You are encouraged to solve this task according to the task description, using any language you may know.

Sorting Algorithm
This is a sorting algorithm. It may be applied to a set of data in order to sort it.

For other sorting algorithms, see Category:Sorting Algorithms, or:
O(n logn) Sorts
Heapsort | Mergesort | Quicksort
O(n log2n) Sorts
Shell Sort
O(n2) Sorts
Bubble sort | Cocktail sort | Comb sort | Gnome sort | Insertion sort | Selection sort | Strand sort
Other Sorts
Bead sort | Bogosort | Counting sort | Pancake sort | Permutation sort | Radix sort | Sleep sort | Stooge sort

Sort an integer array with the   radix sort algorithm.

The primary purpose is to complete the characterization of sort algorithms task.

`with Ada.Text_IO;procedure Radix_Sort is   type Integer_Array is array (Positive range <>) of Integer;    procedure Least_Significant_Radix_Sort (Data : in out Integer_Array; Base : Positive := 10) is      type Bucket is record         Count   : Natural := 0;         Content : Integer_Array (Data'Range);      end record;       subtype Bucket_Index is Integer range -Base + 1 .. Base - 1;      type Bucket_Array is array (Bucket_Index) of Bucket;       procedure Append (To : in out Bucket; Item : Integer) is      begin         To.Count := To.Count + 1;         To.Content (To.Count) := Item;      end Append;       function Get_Nth_Digit (Value : Integer; N : Positive) return Integer is         Result : Integer := (Value / (Base ** (N - 1))) mod Base;      begin         if Value < 0 then            Result := -Result;         end if;         return Result;      end Get_Nth_Digit;       function Get_Maximum return Natural is         Result : Natural := 0;      begin         for I in Data'Range loop            if abs (Data (I)) > Result then               Result := abs (Data (I));            end if;         end loop;         return Result;      end Get_Maximum;       function Split (Pass : Positive) return Bucket_Array is         Buckets : Bucket_Array;      begin         for I in Data'Range loop            Append (To   => Buckets (Get_Nth_Digit (Data (I), Pass)),                    Item => Data (I));         end loop;         return Buckets;      end Split;       function Merge (Buckets : Bucket_Array) return Integer_Array is         Result        : Integer_Array (Data'Range);         Current_Index : Positive := 1;      begin         for Sublist in Buckets'Range loop            for Item in 1 .. Buckets (Sublist).Count loop               Result (Current_Index) := Buckets (Sublist).Content (Item);               Current_Index := Current_Index + 1;            end loop;         end loop;         return Result;      end Merge;       Max_Number  : Natural := Get_Maximum;      Digit_Count : Positive := 1;   begin      -- count digits of biggest number      while Max_Number > Base loop         Digit_Count := Digit_Count + 1;         Max_Number := Max_Number / Base;      end loop;      for Pass in 1 .. Digit_Count loop         Data := Merge (Split (Pass));      end loop;   end Least_Significant_Radix_Sort;    Test_Array : Integer_Array := (170, 45, 75, -90, -802, 24, 2, 66);begin   Least_Significant_Radix_Sort (Test_Array, 4);   for I in Test_Array'Range loop      Ada.Text_IO.Put (Integer'Image (Test_Array (I)));   end loop;   Ada.Text_IO.New_Line;end Radix_Sort;`

output:

`-802-90 2 24 45 66 75 170`

## ALGOL 68

`PROC radixsort = (REF []INT array) VOID:(    [UPB array]INT zero;      [UPB array]INT one;       BITS mask := 16r01;      INT zero_index  := 0,         one_index   := 0,        array_index := 1;      WHILE ABS(mask) > 0 DO         WHILE array_index <= UPB array DO             IF (BIN(array[array_index]) AND mask) = 16r0 THEN                 zero_index +:= 1;                zero[zero_index] := array[array_index]            ELSE                            one_index +:= 1;                one[one_index] := array[array_index]            FI;            array_index +:= 1         OD;         array_index := 1;         FOR i FROM 1 TO zero_index DO             array[array_index] := zero[i];            array_index +:= 1        OD;         FOR i FROM 1 TO one_index DO             array[array_index] := one[i];            array_index +:=1        OD;         array_index := 1;        zero_index := one_index := 0;        mask := mask SHL 1     OD); main:(    [10]INT a;    FOR i FROM 1 TO UPB a DO        a[i] := ROUND(random*1000)    OD;     print(("Before:", a));    print((newline, newline));    radixsort(a);    print(("After: ", a)))`
Output:
```Before:       +459       +941       +623       +386       +263       +766       +129       +554       +160       +328

After:        +129       +160       +263       +328       +386       +459       +554       +623       +766       +941
```

## AutoHotkey

`Radix_Sort(data){	loop, parse, data, `,		n := StrLen(A_LoopField)>n?StrLen(A_LoopField):n	loop % n {		bucket := []	,	i := A_Index		loop, parse, data, `,			bucket[SubStr(A_LoopField,1-i)] .= (bucket[SubStr(A_LoopField,1-i)]?",":"") A_LoopField		data := ""		for i, v in bucket			data .= (data?",":"") v	}	return data}`
Examples:
`d = 170,45,75,90,802,2,24,66MsgBox, 262144, , % Radix_Sort(d)`
Outputs:
`2,24,45,66,75,90,170,802`

## BBC BASIC

The array index is assumed to start at zero. The third parameter of PROCradixsort() is the radix used.

`      DIM test%(9)      test%() = 4, 65, 2, -31, 0, 99, 2, 83, 782, 1      PROCradixsort(test%(), 10, 10)      FOR i% = 0 TO 9        PRINT test%(i%) ;      NEXT      PRINT      END       DEF PROCradixsort(a%(), n%, r%)      LOCAL d%, e%, i%, l%, m%, b%(), bucket%()      DIM b%(n%-1), bucket%(r%-1)      FOR i% = 0 TO n%-1        IF a%(i%) < l% l% = a%(i%)        IF a%(i%) > m% m% = a%(i%)      NEXT      a%() -= l%      m% -= l%      e% = 1      WHILE m% DIV e%        bucket%() = 0        FOR i% = 0 TO n%-1          bucket%(a%(i%) DIV e% MOD r%) += 1        NEXT        FOR i% = 1 TO r%-1          bucket%(i%) += bucket%(i% - 1)        NEXT        FOR i% = n%-1 TO 0 STEP -1          d% = a%(i%) DIV e% MOD r%          bucket%(d%) -= 1          b%(bucket%(d%)) = a%(i%)        NEXT        a%() = b%()        e% *= r%      ENDWHILE      a%() += l%      ENDPROC`

Output:

```       -31         0         1         2         2         4        65        83        99       782
```

## C

Radix sort, "digits" are most significant bits.
`#include <stdio.h>#include <limits.h>#include <stdlib.h>#include <time.h> // Get size of statically allocated array#define ARR_LEN(ARR) (sizeof ARR / sizeof *ARR)// Generate random number in the interval [M,N]#define RAND_RNG(M,N) (M + rand() / (RAND_MAX / (N - M + 1) + 1)); static void swap(unsigned *a, unsigned *b) {    unsigned tmp = *a;    *a = *b;    *b = tmp;} /* sort unsigned ints */static void rad_sort_u(unsigned *from, unsigned *to, unsigned bit){	if (!bit || to < from + 1) return; 	unsigned *ll = from, *rr = to - 1;	for (;;) {		/* find left most with bit, and right most without bit, swap */		while (ll < rr && !(*ll & bit)) ll++;		while (ll < rr &&  (*rr & bit)) rr--;		if (ll >= rr) break;		swap(ll, rr);	} 	if (!(bit & *ll) && ll < to) ll++;	bit >>= 1; 	rad_sort_u(from, ll, bit);	rad_sort_u(ll, to, bit);} /* sort signed ints: flip highest bit, sort as unsigned, flip back */static void radix_sort(int *a, const size_t len){	size_t i;	unsigned *x = (unsigned*) a; 	for (i = 0; i < len; i++)             x[i] ^= INT_MIN;         rad_sort_u(x, x + len, INT_MIN);         for (i = 0; i < len; i++)             x[i] ^= INT_MIN;} int main(void){     srand(time(NULL));    int x[16];      for (size_t i = 0; i < ARR_LEN(x); i++)         x[i] = RAND_RNG(-128,127)     radix_sort(x, ARR_LEN(x));     for (size_t i = 0; i < ARR_LEN(x); i++)         printf("%d%c", x[i], i + 1 < ARR_LEN(x) ? ' ' : '\n');}`
output
`-182 -175 -151 -141 -70 -51 -20 -5 -1 41 70 103 171 198 227 242`

## C++

Implements a least significant digit radix sort and a recursive most significant digit radix sort.

Note: the LSD radix sort uses the standard library std::stable_partition algorithm. This algorithm is guaranteed to preserve relative order and has a higher runtime cost. The MSD radix sort uses std::partition and can be significantly faster.

