[MLIR][Presburger] Fix Gaussian elimination (#164437)

In the Presburger library, there are two minor bugs of Gaussian
elimination.

In Barvinok.cpp, the `if (equations(i, i) != 0) continue;` is intended
to skip only the row-swapping, but it in fact skipped the whole loop
body altogether, including the elimination parts.

In IntegerRelation.cpp, the Gaussian elimination forgets to advance
`firstVar` (the number of finished columns) when it finishes a column.
Moreover, when it checks the pivot row of each column, it didn't ignore
the rows considered.

As an example, suppose the constraints are
```
1 0 0 1 2 = 0
0 1 0 0 3 = 0
0 0 0 1 4 = 0
...
```
For the 4th column, it will think the pivot is the first row `1 0 0 1 2
= 0`, rather than the correct 3rd row `0 0 0 1 4 = 0`.

(This bug is left undiscovered, because if we don't advance `firstVar`
then this Gaussian elimination process will simply do nothing. Moreover,
it is called only in `simplify()`, and the existing test cases doesn't
care whether a set has been simplified.)
4 files changed
tree: 6f51572f1f8cbf194308e63042d597e1cfde5079
  1. .ci/
  2. .github/
  3. bolt/
  4. clang/
  5. clang-tools-extra/
  6. cmake/
  7. compiler-rt/
  8. cross-project-tests/
  9. flang/
  10. flang-rt/
  11. libc/
  12. libclc/
  13. libcxx/
  14. libcxxabi/
  15. libsycl/
  16. libunwind/
  17. lld/
  18. lldb/
  19. llvm/
  20. llvm-libgcc/
  21. mlir/
  22. offload/
  23. openmp/
  24. orc-rt/
  25. polly/
  26. runtimes/
  27. third-party/
  28. utils/
  29. .clang-format
  30. .clang-format-ignore
  31. .clang-tidy
  32. .git-blame-ignore-revs
  33. .gitattributes
  34. .gitignore
  35. .mailmap
  36. CODE_OF_CONDUCT.md
  37. CONTRIBUTING.md
  38. LICENSE.TXT
  39. pyproject.toml
  40. README.md
  41. SECURITY.md
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