| Safe Haskell | Safe-Inferred |
|---|---|
| Language | GHC2021 |
Integer
Synopsis
- data Integer
- data Natural
- data Positive
- data Signed where
- data Sign
- class Increase a where
- class StrictlyIncrease a where
- strictlyIncrease :: Positive -> a -> a
- class Subtraction a where
- subtractInteger :: a -> a -> Integer
- subtractSigned :: a -> a -> Signed
- class Subtraction' b where
- subtract :: Subtraction a => a -> a -> b
- class AbsoluteDifference a b where
- absoluteDifference :: a -> b -> Natural
- class IntegerNarrow a b where
- class IntegerNarrow a b => IntegerConvert a b where
- convert :: a -> b
- class (IntegerConvert a b, IntegerConvert b a) => IntegerEquiv a b
- yolo :: (Integral a, Num b) => a -> b
- class ConvertWithFinite a where
- class (Bounded b, Integral b) => Finite b where
- toFinite :: ConvertWithFinite a => a -> Maybe b
- fromFinite :: ConvertWithFinite a => b -> Maybe a
- class BoundedBelow a where
- minBound :: a
Types
Arbitrary precision integers. In contrast with fixed-size integral types
such as Int, the Integer type represents the entire infinite range of
integers.
Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.
If the value is small (fit into an Int), IS constructor is used.
Otherwise Integer and IN constructors are used to store a BigNat
representing respectively the positive or the negative value magnitude.
Invariant: Integer and IN are used iff value doesn't fit in IS
Instances
Natural number
Invariant: numbers <= 0xffffffffffffffff use the NS constructor
Instances
Instances
Instances
Addition
class Increase a where Source #
Class of numbers are closed under addition with Natural
class StrictlyIncrease a where Source #
Class of numbers that are closed under addition with Positive
Instances
| StrictlyIncrease Positive Source # | |
Defined in Integer.StrictlyIncrease | |
| StrictlyIncrease Signed Source # | |
Defined in Integer.StrictlyIncrease | |
| StrictlyIncrease Integer Source # | |
Defined in Integer.StrictlyIncrease | |
| StrictlyIncrease Natural Source # | |
Defined in Integer.StrictlyIncrease | |
Subtraction
class Subtraction a where Source #
Domain of a subtraction operation
Minimal complete definition
Nothing
Instances
| Subtraction Positive Source # | |
Defined in Integer.Subtraction | |
| Subtraction Signed Source # | |
Defined in Integer.Subtraction | |
| Subtraction Integer Source # | |
Defined in Integer.Subtraction | |
| Subtraction Natural Source # | |
Defined in Integer.Subtraction | |
class Subtraction' b where Source #
Codomain of a subtraction operation
Methods
subtract :: Subtraction a => a -> a -> b Source #
Instances
| Subtraction' Signed Source # | |
Defined in Integer.Subtraction Methods subtract :: Subtraction a => a -> a -> Signed Source # | |
| Subtraction' Integer Source # | |
Defined in Integer.Subtraction Methods subtract :: Subtraction a => a -> a -> Integer Source # | |
class AbsoluteDifference a b where Source #
Methods
absoluteDifference :: a -> b -> Natural Source #
Instances
Conversion
class IntegerNarrow a b where Source #
Instances
class IntegerNarrow a b => IntegerConvert a b where Source #
Instances
class (IntegerConvert a b, IntegerConvert b a) => IntegerEquiv a b Source #
Instances
| IntegerEquiv Positive Positive Source # | |
Defined in Integer.Conversion | |
| IntegerEquiv Signed Signed Source # | |
Defined in Integer.Conversion | |
| IntegerEquiv Signed Integer Source # | |
Defined in Integer.Conversion | |
| IntegerEquiv Integer Signed Source # | |
Defined in Integer.Conversion | |
| IntegerEquiv Integer Integer Source # | |
Defined in Integer.Conversion | |
| IntegerEquiv Natural Natural Source # | |
Defined in Integer.Conversion | |
yolo :: (Integral a, Num b) => a -> b Source #
Partial conversion between Integral types via Integer
yolo =fromInteger.toInteger
class ConvertWithFinite a where Source #
Methods
toWord :: a -> Maybe Word Source #
fromWord :: Word -> Maybe a Source #
class (Bounded b, Integral b) => Finite b where Source #
Methods
toFinite :: ConvertWithFinite a => a -> Maybe b Source #
fromFinite :: ConvertWithFinite a => b -> Maybe a Source #
Instances
| Finite Int Source # | |
Defined in Integer.Finite Methods toFinite :: ConvertWithFinite a => a -> Maybe Int Source # fromFinite :: ConvertWithFinite a => Int -> Maybe a Source # | |
| Finite Word Source # | |
Defined in Integer.Finite Methods toFinite :: ConvertWithFinite a => a -> Maybe Word Source # fromFinite :: ConvertWithFinite a => Word -> Maybe a Source # | |
Lower bound
class BoundedBelow a where Source #
Instances
| BoundedBelow Positive Source # | |
Defined in Integer.Positive.Unsafe | |
| BoundedBelow Natural Source # | |
Defined in Integer.BoundedBelow | |