sbv-10.2: SBVTestSuite/TestSuite/Overflows/Arithmetic.hs
-----------------------------------------------------------------------------
-- |
-- Module : TestSuite.Overflows.Arithmetic
-- Copyright : (c) Levent Erkok
-- License : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- Test suite for overflow checking
-----------------------------------------------------------------------------
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# OPTIONS_GHC -Wall -Werror #-}
module TestSuite.Overflows.Arithmetic(tests) where
import Data.SBV
import Data.SBV.Dynamic
import Data.SBV.Internals (unSBV, SBV(..))
import Data.SBV.Tools.Overflow
import Utils.SBVTestFramework
-- Test suite
tests :: TestTree
tests = testGroup "Overflows" [testGroup "Arithmetic" ts]
where ts = [ testGroup "add-uf" [ testCase "w8" $ assertIsThm $ underflow svPlus (bvAddO :: SWord8 -> SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ underflow svPlus (bvAddO :: SWord16 -> SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ underflow svPlus (bvAddO :: SWord32 -> SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ underflow svPlus (bvAddO :: SWord64 -> SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ underflow svPlus (bvAddO :: SInt8 -> SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ underflow svPlus (bvAddO :: SInt16 -> SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ underflow svPlus (bvAddO :: SInt32 -> SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ underflow svPlus (bvAddO :: SInt64 -> SInt64 -> (SBool, SBool))
]
, testGroup "add-of" [ testCase "w8" $ assertIsThm $ overflow svPlus (bvAddO :: SWord8 -> SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ overflow svPlus (bvAddO :: SWord16 -> SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ overflow svPlus (bvAddO :: SWord32 -> SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ overflow svPlus (bvAddO :: SWord64 -> SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ overflow svPlus (bvAddO :: SInt8 -> SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ overflow svPlus (bvAddO :: SInt16 -> SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ overflow svPlus (bvAddO :: SInt32 -> SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ overflow svPlus (bvAddO :: SInt64 -> SInt64 -> (SBool, SBool))
]
, testGroup "sub-uf" [ testCase "w8" $ assertIsThm $ underflow svMinus (bvSubO :: SWord8 -> SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ underflow svMinus (bvSubO :: SWord16 -> SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ underflow svMinus (bvSubO :: SWord32 -> SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ underflow svMinus (bvSubO :: SWord64 -> SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ underflow svMinus (bvSubO :: SInt8 -> SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ underflow svMinus (bvSubO :: SInt16 -> SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ underflow svMinus (bvSubO :: SInt32 -> SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ underflow svMinus (bvSubO :: SInt64 -> SInt64 -> (SBool, SBool))
]
, testGroup "sub-of" [ testCase "w8" $ assertIsThm $ overflow svMinus (bvSubO :: SWord8 -> SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ overflow svMinus (bvSubO :: SWord16 -> SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ overflow svMinus (bvSubO :: SWord32 -> SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ overflow svMinus (bvSubO :: SWord64 -> SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ overflow svMinus (bvSubO :: SInt8 -> SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ overflow svMinus (bvSubO :: SInt16 -> SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ overflow svMinus (bvSubO :: SInt32 -> SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ overflow svMinus (bvSubO :: SInt64 -> SInt64 -> (SBool, SBool))
]
, testGroup "mul-uf" [ testCase "w8" $ assertIsThm $ underflow svTimes (bvMulO :: SWord8 -> SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ underflow svTimes (bvMulO :: SWord16 -> SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ underflow svTimes (bvMulO :: SWord32 -> SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ underflow svTimes (bvMulO :: SWord64 -> SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ mulChkU bvMulOFast (bvMulO :: SInt8 -> SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ mulChkU bvMulOFast (bvMulO :: SInt16 -> SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ mulChkU bvMulOFast (bvMulO :: SInt32 -> SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ mulChkU bvMulOFast (bvMulO :: SInt64 -> SInt64 -> (SBool, SBool))
