| License | BSD-style |
|---|---|
| Maintainer | Vincent Hanquez <vincent@snarc.org> |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | None |
| Language | Haskell2010 |
Foundation.Numerical
Description
Compared to the Haskell hierarchy of number classes this provide a more flexible approach that is closer to the mathematical foundation (group, field, etc)
This try to only provide one feature per class, at the expense of the number of classes.
- class (Enum a, Eq a, Ord a, Integral a) => IsIntegral a where
- class (Enum a, Eq a, Ord a, Integral a, IsIntegral a) => IsNatural a where
- class Signed a where
- class Additive a where
- class Subtractive a where
- type Difference a :: *
- class Multiplicative a where
- class (Additive a, Multiplicative a) => IDivisible a where
- class Multiplicative a => Divisible a where
- data Sign
- recip :: Divisible a => a -> a
- class IntegralRounding a where
- class FloatingPoint a where
Documentation
class (Enum a, Eq a, Ord a, Integral a) => IsIntegral a where #
Number literals, convertible through the generic Integer type.
all number are Enum'erable, meaning that you can move to next element
Minimal complete definition
Instances
class (Enum a, Eq a, Ord a, Integral a, IsIntegral a) => IsNatural a where #
Non Negative Number literals, convertible through the generic Natural type
Minimal complete definition
types that have sign and can be made absolute
Represent class of things that can be added together, contains a neutral element and is commutative.
x + azero = x azero + x = x x + y = y + x
Instances
class Subtractive a where #
Represent class of things that can be subtracted.
Note that the result is not necessary of the same type as the operand depending on the actual type.
For example:
(-) :: Int -> Int -> Int (-) :: DateTime -> DateTime -> Seconds (-) :: Ptr a -> Ptr a -> PtrDiff (-) :: Natural -> Natural -> Maybe Natural
Minimal complete definition
Associated Types
type Difference a :: * #
Methods
(-) :: a -> a -> Difference a infixl 6 #
Instances
class Multiplicative a where #
Represent class of things that can be multiplied together
x * midentity = x midentity * x = x
Methods
Identity element over multiplication
Multiplication of 2 elements that result in another element
(^) :: (IsNatural n, IDivisible n) => a -> n -> a infixr 8 #
Raise to power, repeated multiplication e.g. > a ^ 2 = a * a > a ^ 10 = (a ^ 5) * (a ^ 5) .. (^) :: (IsNatural n) => a -> n -> a
Instances
class (Additive a, Multiplicative a) => IDivisible a where #
Represent types that supports an euclidian division
(x ‘div‘ y) * y + (x ‘mod‘ y) == x
class Multiplicative a => Divisible a where #
Support for division between same types
This is likely to change to represent specific mathematic divisions
Minimal complete definition
Sign of a signed number
Constructors
| SignNegative | |
| SignZero | |
| SignPositive |
class IntegralRounding a where #
Minimal complete definition
Methods
roundUp :: Integral n => a -> n #
Round up, to the next integral.
Also known as ceiling
roundDown :: Integral n => a -> n #
Round down, to the previous integral
Also known as floor
roundTruncate :: Integral n => a -> n #
Truncate to the closest integral to the fractional number closer to 0.
This is equivalent to roundUp for negative Number and roundDown for positive Number
roundNearest :: Integral n => a -> n #
Round to the nearest integral
roundNearest 3.6
4 > roundNearest 3.4 3
Instances
class FloatingPoint a where #
IEEE754 Floating Point
Minimal complete definition
floatRadix, floatDigits, floatRange, floatDecode, floatEncode
Methods
floatRadix :: Proxy a -> Integer #
floatDigits :: Proxy a -> Int #
floatRange :: Proxy a -> (Int, Int) #
floatDecode :: a -> (Integer, Int) #
floatEncode :: Integer -> Int -> a #
Instances