`#include <algorithm>#include <iostream>#include <iterator> // Radix sort comparator for 32-bit two's complement integersclass radix_test{    const int bit; // bit position [0..31] to examinepublic:    radix_test(int offset) : bit(offset) {} // constructor     bool operator()(int value) const // function call operator    {        if (bit == 31) // sign bit            return value < 0; // negative int to left partition        else            return !(value & (1 << bit)); // 0 bit to left partition    }}; // Least significant digit radix sortvoid lsd_radix_sort(int *first, int *last){    for (int lsb = 0; lsb < 32; ++lsb) // least-significant-bit    {        std::stable_partition(first, last, radix_test(lsb));    }} // Most significant digit radix sort (recursive)void msd_radix_sort(int *first, int *last, int msb = 31){    if (first != last && msb >= 0)    {        int *mid = std::partition(first, last, radix_test(msb));        msb--; // decrement most-significant-bit        msd_radix_sort(first, mid, msb); // sort left partition        msd_radix_sort(mid, last, msb); // sort right partition    }} // test radix_sortint main(){    int data[] = { 170, 45, 75, -90, -802, 24, 2, 66 };     lsd_radix_sort(data, data + 8);    // msd_radix_sort(data, data + 8);     std::copy(data, data + 8, std::ostream_iterator<int>(std::cout, " "));     return 0;}`

Output:

`-802 -90 2 24 45 66 75 170 `

## C#

Works with: C# version 3.0+
`using System; namespace RadixSort{    class Program    {        static void Sort(int[] old)        {            int i, j;            int[] tmp = new int[old.Length];            for (int shift = 31; shift > -1; --shift)            {                j = 0;                for (i = 0; i < old.Length; ++i)                {                    bool move = (old[i] << shift) >= 0;                    if (shift == 0 ? !move : move)  // shift the 0's to old's head                        old[i-j] = old[i];                    else                            // move the 1's to tmp                        tmp[j++] = old[i];                }                Array.Copy(tmp, 0, old, old.Length-j, j);            }        }        static void Main(string[] args)        {            int[] old = new int[] { 2, 5, 1, -3, 4 };            Console.WriteLine(string.Join(", ", old));            Sort(old);            Console.WriteLine(string.Join(", ", old));            Console.Read();        }    }}`

## D

### Shorter Version

`import std.stdio, std.math, std.traits, std.range, std.algorithm; ElementType!R[] radixSort(size_t N=10, R)(R r)if (hasLength!R && isRandomAccessRange!R &&    isIntegral!(ElementType!R)) {    alias ElementType!R E;     static if (isDynamicArray!R)        alias r res;         // input is array => in place sort    else        E[] res = r.array(); // input is Range => return a new array     E absMax = r.map!abs().reduce!max();    immutable nPasses = 1 + cast(int)(log(absMax) / log(N));     foreach (pass; 0 .. nPasses) {        auto bucket = new E[][](2 * N - 1, 0);        foreach (v; res) {            int bIdx = abs(v / (N ^^ pass)) % N;            bIdx = (v < 0) ? -bIdx : bIdx;            bucket[N + bIdx - 1] ~= v;        }        res = bucket.join();    }     return res;} void main() {    auto items = [170, 45, 75, -90, 2, 24, -802, 66];    items.radixSort().writeln();    items.map!q{1 - a}().radixSort().writeln();}`
Output:
```[-802, -90, 2, 24, 45, 66, 75, 170]
[-1, -23, -44, -65, -74, -169, 91, 803]```

### More Efficient Version

`import std.array, std.traits; // considered pure for this programextern(C) void* alloca(in size_t length) pure nothrow; void radixSort(size_t MAX_ALLOCA=5_000, U)(U[] data)pure nothrow if (isUnsigned!U) {    static void radix(in uint byteIndex, in U[] source, U[] dest)    pure nothrow {        immutable size_t sourceSize = source.length;        ubyte* curByte = (cast(ubyte*)source.ptr) + byteIndex;        uint[ubyte.max + 1] byteCounter;        for (size_t i = 0; i < sourceSize; i++, curByte += U.sizeof)            byteCounter[*curByte]++;         {            uint indexStart;            foreach (uint i; 0 .. byteCounter.length) {                immutable size_t tempCount = byteCounter[i];                byteCounter[i] = indexStart;                indexStart += tempCount;            }        }         curByte = (cast(ubyte*)source.ptr) + byteIndex;        for (size_t i = 0; i < sourceSize; i++, curByte += U.sizeof) {            uint* countPtr = byteCounter.ptr + *curByte;            dest[*countPtr] = source[i];            (*countPtr)++;        }    }     U[] tempData;    if (U.sizeof * data.length <= MAX_ALLOCA) {        U* ptr = cast(U*)alloca(data.length * U.sizeof);        if (ptr != null)            tempData = ptr[0 .. data.length];    }    if (tempData.empty)        tempData = uninitializedArray!(U[])(data.length);     static if (U.sizeof == 1) {        radix(0, data, tempData);        data[] = tempData[];    } else {        for (uint i = 0; i < U.sizeof; i += 2) {            radix(i + 0, data, tempData);            radix(i + 1, tempData, data);        }    }} void main() {    import std.stdio;    uint[] items = [170, 45, 75, 4294967206, 2, 24, 4294966494, 66];    items.radixSort();    writeln(items);}`
Output:
`[2, 24, 45, 66, 75, 170, 4294966494, 4294967206]`

## Eiffel

Works for positive integers. Splits up into two buckets according to the binary representation of the number.

` class	RADIX_SORT feature 	radix_sort (ar: ARRAY [INTEGER])			-- Array 'ar' sorted in ascending order.		require			ar_not_void: ar /= Void			not_negative: across ar as a all a.item >= 0 end		local			bucket_1, bucket_0: LINKED_LIST [INTEGER]			j, k, dig: INTEGER		do			create bucket_0.make			create bucket_1.make			dig := digits (ar)			across				0 |..| dig as c			loop				across					ar as r				loop					if r.item.bit_test (c.item) then						bucket_1.extend (r.item)					else						bucket_0.extend (r.item)					end				end				from					j := 1				until					j > bucket_0.count				loop					ar [j] := bucket_0 [j]					j := j + 1				end				from					k := j					j := 1				until					j > bucket_1.count				loop					ar [k] := bucket_1 [j]					k := k + 1					j := j + 1				end				bucket_0.wipe_out				bucket_1.wipe_out			end		ensure			is_sorted: is_sorted (ar)		end feature {NONE} 	digits (ar: ARRAY [INTEGER]): INTEGER			-- Number of digits of the largest item in 'ar'.		local			max: INTEGER			math: DOUBLE_MATH		do			create math			across				ar as a			loop				if a.item > max then					max := a.item				end			end			Result := math.log_2 (max).ceiling + 1		end 	is_sorted (ar: ARRAY [INTEGER]): BOOLEAN			--- Is 'ar' sorted in ascending order?		local			i: INTEGER		do			Result := True			from				i := ar.lower			until				i >= ar.upper			loop				if ar [i] > ar [i + 1] then					Result := False				end				i := i + 1			end		end end `

Test:

` class	APPLICATION create	make feature 	make		local			test: ARRAY [INTEGER]		do			create rs			create test.make_empty			test := <<5, 4, 999, 5, 70, 0, 1000, 55, 1, 2, 3>>			io.put_string ("Unsorted:%N")			across				test as t			loop				io.put_string (t.item.out + " ")			end			rs.radix_sort (test)			io.put_string ("%NSorted:%N")			across				test as t			loop				io.put_string (t.item.out + " ")			end		end 	rs: RADIX_SORT end `
Output:
```Unsorted:
5 4 999 5 70 0 1000 55 1 2 3
Sorted:
0 1 2 3 4 5 5 55 70 999 1000
```

## Elixir

Translation of: Ruby
`defmodule Sort do  def radix_sort(list), do: radix_sort(list, 10)   def radix_sort([], _), do: []  def radix_sort(list, base) do    max = abs(Enum.max_by(list, &abs(&1)))    sorted = radix_sort(list, base, max, 1)    {minus, plus} = Enum.partition(sorted, &(&1<0))    Enum.reverse(minus, plus)  end   defp radix_sort(list, _, max, m) when max<m, do: list  defp radix_sort(list, base, max, m) do    buckets = List.to_tuple(for _ <- 0..base-1, do: [])    bucket2 = Enum.reduce(list, buckets, fn x,acc ->      i = abs(x) |> div(m) |> rem(base)      put_elem(acc, i, [x | elem(acc, i)])    end)    list2 = Enum.reduce(base-1..0, [], fn i,acc -> Enum.reverse(elem(bucket2, i), acc) end)    radix_sort(list2, base, max, m*base)  endend IO.inspect Sort.radix_sort([-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028])`
Output:
```[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]
```

## Fortran

` *=======================================================================* RSORT - sort a list of integers by the Radix Sort algorithm* Public domain.  This program may be used by any person for any purpose.* Origin:  Herman Hollerith, 1887**___Name____Type______In/Out____Description_____________________________*   IX(N)   Integer   Both      Array to be sorted in increasing order*   IW(N)   Integer   Neither   Workspace*   N       Integer   In        Length of array** ASSUMPTIONS:  Bits in an INTEGER is an even number.*               Integers are represented by twos complement.** NOTE THAT:  Radix sorting has an advantage when the input is known *             to be less than some value, so that only a few bits need *             to be compared.  This routine looks at all the bits, *             and is thus slower than Quicksort.*=======================================================================      SUBROUTINE RSORT (IX, IW, N)             IMPLICIT NONE       INTEGER IX, IW, N       DIMENSION IX(N), IW(N)        INTEGER I,                        ! count bits     \$         ILIM,                     ! bits in an integer     \$         J,                        ! count array elements     \$         P1OLD, P0OLD, P1, P0,     ! indices to ones and zeros     \$         SWAP       LOGICAL ODD                       ! even or odd bit position *      IF (N < 2) RETURN      ! validate*        ILIM = Bit_size(i)    !Get the fixed number of bits*=======================================================================* Alternate between putting data into IW and into IX*=======================================================================       P1 = N+1       P0 = N                ! read from 1, N on first pass thru       ODD = .FALSE.       DO I = 0, ILIM-2         P1OLD = P1         P0OLD = P0         ! save the value from previous bit         P1 = N+1         P0 = 0                 ! start a fresh count for next bit          IF (ODD) THEN           DO J = 1, P0OLD, +1             ! copy data from the zeros             IF ( BTEST(IW(J), I) ) THEN               P1 = P1 - 1               IX(P1) = IW(J)             ELSE               P0 = P0 + 1               IX(P0) = IW(J)             END IF           END DO           DO J = N, P1OLD, -1             ! copy data from the ones             IF ( BTEST(IW(J), I) ) THEN               P1 = P1 - 1               IX(P1) = IW(J)             ELSE               P0 = P0 + 1              IX(P0) = IW(J)             END IF           END DO          ELSE            DO J = 1, P0OLD, +1             ! copy data from the zeros             IF ( BTEST(IX(J), I) ) THEN               P1 = P1 - 1               IW(P1) = IX(J)              ELSE               P0 = P0 + 1               IW(P0) = IX(J)             END IF           END DO           DO J = N, P1OLD, -1            ! copy data from the ones             IF ( BTEST(IX(J), I) ) THEN               P1 = P1 - 1               IW(P1) = IX(J)             ELSE               P0 = P0 + 1               IW(P0) = IX(J)             END IF          END DO         END IF  ! even or odd i          ODD = .NOT. ODD       END DO  ! next i *=======================================================================*        the sign bit*=======================================================================       P1OLD = P1       P0OLD = P0       P1 = N+1       P0 = 0  *          if sign bit is set, send to the zero end       DO J = 1, P0OLD, +1         IF ( BTEST(IW(J), ILIM-1) ) THEN            P0 = P0 + 1           IX(P0) = IW(J)         ELSE           P1 = P1 - 1           IX(P1) = IW(J)         END IF       END DO                 DO J = N, P1OLD, -1         IF ( BTEST(IW(J), ILIM-1) ) THEN           P0 = P0 + 1           IX(P0) = IW(J)         ELSE           P1 = P1 - 1           IX(P1) = IW(J)         END IF       END DO *=======================================================================*       Reverse the order of the greater value partition*=======================================================================       P1OLD = P1       DO J = N, (P1OLD+N)/2+1, -1         SWAP = IX(J)         IX(J) = IX(P1)         IX(P1) = SWAP         P1 = P1 + 1       END DO       RETURN      END ! of RSORT  ************************************************************************         test program***********************************************************************      PROGRAM t_sort       IMPLICIT NONE       INTEGER I, N       PARAMETER (N = 11)       INTEGER IX(N), IW(N)       LOGICAL OK        DATA IX / 2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666 /        PRINT *, 'before: ', IX       CALL RSORT (IX, IW, N)       PRINT *, 'after: ', IX *              compare       OK = .TRUE.       DO I = 1, N-1         IF (IX(I) > IX(I+1)) OK = .FALSE.       END DO       IF (OK) THEN         PRINT *, 't_sort: successful test'       ELSE         PRINT *, 't_sort: failure!'       END IF      END ! of test program `
Output:
``` before:  2 24 45 0 66 75 170 -802 -90 1066 666
after:  -802 -90 0 2 24 45 66 75 170 666 1066
t_sort: successful test
```

## Go

LSD radix 256, negatives handled by flipping the high bit.

`package main import (    "bytes"    "encoding/binary"    "fmt") // declarations for word size of datatype word int32const wordLen = 4const highBit = -1 << 31 var data = []word{170, 45, 75, -90, -802, 24, 2, 66} func main() {    buf := bytes.NewBuffer(nil)    ds := make([][]byte, len(data))    for i, x := range data {        binary.Write(buf, binary.LittleEndian, x^highBit)        b := make([]byte, wordLen)        buf.Read(b)        ds[i] = b    }    bins := make([][][]byte, 256)    for i := 0; i < wordLen; i++ {        for _, b := range ds {            bins[b[i]] = append(bins[b[i]], b)        }        j := 0        for k, bs := range bins {            copy(ds[j:], bs)            j += len(bs)            bins[k] = bs[:0]        }    }    fmt.Println("original:", data)    var w word    for i, b := range ds {        buf.Write(b)        binary.Read(buf, binary.LittleEndian, &w)        data[i] = w^highBit    }    fmt.Println("sorted:  ", data)}`

Output:

