schedule Affine schedule Multi-dimensional schedule Case Study Convolution FIR filter Selection sort A complex loop case