----------------------------------------------------------------------------- -- | -- Module : TestSuite.Basics.ArithNoSolver -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- -- Test suite for basic concrete arithmetic, i.e., testing all -- the constant folding based arithmetic implementation in SBV ----------------------------------------------------------------------------- {-# LANGUAGE Rank2Types #-} {-# LANGUAGE TupleSections #-} module TestSuite.Basics.ArithNoSolver(testSuite) where import Data.SBV import Data.SBV.Internals import Data.Maybe(fromJust, fromMaybe) import SBVTest import qualified Data.Binary.IEEE754 as DB (wordToFloat, wordToDouble, floatToWord, doubleToWord) ghcBitSize :: Bits a => a -> Int ghcBitSize x = fromMaybe (error "SBV.ghcBitSize: Unexpected non-finite usage!") (bitSizeMaybe x) -- Test suite testSuite :: SBVTestSuite testSuite = mkTestSuite $ \_ -> test $ genReals ++ genFloats ++ genQRems ++ genBinTest "+" (+) ++ genBinTest "-" (-) ++ genBinTest "*" (*) ++ genUnTest "negate" negate ++ genUnTest "abs" abs ++ genUnTest "signum" signum ++ genBinTest ".&." (.&.) ++ genBinTest ".|." (.|.) ++ genBoolTest "<" (<) (.<) ++ genBoolTest "<=" (<=) (.<=) ++ genBoolTest ">" (>) (.>) ++ genBoolTest ">=" (>=) (.>=) ++ genBoolTest "==" (==) (.==) ++ genBoolTest "/=" (/=) (./=) ++ genBinTest "xor" xor ++ genUnTest "complement" complement ++ genIntTest "shift" shift ++ genIntTest "rotate" rotate ++ genIntTestS "setBit" setBit ++ genIntTestS "clearBit" clearBit ++ genIntTestS "complementBit" complementBit ++ genIntTest "shift" shift ++ genIntTestS "shiftL" shiftL ++ genIntTestS "shiftR" shiftR ++ genIntTest "rotate" rotate ++ genIntTestS "rotateL" rotateL ++ genIntTestS "rotateR" rotateR ++ genBlasts ++ genIntCasts genBinTest :: String -> (forall a. (Num a, Bits a) => a -> a -> a) -> [Test] genBinTest nm op = map mkTest $ zipWith pair [(show x, show y, x `op` y) | x <- w8s, y <- w8s ] [x `op` y | x <- sw8s, y <- sw8s] ++ zipWith pair [(show x, show y, x `op` y) | x <- w16s, y <- w16s] [x `op` y | x <- sw16s, y <- sw16s] ++ zipWith pair [(show x, show y, x `op` y) | x <- w32s, y <- w32s] [x `op` y | x <- sw32s, y <- sw32s] ++ zipWith pair [(show x, show y, x `op` y) | x <- w64s, y <- w64s] [x `op` y | x <- sw64s, y <- sw64s] ++ zipWith pair [(show x, show y, x `op` y) | x <- i8s, y <- i8s ] [x `op` y | x <- si8s, y <- si8s] ++ zipWith pair [(show x, show y, x `op` y) | x <- i16s, y <- i16s] [x `op` y | x <- si16s, y <- si16s] ++ zipWith pair [(show x, show y, x `op` y) | x <- i32s, y <- i32s] [x `op` y | x <- si32s, y <- si32s] ++ zipWith pair [(show x, show y, x `op` y) | x <- i64s, y <- i64s] [x `op` y | x <- si64s, y <- si64s] ++ zipWith pair [(show x, show y, x `op` y) | x <- iUBs, y <- iUBs] [x `op` y | x <- siUBs, y <- siUBs] where pair (x, y, a) b = (x, y, show (fromIntegral a `asTypeOf` b) == show b) mkTest (x, y, s) = "arithCF-" ++ nm ++ "." ++ x ++ "_" ++ y ~: s `showsAs` "True" genBoolTest :: String -> (forall a. Ord a => a -> a -> Bool) -> (forall a. OrdSymbolic a => a -> a -> SBool) -> [Test] genBoolTest nm op opS = map mkTest $ zipWith pair [(show x, show y, x `op` y) | x <- w8s, y <- w8s ] [x `opS` y | x <- sw8s, y <- sw8s] ++ zipWith pair [(show x, show y, x `op` y) | x <- w16s, y <- w16s] [x `opS` y | x <- sw16s, y <- sw16s] ++ zipWith pair [(show x, show y, x `op` y) | x <- w32s, y <- w32s] [x `opS` y | x <- sw32s, y <- sw32s] ++ zipWith pair [(show x, show y, x `op` y) | x <- w64s, y <- w64s] [x `opS` y | x <- sw64s, y <- sw64s] ++ zipWith pair [(show x, show y, x `op` y) | x <- i8s, y <- i8s ] [x `opS` y | x <- si8s, y <- si8s] ++ zipWith pair [(show x, show y, x `op` y) | x <- i16s, y <- i16s] [x `opS` y | x <- si16s, y <- si16s] ++ zipWith pair [(show x, show y, x `op` y) | x <- i32s, y <- i32s] [x `opS` y | x <- si32s, y <- si32s] ++ zipWith pair [(show x, show y, x `op` y) | x <- i64s, y <- i64s] [x `opS` y | x <- si64s, y <- si64s] ++ zipWith pair [(show x, show y, x `op` y) | x <- iUBs, y <- iUBs] [x `opS` y | x <- siUBs, y <- siUBs] where pair (x, y, a) b = (x, y, Just a == unliteral b) mkTest (x, y, s) = "arithCF-" ++ nm ++ "." ++ x ++ "_" ++ y ~: s `showsAs` "True" genUnTest :: String -> (forall a. (Num a, Bits a) => a -> a) -> [Test] genUnTest nm op = map mkTest $ zipWith pair [(show x, op x) | x <- w8s ] [op x | x <- sw8s ] ++ zipWith pair [(show x, op x) | x <- w16s] [op x | x <- sw16s] ++ zipWith pair [(show x, op x) | x <- w32s] [op x | x <- sw32s] ++ zipWith pair [(show x, op x) | x <- w64s] [op x | x <- sw64s] ++ zipWith pair [(show x, op x) | x <- i8s ] [op x | x <- si8s ] ++ zipWith pair [(show x, op x) | x <- i16s] [op x | x <- si16s] ++ zipWith pair [(show x, op x) | x <- i32s] [op x | x <- si32s] ++ zipWith pair [(show x, op x) | x <- i64s] [op x | x <- si64s] ++ zipWith pair [(show x, op x) | x <- iUBs] [op x | x <- siUBs] where pair (x, a) b = (x, show (fromIntegral a `asTypeOf` b) == show b) mkTest (x, s) = "arithCF-" ++ nm ++ "." ++ x ~: s `showsAs` "True" genIntTest :: String -> (forall a. (Num a, Bits a) => a -> Int -> a) -> [Test] genIntTest nm op = map mkTest $ zipWith pair [("u8", show x, show y, x `op` y) | x <- w8s, y <- is] [x `op` y | x <- sw8s, y <- is] ++ zipWith pair [("u16", show x, show y, x `op` y) | x <- w16s, y <- is] [x `op` y | x <- sw16s, y <- is] ++ zipWith pair [("u32", show x, show y, x `op` y) | x <- w32s, y <- is] [x `op` y | x <- sw32s, y <- is] ++ zipWith pair [("u64", show x, show y, x `op` y) | x <- w64s, y <- is] [x `op` y | x <- sw64s, y <- is] ++ zipWith pair [("s8", show x, show y, x `op` y) | x <- i8s, y <- is] [x `op` y | x <- si8s, y <- is] ++ zipWith pair [("s16", show x, show y, x `op` y) | x <- i16s, y <- is] [x `op` y | x <- si16s, y <- is] ++ zipWith pair [("s32", show x, show y, x `op` y) | x <- i32s, y <- is] [x `op` y | x <- si32s, y <- is] ++ zipWith pair [("s64", show x, show y, x `op` y) | x <- i64s, y <- is] [x `op` y | x <- si64s, y <- is] ++ zipWith pair [("iUB", show x, show y, x `op` y) | x <- iUBs, y <- is] [x `op` y | x <- siUBs, y <- is] where pair (t, x, y, a) b = (t, x, y, show a, show b, show (fromIntegral a `asTypeOf` b) == show b) mkTest (t, x, y, a, b, s) = "arithCF-" ++ nm ++ "." ++ t ++ "_" ++ x ++ "_" ++ y ++ "_" ++ a ++ "_" ++ b ~: s `showsAs` "True" is = [-10 .. 10] genIntTestS :: String -> (forall a. (Num a, Bits a) => a -> Int -> a) -> [Test] genIntTestS nm op = map mkTest $ zipWith pair [("u8", show x, show y, x `op` y) | x <- w8s, y <- [0 .. (ghcBitSize x - 1)]] [x `op` y | x <- sw8s, y <- [0 .. (ghcBitSize x - 1)]] ++ zipWith pair [("u16", show x, show y, x `op` y) | x <- w16s, y <- [0 .. (ghcBitSize x - 1)]] [x `op` y | x <- sw16s, y <- [0 .. (ghcBitSize x - 1)]] ++ zipWith pair [("u32", show x, show y, x `op` y) | x <- w32s, y <- [0 .. (ghcBitSize x - 1)]] [x `op` y | x <- sw32s, y <- [0 .. (ghcBitSize x - 1)]] ++ zipWith pair [("u64", show x, show y, x `op` y) | x <- w64s, y <- [0 .. (ghcBitSize x - 1)]] [x `op` y | x <- sw64s, y <- [0 .. (ghcBitSize x - 1)]] ++ zipWith pair [("s8", show x, show y, x `op` y) | x <- i8s, y <- [0 .. (ghcBitSize x - 1)]] [x `op` y | x <- si8s, y <- [0 .. (ghcBitSize x - 1)]] ++ zipWith pair [("s16", show x, show y, x `op` y) | x <- i16s, y <- [0 .. (ghcBitSize x - 1)]] [x `op` y | x <- si16s, y <- [0 .. (ghcBitSize x - 1)]] ++ zipWith pair [("s32", show x, show y, x `op` y) | x <- i32s, y <- [0 .. (ghcBitSize x - 1)]] [x `op` y | x <- si32s, y <- [0 .. (ghcBitSize x - 1)]] ++ zipWith pair [("s64", show x, show y, x `op` y) | x <- i64s, y <- [0 .. (ghcBitSize x - 1)]] [x `op` y | x <- si64s, y <- [0 .. (ghcBitSize x - 1)]] ++ zipWith pair [("iUB", show x, show y, x `op` y) | x <- iUBs, y <- [0 .. 10]] [x `op` y | x <- siUBs, y <- [0 .. 10 ]] where pair (t, x, y, a) b = (t, x, y, show a, show b, show (fromIntegral a `asTypeOf` b) == show b) mkTest (t, x, y, a, b, s) = "arithCF-" ++ nm ++ "." ++ t ++ "_" ++ x ++ "_" ++ y ++ "_" ++ a ++ "_" ++ b ~: s `showsAs` "True" genBlasts :: [Test] genBlasts = map mkTest $ [(show x, fromBitsLE (blastLE x) .== x) | x <- sw8s ] ++ [(show x, fromBitsBE (blastBE x) .== x) | x <- sw8s ] ++ [(show x, fromBitsLE (blastLE x) .== x) | x <- si8s ] ++ [(show x, fromBitsBE (blastBE x) .== x) | x <- si8s ] ++ [(show x, fromBitsLE (blastLE x) .== x) | x <- sw16s] ++ [(show x, fromBitsBE (blastBE x) .== x) | x <- sw16s] ++ [(show x, fromBitsLE (blastLE x) .== x) | x <- si16s] ++ [(show x, fromBitsBE (blastBE x) .== x) | x <- si16s] ++ [(show x, fromBitsLE (blastLE x) .== x) | x <- sw32s] ++ [(show x, fromBitsBE (blastBE x) .== x) | x <- sw32s] ++ [(show x, fromBitsLE (blastLE x) .== x) | x <- si32s] ++ [(show x, fromBitsBE (blastBE x) .== x) | x <- si32s] ++ [(show x, fromBitsLE (blastLE x) .== x) | x <- sw64s] ++ [(show x, fromBitsBE (blastBE x) .== x) | x <- sw64s] ++ [(show x, fromBitsLE (blastLE x) .== x) | x <- si64s] ++ [(show x, fromBitsBE (blastBE x) .== x) | x <- si64s] where mkTest (x, r) = "blast-" ++ x ~: r `showsAs` "True" genIntCasts :: [Test] genIntCasts = map mkTest $ cast w8s ++ cast w16s ++ cast w32s ++ cast w64s ++ cast i8s ++ cast i16s ++ cast i32s ++ cast i64s ++ cast iUBs where mkTest (x, r) = "intCast-" ++ x ~: r `showsAs` "True" lhs x = sFromIntegral (literal x) rhs x = literal (fromIntegral x) cast :: forall a. (Show a, Integral a, Bits a, SymWord a) => [a] -> [(String, SBool)] cast xs = toWords xs ++ toInts xs toWords xs = [(show x, lhs x .== (rhs x :: SWord8 )) | x <- xs] ++ [(show x, lhs x .== (rhs x :: SWord16)) | x <- xs] ++ [(show x, lhs x .== (rhs x :: SWord32)) | x <- xs] ++ [(show x, lhs x .== (rhs x :: SWord64)) | x <- xs] toInts xs = [(show x, lhs x .== (rhs x :: SInt8 )) | x <- xs] ++ [(show x, lhs x .== (rhs x :: SInt16)) | x <- xs] ++ [(show x, lhs x .== (rhs x :: SInt32)) | x <- xs] ++ [(show x, lhs x .== (rhs x :: SInt64)) | x <- xs] ++ [(show x, lhs x .== (rhs x :: SInteger)) | x <- xs] genQRems :: [Test] genQRems = map mkTest $ zipWith pair [("divMod", show x, show y, x `divMod0` y) | x <- w8s, y <- w8s ] [x `sDivMod` y | x <- sw8s, y <- sw8s ] ++ zipWith pair [("divMod", show x, show y, x `divMod0` y) | x <- w16s, y <- w16s] [x `sDivMod` y | x <- sw16s, y <- sw16s] ++ zipWith pair [("divMod", show x, show y, x `divMod0` y) | x <- w32s, y <- w32s] [x `sDivMod` y | x <- sw32s, y <- sw32s] ++ zipWith pair [("divMod", show x, show y, x `divMod0` y) | x <- w64s, y <- w64s] [x `sDivMod` y | x <- sw64s, y <- sw64s] ++ zipWith pair [("divMod", show x, show y, x `divMod1` y) | x <- i8s, y <- i8s ] [x `sDivMod` y | x <- si8s, y <- si8s ] ++ zipWith pair [("divMod", show x, show y, x `divMod1` y) | x <- i16s, y <- i16s] [x `sDivMod` y | x <- si16s, y <- si16s] ++ zipWith pair [("divMod", show x, show y, x `divMod1` y) | x <- i32s, y <- i32s] [x `sDivMod` y | x <- si32s, y <- si32s] ++ zipWith pair [("divMod", show x, show y, x `divMod1` y) | x <- i64s, y <- i64s] [x `sDivMod` y | x <- si64s, y <- si64s] ++ zipWith pair [("divMod", show x, show y, x `divMod0` y) | x <- iUBs, y <- iUBs] [x `sDivMod` y | x <- siUBs, y <- siUBs] ++ zipWith pair [("quotRem", show x, show y, x `quotRem0` y) | x <- w8s, y <- w8s ] [x `sQuotRem` y | x <- sw8s, y <- sw8s ] ++ zipWith pair [("quotRem", show x, show y, x `quotRem0` y) | x <- w16s, y <- w16s] [x `sQuotRem` y | x <- sw16s, y <- sw16s] ++ zipWith pair [("quotRem", show x, show y, x `quotRem0` y) | x <- w32s, y <- w32s] [x `sQuotRem` y | x <- sw32s, y <- sw32s] ++ zipWith pair [("quotRem", show x, show y, x `quotRem0` y) | x <- w64s, y <- w64s] [x `sQuotRem` y | x <- sw64s, y <- sw64s] ++ zipWith pair [("quotRem", show x, show y, x `quotRem1` y) | x <- i8s, y <- i8s ] [x `sQuotRem` y | x <- si8s, y <- si8s ] ++ zipWith pair [("quotRem", show x, show y, x `quotRem1` y) | x <- i16s, y <- i16s] [x `sQuotRem` y | x <- si16s, y <- si16s] ++ zipWith pair [("quotRem", show x, show y, x `quotRem1` y) | x <- i32s, y <- i32s] [x `sQuotRem` y | x <- si32s, y <- si32s] ++ zipWith pair [("quotRem", show x, show y, x `quotRem1` y) | x <- i64s, y <- i64s] [x `sQuotRem` y | x <- si64s, y <- si64s] ++ zipWith pair [("quotRem", show x, show y, x `quotRem0` y) | x <- iUBs, y <- iUBs] [x `sQuotRem` y | x <- siUBs, y <- siUBs] where pair (nm, x, y, (r1, r2)) (e1, e2) = (nm, x, y, show (fromIntegral r1 `asTypeOf` e1, fromIntegral r2 `asTypeOf` e2) == show (e1, e2)) mkTest (nm, x, y, s) = "arithCF-" ++ nm ++ "." ++ x ++ "_" ++ y ~: s `showsAs` "True" -- Haskell's divMod and quotRem differs from SBV's in two ways: -- - when y is 0, Haskell throws an exception, SBV sets the result to 0; like in division -- - Haskell overflows if x == minBound and y == -1 for bounded signed types; but SBV returns minBound, 0; which is more meaningful -- NB. There was a ticket filed against the second anomaly above, See: https://ghc.haskell.org/trac/ghc/ticket/8695 -- But the Haskell folks decided not to fix it. Sigh.. overflow x y = x == minBound && y == -1 divMod0 x y = if y == 0 then (0, x) else x `divMod` y divMod1 x y = if overflow x y then (x, 0) else x `divMod0` y quotRem0 x y = if y == 0 then (0, x) else x `quotRem` y quotRem1 x y = if overflow x y then (x, 0) else x `quotRem0` y genReals :: [Test] genReals = map mkTest $ map ("+",) (zipWith pair [(show x, show y, x + y) | x <- rs, y <- rs ] [x + y | x <- srs, y <- srs ]) ++ map ("-",) (zipWith pair [(show x, show y, x - y) | x <- rs, y <- rs ] [x - y | x <- srs, y <- srs ]) ++ map ("*",) (zipWith pair [(show x, show y, x * y) | x <- rs, y <- rs ] [x * y | x <- srs, y <- srs ]) ++ map ("<",) (zipWith pair [(show x, show y, x < y) | x <- rs, y <- rs ] [x .< y | x <- srs, y <- srs ]) ++ map ("<=",) (zipWith pair [(show x, show y, x <= y) | x <- rs, y <- rs ] [x .<= y | x <- srs, y <- srs ]) ++ map (">",) (zipWith pair [(show x, show y, x > y) | x <- rs, y <- rs ] [x .> y | x <- srs, y <- srs ]) ++ map (">=",) (zipWith pair [(show x, show y, x >= y) | x <- rs, y <- rs ] [x .>= y | x <- srs, y <- srs ]) ++ map ("==",) (zipWith pair [(show x, show y, x == y) | x <- rs, y <- rs ] [x .