```original: [170 45 75 -90 -802 24 2 66]
sorted:   [-802 -90 2 24 45 66 75 170]
```

## Groovy

This solution assumes the radix is a power of 2:

`def radixSort = { final radixExponent, list ->    def fromBuckets = new TreeMap([0:list])    def toBuckets = new TreeMap()    final radix = 2**radixExponent    final mask = radix - 1    final radixDigitSize = (int)Math.ceil(64/radixExponent)    final digitWidth = radixExponent    (0..<radixDigitSize).each { radixDigit ->        fromBuckets.values().findAll { it != null }.flatten().each {            print '.'            long bucketNumber = (long)((((long)it) >>> digitWidth*radixDigit) & mask)            toBuckets[bucketNumber] = toBuckets[bucketNumber] ?: []            toBuckets[bucketNumber] << it        }        (fromBuckets, toBuckets) = [toBuckets, fromBuckets]        toBuckets.clear()    }    final overflow = 2**(63 % radixExponent)    final pos = {it < overflow}    final neg = {it >= overflow}    final keys = fromBuckets.keySet()    final twosComplIndx = [] + (keys.findAll(neg)) + (keys.findAll(pos))    twosComplIndx.collect { fromBuckets[it] }.findAll { it != null }.flatten()}`

Test:

`println (radixSort(3, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))println (radixSort(3, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))println (radixSort(3, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))println ()println (radixSort(8, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))println (radixSort(8, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))println (radixSort(8, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))println ()println (radixSort(11, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))println (radixSort(11, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))println (radixSort(11, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))println ()println (radixSort(16, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))println (radixSort(16, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))println (radixSort(16, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))println ()println (radixSort(32, [23,76,99,58,97,57,35,89,51,38,95,92,24,46,31,24,14,12,57,78,4]))println (radixSort(32, [88,18,31,44,4,0,8,81,14,78,20,76,84,33,73,75,82,5,62,70,12,7,1]))println (radixSort(32, [23,-76,-990,580,97,57,350000,Long.MAX_VALUE,89,Long.MIN_VALUE,51,38,95*2**48,92,-24*2**48,46,31*2**32,24,14,12,57,78,4]))`

Output:

```..............................................................................................................................................................................................................................................................................................................................................................................................................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

........................................................................................................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
........................................................................................................................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
........................................................................................................................................................................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

..............................................................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
..........................................................................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
..........................................................................................................................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

....................................................................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
............................................................................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
............................................................................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]

..........................................[4, 12, 14, 23, 24, 24, 31, 35, 38, 46, 51, 57, 57, 58, 76, 78, 89, 92, 95, 97, 99]
..............................................[0, 1, 4, 5, 7, 8, 12, 14, 18, 20, 31, 33, 44, 62, 70, 73, 75, 76, 78, 81, 82, 84, 88]
..............................................[-9223372036854775808, -6755399441055744, -990, -76, 4, 12, 14, 23, 24, 38, 46, 51, 57, 57, 78, 89, 92, 97, 580, 350000, 133143986176, 26740122787512320, 9223372036854775807]```

`import Data.Bits (Bits(testBit, bitSize))import Data.List (partition) lsdSort :: (Ord a, Bits a) => [a] -> [a]lsdSort = fixSort positiveLsdSort msdSort :: (Ord a, Bits a) => [a] -> [a]msdSort = fixSort positiveMsdSort -- Fix a sort that puts negative numbers at the end, like positiveLsdSort and positiveMsdSortfixSort sorter list = uncurry (flip (++)) (break (< 0) (sorter list)) positiveLsdSort :: (Bits a) => [a] -> [a]positiveLsdSort list = foldl step list [0..bitSize (head list)] where	step list bit = uncurry (++) (partition (not . flip testBit bit) list) positiveMsdSort :: (Bits a) => [a] -> [a]positiveMsdSort list = aux (bitSize (head list) - 1) list where	aux _ [] = []	aux (-1) list = list	aux bit list = aux (bit - 1) lower ++ aux (bit - 1) upper where		(lower, upper) = partition (not . flip testBit bit) list`

## Icon and Unicon

The following is nice and short and works in both languages. However it contains a subtle inefficiency: subscripting a numeric value first coerces it into a string.

`procedure main(A)    every writes((!rSort(A)||" ")|"\n")end procedure rSort(A)    every (min := A[1]) >:= !A    every (mlen := *(A[1]-min)) <:= (!A - min)    every i := !*mlen do {        every put(b := [], |[]\12)        every a := !A do put(b[(a-min)[-i]+2|1], a)        every put(A := [],!!b)        }    return Aend`

Sample run:

```->radix 31 123 -98 7090 802 2
-98 2 31 123 802 7090
->
```

## J

Generally, this task should be accomplished in J using `/:~`. Here we take an approach that's more comparable with the other examples on this page.

`keys f/. data ` evaluates the function f on each group of data at the same position as similar keys. Sorting requires ordered keys. This code uses a J idiom: prepend the keys and matching data. The extra data is removed by behead `}.`.

` radixSortR =: 3 : 0  NB. base radixSort data16 radixSortR y:keys =. x #.^:_1 y NB. compute keyslength =. #{.keysextra =. (-length) {."0 buckets =. i.xfor_pass. i.-length do.   keys =. ; (buckets,pass{"1 keys) <@:}./.extra,keysend.x#.keys NB. restore the data)`

An alternate implementation is

`radixsort=: (] #~ [: +/ =/) [email protected](>./)`

This uses the maximum value of the list for the base, which allows the list to be sorted in one pass.

