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Optimizing Uniform Recurrence Equations Scheduling Strategies

This study delves into the On-the-Time Scheduling Problem of Uniform Recurrence Equations in VLSI Array Structures for Digital Signal Processing. It defines URE, explains linear, uniform, and affine schedules, and execution time computations. The scheduling vector X is crucial, obtained through solving linear programming problems. A case study involving a complex loop is presented, highlighting execution sequences and insights from linear, uniform, affine, and multi-dimensional scheduling strategies. Examples include Convolution, FIR filter, Selection sort, and a complex loop scenario.

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Optimizing Uniform Recurrence Equations Scheduling Strategies

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  1. 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

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

  3. Linear Schedule: Xp

  4. Uniform Schedule: Xp+ci

  5. Affine Schedule: Xip+ci • Execution Time: • Linear schedule: 2N-1. Affine: N

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

  7. Multi-dimensional Schedule • Multi-dimensional Uniform Schedule • Multi-dimensional Affine Schedule

  8. Multi-dimensional Affine Schedule

  9. Case Study • EX:A complex loop

  10. Solution

  11. Execution sequence

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

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