File size: 2,505 Bytes
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 | import Mathlib
import OAI.Computability.QuantumFactoring.BitArithmetic
import OAI.Computability.QuantumFactoring.AIGDivisionBounds
namespace OAI
section
open scoped BigOperators
namespace ExactQuantumFactoring.BitArithmetic
open Std.Sat Std.Tactic.BVDecide.BVExpr.bitblast
open AIGCompiler BooleanNetwork
def sub (w : ℕ) : BooleanNetwork (w+w) w :=
let res := blastSub (inputs (w+w)).1 (binaryInputs w)
compileVec res.aig res.vec
lemma sub_correct (w : ℕ) (x : Fin (w+w) → Bool) (i : Fin w) :
(sub w).eval x i = (leftWord x - rightWord x).getLsbD i.val := by
rw [sub, compileVec_correct]
exact denote_blastSub _ _ _ _ _ (binaryInputs_left w x) (binaryInputs_right w x) _ _
lemma sub_count (w : ℕ) : (sub w).net.count ≤ 158*w+6 := by
have h := compileVec_count (blastSub (inputs (w+w)).1 (binaryInputs w)).aig
(blastSub (inputs (w+w)).1 (binaryInputs w)).vec
have hs := AIGBounds.sub_size (inputs (w+w)).1 (binaryInputs w)
rw [inputs_size] at hs
dsimp only [sub]
nlinarith
def div (w : ℕ) : BooleanNetwork (w+w) w :=
let res := blastUdiv (inputs (w+w)).1 (binaryInputs w)
compileVec res.aig res.vec
lemma div_correct (w : ℕ) (x : Fin (w+w) → Bool) (i : Fin w) :
(div w).eval x i = (leftWord x / rightWord x).getLsbD i.val := by
rw [div, compileVec_correct]
exact denote_blastUdiv _ _ _ _ _ (binaryInputs_left w x) (binaryInputs_right w x) _ _
lemma div_count (w : ℕ) : (div w).net.count ≤ 216*w*w+56*w+6 := by
have h := compileVec_count (blastUdiv (inputs (w+w)).1 (binaryInputs w)).aig
(blastUdiv (inputs (w+w)).1 (binaryInputs w)).vec
have hs := AIGBounds.div_size (inputs (w+w)).1 (binaryInputs w)
rw [inputs_size] at hs
dsimp only [div]
nlinarith
def mod (w : ℕ) : BooleanNetwork (w+w) w :=
let res := blastUmod (inputs (w+w)).1 (binaryInputs w)
compileVec res.aig res.vec
lemma mod_correct (w : ℕ) (x : Fin (w+w) → Bool) (i : Fin w) :
(mod w).eval x i = (leftWord x % rightWord x).getLsbD i.val := by
rw [mod, compileVec_correct]
exact denote_blastUmod _ _ _ _ _ (binaryInputs_left w x) (binaryInputs_right w x) _ _
lemma mod_count (w : ℕ) : (mod w).net.count ≤ 216*w*w+56*w+6 := by
have h := compileVec_count (blastUmod (inputs (w+w)).1 (binaryInputs w)).aig
(blastUmod (inputs (w+w)).1 (binaryInputs w)).vec
have hs := AIGBounds.mod_size (inputs (w+w)).1 (binaryInputs w)
rw [inputs_size] at hs
dsimp only [mod]
nlinarith
end ExactQuantumFactoring.BitArithmetic
end
end OAI
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