Bounded integer ranges
 data Range a = Range {
 lowerBound :: a
 upperBound :: a
 class (Eq a, Ord a, Show a, Num a, Bounded a, Integral a, Bits a) => BoundedInt a
 handleSign :: forall a b. BoundedInt a => (Range a > b) > (Range a > b) > Range a > b
 showBound :: BoundedInt a => a > String
 showRange :: BoundedInt a => Range a > String
 mapMonotonic :: (a > b) > Range a > Range b
 mapMonotonic2 :: (a > b > c) > Range a > Range b > Range c
 emptyRange :: BoundedInt a => Range a
 fullRange :: BoundedInt a => Range a
 range :: a > a > Range a
 rangeByRange :: Range a > Range a > Range a
 singletonRange :: a > Range a
 naturalRange :: BoundedInt a => Range a
 negativeRange :: BoundedInt a => Range a
 rangeSize :: BoundedInt a => Range a > a
 isEmpty :: BoundedInt a => Range a > Bool
 isFull :: BoundedInt a => Range a > Bool
 isSingleton :: BoundedInt a => Range a > Bool
 isSubRangeOf :: BoundedInt a => Range a > Range a > Bool
 isNatural :: BoundedInt a => Range a > Bool
 isNegative :: BoundedInt a => Range a > Bool
 inRange :: BoundedInt a => a > Range a > Bool
 rangeOp :: BoundedInt a => (Range a > Range a) > Range a > Range a
 rangeOp2 :: BoundedInt a => (Range a > Range a > Range a) > Range a > Range a > Range a
 rangeUnion :: BoundedInt a => Range a > Range a > Range a
 rangeIntersection :: BoundedInt a => Range a > Range a > Range a
 disjoint :: BoundedInt a => Range a > Range a > Bool
 rangeGap :: BoundedInt a => Range a > Range a > Range a
 rangeLess :: BoundedInt a => Range a > Range a > Bool
 rangeLessEq :: BoundedInt a => Range a > Range a > Bool
 rangeAbs :: BoundedInt a => Range a > Range a
 rangeSignum :: BoundedInt a => Range a > Range a
 rangeSignumSigned :: BoundedInt a => Range a > Range a
 rangeSignumUnsigned :: BoundedInt a => Range a > Range a
 rangeNeg :: BoundedInt a => Range a > Range a
 rangeNegUnsigned :: BoundedInt a => Range a > Range a
 rangeNegSigned :: BoundedInt a => Range a > Range a
 rangeAdd :: BoundedInt a => Range a > Range a > Range a
 rangeAddUnsigned :: BoundedInt a => Range a > Range a > Range a
 rangeAddSigned :: BoundedInt a => Range a > Range a > Range a
 rangeSub :: BoundedInt a => Range a > Range a > Range a
 rangeSubUnsigned :: BoundedInt a => Range a > Range a > Range a
 rangeMul :: BoundedInt a => Range a > Range a > Range a
 rangeMulSigned :: forall a. BoundedInt a => Range a > Range a > Range a
 rangeMulUnsigned :: forall a. BoundedInt a => Range a > Range a > Range a
 bits :: Bits b => b > Int
 rangeExp :: BoundedInt a => Range a > Range a > Range a
 rangeExpUnsigned :: BoundedInt a => Range a > Range a > Range a
 rangeExpSigned :: BoundedInt a => Range a > Range a > Range a
 rangeOr :: forall a. BoundedInt a => Range a > Range a > Range a
 rangeOrUnsignedCheap :: BoundedInt a => Range a > Range a > Range a
 maxPlus :: BoundedInt a => a > a > a
 minOrUnsigned :: BoundedInt a => a > a > a > a > a
 maxOrUnsigned :: BoundedInt a => a > a > a > a > a
 rangeOrUnsignedAccurate :: BoundedInt a => Range a > Range a > Range a
 rangeAnd :: forall a. BoundedInt a => Range a > Range a > Range a
 rangeAndUnsignedCheap :: BoundedInt a => Range a > Range a > Range a
 rangeXor :: forall a. BoundedInt a => Range a > Range a > Range a
 rangeXorUnsigned :: BoundedInt a => Range a > Range a > Range a
 rangeShiftLU :: BoundedInt a => Range a > Range Word32 > Range a
 rangeShiftRU :: BoundedInt a => Range a > Range Word32 > Range a
 correctShiftRU :: Bits a => a > Word32 > a
 rangeMax :: BoundedInt a => Range a > Range a > Range a
 rangeMin :: BoundedInt a => Range a > Range a > Range a
 rangeMod :: BoundedInt a => Range a > Range a > Range a
 rangeRem :: BoundedInt a => Range a > Range a > Range a
 rangeQuot :: BoundedInt a => Range a > Range a > Range a
 rangeQuotU :: BoundedInt a => Range a > Range a > Range a
 fromRange :: Random a => Range a > Gen a
 rangeTy :: Range t > t > Range t
 atAllTypes :: Monad m => (forall t. (BoundedInt t, Random t, Arbitrary t, Typeable t) => t > m a) > m ()
 prop_propagation1 :: (BoundedInt t, Random t) => t > (forall a. Num a => a > a) > Range t > Property