== y | x <- srs, y <- srs ]) ++ map ("/=",) (zipWith pair [(show x, show y, x /= y) | x <- rs, y <- rs ] [x ./= y | x <- srs, y <- srs ]) ++ map ("/",) (zipWith pair [(show x, show y, x / y) | x <- rs, y <- rs, y /= 0] [x / y | x <- srs, y <- srs, unliteral y /= Just 0]) where pair (x, y, a) b = (x, y, Just a == unliteral b) mkTest (nm, (x, y, s)) = "arithCF-" ++ nm ++ "." ++ x ++ "_" ++ y ~: s `showsAs` "True" genFloats :: [Test] genFloats = bTests ++ uTests ++ fpTests1 ++ fpTests2 ++ converts where bTests = map mkTest2 $ floatRun2 "+" (+) (+) comb ++ doubleRun2 "+" (+) (+) comb ++ floatRun2 "-" (-) (-) comb ++ doubleRun2 "-" (-) (-) comb ++ floatRun2 "*" (*) (*) comb ++ doubleRun2 "*" (*) (*) comb ++ floatRun2 "/" (/) (/) comb ++ doubleRun2 "/" (/) (/) comb ++ floatRun2 "<" (<) (.<) combB ++ doubleRun2 "<" (<) (.<) combB ++ floatRun2 "<=" (<=) (.<=) combB ++ doubleRun2 "<=" (<=) (.<=) combB ++ floatRun2 ">" (>) (.>) combB ++ doubleRun2 ">" (>) (.>) combB ++ floatRun2 ">=" (>=) (.>=) combB ++ doubleRun2 ">=" (>=) (.>=) combB ++ floatRun2 "==" (==) (.==) combB ++ doubleRun2 "==" (==) (.==) combB ++ floatRun2 "/=" (/=) (./=) combN ++ doubleRun2 "/=" (/=) (./=) combN fpTests1 = map mkTest1 $ floatRun1 "abs" abs abs comb1 ++ floatRun1 "fpAbs" abs fpAbs comb1 ++ doubleRun1 "abs" abs abs comb1 ++ doubleRun1 "fpAbs" abs fpAbs comb1 ++ floatRun1 "negate" negate negate comb1 ++ floatRun1 "fpNeg" negate fpNeg comb1 ++ doubleRun1 "negate" negate negate comb1 ++ doubleRun1 "fpNeg" negate fpNeg comb1 ++ floatRun1M "fpSqrt" sqrt fpSqrt comb1 ++ doubleRun1M "fpSqrt" sqrt fpSqrt comb1 ++ floatRun1M "fpRoundToIntegral" fpRoundToIntegralH fpRoundToIntegral comb1 ++ doubleRun1M "fpRoundToIntegral" fpRoundToIntegralH fpRoundToIntegral comb1 ++ floatRun1 "signum" signum signum comb1 ++ doubleRun1 "signum" signum signum comb1 -- TODO. Can't possibly test fma, unless we FFI out to C. Leave it out for the time being fpTests2 = map mkTest2 $ floatRun2M "fpAdd" (+) fpAdd comb ++ doubleRun2M "fpAdd" (+) fpAdd comb ++ floatRun2M "fpSub" (-) fpSub comb ++ doubleRun2M "fpSub" (-) fpSub comb ++ floatRun2M "fpMul" (*) fpMul comb ++ doubleRun2M "fpMul" (*) fpMul comb ++ floatRun2M "fpDiv" (/) fpDiv comb ++ doubleRun2M "fpDiv" (/) fpDiv comb ++ floatRunMM "fpMin" fpMinH fpMin comb ++ doubleRunMM "fpMin" fpMinH fpMin comb ++ floatRunMM "fpMax" fpMaxH fpMax comb ++ doubleRunMM "fpMax" fpMaxH fpMax comb ++ floatRun2 "fpRem" fpRemH fpRem comb ++ doubleRun2 "fpRem" fpRemH fpRem comb ++ floatRun2 "fpIsEqualObject" fpIsEqualObjectH fpIsEqualObject combE ++ doubleRun2 "fpIsEqualObject" fpIsEqualObjectH fpIsEqualObject combE converts = map cvtTest [("toFP_Int8_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- i8s ] ++ map cvtTest [("toFP_Int16_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- i16s] ++ map cvtTest [("toFP_Int32_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- i32s] ++ map cvtTest [("toFP_Int64_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- i64s] ++ map cvtTest [("toFP_Word8_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- w8s ] ++ map cvtTest [("toFP_Word16_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- w16s] ++ map cvtTest [("toFP_Word32_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- w32s] ++ map cvtTest [("toFP_Word64_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- w64s] ++ map cvtTest [("toFP_Float_ToFloat", show x, toSFloat sRNE (literal x), literal x ) | x <- fs ] ++ map cvtTest [("toFP_Double_ToFloat", show x, toSFloat sRNE (literal x), literal (fp2fp x)) | x <- ds ] ++ map cvtTest [("toFP_Integer_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- iUBs] ++ map cvtTest [("toFP_Real_ToFloat", show x, toSFloat sRNE (literal x), fromRational (toRational x)) | x <- rs ] ++ map cvtTest [("toFP_Int8_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- i8s ] ++ map cvtTest [("toFP_Int16_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- i16s] ++ map cvtTest [("toFP_Int32_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- i32s] ++ map cvtTest [("toFP_Int64_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- i64s] ++ map cvtTest [("toFP_Word8_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- w8s ] ++ map cvtTest [("toFP_Word16_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- w16s] ++ map cvtTest [("toFP_Word32_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- w32s] ++ map cvtTest [("toFP_Word64_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- w64s] ++ map cvtTest [("toFP_Float_ToDouble", show x, toSDouble sRNE (literal x), literal (fp2fp x)) | x <- fs ] ++ map cvtTest [("toFP_Double_ToDouble", show x, toSDouble sRNE (literal x), literal x) | x <- ds ] ++ map cvtTest [("toFP_Integer_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- iUBs] ++ map cvtTest [("toFP_Real_ToDouble", show x, toSDouble sRNE (literal x), fromRational (toRational x)) | x <- rs ] ++ map cvtTestI [("fromFP_Float_ToInt8", show x, (fromSFloat sRNE :: SFloat -> SInt8) (literal x), ((fromIntegral :: Integer -> SInt8) . fpRound0) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToInt16", show x, (fromSFloat sRNE :: SFloat -> SInt16) (literal x), ((fromIntegral :: Integer -> SInt16) . fpRound0) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToInt32", show x, (fromSFloat sRNE :: SFloat -> SInt32) (literal x), ((fromIntegral :: Integer -> SInt32) . fpRound0) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToInt64", show x, (fromSFloat sRNE :: SFloat -> SInt64) (literal x), ((fromIntegral :: Integer -> SInt64) . fpRound0) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToWord8", show x, (fromSFloat sRNE :: SFloat -> SWord8) (literal x), ((fromIntegral :: Integer -> SWord8) . fpRound0) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToWord16", show x, (fromSFloat sRNE :: SFloat -> SWord16) (literal x), ((fromIntegral :: Integer -> SWord16) . fpRound0) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToWord32", show x, (fromSFloat sRNE :: SFloat -> SWord32) (literal x), ((fromIntegral :: Integer -> SWord32) . fpRound0) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToWord64", show x, (fromSFloat sRNE :: SFloat -> SWord64) (literal x), ((fromIntegral :: Integer -> SWord64) . fpRound0) x) | x <- fs] ++ map cvtTest [("fromFP_Float_ToFloat", show x, (fromSFloat sRNE :: SFloat -> SFloat) (literal x), literal x) | x <- fs] ++ map cvtTest [("fromFP_Float_ToDouble", show x, (fromSFloat sRNE :: SFloat -> SDouble) (literal x), (literal . fp2fp) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToInteger", show x, (fromSFloat sRNE :: SFloat -> SInteger) (literal x), ((fromIntegral :: Integer -> SInteger) . fpRound0) x) | x <- fs] ++ map cvtTestI [("fromFP_Float_ToReal", show x, (fromSFloat sRNE :: SFloat -> SReal) (literal x), (fromRational . fpRatio0) x) | x <- fs] ++ map cvtTestI [("fromFP_Double_ToInt8", show x, (fromSDouble sRNE :: SDouble -> SInt8) (literal x), ((fromIntegral :: Integer -> SInt8) . fpRound0) x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToInt16", show x, (fromSDouble