[Scheduling] Add Presburger Simplex scheduler #4517
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| unsigned latency = *prob.getLatency(*prob.getLinkedOperatorType(src)); | ||
| row.back() = -latency; // note the negation | ||
| if (src != | ||
| dst) { // note that these coefficients just zero out in self-arcs. |
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This formatting seems broken?
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Thanks @Groverkss, this is excellent work that just needs a minor revision. I have a few nits and a clarification request on the approach itself. Also, it looks like you're missing a dependency on the Presburger library in the CMakeList.txt.
| class Solver : private LexSimplex { | ||
| public: | ||
| Solver(Problem &prob, unsigned numObj) | ||
| : LexSimplex(1 + numObj + prob.getOperations().size()), prob(prob) { |
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Please explain the 1+ in a comment.
| /// Create a latency constraint representing the given dependence. | ||
| /// The constraint is represented as: | ||
| /// dstOpStartTime >= srcOpStartTime + latency. | ||
| void createLatencyConstraint(MutableArrayRef<MPInt> row, |
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I think I'd call this precedence constraint.
| /// Create a cyclic latency constraint representing the given dependence and | ||
| /// the given dependence distance. | ||
| /// The constraint is represented as: | ||
| /// dstOpStartTime >= srcOpStartTime + latency + II * distance. |
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Should be minus II * distance, coming from:
srcOpStartTime + latency <= dstOpStartTime + distance * II
| Problem::Dependence dep, | ||
| const MPInt &distance) { | ||
| createLatencyConstraint(row, dep); | ||
| row[0] = distance; |
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Please introduce a constant for the variable representing the II.
| // There is a single objective, minimize the last operation. | ||
| { | ||
| SmallVector<MPInt, 8> row(solver.getNumCols()); | ||
| row[1] = 1; |
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Again, please introduce a constant for the magic number.
| } | ||
| } | ||
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| // The constraints from dependence are built in a way that the solution always |
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| for (auto *op : prob.getOperations()) | ||
| prob.setStartTime(op, | ||
| int64_t(sample[solver.getOpIndex(op)].getAsInteger())); |
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Start times are stored as unsigned in the Problem, so I think it would be clearer to cast directly to unsigned here instead of int64_t.
| } | ||
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| // The constraints from dependence are built in a way that the solution always | ||
| // has integer rational start times. So, we can solve rationally keeping II |
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Isn't the reference to II a copy'n'paste artifact?
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| ArrayRef<Fraction> res = *sample; | ||
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| // If we have an integer II, we can just return the solution. |
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This intuitively makes sense to me, but can you provide a reference to a paper or text book for the underlying theoretical reasoning please?
| // is valid, this is a valid solution. | ||
| MaybeOptimum<SmallVector<Fraction, 8>> solveRationally() { | ||
| MaybeOptimum<SmallVector<Fraction, 8>> sample = | ||
| LexSimplex::findRationalLexMin(); |
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The II is not part of the objective, right? So the solver may theoretically return any value here, because the II is just a normal decision variable if I understand correctly.
I would have expected that you optimize for the smallest II first, ceil/fix it, and then optimize for the start time of the last operation.
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@Groverkss I transitioned (#4523) the scheduling test cases to use the SSP dialect and the |
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Status? |
This patch adds a new scheduler for Scheduling problems. This scheduler utilizes the Presburger library's Simplex to find the optimal solution.
The Presburger scheduler lives in-tree in MLIR, which means there are no external dependencies and allows using arbitrary precision.