vector-algorithms-0.5.2: Efficient algorithms for vector arrays

Portability | Non-portable (scoped type variables, bang patterns)
Stability | Experimental
Maintainer | Dan Doel <dan.doel@gmail.com>

Data.Vector.Algorithms.Radix

Description

This module provides a radix sort for a subclass of unboxed arrays. The radix class gives information on * the number of passes needed for the data type

- the size of the auxiliary arrays
- how to compute the pass-k radix of a value

Radix sort is not a comparison sort, so it is able to achieve O(n) run time, though it also uses O(n) auxiliary space. In addition, there is a constant space overhead of 2*size*sizeOf(Int) for the sort, so it is not advisable to use this sort for large numbers of very small arrays.

A standard example (upon which one could base their own Radix instance) is Word32:

- We choose to sort on r = 8 bits at a time
- A Word32 has b = 32 bits total

Thus, b/r = 4 passes are required, 2^r = 256 elements are needed in an auxiliary array, and the radix function is:

     radix k e = (e `shiftR` (k*8)) .&. 256

Synopsis

- sort :: forall e m v. (PrimMonad m, MVector v e, Radix e) => v (PrimState m) e -> m ()
- sortBy :: (PrimMonad m, MVector v e) => Int -> Int -> (Int -> e -> Int) -> v (PrimState m) e -> m ()
- class Radix e where
  - passes :: e -> Int
  - size :: e -> Int
  - radix :: Int -> e -> Int

# Documentation

sort :: forall e m v. (PrimMonad m, MVector v e, Radix e) => v (PrimState m) e -> m ()

Sorts an array based on the Radix instance.

sortBy

Arguments

:: (PrimMonad m, MVector v e) |
=> Int | the number of passes
-> Int | the size of auxiliary arrays
-> (Int -> e -> Int) | the radix function
-> v (PrimState m) e | the array to be sorted
-> m () |

Radix sorts an array using custom radix information requires the number of passes to fully sort the array, the size of of auxiliary arrays necessary (should be one greater than the maximum value returned by the radix function), and a radix function, which takes the pass and an element, and returns the relevant radix.

class Radix e where

Methods

passes :: e -> Int

The number of passes necessary to sort an array of es

size :: e -> Int

The size of an auxiliary array

radix :: Int -> e -> Int

The radix function parameterized by the current pass

Instances

Radix Int |
Radix Int8 |
Radix Int16 |
Radix Int32 |
Radix Int64 |
Radix Word |
Radix Word8 |
Radix Word16 |
Radix Word32 |
Radix Word64 |
(Radix i, Radix j) => Radix (i, j) |