intervals-0.2.2: Interval Arithmetic

Portability	GHC only
Stability	experimental
Maintainer	ekmett@gmail.com
Safe Haskell	Safe-Inferred

Numeric.Interval

Description

Interval arithmetic

Synopsis

Documentation

data Interval a Source

Constructors

I !a !a

Instances

Eq a => Eq (Interval a)
(RealExtras a, Ord a) => Floating (Interval a)
(Fractional a, Ord a) => Fractional (Interval a)
(Num a, Ord a) => Num (Interval a)
Ord a => Ord (Interval a)
Real a => Real (Interval a)	This means that realToFrac will use the midpoint What moron put an Ord instance requirement on Real!
RealExtras a => RealFloat (Interval a)	We have to play some semantic games to make these methods make sense. Most compute with the midpoint of the interval.
RealFloat a => RealFrac (Interval a)
Show a => Show (Interval a)
RealExtras a => RealExtras (Interval a)

(...) :: a -> a -> Interval aSource

The rule of thumb is you should only use this to construct using values that you took out of the interval. Otherwise, use I, to force rounding

whole :: Fractional a => Interval aSource

The whole real number line

empty :: Fractional a => Interval aSource

An empty interval

null :: Ord a => Interval a -> Bool Source

negation handles NaN properly

singleton :: a -> Interval aSource

A singleton point

elem :: Ord a => a -> Interval a -> Bool Source

notElem :: Ord a => a -> Interval a -> Bool Source

inf :: Interval a -> aSource

The infinumum (lower bound) of an interval

sup :: Interval a -> aSource

The supremum (upper bound) of an interval

singular :: Ord a => Interval a -> Bool Source

Is the interval a singleton point? N.B. This is fairly fragile and likely will not hold after even a few operations that only involve singletons

width :: Num a => Interval a -> aSource

Calculate the width of an interval.

midpoint :: Fractional a => Interval a -> aSource

Nearest point to the midpoint of the interval.

intersection :: (Fractional a, Ord a) => Interval a -> Interval a -> Interval aSource

Calculate the intersection of two intervals.

hull :: Ord a => Interval a -> Interval a -> Interval aSource

Calculate the convex hull of two intervals

bisection :: Fractional a => Interval a -> (Interval a, Interval a)Source

Bisect an interval at its midpoint.

magnitude :: (Num a, Ord a) => Interval a -> aSource

magnitude

mignitude :: (Num a, Ord a) => Interval a -> aSource

contains :: Ord a => Interval a -> Interval a -> Bool Source

isSubsetOf :: Ord a => Interval a -> Interval a -> Bool Source

certainly :: Ord a => (forall b. Ord b => b -> b -> Bool) -> Interval a -> Interval a -> Bool Source

For all x in X, y in Y. x op y

(<!) :: Ord a => Interval a -> Interval a -> Bool Source

For all x in X, y in Y. x < y

(<=!) :: Ord a => Interval a -> Interval a -> Bool Source

For all x in X, y in Y. x <= y

(==!) :: Eq a => Interval a -> Interval a -> Bool Source

For all x in X, y in Y. x == y

(>=!) :: Ord a => Interval a -> Interval a -> Bool Source

For all x in X, y in Y. x >= y

(>!) :: Ord a => Interval a -> Interval a -> Bool Source

For all x in X, y in Y. x > y

possibly :: Ord a => (forall b. Ord b => b -> b -> Bool) -> Interval a -> Interval a -> Bool Source

Does there exist an x in X, y in Y such that x op y?

(<?) :: Ord a => Interval a -> Interval a -> Bool Source

Does there exist an x in X, y in Y such that x < y?

(<=?) :: Ord a => Interval a -> Interval a -> Bool Source

Does there exist an x in X, y in Y such that x <= y?

(==?) :: Ord a => Interval a -> Interval a -> Bool Source

Does there exist an x in X, y in Y such that x == y?

(>=?) :: Ord a => Interval a -> Interval a -> Bool Source

Does there exist an x in X, y in Y such that x >= y?

(>?) :: Ord a => Interval a -> Interval a -> Bool Source

Does there exist an x in X, y in Y such that x > y?

idouble :: Interval Double -> Interval Double Source

ifloat :: Interval Float -> Interval Float Source