19e06acc65
I made a few choices so far that can probably be discussed: - got rid of `modn` on `UInt`, nobody seems to use it apart from the definition of `shift` which can use normal `mod` - removed the previous defeq optimized definition of `USize.size` in favor for a normal one. The motivation was to allow `OfNat` to work which doesn't seem to be necessary anymore afaict. - Minimized uses of `.val`, should we maybe mark it deprecated? - Mostly got rid of `.val` in basically all theorems as the proper next level of API would now be `.toBitVec`. We could probably re-prove them but it would be more annoying given the change of definition. - Did not yet redefine `log2` in terms of `BitVec` as this would require a `log2` in `BitVec` as well, do we want this? - I added a couple of theorems around the relation of `<` on `UInt` and `Nat`. These were previously not needed because defeq was used all over the place to save us. I did not yet generalize these to all types as I wasn't sure if they are the appropriate lemma that we want to have.
52 lines
1.3 KiB
Text
52 lines
1.3 KiB
Text
/-
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Copyright (c) 2024 Lean FRO, LLC. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joe Hendrix, Wojciech Nawrocki, Leonardo de Moura, Mario Carneiro, Alex Keizer, Harun Khan, Abdalrhman M Mohamed
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-/
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prelude
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import Init.Data.Fin.Basic
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set_option linter.missingDocs true
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/-!
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This module exists to provide the very basic `BitVec` definitions required for
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`Init.Data.UInt.BasicAux`.
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-/
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namespace BitVec
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section Nat
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/-- The `BitVec` with value `i mod 2^n`. -/
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@[match_pattern]
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protected def ofNat (n : Nat) (i : Nat) : BitVec n where
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toFin := Fin.ofNat' (2^n) i
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instance instOfNat : OfNat (BitVec n) i where ofNat := .ofNat n i
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/-- Return the bound in terms of toNat. -/
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theorem isLt (x : BitVec w) : x.toNat < 2^w := x.toFin.isLt
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end Nat
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section arithmetic
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/--
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Addition for bit vectors. This can be interpreted as either signed or unsigned addition
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modulo `2^n`.
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SMT-Lib name: `bvadd`.
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-/
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protected def add (x y : BitVec n) : BitVec n := .ofNat n (x.toNat + y.toNat)
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instance : Add (BitVec n) := ⟨BitVec.add⟩
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/--
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Subtraction for bit vectors. This can be interpreted as either signed or unsigned subtraction
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modulo `2^n`.
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-/
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protected def sub (x y : BitVec n) : BitVec n := .ofNat n ((2^n - y.toNat) + x.toNat)
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instance : Sub (BitVec n) := ⟨BitVec.sub⟩
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end arithmetic
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end BitVec
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