NumHask.Examples

NumHask usage examples

Imports and Pragmas

NumHask.Prelude is a replacement for the standard prelude with the NoImplicitPrelude extension explicitly required.

>>> :set -XNoImplicitPrelude
>>> import NumHask.Prelude

Int, Integer, Double and Float are from base. NumHask takes these classes and redefines the basic arithmetic operators.

>>> 1 + 1
2
>>> 1 - 1
0
>>> 1 * 1
1
>>> 1 / 1
1.0

Note that the literal numbers in the divide above defaulted to Float rather than Int.

>>> 1 / (1::Int)
...
... No instance for (MultiplicativeGroup Int)
...

>>> 1 / fromIntegral (1::Int)
1.0

RebindableSyntax removes the Haskell98 link between literal numbers and base classes. Literal numbers are pre-processed by ghc as `fromInteger 1` and `fromRational 1.0`.

>>> :t 1
1 :: Num p => p

>>> :t 1.0
1.0 :: Fractional p => p

>>> :set -XRebindableSyntax
>>> :t 1
1 :: FromInteger a => a

>>> :t 1.0
1.0 :: FromRatio b => b

Float and Double are Field instances.

>>> zero == 0.0
True
>>> one == 1.0
True
>>> 1.0 + 1.0
2.0
>>> 1.0 - 1.0
0.0
>>> 1.0 * 1.0
1.0
>>> 1.0 / 1.0
1.0

QuotientField

>>> 1 `div` 2
0
>>> 3 `mod` 2
1

BoundedField

>>> one/zero
Infinity
>>> -one/zero
-Infinity
>>> zero/zero+one
NaN

ExpField

>>> logBase 2 4
2.0
>>> 2 ** 2
4.0
>>> sqrt 4
2.0
>>> exp 2
7.38905609893065
>>> log 2
0.6931471805599453

Complex numbers

>>> let a = 1 :+ 2
>>> a
1 :+ 2
>>> zero - a
(-1) :+ (-2)
>>> (1 :+ (-2)) * ((-2) :+ 4)
6 :+ 8
>>> (1 :+ (-1)) / (2 :+ 2)
0.0 :+ (-0.5)

Vectors

Matrices