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{-# LANGUAGE CPP #-}
{-# LANGUAGE RecordWildCards #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
module Tests.Reference.Generators (
-- * Integer with a large range
LargeInteger(..)
-- * Floats with NaNs
, FloatNaN(..)
, canonicaliseNaN
-- * Floats with special values
, HalfSpecials(..)
, FloatSpecials(..)
, DoubleSpecials(..)
-- * Floating types to bit representation conversion
, halfToWord
, floatToWord
, doubleToWord
, wordToHalf
, wordToFloat
, wordToDouble
) where
import Data.Word
import Numeric (showHex)
import Numeric.Half as Half
import GHC.Float (float2Double)
import Data.Proxy
import Foreign
import System.IO.Unsafe
import System.Random (Random)
import Test.QuickCheck
#if !MIN_VERSION_base(4,8,0)
import Control.Applicative
#endif
-- | QuickCheck generator for large integers
--
newtype LargeInteger = LargeInteger { getLargeInteger :: Integer }
deriving (Show, Eq)
instance Arbitrary LargeInteger where
arbitrary =
sized $ \n ->
oneof $ take (1 + n `div` 10)
[ LargeInteger . fromIntegral <$> (arbitrary :: Gen Int8)
, LargeInteger . fromIntegral <$> choose (minBound, maxBound :: Int64)
, LargeInteger . bigger . fromIntegral <$> choose (minBound, maxBound :: Int64)
]
where
bigger n = n * abs n
----------------------------------------
-- Float <-> Integral conversions
--
wordToHalf :: Word16 -> Half
wordToHalf = Half.Half . fromIntegral
wordToFloat :: Word32 -> Float
wordToFloat = toFloat
wordToDouble :: Word64 -> Double
wordToDouble = toFloat
toFloat :: (Storable word, Storable float) => word -> float
toFloat w =
unsafeDupablePerformIO $ alloca $ \buf -> do
poke (castPtr buf) w
peek buf
halfToWord :: Half -> Word16
halfToWord (Half.Half w) = fromIntegral w
floatToWord :: Float -> Word32
floatToWord = fromFloat
doubleToWord :: Double -> Word64
doubleToWord = fromFloat
fromFloat :: (Storable word, Storable float) => float -> word
fromFloat float =
unsafeDupablePerformIO $ alloca $ \buf -> do
poke (castPtr buf) float
peek buf
---------------------------------------------------
-- Floats with NaNs
--
class RealFloat n => FloatNaN n where
canonicalNaN :: n
canonicaliseNaN :: FloatNaN n => n -> n
canonicaliseNaN n | isNaN n = canonicalNaN
| otherwise = n
instance FloatNaN Half where
canonicalNaN = Half 0x7e00
instance FloatNaN Float where
canonicalNaN = Half.fromHalf canonicalNaN
instance FloatNaN Double where
canonicalNaN = float2Double canonicalNaN
---------------------------------------------------
-- Generators for float types with special values
--
instance Arbitrary Half where
arbitrary = getHalfSpecials <$> arbitrary
shrink = shrinkRealFrac
newtype HalfSpecials = HalfSpecials { getHalfSpecials :: Half }
deriving (Ord, Num, Fractional, RealFrac, Real, Floating, RealFloat, FloatNaN)
newtype FloatSpecials = FloatSpecials { getFloatSpecials :: Float }
deriving (Ord, Num, Fractional, RealFrac, Real, Floating, RealFloat, FloatNaN)
newtype DoubleSpecials = DoubleSpecials { getDoubleSpecials :: Double }
deriving (Ord, Num, Fractional, RealFrac, Real, Floating, RealFloat, FloatNaN)
instance Eq HalfSpecials where
HalfSpecials a == HalfSpecials b = halfToWord a == halfToWord b
instance Eq FloatSpecials where
FloatSpecials a == FloatSpecials b = floatToWord a == floatToWord b
instance Eq DoubleSpecials where
DoubleSpecials a == DoubleSpecials b = doubleToWord a == doubleToWord b
instance Show HalfSpecials where
showsPrec p (HalfSpecials n)
| isNaN n = showString "NaN{-0x" . showHex (halfToWord n) . showString "-}"
| otherwise = showsPrec p n
instance Show FloatSpecials where