]
, testGroup "mul-of" [ testCase "w8" $ assertIsThm $ mulChkO bvMulOFast (bvMulO :: SWord8 -> SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ mulChkO bvMulOFast (bvMulO :: SWord16 -> SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ mulChkO bvMulOFast (bvMulO :: SWord32 -> SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ mulChkO bvMulOFast (bvMulO :: SWord64 -> SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ mulChkO bvMulOFast (bvMulO :: SInt8 -> SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ mulChkO bvMulOFast (bvMulO :: SInt16 -> SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ mulChkO bvMulOFast (bvMulO :: SInt32 -> SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ mulChkO bvMulOFast (bvMulO :: SInt64 -> SInt64 -> (SBool, SBool))
]
, testGroup "div-uf" [ testCase "w8" $ assertIsThm $ never svDivide (bvDivO :: SWord8 -> SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ never svDivide (bvDivO :: SWord16 -> SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ never svDivide (bvDivO :: SWord32 -> SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ never svDivide (bvDivO :: SWord64 -> SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ never svDivide (bvDivO :: SInt8 -> SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ never svDivide (bvDivO :: SInt16 -> SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ never svDivide (bvDivO :: SInt32 -> SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ never svDivide (bvDivO :: SInt64 -> SInt64 -> (SBool, SBool))
]
, testGroup "div-of" [ testCase "w8" $ assertIsThm $ never svDivide (bvDivO :: SWord8 -> SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ never svDivide (bvDivO :: SWord16 -> SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ never svDivide (bvDivO :: SWord32 -> SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ never svDivide (bvDivO :: SWord64 -> SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ divChk svDivide (bvDivO :: SInt8 -> SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ divChk svDivide (bvDivO :: SInt16 -> SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ divChk svDivide (bvDivO :: SInt32 -> SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ divChk svDivide (bvDivO :: SInt64 -> SInt64 -> (SBool, SBool))
]
, testGroup "neg-uf" [ testCase "w8" $ assertIsThm $ never1 svNeg0 (bvNegO :: SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ never1 svNeg0 (bvNegO :: SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ never1 svNeg0 (bvNegO :: SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ never1 svNeg0 (bvNegO :: SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ underflow1 svNeg0 (bvNegO :: SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ underflow1 svNeg0 (bvNegO :: SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ underflow1 svNeg0 (bvNegO :: SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ underflow1 svNeg0 (bvNegO :: SInt64 -> (SBool, SBool))
]
, testGroup "neg-of" [ testCase "w8" $ assertIsThm $ never1 svNeg0 (bvNegO :: SWord8 -> (SBool, SBool))
, testCase "w16" $ assertIsThm $ never1 svNeg0 (bvNegO :: SWord16 -> (SBool, SBool))
, testCase "w32" $ assertIsThm $ never1 svNeg0 (bvNegO :: SWord32 -> (SBool, SBool))
, testCase "w64" $ assertIsThm $ never1 svNeg0 (bvNegO :: SWord64 -> (SBool, SBool))
, testCase "i8" $ assertIsThm $ overflow1 svNeg0 (bvNegO :: SInt8 -> (SBool, SBool))
, testCase "i16" $ assertIsThm $ overflow1 svNeg0 (bvNegO :: SInt16 -> (SBool, SBool))
, testCase "i32" $ assertIsThm $ overflow1 svNeg0 (bvNegO :: SInt32 -> (SBool, SBool))
, testCase "i64" $ assertIsThm $ overflow1 svNeg0 (bvNegO :: SInt64 -> (SBool, SBool))
]
]
-- 256 bits is large enough to do all these proofs
large :: Int
large = 256
type SLarge = SVal
svNeg0 :: SLarge -> SLarge
svNeg0 v = z `svMinus` v
where z = svInteger (KBounded (hasSign v) large) 0
exactlyWhen :: SBool -> SVal -> SBool
exactlyWhen (SBV a) b = SBV $ (a `svAnd` b) `svOr` (svNot a `svAnd` svNot b)
-- Properly extend to a dynamic signed large vector. This works because we grow to 256 bits, which is high enough.
