# bit-stream

Lazy, infinite, compact stream of Bool with O(1) indexing. https://github.com/Bodigrim/bit-stream#readme

 Version on this page: 0.1.0.2 LTS Haskell 12.22: 0.1.0.2 Stackage Nightly 2018-12-15: 0.1.0.2 Latest on Hackage: 0.1.0.2

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#### Module documentation for 0.1.0.2

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# bit-stream

Lazy, infinite, compact stream of `Bool` with O(1) indexing. Most useful for memoization of predicates.

## Example 1

Consider following predicate:

``````isOdd :: Word -> Bool
isOdd 0 = False
isOdd n = not (isOdd (n - 1))
``````

Its computation is expensive, so we’d like to memoize its values into `BitStream` using `tabulate` and access this stream via `index` instead of recalculation of `isOdd`:

``````isOddBS :: BitStream
isOddBS = tabulate isOdd

isOdd' :: Word -> Bool
isOdd' = index isOddBS
``````

We can do even better by replacing part of recursive calls to `isOdd` by indexing memoized values. Write `isOddF` such that `isOdd = fix isOddF`:

``````isOddF :: (Word -> Bool) -> Word -> Bool
isOddF _ 0 = False
isOddF f n = not (f (n - 1))
``````

and use `tabulateFix`:

``````isOddBS :: BitStream
isOddBS = tabulateFix isOddF

isOdd' :: Word -> Bool
isOdd' = index isOddBS
``````

## Example 2

Define a predicate, which checks whether its argument is a prime number by trial division.

``````isPrime :: Word -> Bool
isPrime n
| n < 2     = False
| n < 4     = True
| even n    = False
| otherwise = and [ n `rem` d /= 0 | d <- [3, 5 .. ceiling (sqrt (fromIntegral n))], isPrime d]
``````

Convert it to unfixed form:

``````isPrimeF :: (Word -> Bool) -> Word -> Bool
isPrimeF f n
| n < 2     = False
| n < 4     = True
| even n    = False
| otherwise = and [ n `rem` d /= 0 | d <- [3, 5 .. ceiling (sqrt (fromIntegral n))], f d]
``````

Create its memoized version for faster evaluation:

``````isPrimeBS :: BitStream
isPrimeBS = tabulateFix isPrimeF

isPrime' :: Word -> Bool
isPrime' = index isPrimeBS
``````
Depends on 4 packages:
Used by 2 packages:
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