sRNE :: SDouble -> SInt16) (literal x), ((fromIntegral :: Integer -> SInt16) . fpRound0) x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToInt32", show x, (fromSDouble sRNE :: SDouble -> SInt32) (literal x), ((fromIntegral :: Integer -> SInt32) . fpRound0) x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToInt64", show x, (fromSDouble sRNE :: SDouble -> SInt64) (literal x), ((fromIntegral :: Integer -> SInt64) . fpRound0) x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToWord8", show x, (fromSDouble sRNE :: SDouble -> SWord8) (literal x), ((fromIntegral :: Integer -> SWord8) . fpRound0) x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToWord16", show x, (fromSDouble sRNE :: SDouble -> SWord16) (literal x), ((fromIntegral :: Integer -> SWord16) . fpRound0) x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToWord32", show x, (fromSDouble sRNE :: SDouble -> SWord32) (literal x), ((fromIntegral :: Integer -> SWord32) . fpRound0) x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToWord64", show x, (fromSDouble sRNE :: SDouble -> SWord64) (literal x), ((fromIntegral :: Integer -> SWord64) . fpRound0) x) | x <- ds] ++ map cvtTest [("fromFP_Double_ToFloat", show x, (fromSDouble sRNE :: SDouble -> SFloat) (literal x), (literal . fp2fp) x) | x <- ds] ++ map cvtTest [("fromFP_Double_ToDouble", show x, (fromSDouble sRNE :: SDouble -> SDouble) (literal x), literal x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToInteger", show x, (fromSDouble sRNE :: SDouble -> SInteger) (literal x), ((fromIntegral :: Integer -> SInteger) . fpRound0) x) | x <- ds] ++ map cvtTestI [("fromFP_Double_ToReal", show x, (fromSDouble sRNE :: SDouble -> SReal) (literal x), (fromRational . fpRatio0) x) | x <- ds] ++ map cvtTest [("reinterp_Word32_Float", show x, sWord32AsSFloat (literal x), literal (DB.wordToFloat x)) | x <- w32s] ++ map cvtTest [("reinterp_Word64_Double", show x, sWord64AsSDouble (literal x), literal (DB.wordToDouble x)) | x <- w64s] ++ map cvtTestI [("reinterp_Float_Word32", show x, sFloatAsSWord32 (literal x), literal (DB.floatToWord x)) | x <- fs, not (isNaN x)] -- Not unique for NaN ++ map cvtTestI [("reinterp_Double_Word64", show x, sDoubleAsSWord64 (literal x), literal (DB.doubleToWord x)) | x <- ds, not (isNaN x)] -- Not unique for NaN floatRun1 nm f g cmb = map (nm,) [cmb (x, f x, extract (g (literal x))) | x <- fs] doubleRun1 nm f g cmb = map (nm,) [cmb (x, f x, extract (g (literal x))) | x <- ds] floatRun1M nm f g cmb = map (nm,) [cmb (x, f x, extract (g sRNE (literal x))) | x <- fs] doubleRun1M nm f g cmb = map (nm,) [cmb (x, f x, extract (g sRNE (literal x))) | x <- ds] floatRun2 nm f g cmb = map (nm,) [cmb (x, y, f x y, extract (g (literal x) (literal y))) | x <- fs, y <- fs] doubleRun2 nm f g cmb = map (nm,) [cmb (x, y, f x y, extract (g (literal x) (literal y))) | x <- ds, y <- ds] floatRun2M nm f g cmb = map (nm,) [cmb (x, y, f x y, extract (g sRNE (literal x) (literal y))) | x <- fs, y <- fs] doubleRun2M nm f g cmb = map (nm,) [cmb (x, y, f x y, extract (g sRNE (literal x) (literal y))) | x <- ds, y <- ds] floatRunMM nm f g cmb = map (nm,) [cmb (x, y, f x y, extract (g (literal x) (literal y))) | x <- fs, y <- fs, not (alt0 x y || alt0 y x)] doubleRunMM nm f g cmb = map (nm,) [cmb (x, y, f x y, extract (g (literal x) (literal y))) | x <- ds, y <- ds, not (alt0 x y || alt0 y x)] -- fpMin/fpMax: skip +0/-0 case as this is underspecified alt0 x y = isNegativeZero x && y == 0 && not (isNegativeZero y) uTests = map mkTest1 $ concatMap (checkPred fs sfs) predicates ++ concatMap (checkPred ds sds) predicates extract :: SymWord a => SBV a -> a extract = fromJust . unliteral comb (x, y, a, b) = (show x, show y, same a b) combB (x, y, a, b) = (show x, show y, checkNaN f x y a b) where f v w = not (v || w) -- All comparisons except /=: Both should be False if we have a NaN argument combN (x, y, a, b) = (show x, show y, checkNaN f x y a b) where f v w = v && w -- /=: Both should be True combE (x, y, a, b) = (show x, show y, a == b) comb1 (x, a, b) = (show x, same a b) same a b = (isNaN a &&& isNaN b) || (a == b) checkNaN f x y a b | isNaN x || isNaN y = f a b | True = a == b cvtTest (nm, x, a, b) = "arithCF-" ++ nm ++ "." ++ x ~: same (extract a) (extract b) `showsAs` "True" cvtTestI (nm, x, a, b) = "arithCF-" ++ nm ++ "." ++ x ~: (a == b) `showsAs` "True" mkTest1 (nm, (x, s)) = "arithCF-" ++ nm ++ "." ++ x ~: s `showsAs` "True" mkTest2 (nm, (x, y, s)) = "arithCF-" ++ nm ++ "." ++ x ++ "_" ++ y ~: s `showsAs` "True" checkPred :: (Show a, RealFloat a, Floating a, SymWord a) => [a] -> [SBV a] -> (String, SBV a -> SBool, a -> Bool) -> [(String, (String, Bool))] checkPred xs sxs (n, ps, p) = zipWith (chk n) (map (\x -> (x, p x)) xs) (map ps sxs) where chk nm (x, v) sv = (nm, (show x, Just v == unliteral sv)) predicates :: IEEEFloating a => [(String, SBV a -> SBool, a -> Bool)] predicates = [ ("fpIsNormal", fpIsNormal, fpIsNormalizedH) , ("fpIsSubnormal", fpIsSubnormal, isDenormalized) , ("fpIsZero", fpIsZero, (== 0)) , ("fpIsInfinite", fpIsInfinite, isInfinite) , ("fpIsNaN", fpIsNaN, isNaN) , ("fpIsNegative", fpIsNegative, \x -> x < 0 || isNegativeZero x) , ("fpIsPositive", fpIsPositive, \x -> x >= 0 && not (isNegativeZero x)) , ("fpIsNegativeZero", fpIsNegativeZero, isNegativeZero) , ("fpIsPositiveZero", fpIsPositiveZero, \x -> x == 0 && not (isNegativeZero x)) , ("fpIsPoint", fpIsPoint, \x -> not (isNaN x || isInfinite x)) ] -- Concrete test data xsSigned, xsUnsigned :: (Num a, Enum a, Bounded a) => [a] xsUnsigned = take 5 (iterate (1+) minBound) ++ take 5 (iterate (\x -> x-1) maxBound) xsSigned = xsUnsigned ++ [-5 .. 5] w8s :: [Word8] w8s = xsUnsigned sw8s :: [SWord8] sw8s = xsUnsigned w16s :: [Word16] w16s = xsUnsigned sw16s :: [SWord16] sw16s = xsUnsigned w32s :: [Word32] w32s = xsUnsigned sw32s :: [SWord32] sw32s = xsUnsigned w64s :: [Word64] w64s = xsUnsigned sw64s :: [SWord64] sw64s = xsUnsigned i8s :: [Int8] i8s = xsSigned si8s :: [SInt8] si8s = xsSigned i16s :: [Int16] i16s = xsSigned si16s :: [SInt16] si16s = xsSigned i32s :: [Int32] i32s = xsSigned si32s :: [SInt32] si32s = xsSigned i64s :: [Int64] i64s = xsSigned si64s :: [SInt64] si64s = xsSigned iUBs :: [Integer] iUBs = [-1000000 .. -999995] ++ [-5 .. 5] ++ [999995 .. 1000000] siUBs :: [SInteger] siUBs = map literal iUBs rs :: [AlgReal] rs = [fromRational (i % d) | i <- nums, d <- dens] where nums = [-1000000 .. -999998] ++ [-2 .. 2] ++ [999998 .. 1000001] dens = [2 .. 5] ++ [98 .. 102] ++ [999998 .. 1000000] srs :: [SReal] srs = map literal rs fs :: [Float] fs = xs ++ map (* (-1)) (filter (not . isNaN) xs) -- -nan is the same as nan where xs = [nan, infinity, 0, 0.5, 0.68302244, 0.5268265, 0.10283524, 5.8336496e-2, 1.0e-45] sfs :: [SFloat] sfs = map literal fs ds :: [Double] ds = xs ++ map (* (-1)) (filter (not . isNaN) xs) -- -nan is the same as nan where xs = [nan, infinity, 0, 0.5, 2.516632060108026e-2, 0.8601891300751106, 7.518897767550192e-2, 1.1656043286207285e-2, 5.0e-324] sds :: [SDouble] sds = map literal ds