feat: add BitVec.(getElem, getLsbD, getMsbD, msb)_(srem, sdiv)
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bollu
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Feb 21, 2025
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| theorem msb_srem {x y : BitVec w} : | ||
| (BitVec.srem x y).msb | ||
| = (match x.msb, y.msb with | ||
| | false, false => BitVec.umod x y | ||
| | false, true => BitVec.umod x (.neg y) | ||
| | true, false => .neg (umod (.neg x) y) | ||
| | true, true => .neg (umod (.neg x) (.neg y))).msb := by | ||
| rfl |
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We should drop msb, since there is a theorem statement one should be able to write about the sign of the result of srem that does not express it directly in terms of the case-split of umod, plus a msb.
bollu
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Feb 21, 2025
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| theorem msb_sdiv {x y : BitVec w} : | ||
| (BitVec.sdiv x y).msb | ||
| = (match x.msb, y.msb with | ||
| | false, false => udiv x y | ||
| | false, true => .neg (udiv x (.neg y)) | ||
| | true, false => .neg (udiv (.neg x) y) | ||
| | true, true => udiv (.neg x) (.neg y)).msb := by |
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Same comment as above, this time for sdiv. There's a legible theorem statement to be written here, and we should find it.
|
the correct lemmas now exist. |
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