Number.NonNegativeChunky

A lazy number type, which is a generalization of lazy Peano numbers. Comparisons can be made lazy and thus computations are possible which are impossible with strict number types, e.g. you can compute let y = min (1+y) 2 in y. You can even work with infinite values. However, depending on the granularity, the memory consumption is higher than that for strict number types. This number type is of interest for the merge operation of event lists, which allows for co-recursive merges.

Documentation

data T a

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.

The type is equivalent to Chunky.

Instances

C a => Eq (T a)

Methods

(==) :: T a -> T a -> Bool

(/=) :: T a -> T a -> Bool

(C a, Fractional a) => Fractional (T a)

Methods

(/) :: T a -> T a -> T a

recip :: T a -> T a

fromRational :: Rational -> T a

(C a, Num a) => Num (T a)

Methods

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

(*) :: T a -> T a -> T a

negate :: T a -> T a

abs :: T a -> T a

signum :: T a -> T a

fromInteger :: Integer -> T a

C a => Ord (T a)

Methods

compare :: T a -> T a -> Ordering

(<) :: T a -> T a -> Bool

(<=) :: T a -> T a -> Bool

(>) :: T a -> T a -> Bool

(>=) :: T a -> T a -> Bool

max :: T a -> T a -> T a

min :: T a -> T a -> T a

Show a => Show (T a)

Methods

showsPrec :: Int -> T a -> ShowS

show :: T a -> String

showList :: [T a] -> ShowS

C a => Semigroup (T a)

Methods

(<>) :: T a -> T a -> T a

sconcat :: NonEmpty (T a) -> T a

stimes :: Integral b => b -> T a -> T a

C a => Monoid (T a)

Methods

mempty :: T a

mappend :: T a -> T a -> T a

mconcat :: [T a] -> T a

(C a, Arbitrary a) => Arbitrary (T a)

Methods

arbitrary :: Gen (T a)

shrink :: T a -> [T a]

C a => C (T a)

Methods

zero :: T a

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

negate :: T a -> T a

C a => C (T a)

Methods

isZero :: T a -> Bool

(C a, C a) => C (T a)

Methods

(*) :: T a -> T a -> T a

one :: T a

fromInteger :: Integer -> T a

(^) :: T a -> Integer -> T a

C a => C (T a)

Methods

idt :: T a

(<*>) :: T a -> T a -> T a

cumulate :: [T a] -> T a

C a => C (T a)

Methods

split :: T a -> T a -> (T a, (Bool, T a))

(Ord a, C a, C a) => C (T a)

divMod is implemented in terms of divModStrict. If it is needed we could also provide a function that accesses the divisor first in a lazy way and then uses a strict divisor for subsequent rounds of the subtraction loop. This way we can handle the cases "dividend smaller than divisor" and "dividend greater than divisor" in a lazy and efficient way. However changing the way of operation within one number is also not nice.

Methods

div :: T a -> T a -> T a

mod :: T a -> T a -> T a

divMod :: T a -> T a -> (T a, T a)

(C a, C a, C a) => C (T a)

Methods

abs :: T a -> T a

signum :: T a -> T a

(C a, C a) => C (T a)

Methods

toRational :: T a -> Rational

(C a, C a) => C (T a)

Methods

quot :: T a -> T a -> T a

rem :: T a -> T a -> T a

quotRem :: T a -> T a -> (T a, T a)

(C a, C a) => C (T a)

Methods

toInteger :: T a -> Integer

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

toChunks :: C a => T a -> [a]

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

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

fromChunky98 :: (C a, C a) => T a -> T a

toChunky98 :: (C a, C a) => T a -> T a

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

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

Remove zero chunks.

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

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

divModLazy :: (C a, C a) => T a -> T a -> (T a, T a)

divModLazy accesses the divisor in a lazy way. However this is only relevant if the dividend is smaller than the divisor. For large dividends the divisor will be accessed multiple times but since it is already fully evaluated it could also be strict.

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

This function has a strict divisor and maintains the chunk structure of the dividend at a smaller scale.