Example use:

`   radixsort [email protected]#~104 5 6 6 6 6 6 8 8`

Or, for negative number support:

`rsort=: (] + [email protected]:-) <./`

Example:

`   rsort _6[email protected]#~10_2 _1 0 0 0 0 0 2 2`

## Java

`public static int[] sort(int[] old) {    // Loop for every bit in the integers    for (int shift = Integer.SIZE - 1; shift > -1; shift--) {        // The array to put the partially sorted array into        int[] tmp = new int[old.length];        // The number of 0s        int j = 0;         // Move the 0s to the new array, and the 1s to the old one        for (int i = 0; i < old.length; i++) {            // If there is a 1 in the bit we are testing, the number will be negative            boolean move = old[i] << shift >= 0;             // If this is the last bit, negative numbers are actually lower            if (shift == 0 ? !move : move) {                tmp[j] = old[i];                j++;            } else {                // It's a 1, so stick it in the old array for now                old[i - j] = old[i];            }        }         // Copy over the 1s from the old array        for (int i = j; i < tmp.length; i++) {            tmp[i] = old[i - j];        }         // And now the tmp array gets switched for another round of sorting        old = tmp;    }     return old;}`
Translation of: NetRexx
` import java.util.ArrayList;import java.util.Arrays;import java.util.LinkedList;import java.util.List;import java.util.Queue; public class RSortingRadixsort00 {   public RSortingRadixsort00() {     return;  }   public static int[] lsdRadixSort(int[] tlist) {     List<Integer> intermediates;    int[] limits = getLimits(tlist);    tlist = rescale(tlist, limits[1]);     for (int px = 1; px <= limits[2]; ++px) {      @SuppressWarnings("unchecked")      Queue<Integer> bukits[] = new Queue[10];      for (int ix = 0; ix < tlist.length; ++ix) {        int cval = tlist[ix];        int digit = (int) (cval / Math.pow(10, px - 1) % 10);        if (bukits[digit] == null) {          bukits[digit] = new LinkedList<>();        }        bukits[digit].add(cval);      }       intermediates = new ArrayList<>();      for (int bi = 0; bi < 10; ++bi) {        if (bukits[bi] != null) {          while (bukits[bi].size() > 0) {            int nextd;            nextd = bukits[bi].poll();            intermediates.add(nextd);          }        }      }       for (int iw = 0; iw < intermediates.size(); ++iw) {        tlist[iw] = intermediates.get(iw);      }    }     tlist = rescale(tlist, -limits[1]);     return tlist;  }   private static int[] rescale(int[] arry, int delta) {     for (int ix = 0; ix < arry.length; ++ix) {      arry[ix] -= delta;    }     return arry;  }   private static int[] getLimits(int[] tlist) {     int[] lims = new int[3];     for (int i_ = 0; i_ < tlist.length; ++i_) {      lims[0] = Math.max(lims[0], tlist[i_]);      lims[1] = Math.min(lims[1], tlist[i_]);    }    lims[2] = (int) Math.ceil(Math.log10(lims[0] - lims[1]));     return lims;  }   private static void runSample(String[] args) {     int[][] lists = {      new int[] { 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, },      new int[] { -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, -0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, },      new int[] { 2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666, },      new int[] { 170, 45, 75, 90, 2, 24, 802, 66, },      new int[] { -170, -45, -75, -90, -2, -24, -802, -66, },    };     long etime;    lsdRadixSort(Arrays.copyOf(lists[0], lists[0].length)); // do one pass to set up environment to remove it from timings     for (int[] tlist : lists) {      System.out.println(array2list(tlist));      etime = System.nanoTime();      tlist = lsdRadixSort(tlist);      etime = System.nanoTime() - etime;      System.out.println(array2list(tlist));      System.out.printf("Elapsed time: %fs%n", ((double) etime / 1_000_000_000.0));      System.out.println();    }     return;  }   private static List<Integer> array2list(int[] arry) {     List<Integer> target = new ArrayList<>(arry.length);     for (Integer iv : arry) {      target.add(iv);    }     return target;  }   public static void main(String[] args) {     runSample(args);     return;  }} `
Output:
```[10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]
[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Elapsed time: 0.000256s

[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
[-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Elapsed time: 0.000198s

[2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666]
[-802, -90, 0, 2, 24, 45, 66, 75, 170, 666, 1066]
Elapsed time: 0.000187s

[170, 45, 75, 90, 2, 24, 802, 66]
[2, 24, 45, 66, 75, 90, 170, 802]
Elapsed time: 0.000088s

[-170, -45, -75, -90, -2, -24, -802, -66]
[-802, -170, -90, -75, -66, -45, -24, -2]
Elapsed time: 0.000113s

```

## jq

`# Sort the input array;# "base" must be an integer greater than 1def radix_sort(base):  # We only need the ceiling of non-negatives:  def ceil: if . == floor then . else (. + 1 | floor) end;   min as \$min  | map(. - \$min)  | ((( max|log) / (base|log)) | ceil) as \$rounds  | reduce range(0; \$rounds) as \$i      # state: [ base^i, buckets ]      ( [1, .];        .[0] as \$base_i        | reduce .[1][] as \$n             ([];             ((\$n/\$base_i) % base) as \$digit             | .[\$digit] += [\$n] )        | [(\$base_i * base), (map(select(. != null)) | flatten)] )  | .[1]  | map(. + \$min) ; def radix_sort:  radix_sort(10); `

Example

` # Verify that radix_sort agrees with sort( [1, 3, 8, 9, 0, 0, 8, 7, 1, 6],  [170, 45, 75, 90, 2, 24, 802, 66],  [170, 45, 75, 90, 2, 24, -802, -66] ) | (radix_sort == sort) `
Output:
```true
true
true
```

## Julia

Translation of: Scala
`function radixsort(tobesorted::Vector{Int64})    arr = deepcopy(tobesorted)    for shift in 63:-1:0        tmp = Vector{Int64}(undef, length(arr))        j = 0        for i in 1:length(arr)            if (shift == 0) == ((arr[i] << shift) >= 0)                arr[i - j] = arr[i]            else                tmp[j + 1] = arr[i]                j += 1            end        end        tmp[j+1:end] .= arr[1:length(tmp)-j]        arr = tmp    end    arrend function testradixsort()    arrays = [[170, 45, 75, -90, -802, 24, 2, 66], [-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028]]    for array in arrays         println(radixsort(array))    endend testradixsort() `
Output:
```
[-802, -90, 2, 24, 45, 66, 75, 170]
[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]

```

## Kotlin

Translation of: Java
`// version 1.1.2 fun radixSort(original: IntArray): IntArray {    var old = original // Need this to be mutable    // Loop for every bit in the integers    for (shift in 31 downTo 0) {        val tmp = IntArray(old.size)  // The array to put the partially sorted array into        var j = 0                     // The number of 0s        // Move the 0s to the new array, and the 1s to the old one        for (i in 0 until old.size) {            // If there is a 1 in the bit we are testing, the number will be negative            val move = (old[i] shl shift) >= 0            // If this is the last bit, negative numbers are actually lower            val toBeMoved = if (shift == 0) !move else move            if (toBeMoved)                tmp[j++] = old[i]            else {                // It's a 1, so stick it in the old array for now                old[i - j] = old[i]            }        }        // Copy over the 1s from the old array        for (i in j until tmp.size) tmp[i] = old[i - j]        // And now the tmp array gets switched for another round of sorting        old = tmp    }    return old} fun main(args: Array<String>) {    val arrays = arrayOf(        intArrayOf(170, 45, 75, -90, -802, 24, 2, 66),        intArrayOf(-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028)    )    for (array in arrays) println(radixSort(array).contentToString())}`
Output:
```[-802, -90, 2, 24, 45, 66, 75, 170]
[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]
```

## Mathematica

`ClearAll[SortByPos, RadixSort]SortByPos[data : {_List ..}, pos_Integer] := Module[{digs, order},  digs = data[[All, pos]];  order = Ordering[digs];  data[[order]]  ]RadixSort[x : {_Integer ..}] := Module[{y, digs, maxlen, offset},  offset = Min[x];  y = x - offset;  digs = IntegerDigits /@ y;  maxlen = Max[Length /@ digs];  digs = IntegerDigits[#, 10, maxlen] & /@ y;  digs = Fold[SortByPos, digs, -Range[maxlen]];  digs = FromDigits /@ digs;  digs += offset;  digs  ]`

Testing out the algorithm:

`RadixSort[{170,45,75,-90,-802,24,2,66}]RadixSort[{170,45,75,90,802,2,24,66}]`
Output:
```{-802,-90,2,24,45,66,75,170}
{2,24,45,66,75,90,170,802}```

## NetRexx

Uses a suggestion in the discussion page to handle negative values.
Limitations - Handles decimal digits only.

### Using the Rexx class

`/* NetRexx */options replace format comments java crossref symbols nobinary runSample(arg)return -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method radixSort(tlist = Rexx[]) public static returns Rexx[]   -- scale the array to start at zero to allow handling of -ve values  parse getLimits(tlist) maxn minn maxl .  tlist = rescale(tlist, minn)   loop px = maxl to 1 by -1    bukits = ''    loop ix = 0 to tlist.length - 1      cval = tlist[ix].right(maxl, 0)      parse cval . =(px) digit +1 .      bukits[digit] = bukits[digit] (cval + 0) -- simulates a stack      end ix    intermediates = ''    loop bi = 0 to 9      intermediates = intermediates bukits[bi] -- sumulates unstack      end bi    -- reload array    loop iw = 1 to intermediates.words()      tlist[iw - 1] = intermediates.word(iw)      end iw    end px   -- restore the array to original scale  tlist = rescale(tlist, -minn)  return tlist -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method rescale(arry = Rexx[], newbase) private static returns Rexx[]  loop ix = 0 to arry.length - 1    arry[ix] = arry[ix] - newbase    end ix  return arry-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method getLimits(arry = Rexx[]) private static returns Rexx  maxn = 0  minn = 0  maxl = 0  loop i_ = 0 to arry.length - 1    maxn = maxn.max(arry[i_])    minn = minn.min(arry[i_])    end i_  maxl = (maxn - minn).length()  return maxn minn maxl-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method runSample(arg) private static  lists = [-    [2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666], -    [170, 45, 75, 90, 2, 24, 802, 66], -    [10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0], -    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], -    [-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, -0], -    [-0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10], -    [-10, -19, -18, -17, -18, -15, -14, -13, -12, -11, -100], -    [10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0, -0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10], -    [-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, -0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] -  ]   loop il = 0 to lists.length - 1    tlist = lists[il]    say ' Input:' Arrays.asList(tlist)    say 'Output:' Arrays.asList(radixSort(tlist))    say    end il  return `
Output:
``` Input: [2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666]
Output: [-802, -90, 0, 2, 24, 45, 66, 75, 170, 666, 1066]

Input: [170, 45, 75, 90, 2, 24, 802, 66]
Output: [2, 24, 45, 66, 75, 90, 170, 802]

Input: [10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0]
Output: [0, 1, 2, 3, 4, 5, 7, 8, 8, 9, 10]

