Skip to content

Commit

Permalink
Playing with the RShr proof
Browse files Browse the repository at this point in the history
  • Loading branch information
pennyannn committed Sep 13, 2024
1 parent c938b29 commit d079364
Show file tree
Hide file tree
Showing 3 changed files with 67 additions and 35 deletions.
1 change: 1 addition & 0 deletions Arm/BitVec.lean
Original file line number Diff line number Diff line change
Expand Up @@ -287,6 +287,7 @@ abbrev lsb (x : BitVec n) (i : Nat) : BitVec 1 :=
-- by LeanSAT.
(BitVec.extractLsb i i x).cast (by omega)

@[state_simp_rules]
abbrev partInstall (hi lo : Nat) (val : BitVec (hi - lo + 1)) (x : BitVec n): BitVec n :=
let mask := allOnes (hi - lo + 1)
let val_aligned := (zeroExtend n val) <<< lo
Expand Down
98 changes: 64 additions & 34 deletions Arm/Insts/Common.lean
Original file line number Diff line number Diff line change
Expand Up @@ -643,7 +643,8 @@ def RShr (unsigned : Bool) (value : Int) (shift : Nat) (round : Bool) (h : n > 0
BitVec.ofInt (n + 1) rounded
else
BitVec.ofInt (n + 1) value
extractLsb' 0 n (fn rounded_bv shift)
have h₀ : n - 1 - 0 + 1 = n := by omega
BitVec.cast h₀ $ extractLsb (n-1) 0 (fn rounded_bv shift)

@[state_simp_rules]
def Int_with_unsigned (unsigned : Bool) (value : BitVec n) : Int :=
Expand All @@ -664,52 +665,81 @@ def shift_right_common_aux
termination_by (info.elements - e)


theorem crock (operand : BitVec 128) :
(BitVec.ofNat 65 (operand.toNat % 18446744073709551616)) = zeroExtend 65 (extractLsb' 0 64 operand)
:= by sorry

theorem crock1 (operand : BitVec 128) :
(BitVec.ofNat 65 (operand.toNat >>> 64 % 18446744073709551616)) = zeroExtend 65 (extractLsb' 64 64 operand)
:= by sorry


/-
unsolved goals
operand : BitVec 128
shift : Nat
result : BitVec 128
⊢ (result &&& 340282366920938463444927863358058659840#128 |||
zeroExtend 128
(extractLsb' 0 64 ((BitVec.ofNat 65 (operand.toNat % 18446744073709551616)).ushiftRight shift))) &&&
18446744073709551615#128 |||
zeroExtend 128
(extractLsb' 0 64 ((BitVec.ofNat 65 (operand.toNat >>> 64 % 18446744073709551616)).ushiftRight shift)) <<<
64 =
(extractLsb' 64 64 operand).ushiftRight shift ++ (extractLsb' 0 64 operand).ushiftRight shift
-/


-- @[app_unexpander BitVec.ofNat] def unexpandBitVecOfNatToHex : Lean.PrettyPrinter.Unexpander
-- | `($(_) $n:num $i:num) =>
-- let i' := i.getNat
-- let n' := n.getNat
-- let trimmed_hex := -- Remove leading zeroes...
-- String.dropWhile (BitVec.ofNat n' i').toHex
-- (fun c => c = '0')
-- -- ... but keep one if the literal is all zeros.
-- let trimmed_hex := if trimmed_hex.isEmpty then "0" else trimmed_hex
-- let bv := Lean.Syntax.mkNumLit s!"0x{trimmed_hex}#{n'}"
-- `($bv:num)
-- | _ => throw ()

theorem crock1 (x : BitVec 64): BitVec.ofInt 65 (Int.ofNat x.toNat) = zeroExtend 65 x := by
simp only [Int.ofNat_eq_coe, ofInt_natCast, ofNat_toNat]

theorem crock2 (operand : BitVec 128) (shift : Nat) (result : BitVec 128)
(x : BitVec 64) (y : BitVec 64)
: (result &&& 340282366920938463444927863358058659840#128 |||
zeroExtend 128 (extractLsb 63 0 (zeroExtend 65 x >>> shift))) &&&
18446744073709551615#128 |||
zeroExtend 128 (extractLsb 63 0 (zeroExtend 65 y >>> shift)) <<< 64 =
y >>> shift ++ x >>> shift := by
sorry

