non-negative-0.0.6: Non-negative numbers

PortabilityHaskell 98



This module contains internal functions (*Unsafe) that I had liked to re-use in the NumericPrelude type hierarchy. However since the Eq and Ord instance already require the Num class, we cannot use that in the NumericPrelude.



data T a Source

A chunky non-negative number is a list of non-negative numbers. It represents the sum of the list elements. It is possible to represent a finite number with infinitely many chunks by using an infinite number of zeros.

Note the following problems:

Addition is commutative only for finite representations. E.g. let y = min (1+y) 2 in y is defined, let y = min (y+1) 2 in y is not.


(Enum a, C a) => Enum (T a) 
C a => Eq (T a) 
(Integral a, C a) => Integral (T a) 
C a => Num (T a) 
C a => Ord (T a) 
(Real a, C a) => Real (T a) 
Show a => Show (T a) 
(C a, Arbitrary a) => Arbitrary (T a) 
Monoid (T a) 
C a => C (T a) 

fromChunks :: C a => [a] -> T aSource

fromNumber :: C a => a -> T aSource

toChunks :: T a -> [a]Source

This routine exposes the inner structure of the lazy number.

toNumber :: C a => T a -> aSource

normalize :: C a => T a -> T aSource

Remove zero chunks.

isNull :: C a => T a -> BoolSource

isPositive :: C a => T a -> BoolSource

minMaxDiff :: C a => T a -> T a -> (T a, T a, Bool)Source

In minMaxDiff x y == (z,r,b) z represents min x y, r represents max x y - min x y, and xy == b or x>y ==> not b, for x==y the value of b is arbitrary.

divModStrict :: (Integral a, C a) => T a -> a -> (T a, a)Source

toChunksUnsafe :: T a -> [a]Source

This routine exposes the inner structure of the lazy number and is actually the same as toChunks. It was considered dangerous, but you can observe the lazy structure in tying-the-knot applications anyway. So the explicit revelation of the chunks seems not to be worse.