Input: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Output: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

Input: [-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, 0]
Output: [-10, -9, -8, -8, -7, -5, -4, -3, -2, -1, 0]

Input: [0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]
Output: [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0]

Input: [-10, -19, -18, -17, -18, -15, -14, -13, -12, -11, -100]
Output: [-100, -19, -18, -18, -17, -15, -14, -13, -12, -11, -10]

Input: [10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10]
Output: [-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 7, 8, 8, 9, 10]

Input: [-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Output: [-10, -9, -8, -8, -7, -5, -4, -3, -2, -1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
```

### Using Collection classes

`/* NetRexx */options replace format comments java crossref symbols nobinary import java.util.Queue runSample(arg)return -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method radixSort(tlist = Rexx[]) public static returns Rexx[]   -- scale the array to start at zero to allow handling of -ve values  limits = ''  parse '!MAXN !MINN !MAXL' maxn_ minn_ maxl_ .  parse getLimits(tlist) maxn minn maxl .  limits[maxn_] = maxn  limits[minn_] = minn  limits[maxl_] = maxl  tlist = rescale(tlist, limits[minn_])   loop px = limits[maxl_] to 1 by -1    bukits = Queue[10] -- stacks for digits 0 .. 9    loop ix = 0 while ix < tlist.length      cval = tlist[ix].right(limits[maxl_], 0)      parse cval . =(px) digit +1 . -- extract next digit (fun with parse)      -- alternatively: digit = (cval % (10 ** (px - 1))) // 10      if bukits[digit] == null then bukits[digit] = LinkedList()      bukits[digit].add((cval + 0))      end ix     intermediates = ArrayList()    loop bi = 0 to 9      if bukits[bi] \= null then loop while bukits[bi].size() > 0        nextd = bukits[bi].poll()        intermediates.add(nextd)        end      end bi     -- reload result array    loop iw = 0 while iw < intermediates.size()      tlist[iw] = Rexx intermediates.get(iw)      end iw    end px   -- restore the array to original scale  tlist = rescale(tlist, -limits[minn_])  return tlist -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method rescale(arry = Rexx[], newbase) private static returns Rexx[]  loop ix = 0 to arry.length - 1    arry[ix] = arry[ix] - newbase    end ix  return arry-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method getLimits(arry = Rexx[]) private static returns Rexx  maxn = 0  minn = 0  maxl = 0  loop i_ = 0 to arry.length - 1    maxn = maxn.max(arry[i_])    minn = minn.min(arry[i_])    end i_  maxl = (maxn - minn).length()  return maxn minn maxl-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~method runSample(arg) private static  lists = [-    [2, 24, 45, 0, 66, 75, 170, -802, -90, 1066, 666], -    [170, 45, 75, 90, 2, 24, 802, 66], -    [10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0], -    [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], -    [-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, -0], -    [-0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10], -    [-10, -19, -18, -17, -18, -15, -14, -13, -12, -11, -100], -    [10, 9, 8, 7, 8, 5, 4, 3, 2, 1, 0, -0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10], -    [-10, -9, -8, -7, -8, -5, -4, -3, -2, -1, -0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10] -  ]   loop il = 0 to lists.length - 1    tlist = lists[il]    say ' Input:' Arrays.asList(tlist)    say 'Output:' Arrays.asList(radixSort(tlist))    say    end il  return `

## Perl

`#!/usr/bin/perluse warnings;use strict; sub radix {    my @tab = ([@_]);     my \$max_length = 0;    length > \$max_length and \$max_length = length for @_;    \$_ = sprintf "%0\${max_length}d", \$_ for @{ \$tab[0] }; # Add zeros.     for my \$pos (reverse -\$max_length .. -1) {        my @newtab;        for my \$bucket (@tab) {            for my \$n (@\$bucket) {                my \$char = substr \$n, \$pos, 1;                \$char = -1 if '-' eq \$char;                \$char++;                push @{ \$newtab[\$char] }, \$n;            }        }        @tab = @newtab;    }     my @return;    my \$negative = shift @tab;                            # Negative bucket must be reversed.    push @return, reverse @\$negative;    for my \$bucket (@tab) {        push @return, @{ \$bucket // [] };    }    \$_ = 0 + \$_ for @return;                              # Remove zeros.    return @return;}`

To test, add the following lines:

`use Test::More tests => 1000; for (1 .. 1000) {    my @l = map int rand(2000) - 1000, 0 .. 20;    is_deeply([radix(@l)], [sort { \$a <=> \$b } @l]);}`

## Perl 6

A base-10 radix sort, done on the string representation of the integers. Signs are handled by in-place reversal of the '-' bucket on the last iteration. (The sort in there is not cheating; it only makes sure we process the buckets in the right order, since classify might return the buckets in random order. It might be more efficient to create our own ordered buckets, but this is succinct.)

`sub radsort (@ints) {    my \$maxlen = [max] @ints».chars;    my @list = @ints».fmt("\%0{\$maxlen}d");     for reverse ^\$maxlen -> \$r {        my @buckets = @list.classify( *.substr(\$r,1) ).sort: *.key;        @buckets[0].value = @buckets[0].value.reverse.List            if !\$r and @buckets[0].key eq '-';        @list = flat map *.value.values, @buckets;    }    @list».Int;} .say for radsort (-2_000 .. 2_000).roll(20);`
Output:
```-1585
-1427
-1228
-1067
-945
-657
-643
-232
-179
-28
37
411
488
509
716
724
1504
1801
1864
1939```

## Phix

`function radixSortn(sequence s, integer n)sequence buckets = repeat({},10)sequence res = {}    for i=1 to length(s) do        integer digit = remainder(floor(s[i]/power(10,n-1)),10)+1        buckets[digit] = append(buckets[digit],s[i])    end for    for i=1 to length(buckets) do        integer len = length(buckets[i])        if len!=0 then            if len=1 or n=1 then                res &= buckets[i]            else                res &= radixSortn(buckets[i],n-1)            end if        end if    end for    return resend function function split_by_sign(sequence s)sequence buckets = {{},{}}    for i=1 to length(s) do        integer si = s[i]        if si<0 then            buckets[1] = append(buckets[1],-si)        else            buckets[2] = append(buckets[2],si)        end if    end for    return bucketsend function function radixSort(sequence s)integer mins = min(s)integer passes = max(max(s),abs(mins))    passes = floor(log10(passes))+1    if mins<0 then        sequence buckets = split_by_sign(s)        buckets[1] = reverse(sq_uminus(radixSortn(buckets[1],passes)))        buckets[2] = radixSortn(buckets[2],passes)        s = buckets[1]&buckets[2]    else        s = radixSortn(s,passes)    end if    return send function ?radixSort({1, 3, 8, 9, 0, 0, 8, 7, 1, 6})?radixSort({170, 45, 75, 90, 2, 24, 802, 66})?radixSort({170, 45, 75, 90, 2, 24, -802, -66})?radixSort({100000, -10000, 400, 23, 10000})`
Output:
```{0,0,1,1,3,6,7,8,8,9}
{2,24,45,66,75,90,170,802}
{-802,-66,2,24,45,75,90,170}
{-10000,23,400,10000,100000}
```

## PicoLisp

This is a LSD base-2 radix sort using queues:

`(de radixSort (Lst)   (let Mask 1      (while         (let (Pos (list NIL NIL)  Neg (list NIL NIL)  Flg)            (for N Lst               (queue                  (if2 (ge0 N) (bit? Mask N)                     (cdr Pos) Pos Neg (cdr Neg) )                  N )               (and (>= (abs N) Mask) (on Flg)) )            (setq               Lst (conc (apply conc Neg) (apply conc Pos))               Mask (* 2 Mask) )            Flg ) ) )   Lst )`

Output:

```: (radixSort (make (do 12 (link (rand -999 999)))))
-> (-999 -930 -666 -336 -218 68 79 187 391 405 697 922)```

## PureBasic

`Structure bucket  List i.i()EndStructure DataSection  ;sets specify the size (1 based) followed by each integer  set1:  Data.i 10 ;size  Data.i 1, 3, 8, 9, 0, 0, 8, 7, 1, 6 ;data  set2:  Data.i 8   Data.i 170, 45, 75, 90, 2, 24, 802, 66  set3:  Data.i 8  Data.i 170, 45, 75, 90, 2, 24, -802, -66EndDataSection Procedure setIntegerArray(Array x(1), *setPtr)   Protected i, count  count = PeekI(*setPtr) - 1 ;convert to zero based count  *setPtr + SizeOf(Integer) ;move pointer forward to data  Dim x(count)  For i = 0 To count    x(i) = PeekI(*setPtr + i * SizeOf(Integer))  Next EndProcedure Procedure displayArray(Array x(1))  Protected i, Size = ArraySize(x())  For i = 0 To Size    Print(Str(x(i)))    If i < Size: Print(", "): EndIf  Next   PrintN("")EndProcedure Procedure radixSort(Array x(1), Base = 10)  Protected count = ArraySize(x())  If Base < 1 Or count < 1: ProcedureReturn: EndIf ;exit due to invalid values   Protected i, pv, digit, digitCount, maxAbs, pass, index  ;find element with largest number of digits  For i = 0 To count    If Abs(x(i)) > maxAbs      maxAbs = Abs(x(i))    EndIf   Next   digitCount = Int(Log(maxAbs)/Log(Base)) + 1   For pass = 1 To digitCount    Dim sortBuckets.bucket(Base * 2 - 1)    pv = Pow(Base, pass - 1)     ;place elements in buckets according to the current place-value's digit    For index = 0 To count      digit = Int(x(index)/pv) % Base + Base      AddElement(sortBuckets(digit)\i())      sortBuckets(digit)\i() = x(index)    Next     ;transfer contents of buckets back into array    index = 0    For digit = 1 To (Base * 2) - 1      ForEach sortBuckets(digit)\i()        x(index) = sortBuckets(digit)\i()        index + 1      Next     Next  NextEndProcedure If OpenConsole()  Dim x(0)  setIntegerArray(x(), ?set1)  radixSort(x()): displayArray(x())   setIntegerArray(x(), ?set2)  radixSort(x()): displayArray(x())   setIntegerArray(x(), ?set3)  radixSort(x(), 2): displayArray(x())   Print(#CRLF\$ + #CRLF\$ + "Press ENTER to exit"): Input()  CloseConsole()EndIf`

Sample output:

```0, 0, 1, 1, 3, 6, 7, 8, 8, 9
2, 24, 45, 66, 75, 90, 170, 802
-802, -66, 2, 24, 45, 75, 90, 170```

## Python

Works with: Python version 2.6

This is the Wikipedia example code extended with an extra pass to sort negative values correctly.

