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On the Time Scheduling Problem of Uniform Recurrence Equations

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.

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On the Time Scheduling Problem of Uniform Recurrence Equations

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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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