toLarge :: HasKind a => SBV a -> SLarge
toLarge v
| extra < 0 = error $ "toLarge: Unexpected size: " ++ show (n, large)
| hasSign v = svSignExtend extra (unSBV v)
| True = mkSigned $ svZeroExtend extra (unSBV v)
where n = intSizeOf v
extra = large - n
mkSigned = svFromIntegral (KBounded True large)
-- Multiplication checks are expensive. For these, we simply check that the SBV encodings and the z3 versions are equivalent
mulChkO :: forall a. SymVal a => (SBV a -> SBV a -> (SBool, SBool)) -> (SBV a -> SBV a -> (SBool, SBool)) -> Predicate
mulChkO fast slow = do setLogic Logic_NONE
x <- free "x"
y <- free "y"
let (_, ov1) = x `fast` y
(_, ov2) = x `slow` y
return $ ov1 .== ov2
-- Underflow mults
mulChkU :: forall a. SymVal a => (SBV a -> SBV a -> (SBool, SBool)) -> (SBV a -> SBV a -> (SBool, SBool)) -> Predicate
mulChkU fast slow = do setLogic Logic_NONE
x <- free "x"
y <- free "y"
let (uf1, _) = x `fast` y
(uf2, _) = x `slow` y
return $ uf1 .== uf2
-- Signed division can only underflow under one condition, check that simply instead of trying to do an expensive embedding proof
divChk :: forall a. (Integral a, Bounded a, SymVal a) => (SLarge -> SLarge -> SLarge) -> (SBV a -> SBV a -> (SBool, SBool)) -> Predicate
divChk _op cond = do x <- free "x"
y <- free "y"
let (_, overflowHappens) = x `cond` y
special = (unSBV x `svEqual` topSet) `svAnd` (unSBV y `svEqual` neg1)
n = intSizeOf x
neg1 = svInteger (KBounded True n) (-1)
topSet = svInteger (KBounded True n) (2^(n-1))
return $ overflowHappens `exactlyWhen` special
-- For a few cases, we expect them to "never" overflow. The "embedding proofs" are either too expensive (in case of division), or
-- not possible (in case of negation). We capture these here.
never :: forall a. (Integral a, Bounded a, SymVal a) => (SLarge -> SLarge -> SLarge) -> (SBV a -> SBV a -> (SBool, SBool)) -> Predicate
never _op cond = do x <- free "x"
y <- free "y"
let (underflowHappens, _) = x `cond` y
return $ underflowHappens `exactlyWhen` svFalse
never1 :: forall a. (Integral a, Bounded a, SymVal a) => (SLarge -> SLarge) -> (SBV a -> (SBool, SBool)) -> Predicate
never1 _op cond = do x <- free "x"
let (underflowHappens, _) = cond x
return $ underflowHappens `exactlyWhen` svFalse
underflow :: forall a. (Integral a, Bounded a, SymVal a) => (SLarge -> SLarge -> SLarge) -> (SBV a -> SBV a -> (SBool, SBool)) -> Predicate
underflow op cond = do x <- free "x"
y <- free "y"
let (underflowHappens, _) = x `cond` y
extResult :: SLarge
extResult = toLarge x `op` toLarge y
return $ underflowHappens `exactlyWhen` (extResult `svLessThan` toLarge (minBound :: SBV a))
overflow :: forall a. (Integral a, Bounded a, SymVal a) => (SLarge -> SLarge -> SLarge) -> (SBV a -> SBV a -> (SBool, SBool)) -> Predicate
overflow op cond = do x <- free "x"
y <- free "y"
let (_, overflowHappens) = x `cond` y
extResult :: SLarge
extResult = toLarge x `op` toLarge y
return $ overflowHappens `exactlyWhen` (extResult `svGreaterThan` toLarge (maxBound :: SBV a))
underflow1 :: forall a. (Integral a, Bounded a, SymVal a) => (SLarge -> SLarge) -> (SBV a -> (SBool, SBool)) -> Predicate
underflow1 op cond = do x <- free "x"
let (underflowHappens, _) = cond x
extResult :: SLarge
extResult = op $ toLarge x
return $ underflowHappens `exactlyWhen` (extResult `svLessThan` toLarge (minBound :: SBV a))
overflow1 :: forall a. (Integral a, Bounded a, SymVal a) => (SLarge -> SLarge) -> (SBV a -> (SBool, SBool)) -> Predicate
overflow1 op cond = do x <- free "x"
let (_, overflowHappens) = cond x
extResult :: SLarge
extResult = op $ toLarge x
return $ overflowHappens `exactlyWhen` (extResult `svGreaterThan` toLarge (maxBound :: SBV a))
{- HLint ignore module "Reduce duplication" -}