`#python2.6 <from math import log def getDigit(num, base, digit_num):    # pulls the selected digit    return (num // base ** digit_num) % base   def makeBlanks(size):    # create a list of empty lists to hold the split by digit    return [ [] for i in range(size) ]   def split(a_list, base, digit_num):    buckets = makeBlanks(base)    for num in a_list:        # append the number to the list selected by the digit        buckets[getDigit(num, base, digit_num)].append(num)      return buckets # concatenate the lists back in order for the next stepdef merge(a_list):    new_list = []    for sublist in a_list:       new_list.extend(sublist)    return new_list def maxAbs(a_list):    # largest abs value element of a list    return max(abs(num) for num in a_list) def split_by_sign(a_list):    # splits values by sign - negative values go to the first bucket,    # non-negative ones into the second    buckets = [[], []]    for num in a_list:        if num < 0:            buckets[0].append(num)        else:            buckets[1].append(num)    return buckets def radixSort(a_list, base):    # there are as many passes as there are digits in the longest number    passes = int(round(log(maxAbs(a_list), base)) + 1)     new_list = list(a_list)    for digit_num in range(passes):        new_list = merge(split(new_list, base, digit_num))    return merge(split_by_sign(new_list)) `

An alternate implementation using which works on Python 3:

`#python3.7 <def flatten(some_list):    """    Flatten a list of lists.    Usage: flatten([[list a], [list b], ...])    Output: [elements of list a, elements of list b]    """    new_list = []    for sub_list in some_list:        new_list += sub_list    return new_list def radix(some_list, idex=None, size=None):    """    Recursive radix sort    Usage: radix([unsorted list])    Output: [sorted list]    """    # Initialize variables not set in the initial call    if size == None:        largest_num = max(some_list)        largest_num_str = str(largest_num)        largest_num_len = len(largest_num_str)        size = largest_num_len     if idex == None:        idex = size     # Translate the index we're looking at into an array index.    # e.g., looking at the 10's place for 100:    # size: 3    # idex: 2    #    i: (3-2) == 1    # str(123)[i] -> 2    i = size - idex      # The recursive base case.    # Hint: out of range indexing errors    if i >= size:        return some_list     # Initialize the bins we will place numbers into    bins = [[] for _ in range(10)]     # Iterate over the list of numbers we are given    for e in some_list:        # The destination bin; e.g.,:        #   size: 5        #      e: 29        #  num_s: '00029'        #      i: 3        # dest_c: '2'        # dest_i: 2        num_s  = str(e).zfill(size)        dest_c = num_s[i]        dest_i = int(dest_c)         bins[dest_i] += [e]     result = []    for b in bins:        # Make the recursive call        # Sort each of the sub-lists in our bins        result.append(radix(b, idex-1, size))     # Flatten our list    # This is also called in our recursive call,    # so we don't need flatten to be recursive.    flattened_result = flatten(result)     return flattened_result `

That same example but more compact:

`#python3.7 <def flatten(l):    return [y for x in l for y in x] def radix(l, p=None, s=None):    if s == None:        s = len(str(max(l)))    if p == None:        p = s     i = s - p     if i >= s:        return l     bins = [[] for _ in range(10)]     for e in l:        bins[int(str(e).zfill(s)[i])] += [e]     return flatten([radix(b, p-1, s) for b in bins] `