showsPrec p (FloatSpecials n)
| isNaN n = showString "NaN{-0x" . showHex (floatToWord n) . showString "-}"
| otherwise = showsPrec p n
instance Show DoubleSpecials where
showsPrec p (DoubleSpecials n)
| isNaN n = showString "NaN{-0x" . showHex (doubleToWord n) . showString "-}"
| otherwise = showsPrec p n
instance Arbitrary HalfSpecials where
arbitrary = HalfSpecials <$> frequency [ (2, arbitraryFloating)
, (1, arbitraryFloatSpecials) ]
shrink (HalfSpecials n) = [ HalfSpecials n' | n' <- shrinkRealFrac n ]
instance Arbitrary FloatSpecials where
arbitrary = FloatSpecials <$> frequency [ (2, arbitraryFloating)
, (1, arbitraryFloatSpecials) ]
shrink (FloatSpecials n) = [ FloatSpecials n' | n' <- shrinkRealFrac n ]
instance Arbitrary DoubleSpecials where
arbitrary = DoubleSpecials <$> frequency [ (2, arbitraryFloating)
, (1, arbitraryFloatSpecials) ]
shrink (DoubleSpecials n) = [ DoubleSpecials n' | n' <- shrinkRealFrac n ]
-- | Generate a float from a uniformly random bit pattern
--
arbitraryFloating :: forall n. RealFloatIEEE n => Gen n
arbitraryFloating = wordToFloating <$> arbitraryBoundedIntegral
-- | Generate float special values, see 'IeeeSpecials',
--
-- In particular we generate more than a single NaN bit pattern so that we can
-- test non-canonical representations. The other special values have a single
-- bit pattern.
--
arbitraryFloatSpecials :: forall n. (RealFloatIEEE n, Random (FloatWord n))
=> Gen n
arbitraryFloatSpecials =
frequency
[ (1, pure (wordToFloating positiveInfinity))
, (1, pure (wordToFloating negativeInfinity))
, (1, pure (wordToFloating negativeZero))
, (3, wordToFloating <$> choose nanRange)
]
where
IeeeSpecials {..} = floatIeeeSpecials (Proxy :: Proxy n)
-- | Special values for IEEE float types, including negative 0,
-- positive and negative infinity and a range of NaN values.
--
data IeeeSpecials n = IeeeSpecials {
positiveInfinity :: n,
negativeInfinity :: n,
negativeZero :: n,
nanRange :: (n, n)
}
deriving (Eq, Functor, Show)
-- | The 'IeeeSpecials' values for 'RealFloatIEEE' types (i.e. 'Half', 'Float'
-- and 'Double').
--
-- To make sense of the bit-twiddling here, see
--
-- <https://en.wikipedia.org/wiki/Single-precision_floating-point_format>
-- <https://en.wikipedia.org/wiki/Half-precision_floating-point_format>
-- <https://en.wikipedia.org/wiki/Double-precision_floating-point_format>
--
floatIeeeSpecials :: RealFloatIEEE n => Proxy n -> IeeeSpecials (FloatWord n)
floatIeeeSpecials p =
IeeeSpecials {..}
where
positiveInfinity = (setBit 0 (exponentBits p) - 1)
`shiftL` significandBits p
negativeInfinity = (setBit 0 (exponentBits p +1) - 1)
`shiftL` significandBits p
negativeZero = setBit 0 (exponentBits p + significandBits p)
nanRange = (positiveInfinity, negativeZero - 1)
class (RealFloat n, Integral (FloatWord n), Show (FloatWord n),
Bounded (FloatWord n), Bits (FloatWord n))
=> RealFloatIEEE n where
exponentBits :: Proxy n -> Int
significandBits :: Proxy n -> Int
type FloatWord n :: *
wordToFloating :: FloatWord n -> n
--floatingToWord :: n -> FloatWord n
instance RealFloatIEEE Half where
exponentBits _ = 5
significandBits _ = 10
type FloatWord Half = Word16
wordToFloating = wordToHalf
--floatingToWord = halfToWord
instance RealFloatIEEE Float where
exponentBits _ = 8
significandBits _ = 23
type FloatWord Float = Word32
wordToFloating = wordToFloat
--floatingToWord = floatToWord
instance RealFloatIEEE Double where
exponentBits _ = 11
significandBits _ = 52
type FloatWord Double = Word64
wordToFloating = wordToDouble
--floatingToWord = doubleToWord
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