| Issue |
151043
|
| Summary |
Additional missing known bits info for x * x
|
| Labels |
new issue
|
| Assignees |
|
| Reporter |
ZERICO2005
|
https://github.com/llvm/llvm-project/issues/48027 outlines that `x * x` will always have bit 1 cleared. I have also discovered three additional tricks that can resolve additional unknown bits:
A: If bit 0 of the input is set, then bit 2 of the output must be cleared.
B: If bit 0 of the input is cleared, then bit 3 of the output must be cleared.
C: If the input % 4 == 2, then bits 3 and 4 of the output must be cleared.
Alternatively, `A` and `C` can be rephrased as:
A: If bit 0 of the output is set, then bit 2 of the output must be cleared.
C: If bit 2 of the output is set, then bits 3 and 4 of the output must be cleared.
This is because these are the only possible results for `(x * x) % 32`:
```
00: 00000
01: 00001
04: 00100
09: 01001
10: 10000
11: 10001
19: 11001
```
The transformations appear to be valid in alive2:
A: https://alive2.llvm.org/ce/z/wip7Ue
B: https://alive2.llvm.org/ce/z/5etB7b
C: https://alive2.llvm.org/ce/z/BNzk7L
Clang 20.1.0 doesn't optimize these patterns out currently https://godbolt.org/z/M6rj4cG3T.
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