## QB64

` #lang QB64'* don't be an a\$\$. Keep this credit notice with the source:'* written/refactored by CodeGuy, 2018.'* also works with negative numbers.TESTN& = 63A\$ = ""REDIM b(0 TO TESTN&) AS DOUBLEFOR s& = -1 TO 1 STEP 2    A\$ = A\$ + CHR\$(13) + CHR\$(10) + "Random order:"    FOR i = 0 TO TESTN&        b(i) = (1000 * RND) AND 1023        IF i MOD 2 THEN b(i) = -b(i)        IF i < TESTN& THEN            A\$ = A\$ + LTRIM\$(STR\$(b(i))) + ","        ELSE            A\$ = A\$ + LTRIM\$(STR\$(b(i))) + CHR\$(13) + CHR\$(10)        END IF    NEXT    RadixSort b(), 0, TESTN&, s&    IF s& = -1 THEN        A\$ = A\$ + "descending order" + CHR\$(13) + CHR\$(10)    ELSE        A\$ = A\$ + "ascending order" + CHR\$(13) + CHR\$(10)    END IF     FOR i = 0 TO TESTN&        PRINT b(i);        IF i < TESTN& THEN            A\$ = A\$ + LTRIM\$(STR\$(b(i))) + ","        ELSE            A\$ = A\$ + LTRIM\$(STR\$(b(i))) + CHR\$(13) + CHR\$(10)        END IF    NEXTNEXTPRINT A\$TYPE MinMaxRec    min AS LONG    max AS LONGEND TYPE SUB RadixSort (CGSortLibArr() AS DOUBLE, start&, finish&, order&)    ArrayIsInteger CGSortLibArr(), start&, finish&, errindex&, errcon&    IF errcon& THEN        '* use another stable sort and sort anyway        MergeSort CGSortLibArr(), start&, finish&, order&    ELSE        DIM RSMMrec AS MinMaxRec        GetMinMaxArray CGSortLibArr(), start&, finish&, RSMMrec        IF CGSortLibArr(RSMMrec.min) = CGSortLibArr(RSMMrec.max) THEN EXIT SUB '* no div0 bombs        delta# = CGSortLibArr(RSMMrec.max) - CGSortLibArr(RSMMrec.min)        DIM pow2 AS _UNSIGNED _INTEGER64        DIM NtmpN AS _UNSIGNED _INTEGER64        DIM Int64MaxShift AS _INTEGER64: Int64MaxShift = 2 ^ 64        REDIM ct&(-1 TO 1)        REDIM RadixCGSortLibArr(0 TO 1, finish& - start&) AS DOUBLE        SELECT CASE order&            CASE 1                pow2 = Int64MaxShift                bits& = LEN(Int64MaxShift) * 8                DO UNTIL bits& < 0                    FOR i& = start& TO finish&                        NtmpN = Int64MaxShift * (CGSortLibArr(i&) - CGSortLibArr(RSMMrec.min)) / (delta#)                        IF NtmpN AND pow2 THEN                            tmpradix% = 1                        ELSE                            tmpradix% = 0                        END IF                        RadixCGSortLibArr(tmpradix%, ct&(tmpradix%)) = CGSortLibArr(i&)                        ct&(tmpradix%) = ct&(tmpradix%) + 1                    NEXT                    c& = start&                    FOR i& = 0 TO 1                        FOR j& = 0 TO ct&(i&) - 1                            CGSortLibArr(c&) = RadixCGSortLibArr(i&, j&)                            c& = c& + 1                        NEXT                        ct&(i&) = 0                    NEXT                    pow2 = pow2 / 2                    bits& = bits& - 1                LOOP            CASE ELSE                pow2 = 1                FOR bits& = 0 TO 63                    FOR i& = start& TO finish&                        NtmpN = Int64MaxShift * (CGSortLibArr(i&) - CGSortLibArr(RSMMrec.min)) / (delta#)                        IF NtmpN AND pow2 THEN                            tmpradix% = 1                        ELSE                            tmpradix% = 0                        END IF                        RadixCGSortLibArr(tmpradix%, ct&(tmpradix%)) = CGSortLibArr(i&)                        ct&(tmpradix%) = ct&(tmpradix%) + 1                    NEXT                    c& = start&                    FOR i& = 0 TO 1                        FOR j& = 0 TO ct&(i&) - 1                            CGSortLibArr(c&) = RadixCGSortLibArr(i&, j&)                            c& = c& + 1                        NEXT                        ct&(i&) = 0                    NEXT                    pow2 = pow2 * 2                NEXT        END SELECT        ERASE RadixCGSortLibArr, ct&    END IFEND SUB SUB ArrayIsInteger (CGSortLibArr() AS DOUBLE, start&, finish&, errorindex&, IsInt&)    IsInt& = 1    errorindex& = start&    FOR IsIntegerS& = start& TO finish&        IF CGSortLibArr(IsIntegerS&) MOD 1 THEN            errorindex& = IsIntegerS&            IsInt& = 0            EXIT FUNCTION        END IF    NEXTEND FUNCTION SUB MergeSort (CGSortLibArr() AS DOUBLE, start&, finish&, order&)    SELECT CASE finish& - start&        CASE IS > 31            middle& = start& + (finish& - start&) \ 2            MergeSort CGSortLibArr(), start&, middle&, order&            MergeSort CGSortLibArr(), middle& + 1, finish&, order&            'IF order& = 1 THEN            EfficientMerge CGSortLibArr(), start&, finish&, order&            'ELSE            '    MergeRoutine CGSortLibArr(), start&, finish&, order&            'END IF        CASE IS > 0            InsertionSort CGSortLibArr(), start&, finish&, order&    END SELECTEND SUB SUB EfficientMerge (right() AS DOUBLE, start&, finish&, order&)    half& = start& + (finish& - start&) \ 2    REDIM left(start& TO half&) AS DOUBLE '* hold the first half of the array in left() -- must be the same type as right()    FOR LoadLeft& = start& TO half&        left(LoadLeft&) = right(LoadLeft&)    NEXT    SELECT CASE order&        CASE 1            i& = start&            j& = half& + 1            insert& = start&            DO                IF i& > half& THEN '* left() exhausted                    IF j& > finish& THEN '* right() exhausted                        EXIT DO                    ELSE                        '* stuff remains in right to be inserted, so flush right()                        WHILE j& <= finish&                            right(insert&) = right(j&)                            j& = j& + 1                            insert& = insert& + 1                        WEND                        EXIT DO                        '* and exit                    END IF                ELSE                    IF j& > finish& THEN                        WHILE i& < LoadLeft&                            right(insert&) = left(i&)                            i& = i& + 1                            insert& = insert& + 1                        WEND                        EXIT DO                    ELSE                        IF right(j&) < left(i&) THEN                            right(insert&) = right(j&)                            j& = j& + 1                        ELSE                            right(insert&) = left(i&)                            i& = i& + 1                        END IF                        insert& = insert& + 1                    END IF                END IF            LOOP        CASE ELSE            i& = start&            j& = half& + 1            insert& = start&            DO                IF i& > half& THEN '* left() exhausted                    IF j& > finish& THEN '* right() exhausted                        EXIT DO                    ELSE                        '* stuff remains in right to be inserted, so flush right()                        WHILE j& <= finish&                            right(insert&) = right(j&)                            j& = j& + 1                            insert& = insert& + 1                        WEND                        EXIT DO                        '* and exit                    END IF                ELSE                    IF j& > finish& THEN                        WHILE i& < LoadLeft&                            right(insert&) = left(i&)                            i& = i& + 1                            insert& = insert& + 1                        WEND                        EXIT DO                    ELSE                        IF right(j&) > left(i&) THEN                            right(insert&) = right(j&)                            j& = j& + 1                        ELSE                            right(insert&) = left(i&)                            i& = i& + 1                        END IF                        insert& = insert& + 1                    END IF                END IF            LOOP    END SELECT    ERASE leftEND SUB SUB GetMinMaxArray (CGSortLibArr() AS DOUBLE, Start&, Finish&, GetMinMaxArray_minmax AS MinMaxRec)    DIM GetGetMinMaxArray_minmaxArray_i AS LONG    DIM GetMinMaxArray_n AS LONG    DIM GetMinMaxArray_TT AS LONG    DIM GetMinMaxArray_NMod2 AS INTEGER    '* this is a workaround for the irritating malfunction    '* of MOD using larger numbers and small divisors    GetMinMaxArray_n = Finish& - Start&    GetMinMaxArray_TT = GetMinMaxArray_n MOD 10000    GetMinMaxArray_NMod2 = GetMinMaxArray_n - 10000 * ((GetMinMaxArray_n - GetMinMaxArray_TT) / 10000)    IF (GetMinMaxArray_NMod2 MOD 2) THEN        GetMinMaxArray_minmax.min = Start&        GetMinMaxArray_minmax.max = Start&        GetGetMinMaxArray_minmaxArray_i = Start& + 1    ELSE        IF CGSortLibArr(Start&) > CGSortLibArr(Finish&) THEN            GetMinMaxArray_minmax.max = Start&            GetMinMaxArray_minmax.min = Finish&        ELSE            GetMinMaxArray_minmax.min = Finish&            GetMinMaxArray_minmax.max = Start&        END IF        GetGetMinMaxArray_minmaxArray_i = Start& + 2    END IF     WHILE GetGetMinMaxArray_minmaxArray_i < Finish&        IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i) > CGSortLibArr(GetGetMinMaxArray_minmaxArray_i + 1) THEN            IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i) > CGSortLibArr(GetMinMaxArray_minmax.max) THEN                GetMinMaxArray_minmax.max = GetGetMinMaxArray_minmaxArray_i            END IF            IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i + 1) < CGSortLibArr(GetMinMaxArray_minmax.min) THEN                GetMinMaxArray_minmax.min = GetGetMinMaxArray_minmaxArray_i + 1            END IF        ELSE            IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i + 1) > CGSortLibArr(GetMinMaxArray_minmax.max) THEN                GetMinMaxArray_minmax.max = GetGetMinMaxArray_minmaxArray_i + 1            END IF            IF CGSortLibArr(GetGetMinMaxArray_minmaxArray_i) < CGSortLibArr(GetMinMaxArray_minmax.min) THEN                GetMinMaxArray_minmax.min = GetGetMinMaxArray_minmaxArray_i            END IF        END IF        GetGetMinMaxArray_minmaxArray_i = GetGetMinMaxArray_minmaxArray_i + 2    WENDEND SUB SUB InsertionSort (CGSortLibArr() AS DOUBLE, start AS LONG, finish AS LONG, order&)    DIM InSort_Local_ArrayTemp AS DOUBLE    DIM InSort_Local_i AS LONG    DIM InSort_Local_j AS LONG    SELECT CASE order&        CASE 1            FOR InSort_Local_i = start + 1 TO finish                InSort_Local_ArrayTemp = CGSortLibArr(InSort_Local_i)                InSort_Local_j = InSort_Local_i - 1                DO UNTIL InSort_Local_j < start                    IF (InSort_Local_ArrayTemp < CGSortLibArr(InSort_Local_j)) THEN                        CGSortLibArr(InSort_Local_j + 1) = CGSortLibArr(InSort_Local_j)                        InSort_Local_j = InSort_Local_j - 1                    ELSE                        EXIT DO                    END IF                LOOP                CGSortLibArr(InSort_Local_j + 1) = InSort_Local_ArrayTemp            NEXT        CASE ELSE            FOR InSort_Local_i = start + 1 TO finish                InSort_Local_ArrayTemp = CGSortLibArr(InSort_Local_i)                InSort_Local_j = InSort_Local_i - 1                DO UNTIL InSort_Local_j < start                    IF (InSort_Local_ArrayTemp > CGSortLibArr(InSort_Local_j)) THEN                        CGSortLibArr(InSort_Local_j + 1) = CGSortLibArr(InSort_Local_j)                        InSort_Local_j = InSort_Local_j - 1                    ELSE                        EXIT DO                    END IF                LOOP                CGSortLibArr(InSort_Local_j + 1) = InSort_Local_ArrayTemp            NEXT    END SELECTEND SUB `

## Racket

` #lang Racket(define (radix-sort l r)  (define queues (for/vector #:length r ([_ r]) (make-queue)))  (let loop ([l l] [R 1])     (define all-zero? #t)     (for ([x (in-list l)])      (define x/R (quotient x R))      (enqueue! (vector-ref queues (modulo x/R r)) x)      (unless (zero? x/R) (set! all-zero? #f)))    (if all-zero? l	         (loop (let q-loop ([i 0])                (define q (vector-ref queues i))                (let dq-loop ()                  (if (queue-empty? q)                    (if (< i (sub1 r)) (q-loop (add1 i)) '())                    (cons (dequeue! q) (dq-loop)))))              (* R r)))))(for/and ([i 10000]) ; run some tests on random lists with a random radix  (define (make-random-list)     (for/list ([i (+ 10 (random 10))]) (random 100000)))  (define (sorted? l)     (match l [(list) #t] [(list x) #t]          [(list x y more ...) (and (<= x y) (sorted? (cons y more)))]))  (sorted? (radix-sort (make-random-list) (+ 2 (random 98)))));; => #t, so all passed `

## REXX

This REXX version also works with malformed integers.       7,   007,   +7,   .7e1,   7.0   are all treated equally.

`/*REXX program performs a radix sort on an integer array (can be negative/zero/positive)*/call gen                                         /*call subroutine to generate numbers. */call radSort  n                                  /*invoke the  radix sort  subroutine.  */                                                 /* [↓]  display sorted items ───► term.*/     do j=1  for n;   say 'item'  right(j,w)  "after the radix sort:"  right(@.j,w);   endexit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/gen: w=0                                         /*the max width of an number in the ILF*/     ILF=' 0  2  3  4  5  5  7. 6  6  7 11  7 13  9  8  8 17  8 19  9 10 13 23  9 10 15' ,         ' 9 11 29 10 31 10 14 19 12 10 37 21 16 11 41 12 43 15 11 25 47 11 14 12 20 17' ,         '53 11 16 13 22 31 59 12 61 33 13 12 18 16 67 21 26 14 71 12 73 39 13 23 18 18' ,         '79 13 12 43 83 14 22 45 32 17 89 13 20 27 34 49 24 13 97 16 17 14  101'        ,         '22 103 19 15 55 107 13 109 18 40 15 113  -42'              /*excluding -42, abbreviated above list is called the integer log function*/     n=words(ILF)                                             /*    I────── L── F───────*/                    do m=1  for n;  _=word(ILF,m)+0;  @.m=_;  w=max(w,length(_));    end     return                                      /* [↑]       W:  max width of numbers. *//*──────────────────────────────────────────────────────────────────────────────────────*/radSort: procedure expose @. w;   parse arg size;   mote=c2d(' ');    #=1;     !.#._n=size!.#._b=1;!.#._i=1;  do i=1  for size;   [email protected].i;   @.i=right(abs(y), w, 0);   if y<0  then @.i='-'@.i           end  /*i*/                                              /* [↑]  negative case*/      do  while #\==0;   ctr.=0;  L='ffff'x;  low=!.#._b;  n=!.#._n;  \$=!.#._i;   H=     #=#-1                                                       /* [↑]   is the radix. */           do j=low  for n;      parse var  @.j  =(\$)  _  +1;    ctr._=ctr._ + 1           if ctr._==1 & _\==''  then do;  if _<<L  then L=_;    if _>>H  then H=_                                      end  /*  ↑↑                                       */           end   /*j*/                     /*  └┴─────◄───  <<   is a strict comparison.*/     _=                                    /*      ┌──◄───  >>    " "    "        "     */     if L>>H  then iterate                 /*◄─────┘                                    */     if L==H & ctr._==0  then do;  #=#+1;  !.#._b=low;  !.#._n=n;  !.#._i=\$ + 1;   iterate                              end     L=c2d(L);    H=c2d(H);       ?=ctr._ + low;        top._=?;          ts=mote     max=L                  do k=L  to H;   _=d2c(k,1);   c=ctr._   /* [↓]  swap two item radices.*/                  if c>ts  then parse value  c k  with  ts max;       ?=?+c;       top._=?                  end   /*k*/     piv=low                                     /*set PIVot to the low part of the sort*/             do  while  piv < low+n             [email protected].piv                        do forever;     parse var it  =(\$)  _  +1;         c=top._ -1                        if piv>=c  then leave;   top._=c;     [email protected].c;     @.c=it;      it=?                        end   /*forever*/             top._=piv;                          @.piv=it;          piv=piv + ctr._             end   /*while piv<low+n */     i=max          do  until i==max;   _=d2c(i,1);     i=i+1;        if i>H  then i=L;      d=ctr._          if d<=mote then do;         if d<2  then iterate;         b=top._                            do k=b+1  for d-1;                      [email protected].k                              do j=k-1  by -1  to b  while q<<@.j;  jp=j+1; @.[email protected].j;  end                                                                    jp=j+1; @.jp=q                              end   /*k*/                          iterate                          end          #=#+1;  !.#._b=top._;  !.#._n=d;  !.#._i=\$+1          end   /*until i==max*/     end        /*while #\==0 */#=0                                              /* [↓↓↓]  handle neg. and pos. arrays. */        do i=size  by -1  to 1;        if @.i>=0  then iterate;  #=#+1;   @@.#[email protected].i;    end        do j=1  for size;   if @.j>=0  then do;  #=#+1;  @@.#[email protected].j;  end;  @.[email protected]@.j+0;  endreturn                                           /* [↑↑↑]  combine 2 lists into 1 list. */`

