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RadixSort.scala
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RadixSort.scala
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package atrox
import java.util.Arrays
import java.lang.Float.floatToRawIntBits
/** Radix sort is non-comparative sorting alorithm that have linear complexity
* for fixed width integers. In practice it's much faster than
* java.util.Arrays.sort for arrays larger than 1k. The only drawback is that the
* implementation used here is not in-place and needs auxilary array that is as
* big as the input to be sorted.
*
* Based on arcane knowledge of http://www.codercorner.com/RadixSortRevisited.htm
*/
object RadixSort {
protected def computeOffsets(
counts: Array[Int], offsets: Array[Int], bytes: Int, length: Int,
dealWithNegatives: Boolean = true, floats: Boolean = false, detectSkips: Boolean = true
): Int = {
var canSkip = 0
// compute offsets/prefix sums
var byte = 0
while (byte < bytes) {
val b256 = byte * 256
offsets(b256 + 0) = 0
var i = 1
while (i < 256) {
offsets(b256 + i) = counts(b256 + i-1) + offsets(b256 + i-1)
i += 1
}
if (detectSkips) {
// detect radices that can be skipped
var i = 0
var skip = false
while (i < 256 && (counts(b256 + i) == length || counts(b256 + i) == 0) && !skip) {
skip = (counts(b256 + i) == length)
i += 1
}
if (skip) {
canSkip |= (1 << byte)
}
}
byte += 1
}
val lastByte = bytes - 1
val lb256 = lastByte * 256
// deal with negative values
if (dealWithNegatives) {
var negativeValues = 0
var i = 128
while (i < 256) {
negativeValues += counts(lb256 + i)
i += 1
}
if (!floats) {
offsets(lb256 + 0) = negativeValues
offsets(lb256 + 128) = 0
var i = 1 ; while (i < 256) {
val ii = i + 128
val curr = ii % 256
val prev = (ii - 1 + 256) % 256
offsets(lb256 + curr) = counts(lb256 + prev) + offsets(lb256 + prev)
i += 1
}
} else {
offsets(lb256 + 0) = negativeValues
offsets(lb256 + 255) = counts(lb256 + 255) - 1
var i = 1 ; while (i < 128) {
offsets(lb256 + i) = offsets(lb256 + i - 1) + counts(lb256 + i - 1)
i += 1
}
i = 254 ; while (i > 127) {
offsets(lb256 + i) = offsets(lb256 + i + 1) + counts(lb256 + i)
i -= 1
}
}
}
canSkip
}
protected def handleResults[T](arr: Array[T], input: Array[T], output: Array[T], returnResultInSourceArray: Boolean): (Array[T], Array[T]) = {
if (returnResultInSourceArray && !(input eq arr)) {
// copy data into array that was passed as an argument to be sorted
System.arraycopy(input, 0, output, 0, input.length)
assert(input != output)
(output, input)
} else {
// return arrays as they are
assert(input != output)
(input, output)
}
}
def sort(arr: Array[Int]): Unit = {
if (arr.length <= 1024) {
Arrays.sort(arr)
} else {
sort(arr, new Array[Int](arr.length), 0, arr.length, 0, 4, true)
}
}
def sort(arr: Array[Int], scratch: Array[Int]): (Array[Int], Array[Int]) =
sort(arr, scratch, 0, arr.length, 0, 4, false)
def sort(arr: Array[Int], scratch: Array[Int], returnResultInSourceArray: Boolean): (Array[Int], Array[Int]) =
sort(arr, scratch, 0, arr.length, 0, 4, returnResultInSourceArray)
/** Sorts `arr` array using `scratch` as teporary scratchpad. Returns both
* arrays, first sorted, second in undefined state. Both returned arrays are the
* same arrays passed as arguments but it's not specified which is which.
*
* If returnResultInSourceArray is set to true, the sorted array is the one
* passed as argument to be sorted. In this case arrays cannot be swapped.
*
* from and fromByte are inclusive positions
* to and toByte are exclusive positions
*/
def sort(arr: Array[Int], scratch: Array[Int], from: Int, to: Int, fromByte: Int, toByte: Int, returnResultInSourceArray: Boolean): (Array[Int], Array[Int]) = {
require(to <= scratch.length)
require(fromByte < toByte)
require(fromByte >= 0 && fromByte < 4)
require(toByte > 0 && toByte <= 4)
require(from >= 0)
require(to <= arr.length)
var input = arr
var output = scratch
val counts = new Array[Int](4 * 256)
val offsets = new Array[Int](4 * 256)
var sorted = true
var last = input(to - 1)
// collect counts
// This loop iterates backward because this way it brings begining of the
// `arr` array into a cache and that speeds up next iteration.
