An Integer Programming Approach to Instruction Scheduling

1. An Integer Programming Approach to Instruction Scheduling Matt Streeter Carsten Schwicking

2. Objective • To use integer programming to obtain optimal instruction schedules • Assume partioning has already been done (copies inserted, etc.)

3. Optimization & Constraints • Optimize schedule length • Constraints • Single execution (of each instruction) • Resource • Data dependence • Not yet dealing with crossbar constraint

4. Formulation Source • Daniel Kaestner and Sebastian Winkel. “ILP-based Instruction Scheduling for IA-64,” in LCTES 2001. • Used a real multiple issue architecture • IA-64 has VLIW characteristics

5. Integer Programming Formulation • Define a variable for each possible instruction, start time, and function unit tuple • Xkm t  {0,1} • m = instruction id • t = start time (cycle #) • k = execution unit #

6. Constraints:Instruction Executed Once

7. Constraints:Resource • Rk = # of execution units of type k • R(n) = all possible execution units for n

8. Constraints:Data Dependence • where n must not execute until m finishes

9. Preliminary results • Generated random data dependency trees • Each node has degree chosen uniformly at random from {0, 1, 2, 3}; durations chosen from {1, 2, 3, 4}; function unit assigned at random • 4 function units, one of each type • Maximum height H (=6 here)

10. Preliminary results • Optimal scheduling only feasible for basic blocks of ~10 instructions • An alternative is to search for locally optimal schedules

11. Preliminary results • Use simple heuristic (list scheduling) to generate a “center” schedule • Until 10 seconds have elapsed: • For r from 1 to rmax do: • Generate optimal schedule subject to the constraint that the cycle assigned to each instruction is within a distance r of the cycle assigned by the center schedule

12. Preliminary results