 rangePropagationSafetyPre :: (Random t, BoundedInt t, BoundedInt a) => t > (t > t > a) > (Range t > Range t > Range a) > (t > t > Bool) > Range t > Range t > Property
 rangePropagationSafetyPre2 :: (Random t, BoundedInt t, Random t2, BoundedInt t2, BoundedInt a) => t > (t > t2 > a) > (Range t > Range t2 > Range a) > (t > t2 > Bool) > Range t > Range t2 > Property
 prop_propagation2 :: (BoundedInt t, Random t) => t > (forall a. Num a => a > a > a) > Range t > Range t > Property
 data TestCase = forall t . Testable t => TC String t
 typedTests :: forall a. (BoundedInt a, Random a, Arbitrary a, Integral a) => a > [TestCase]
Definition
A bounded range of values of type a
Range  

Eq a => Eq (Range a)  
BoundedInt a => Num (Range a)  Implements 
Show a => Show (Range a)  
(BoundedInt a, Arbitrary a) => Arbitrary (Range a)  
BoundedInt a => Set (Range a)  
BoundedInt a => FullProp (Range a) 
class (Eq a, Ord a, Show a, Num a, Bounded a, Integral a, Bits a) => BoundedInt a Source
Convenience alias for bounded integers
handleSign :: forall a b. BoundedInt a => (Range a > b) > (Range a > b) > Range a > bSource
A convenience function for defining range propagation.
handleSign propU propS
chooses propU
for unsigned types and
propS
for signed types.
showBound :: BoundedInt a => a > StringSource
Shows a bound.
showRange :: BoundedInt a => Range a > StringSource
A textual representation of ranges.
mapMonotonic :: (a > b) > Range a > Range bSource
Requires a monotonic function
mapMonotonic2 :: (a > b > c) > Range a > Range b > Range cSource
Requires a monotonic function
Set operations
emptyRange :: BoundedInt a => Range aSource
The range containing no elements
fullRange :: BoundedInt a => Range aSource
The range containing all elements of a type
rangeByRange :: Range a > Range a > Range aSource
singletonRange :: a > Range aSource
The range containing one element
naturalRange :: BoundedInt a => Range aSource
The range from 0
to the maximum element
negativeRange :: BoundedInt a => Range aSource
The range from the smallest negative element to 1
.
Undefined for unsigned types
rangeSize :: BoundedInt a => Range a > aSource
The size of a range. Beware that the size may not always be representable
for signed types. For instance
rangeSize (range minBound maxBound) :: Int
gives a nonsense answer.
isEmpty :: BoundedInt a => Range a > BoolSource
Checks if the range is empty
isFull :: BoundedInt a => Range a > BoolSource
Checks if the range contains all values of the type
isSingleton :: BoundedInt a => Range a > BoolSource
Checks is the range contains exactly one element
isSubRangeOf :: BoundedInt a => Range a > Range a > BoolSource
r1 `isSubRangeOf` r2
checks is all the elements in r1
are included
in r2
isNatural :: BoundedInt a => Range a > BoolSource
Checks whether a range is a subrange of the natural numbers.
isNegative :: BoundedInt a => Range a > BoolSource
Checks whether a range is a subrange of the negative numbers.
inRange :: BoundedInt a => a > Range a > BoolSource
a `inRange` r
checks is a
is an element of the range r
.
rangeOp :: BoundedInt a => (Range a > Range a) > Range a > Range aSource
A convenience function for defining range propagation. If the input range is empty then the result is also empty.
rangeOp2 :: BoundedInt a => (Range a > Range a > Range a) > Range a > Range a > Range aSource
See rangeOp
.
rangeUnion :: BoundedInt a => Range a > Range a > Range aSource
Union on ranges.
rangeIntersection :: BoundedInt a => Range a > Range a > Range aSource
Intersection on ranges.
disjoint :: BoundedInt a => Range a > Range a > BoolSource
disjoint r1 r2
returns true when r1
and r2
have no elements in
common.
rangeGap :: BoundedInt a => Range a > Range a > Range aSource
rangeGap r1 r2
returns a range of all the elements between r1
and
r2
including the boundary elements. If r1
and r2
have elements in
common the result is an empty range.
rangeLess :: BoundedInt a => Range a > Range a > BoolSource
r1 `rangeLess` r2:
Checks if all elements of r1
are less than all elements of r2
.
rangeLessEq :: BoundedInt a => Range a > Range a > BoolSource
r1 `rangeLessEq` r2:
Checks if all elements of r1
are less than or equal to all elements of
r2
.
