⚠️ Warning: This is a draft ⚠️

This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.

If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.

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

```with Ada.Text_IO;
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;

Test_Array : Integer_Array := (170, 45, 75, -90, -802, 24, 2, 66);
begin
for I in Test_Array'Range loop
end loop;
```

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;
INT zero_index  := 0,
one_index   := 0,
array_index := 1;

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;
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));
print(("After: ", a))
)
```

{{out}}

```
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 = 170,45,75,90,802,2,24,66
```

Outputs:

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

BBC BASIC

{{works with|BBC BASIC for Windows}} 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
FOR i% = 0 TO 9
PRINT test%(i%) ;
NEXT
PRINT
END

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;

}

/* 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;

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)

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 integers
{
const int bit; // bit position [0..31] to examine
public:
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 sort
{
for (int lsb = 0; lsb < 32; ++lsb) // least-significant-bit
{
}
}

// 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
}
}

int main()
{
int data[] = { 170, 45, 75, -90, -802, 24, 2, 66 };

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 sharp|C#|3.0+}}

```using System;

{
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));
}
}
}
```

D

Shorter Version

```import std.stdio, std.math, std.traits, std.range, std.algorithm;

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];
}
```

{{out}}

```[-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 program
extern(C) void* alloca(in size_t length) pure nothrow;

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) {
data[] = tempData[];
} else {
for (uint i = 0; i < U.sizeof; i += 2) {
}
}
}

void main() {
import std.stdio;
uint[] items = [170, 45, 75, 4294967206, 2, 24, 4294966494, 66];
writeln(items);
}
```

{{out}}

```[2, 24, 45, 66, 75, 170, 4294966494, 4294967206]
```

EasyLang

# only works with positive integers

subr sort radix = 16 max = 0 for di range len data[] if data[di] > max max = data[di] . . len buck[][] radix pos = 1 while pos <= max for i range radix len buck[i][] 0 . for di range len data[] h = data[di] / pos mod radix buck[h][] &= data[di] . di = 0 for i range radix for j range len buck[i][] data[di] = buck[i][j] di += 1 . . pos *= radix . . data[] = [ 29 4 72 44 55 26 27 77 92 5 ] call sort print data[]

```

## Eiffel

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

```Eiffel

class

feature

-- Array 'ar' sorted in ascending order.
require
ar_not_void: ar /= Void
not_negative: across ar as a all a.item >= 0 end
local
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
io.put_string ("%NSorted:%N")
across
test as t
loop
io.put_string (t.item.out + " ")
end
end

end

```

{{out}}

```
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

{{trans|Ruby}}

```defmodule Sort 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)
end
end

IO.inspect Sort.radix_sort([-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028])
```

{{out}}

```
[-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

```

{{out}}

```
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 data
type word int32
const wordLen = 4
const 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)
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)
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()
fromBuckets.values().findAll { it != null }.flatten().each {
print '.'
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 ()
println ()
println ()
println ()
```

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 positiveMsdSort
fixSort 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
```

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.

```unicon
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 A
end
```

Sample run:

```txt

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

```

## J

{{eff note|J|/:~}}

`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 `}.`.

```j

:
keys =. x #.^:_1 y NB. compute keys
length =. #{.keys
extra =. (-length) {."0 buckets =. i.x
for_pass. i.-length do.
keys =. ; (buckets,pass{"1 keys) <@:}./.extra,keys
end.
x#.keys NB. restore the data
)
```

An alternate implementation is

```j
radixsort=: (] #~ [: +/ =/) i.@(>./)
```

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

Example use:

```j
4 5 6 6 6 6 6 8 8
```

Or, for negative number support:

```j
```

Example:

```j
rsort _6+?.@#~10
_2 _1 0 0 0 0 0 2 2
```

## Java

```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;
}
```

{{trans|NetRexx}}

```Java

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Queue;

return;
}

public static int[] lsdRadixSort(int[] tlist) {

List intermediates;
int[] limits = getLimits(tlist);
tlist = rescale(tlist, limits[1]);

for (int px = 1; px <= limits[2]; ++px) {
@SuppressWarnings("unchecked")
Queue 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) {
}
}

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();
}
}
}

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();
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 array2list(int[] arry) {

List target = new ArrayList<>(arry.length);

for (Integer iv : arry) {
}

return target;
}

public static void main(String[] args) {

runSample(args);

return;
}
}

```

{{out}}

```txt

[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

```jq
# Sort the input array;
# "base" must be an integer greater than 1
# 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) ;

```

'''Example'''

```jq

# 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] )

```

{{Out}}
true
true
true

## Julia

{{trans|Scala}}

```julia
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
arr
end

arrays = [[170, 45, 75, -90, -802, 24, 2, 66], [-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028]]
for array in arrays
end
end

```
{{output}}
```txt

[-802, -90, 2, 24, 45, 66, 75, 170]
[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]

```

## Kotlin

{{trans|Java}}

```scala
// version 1.1.2

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) {
val arrays = arrayOf(
intArrayOf(170, 45, 75, -90, -802, 24, 2, 66),
intArrayOf(-4, 5, -26, 58, -990, 331, 331, 990, -1837, 2028)
)
}
```

{{out}}

