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2f887db | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 | import Mathlib
import OAI.Computability.QuantumFactoring.AIGCompiler
import OAI.Computability.QuantumFactoring.AIGBounds
import OAI.Computability.QuantumFactoring.AIGInputs
import OAI.Computability.QuantumFactoring.BitEncoding
namespace OAI
section
open scoped BigOperators
namespace ExactQuantumFactoring
namespace BitArithmetic
open Std.Sat Std.Tactic.BVDecide.BVExpr.bitblast
open AIGCompiler BooleanNetwork
/-- The two actual little-endian input words of the bitblaster. -/
def binaryInputs (w : ℕ) : AIG.BinaryRefVec (inputs (w+w)).1 w :=
⟨refVector (fun i => (inputs (w+w)).2 (i.castAdd w)),
refVector (fun i => (inputs (w+w)).2 (Fin.natAdd w i))⟩
def leftWord {w : ℕ} (x : Fin (w+w) → Bool) : BitVec w :=
bitsValue (fun i => x (i.castAdd w))
def rightWord {w : ℕ} (x : Fin (w+w) → Bool) : BitVec w :=
bitsValue (fun i => x (Fin.natAdd w i))
lemma binaryInputs_left (w : ℕ) (x : Fin (w+w) → Bool) (i : ℕ) (hi : i < w) :
AIG.denote x ⟨(inputs (w+w)).1, (binaryInputs w).lhs.get i hi⟩ =
(leftWord x).getLsbD i := by
rw [binaryInputs, refVector_get, inputs_correct]
exact (bitsValue_bit (fun j => x (j.castAdd w)) ⟨i,hi⟩).symm
lemma binaryInputs_right (w : ℕ) (x : Fin (w+w) → Bool) (i : ℕ) (hi : i < w) :
AIG.denote x ⟨(inputs (w+w)).1, (binaryInputs w).rhs.get i hi⟩ =
(rightWord x).getLsbD i := by
rw [binaryInputs, refVector_get, inputs_correct]
exact (bitsValue_bit (fun j => x (Fin.natAdd w j)) ⟨i,hi⟩).symm
def add (w : ℕ) : BooleanNetwork (w+w) w :=
let res := blastAdd (inputs (w+w)).1 (binaryInputs w)
compileVec res.aig res.vec
lemma add_correct (w : ℕ) (x : Fin (w+w) → Bool) (i : Fin w) :
(add w).eval x i = (leftWord x + rightWord x).getLsbD i.val := by
rw [add, compileVec_correct]
exact denote_blastAdd _ _ _ _ _ (binaryInputs_left w x) (binaryInputs_right w x) _ _
def mul (w : ℕ) : BooleanNetwork (w+w) w :=
let res := blastMul (inputs (w+w)).1 (binaryInputs w)
compileVec res.aig res.vec
lemma mul_correct (w : ℕ) (x : Fin (w+w) → Bool) (i : Fin w) :
(mul w).eval x i = (leftWord x * rightWord x).getLsbD i.val := by
rw [mul, compileVec_correct]
exact denote_blastMul _ _ _ _ _ (binaryInputs_left w x) (binaryInputs_right w x) _ _
lemma add_count (w : ℕ) : (add w).net.count ≤ 86*w+6 := by
have h := compileVec_count (blastAdd (inputs (w+w)).1 (binaryInputs w)).aig
(blastAdd (inputs (w+w)).1 (binaryInputs w)).vec
have hs := AIGBounds.add_size (inputs (w+w)).1 (binaryInputs w)
rw [inputs_size] at hs
dsimp only [add]
omega
lemma mul_count (w : ℕ) : (mul w).net.count ≤ 90*w*w+14*w+6 := by
have h := compileVec_count (blastMul (inputs (w+w)).1 (binaryInputs w)).aig
(blastMul (inputs (w+w)).1 (binaryInputs w)).vec
have hs := AIGBounds.mul_size (inputs (w+w)).1 (binaryInputs w)
rw [inputs_size] at hs
dsimp only [mul]
nlinarith
end BitArithmetic
end ExactQuantumFactoring
end
end OAI
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