Propagation
rangeAbs :: BoundedInt a => Range a > Range aSource
Propagates range information through abs
.
rangeSignum :: BoundedInt a => Range a > Range aSource
Propagates range information through signum
.
rangeSignumSigned :: BoundedInt a => Range a > Range aSource
Signed case for rangeSignum
.
rangeSignumUnsigned :: BoundedInt a => Range a > Range aSource
Unsigned case for rangeSignum
.
rangeNeg :: BoundedInt a => Range a > Range aSource
Propagates range information through negation.
rangeNegUnsigned :: BoundedInt a => Range a > Range aSource
Unsigned case for rangeNeg
.
rangeNegSigned :: BoundedInt a => Range a > Range aSource
Signed case for rangeNeg
.
rangeAdd :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through addition.
rangeAddUnsigned :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeAdd
.
rangeAddSigned :: BoundedInt a => Range a > Range a > Range aSource
Signed case for rangeAdd
.
rangeSub :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through subtraction.
rangeSubUnsigned :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeSub
.
rangeMul :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through multiplication
rangeMulSigned :: forall a. BoundedInt a => Range a > Range a > Range aSource
Signed case for rangeMul
.
rangeMulUnsigned :: forall a. BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeMul
.
bits :: Bits b => b > IntSource
Returns the position of the highest bit set to 1. Counting starts at 1. Beware! It doesn't terminate for negative numbers.
rangeExp :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through exponentiation.
rangeExpUnsigned :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeExp
.
rangeExpSigned :: BoundedInt a => Range a > Range a > Range aSource
Sigend case for rangeExp
rangeOr :: forall a. BoundedInt a => Range a > Range a > Range aSource
Propagates range information through ..
.
rangeOrUnsignedCheap :: BoundedInt a => Range a > Range a > Range aSource
Cheap and inaccurate range propagation for ..
on unsigned numbers.
maxPlus :: BoundedInt a => a > a > aSource
a `maxPlus` b
adds a
and b
but if the addition overflows then
maxBound
is returned.
minOrUnsigned :: BoundedInt a => a > a > a > a > aSource
Accurate lower bound for ..
on unsigned numbers.
maxOrUnsigned :: BoundedInt a => a > a > a > a > aSource
Accurate upper bound for ..
on unsigned numbers.
rangeOrUnsignedAccurate :: BoundedInt a => Range a > Range a > Range aSource
Accurate range propagation through ..
for unsigned types.
rangeAnd :: forall a. BoundedInt a => Range a > Range a > Range aSource
Propagating range information through .&.
.
rangeAndUnsignedCheap :: BoundedInt a => Range a > Range a > Range aSource
Cheap and inaccurate range propagation for .&.
on unsigned numbers.
rangeXor :: forall a. BoundedInt a => Range a > Range a > Range aSource
Propagating range information through xor
.
rangeXorUnsigned :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeXor
.
rangeShiftLU :: BoundedInt a => Range a > Range Word32 > Range aSource
Propagating range information through shiftLU
.
rangeShiftRU :: BoundedInt a => Range a > Range Word32 > Range aSource
Unsigned case for rangeShiftLU
.
Propagating range information through shiftRU
.
correctShiftRU :: Bits a => a > Word32 > aSource
Unsigned case for rangeShiftRU
.
This is a replacement fror Haskell's shiftR. If we carelessly use Haskell's variant then we will get left shifts for very large shift values.
rangeMax :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through max
.
rangeQuot :: BoundedInt a => Range a > Range a > Range aSource
Propagates range information through quot
.
rangeQuotU :: BoundedInt a => Range a > Range a > Range aSource
Unsigned case for rangeQuot
.
Testing
atAllTypes :: Monad m => (forall t. (BoundedInt t, Random t, Arbitrary t, Typeable t) => t > m a) > m ()Source
Applies a (monadic) function to all the types we are interested in testing with for Feldspar.
Example usage: 'atAllTypes (quickCheck . prop_mul)'
Set operations
Propagation
prop_propagation1 :: (BoundedInt t, Random t) => t > (forall a. Num a => a > a) > Range t > PropertySource
rangePropagationSafetyPre :: (Random t, BoundedInt t, BoundedInt a) => t > (t > t > a) > (Range t > Range t > Range a) > (t > t > Bool) > Range t > Range t > PropertySource
This function is useful for range propagation functions like
rangeMax
, rangeMod
etc.
It takes two ranges, picks an element out of either ranges and
checks if applying the operation to the individual elements is in
the resulting range after range propagation.
The third argument is a precondition that is satisfied before the test is run. A good example is to make sure that the second argument is nonzero when testing division.
rangePropagationSafetyPre2 :: (Random t, BoundedInt t, Random t2, BoundedInt t2, BoundedInt a) => t > (t > t2 > a) > (Range t > Range t2 > Range a) > (t > t2 > Bool) > Range t > Range t2 > PropertySource
prop_propagation2 :: (BoundedInt t, Random t) => t > (forall a. Num a => a > a > a) > Range t > Range t > PropertySource
Running
typedTests :: forall a. (BoundedInt a, Random a, Arbitrary a, Integral a) => a > [TestCase]Source