Factory.Data.Interval

AUTHOR

Dr. Alistair Ward

DESCRIPTION

• Describes a bounded set of, typically integral, quantities.
• Operations have been defined, on the list of consecutive quantities delimited by these endpoints.
• The point is that if the list is composed from consecutive quantities, the intermediate values can be inferred, rather than physically represented.

CAVEATS

• The API was driven top-down by its caller's requirements, rather than a bottom-up attempt to provide a complete interface. consequently there may be omissions from the view point of future callers.
• Thought similar to the mathematical concept of an interval, the latter technically relates to real numbers; https://en.wikipedia.org/wiki/Interval_%28mathematics%29.
• No account has been made for semi-closed or open intervals.

Types

Type-synonyms

type Interval endPoint = (endPoint, endPoint)

Defines a closed (inclusive) interval of consecutive values.

Constants

closedUnitInterval :: Num n => Interval n

Construct the unsigned closed unit-interval; https://en.wikipedia.org/wiki/Unit_interval.

mkBounded :: Bounded endPoint => Interval endPoint

Construct an interval from a bounded type.

Functions

elem' :: Ord endPoint => endPoint -> Interval endPoint -> Bool

True if the specified value is within the inclusive bounds of the interval.

normalise :: Ord endPoint => Interval endPoint -> Interval endPoint

Swap the end-points where they were originally reversed, but otherwise do nothing.

product'

Arguments

:: (Integral i, Show i)

=> Ratio i

The ratio at which to bisect the Interval.

-> i

For efficiency, the interval will not be bisected, when it's length has been reduced to this value.

-> Interval i

-> i

The resulting product.

• Multiplies the consecutive sequence of integers within Interval.
• Since the result can be large, divideAndConquer is used to form operands of a similar order of magnitude, thus improving the efficiency of the big-number multiplication.

shift

Arguments

:: Num endPoint

=> endPoint

The magnitude of the require shift.

-> Interval endPoint

The interval to be shifted.

-> Interval endPoint

Shift of both end-points of the interval by the specified amount.

splitAt' :: (Enum endPoint, Ord endPoint, Show endPoint) => endPoint -> Interval endPoint -> (Interval endPoint, Interval endPoint)

Bisect the interval at the specified end-point; which should be between the two existing end-points.

toList :: Enum endPoint => Interval endPoint -> [endPoint]

• Converts Interval to a list by enumerating the values.
• CAVEAT: produces rather odd results for Fractional types, but no stranger than considering such types Enumerable in the first place.

Accessors

getMinBound :: Interval endPoint -> endPoint

Accessor.

getMaxBound :: Interval endPoint -> endPoint

Accessor.

Constructor

precisely :: endPoint -> Interval endPoint

Construct an interval from a single value.

Predicates

isReversed :: Ord endPoint => Interval endPoint -> Bool

True if getMinBound exceeds getMaxBound extent.