output   (with the middle section elided.)

```item   1 after the radix sort: -42
item   2 after the radix sort:   0
item   3 after the radix sort:   2
item   4 after the radix sort:   3
item   5 after the radix sort:   4
item   6 after the radix sort:   5
item   7 after the radix sort:   5
item   8 after the radix sort:   6
item   9 after the radix sort:   6
item  10 after the radix sort:   7
item  11 after the radix sort:   7
item  12 after the radix sort:   7
item  13 after the radix sort:   8
.
.
.
(middle section elided.)
.
.
.
item  92 after the radix sort:  40
item  93 after the radix sort:  41
item  94 after the radix sort:  43
item  95 after the radix sort:  43
item  96 after the radix sort:  45
item  97 after the radix sort:  47
item  98 after the radix sort:  49
item  99 after the radix sort:  53
item 100 after the radix sort:  55
item 101 after the radix sort:  59
item 102 after the radix sort:  61
item 103 after the radix sort:  67
item 104 after the radix sort:  71
item 105 after the radix sort:  73
item 106 after the radix sort:  79
item 107 after the radix sort:  83
item 108 after the radix sort:  89
item 109 after the radix sort:  97
item 110 after the radix sort: 101
item 111 after the radix sort: 103
item 112 after the radix sort: 107
item 113 after the radix sort: 109
item 114 after the radix sort: 113
```

## Ruby

Negative number handling courtesy the Tcl solution.

`class Array  def radix_sort(base=10)    ary = dup    rounds = (Math.log(ary.minmax.map(&:abs).max)/Math.log(base)).floor + 1    rounds.times do |i|      buckets = Array.new(2*base){[]}      base_i = base**i      ary.each do |n|        digit = (n/base_i) % base        digit += base if 0<=n        buckets[digit] << n      end      ary = buckets.flatten      p [i, ary] if \$DEBUG    end    ary  end  def radix_sort!(base=10)    replace radix_sort(base)  endend p [1, 3, 8, 9, 0, 0, 8, 7, 1, 6].radix_sortp [170, 45, 75, 90, 2, 24, 802, 66].radix_sortp [170, 45, 75, 90, 2, 24, -802, -66].radix_sortp [100000, -10000, 400, 23, 10000].radix_sort`

running with \$DEBUG on produces:

```[0, [0, 0, 1, 1, 3, 6, 7, 8, 8, 9]]
[0, 0, 1, 1, 3, 6, 7, 8, 8, 9]
[0, [170, 90, 2, 802, 24, 45, 75, 66]]
[1, [2, 802, 24, 45, 66, 170, 75, 90]]
[2, [2, 24, 45, 66, 75, 90, 170, 802]]
[2, 24, 45, 66, 75, 90, 170, 802]
[0, [-66, -802, 170, 90, 2, 24, 45, 75]]
[1, [-66, -802, 2, 24, 45, 170, 75, 90]]
[2, [-802, -66, 2, 24, 45, 75, 90, 170]]
[-802, -66, 2, 24, 45, 75, 90, 170]
[0, [-10000, 100000, 400, 10000, 23]]
[1, [-10000, 100000, 400, 10000, 23]]
[2, [-10000, 100000, 10000, 23, 400]]
[3, [-10000, 100000, 10000, 23, 400]]
[4, [-10000, 100000, 23, 400, 10000]]
[5, [-10000, 23, 400, 10000, 100000]]
[-10000, 23, 400, 10000, 100000]```

another version (After sorting at the absolute value, it makes a negative order reverse.)

`class Array  def radix_sort(base=10)    ary = dup    m, max = 1, ary.minmax.map(&:abs).max    while m <= max      buckets = Array.new(base){[]}      ary.each {|n| buckets[(n.abs / m) % base] << n}      ary = buckets.flatten      m *= base    end    ary.partition{|n| n<0}.inject{|minus,plus| minus.reverse + plus}  endend`

## Scala

`object RadixSort extends App {  def sort(toBeSort: Array[Int]): Array[Int] = { // Loop for every bit in the integers    var arr = toBeSort    for (shift <- Integer.SIZE - 1 until -1 by -1) { // The array to put the partially sorted array into      val tmp = new Array[Int](arr.length)      // The number of 0s      var j = 0      // Move the 0s to the new array, and the 1s to the old one      for (i <- arr.indices) // If there is a 1 in the bit we are testing, the number will be negative        // If this is the last bit, negative numbers are actually lower        if ((shift == 0) == (arr(i) << shift >= 0)) arr(i - j) = arr(i)        else {          tmp(j) = arr(i)          j += 1        }      // Copy over the 1s from the old array      arr.copyToArray(tmp, j, arr.length - j)       // And now the tmp array gets switched for another round of sorting      arr = tmp    }    arr  }   println(sort(Array(170, 45, 75, -90, -802, 24, 2, 66)).mkString(", "))}`

## Sidef

Translation of: Ruby
`class Array {    method radix_sort(base=10) {        var arr = self.clone        var rounds = ([arr.minmax].map{.abs}.max.ilog(base) + 1)        for i in (0..rounds) {            var buckets = (2*base -> of {[]})            var base_i = base**i            for n in arr {                var digit = (n/base_i % base)                digit += base if (0 <= n)                buckets[digit].append(n)            }            arr = buckets.flat        }        return arr    }} for arr in [    [1, 3, 8, 9, 0, 0, 8, 7, 1, 6],    [170, 45, 75, 90, 2, 24, 802, 66],    [170, 45, 75, 90, 2, 24, -802, -66],    [100000, -10000, 400, 23, 10000],] {    say arr.radix_sort}`
Output:
```[0, 0, 1, 1, 3, 6, 7, 8, 8, 9]
[2, 24, 45, 66, 75, 90, 170, 802]
[-802, -66, 2, 24, 45, 75, 90, 170]
[-10000, 23, 400, 10000, 100000]
```

## Tcl

Translation of: Python
`package require Tcl 8.5proc splitByRadix {lst base power} {    # create a list of empty lists to hold the split by digit    set out [lrepeat [expr {\$base*2}] {}]    foreach item \$lst {	# pulls the selected digit	set digit [expr {(\$item / \$base ** \$power) % \$base + \$base * (\$item >= 0)}]	# append the number to the list selected by the digit	lset out \$digit [list {*}[lindex \$out \$digit] \$item]    }    return \$out} # largest abs value element of a listproc tcl::mathfunc::maxabs {lst} {    set max [abs [lindex \$lst 0]]    for {set i 1} {\$i < [llength \$lst]} {incr i} {	set v [abs [lindex \$lst \$i]]	if {\$max < \$v} {set max \$v}    }    return \$max} proc radixSort {lst {base 10}} {    # there are as many passes as there are digits in the longest number    set passes [expr {int(log(maxabs(\$lst))/log(\$base) + 1)}]    # For each pass...    for {set pass 0} {\$pass < \$passes} {incr pass} {	# Split by radix, then merge back into the list	set lst [concat {*}[splitByRadix \$lst \$base \$pass]]    }    return \$lst}`

Demonstrations:

`puts [radixSort {1 3 8 9 0 0 8 7 1 6}]puts [radixSort {170 45 75 90 2 24 802 66}]puts [radixSort {170 45 75 90 2 24 -802 -66}]`

Output:

```0 0 1 1 3 6 7 8 8 9
2 24 45 66 75 90 170 802
-802 -66 2 24 45 75 90 170
```

## zkl

In place int sort, fairly light on garbage creation.

`fcn radixSort(ns){ // ints only, inplace, ns is mutable   b:=(0).pump(20,List,List().copy);  // 20 [empty] buckets: -10..10   z:=ns.reduce(fcn(a,b){ a.abs().max(b.abs()) },0); // |max or min of input|   m:=1;   while(z){      ns.apply2('wrap(n){ b[(n/m)%10 +10].append(n) }); // sort on right digit      ns.clear(); b.pump(ns.extend);		// slam buckets over src      b.apply("clear");			     // reset buckets      m*=10; z/=10;			// move sort digit left   }   ns}`
`radixSort(T(170, 45, 75, 90, 802, 2, 24, 66)).println();radixSort(T(170, 45, 75, -90, -802, 24, 2, 66)).println();`
Output:
```L(2,24,45,66,75,90,170,802)
L(-802,-90,2,24,45,66,75,170)
```