var i = to - 1
while (i >= from) {
sorted &= last >= input(i)
last = input(i)
var byte = 0
while (byte < 4) { // iterates through all 4 bytes on purpose, JVM unrolls this loop
val c = (input(i) >>> (byte * 8)) & 0xff
counts(byte * 256 + c) += 1
byte += 1
}
i -= 1
}
if (sorted) return (input, output)
val canSkip = computeOffsets(counts, offsets, 4, arr.length)
var byte = fromByte
while (byte < toByte) {
if ((canSkip & (1 << byte)) == 0) {
val byteOffsets = Arrays.copyOfRange(offsets, byte * 256, byte * 256 + 256)
var i = from
while (i < to) {
val c = (input(i) >>> (byte * 8)) & 0xff
output(byteOffsets(c)) = input(i)
byteOffsets(c) += 1
i += 1
}
// swap input with output
val tmp = input
input = output
output = tmp
}
byte += 1
}
handleResults(arr, input, output, returnResultInSourceArray)
}
def sort(arr: Array[Long]): Unit = {
if (arr.length <= 1024) {
Arrays.sort(arr)
} else {
sort(arr, new Array[Long](arr.length), 0, arr.length, 0, 8, true)
}
}
def sort(arr: Array[Long], scratch: Array[Long]): (Array[Long], Array[Long]) =
sort(arr, scratch, 0, arr.length, 0, 8, false)
def sort(arr: Array[Long], scratch: Array[Long], returnResultInSourceArray: Boolean): (Array[Long], Array[Long]) =
sort(arr, scratch, 0, arr.length, 0, 8, returnResultInSourceArray)
def sort(arr: Array[Long], scratch: Array[Long], from: Int, to: Int, fromByte: Int, toByte: Int, returnResultInSourceArray: Boolean): (Array[Long], Array[Long]) = {
require(to <= scratch.length)
require(fromByte < toByte)
require(fromByte >= 0 && fromByte < 8)
require(toByte > 0 && toByte <= 8)
require(from >= 0)
require(to <= arr.length)
var input = arr
var output = scratch
val counts = new Array[Int](8 * 256)
val offsets = new Array[Int](8 * 256)
var sorted = true
var last = input(to - 1)
// collect counts
// This loop iterates backward because this way it brings begining of the
// `arr` array into a cache and that speeds up next iteration.
var i = to - 1
while (i >= from) {
sorted &= last >= input(i)
last = input(i)
var byte = 0
while (byte < 8) {
val c = ((input(i) >>> (byte * 8)) & 0xff).toInt
counts(byte * 256 + c) += 1
byte += 1
}
i -= 1
}
if (sorted) return (input, output)
val canSkip = computeOffsets(counts, offsets, 8, arr.length)
var byte = fromByte
while (byte < toByte) {
if ((canSkip & (1 << byte)) == 0) {
val byteOffsets = Arrays.copyOfRange(offsets, byte * 256, byte * 256 + 256)
var i = from
while (i < to) {
val c = ((input(i) >>> (byte * 8)) & 0xff).toInt
output(byteOffsets(c)) = input(i)
byteOffsets(c) += 1
i += 1
}
// swap input with output
val tmp = input
input = output
output = tmp
}
byte += 1
}
handleResults(arr, input, output, returnResultInSourceArray)
}
def sort(arr: Array[Float]): Unit = {
if (arr.length <= 1024) {
Arrays.sort(arr)
} else {
sort(arr, new Array[Float](arr.length), 0, arr.length, 0, 8, true)
}
}
def sort(arr: Array[Float], scratch: Array[Float]): (Array[Float], Array[Float]) =
sort(arr, scratch, 0, arr.length, 0, 4, false)
def sort(arr: Array[Float], scratch: Array[Float], returnResultInSourceArray: Boolean): (Array[Float], Array[Float]) =
sort(arr, scratch, 0, arr.length, 0, 4, returnResultInSourceArray)
def sort(arr: Array[Float], scratch: Array[Float], from: Int, to: Int, fromByte: Int, toByte: Int, returnResultInSourceArray: Boolean): (Array[Float], Array[Float]) = {
require(to <= scratch.length)
require(fromByte < toByte)
require(fromByte >= 0 && fromByte < 4)
require(toByte > 0 && toByte <= 4)
require(from >= 0)
require(to <= arr.length)
var input = arr
var output = scratch
val counts = new Array[Int](4 * 256)
val offsets = new Array[Int](4 * 256)
var sorted = true
var last = input(to - 1)
// collect counts
// This loop iterates backward because this way it brings begining of the
// `arr` array into a cache and that speeds up next iteration.
var i = to - 1
while (i >= from) {
sorted &= last >= input(i)
last = input(i)
var byte = 0
while (byte < 4) {
val c = (floatToRawIntBits(input(i)) >>> (byte * 8)) & 0xff
counts(byte * 256 + c) += 1
byte += 1
}
i -= 1
}
if (sorted) return (input, output)
val canSkip = computeOffsets(counts, offsets, 4, arr.length, floats = true)
var byte = fromByte
while (byte < toByte) {
if ((canSkip & (1 << byte)) == 0) {
val byteOffsets = Arrays.copyOfRange(offsets, byte * 256, byte * 256 + 256)
var i = from
while (i < to) {
val c = (floatToRawIntBits(input(i)) >>> (byte * 8)) & 0xff
output(byteOffsets(c)) = input(i)
byteOffsets(c) += (if (byte < 3 || input(i) >= 0) 1 else -1)
i += 1
}
// swap input with output
val tmp = input
input = output
output = tmp
}
byte += 1
}
handleResults(arr, input, output, returnResultInSourceArray)
}
}