-- (BitVec.cast ⋯ (extractLsb 63 0 operand)).toNat
-- --> (operand.toNat % 18446744073709551616)
-- extractLsb_toNat is the lemma that turned extractLsb into mod operation in Nat
-- This makes it hard to use bv_decide
theorem shift_right_common_aux_64_2_tff (operand : BitVec 128)
(shift : Nat) (result : BitVec 128):
shift_right_common_aux 0
{esize := 64, elements := 2, shift := shift,
unsigned := true, round := false, accumulate := false,
h := (by omega)}
operand 0#128 result =
(ushiftRight (extractLsb' 64 64 operand) shift)
++ (ushiftRight (extractLsb' 0 64 operand) shift) := by
(ushiftRight (extractLsb 127 64 operand) shift)
++ (ushiftRight (extractLsb 63 0 operand) shift) := by
unfold shift_right_common_aux
simp only [minimal_theory, bitvec_rules]
unfold shift_right_common_aux
simp only [minimal_theory, bitvec_rules]
unfold shift_right_common_aux
simp only [minimal_theory, bitvec_rules]
simp only [state_simp_rules, partInstall,
minimal_theory, bitvec_rules,
Nat.shiftRight_zero, Nat.zero_shiftRight,
crock, crock1]
-- bv_decide
simp only [-- -extractLsb_toNat,
state_simp_rules,
minimal_theory,
-- bitvec_rules,
BitVec.cast_eq,
Nat.shiftRight_zero,
Nat.zero_shiftRight,
Nat.reduceMul,
Nat.reduceAdd,
Nat.add_one_sub_one,
Nat.sub_zero,
reduceAllOnes,
reduceZeroExtend,
Nat.zero_mul,
shiftLeft_zero_eq,
reduceNot,
BitVec.extractLsb_ofNat,
Nat.reducePow,
Nat.zero_mod,
Int.ofNat_emod,
Int.Nat.cast_ofNat_Int,
BitVec.zero_add,
Nat.reduceSub,
Nat.one_mul,
reduceHShiftLeft,
ushiftRight_eq,
crock1
]
generalize (extractLsb 63 0 operand) = x
generalize (extractLsb 127 64 operand) = y
apply crock2

theorem shift_right_common_aux_32_4_fff (operand : BitVec 128)
(shift : Nat) (result : BitVec 128):
Expand Down
3 changes: 2 additions & 1 deletion Proofs/AES-GCM/GCMInitV8Sym.lean
Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,7 @@ namespace GCMInitV8Program
abbrev H_addr (s : ArmState) : BitVec 64 := r (StateField.GPR 1#5) s
abbrev Htable_addr (s : ArmState) : BitVec 64 := r (StateField.GPR 0#5) s

-- set_option debug.byAsSorry true in
set_option debug.byAsSorry true in
set_option maxRecDepth 1000000 in
-- set_option profiler true in
theorem gcm_init_v8_program_run_152 (s0 sf : ArmState)
Expand All @@ -35,6 +35,7 @@ theorem gcm_init_v8_program_run_152 (s0 sf : ArmState)

set_option maxRecDepth 1000000 in
set_option maxHeartbeats 2000000 in
-- set_option linter.unusedVariables false
-- set_option profiler true in
theorem gcm_init_v8_program_correct (s0 sf : ArmState)
(h_s0_program : s0.program = gcm_init_v8_program)
Expand Down

0 comments on commit d079364

Please sign in to comment.