```txt

[-802, -90, 2, 24, 45, 66, 75, 170]
[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]

```

## Mathematica

```Mathematica
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:

```Mathematica
```

{{out}}

```txt
{-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
/* 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
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
end il
return

```

{{out}}

```txt

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
/* 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()
end ix

intermediates = ArrayList()
loop bi = 0 to 9
if bukits[bi] \= null then loop while bukits[bi].size() > 0
nextd = bukits[bi].poll()
end
end bi

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
end il
return

```

## Perl

```perl
#!/usr/bin/perl
use warnings;
use strict;

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:

```perl>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.)

```perl6
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);
```

{{out}}

```txt
-1585
-1427
-1228
-1067
-945
-657
-643
-232
-179
-28
37
411
488
509
716
724
1504
1801
1864
1939
```

## Phix

```Phix
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
end if
end if
end for
return res
end 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 buckets
end function

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)
s = buckets[1]&buckets[2]
else
end if
return s
end 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})
```

{{out}}

```txt

{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:

```PicoLisp
(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))
Flg ) ) )
Lst )
```

Output:

```txt
-> (-999 -930 -666 -336 -218 68 79 187 391 405 697 922)
```

## PureBasic

```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, -66
EndDataSection

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
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
Next
EndProcedure

If OpenConsole()
Dim x(0)
setIntegerArray(x(), ?set1)

setIntegerArray(x(), ?set2)

setIntegerArray(x(), ?set3)

Print(#CRLF\$ + #CRLF\$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf
```

Sample output:

```txt
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|2.6}}

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

```python
#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 step
def 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

# 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:

```python
#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

"""
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

# 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:

```python
#python3.7 <
def flatten(l):
return [y for x in l for y in x]

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

```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& = 63
A\$ = ""
REDIM b(0 TO TESTN&) AS DOUBLE
FOR 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
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
NEXT
NEXT
PRINT A\$
TYPE MinMaxRec
min AS LONG
max AS LONG
END 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
ELSE
END IF
NEXT
c& = start&
FOR i& = 0 TO 1
FOR j& = 0 TO ct&(i&) - 1
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
ELSE
END IF
NEXT
c& = start&
FOR i& = 0 TO 1
FOR j& = 0 TO ct&(i&) - 1
c& = c& + 1
NEXT
ct&(i&) = 0
NEXT
pow2 = pow2 * 2
NEXT
END SELECT
END IF
END 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
NEXT
END 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 SELECT
END 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&
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
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
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 left
END 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
WEND
END 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 SELECT
END SUB

```

## Racket

```Racket

#lang Racket
(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 as equal.

```rexx
/*REXX program performs a radix sort on an integer array (can be negative/zero/positive)*/
call gen                                         /*call subroutine to generate numbers. */
do j=1  for n;  say 'item'    right(j, w)    "after the radix sort:"    right(@.j, w)
end   /*j*/                                 /* [↑]  display sorted items ───► term.*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
gen: 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───────*/
w= 0;         do m=1  for n;   _= word(ILF,m) +0;    @.m= _;    w= max(w, length(_) )
end   /*m*/;        return    /*W:  is the maximum 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= 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 _<>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 2 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=c  then leave;   top._= c;    ?= @.c;    @.c= it;    it= ?
end   /*forever*/
top._= piv;                          @.piv=it;          piv=piv + ctr._
end   /*while pivH  then i= L;     d= ctr._
if d<=mote  then do;         if d<2  then iterate;          b= top._
do k=b+1  for d-1;                       q= @.k
do j=k-1  by -1  to b  while q<<@.j;  jp= j+1;   @.jp= @.j
end   /*j*/
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]
end   /*i*/
do j=1  for size;   if @.j>=0  then do;  #= #+1;   @@.#= @.j;  end;    @.j= @@.j+0
end   /*j*/;                   return    /* [↑↑↑]  combine 2 lists into 1 list. */
```

{{out|output|text=    (with the middle section elided.)}}

(Output is shown at   '''3/4'''   size.)
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.

```ruby
class Array
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
end
end

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

running with \$DEBUG on produces:

```txt
[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.)

```ruby
class Array
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}
end
end
```

## Scala

```Scala
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

{{trans|Ruby}}

```ruby
class Array {
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],
] {
}
```

{{out}}

```txt

[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]

```

## Tailspin

```tailspin

sink bucketize
def value: \$;
\$ / [email protected] -> #
<0 ?(\$value <0..>)>
<0>
<>
def bucket: \$ mod \$base -> ()> \$ + 1 ! <0> \$base ! <> \$ !);
end bucketize
// Negatives get completed in wrong length-order, we need to collect by length and correct at the end
@: { done: 1, digit: 1, positives: [], negatives: [[]], buckets: [1..\$base -> []]};
\$... -> !bucketize
[email protected] -> #
<1>
[[email protected](-1..1:-1)... ..., [email protected]...] !
<>
def previous: [email protected];
..|@: {done: 1, digit: [email protected] * \$base, buckets:[1..\$base -> []]};
..|@.negatives: [];
\$previous... ... -> !bucketize
[email protected] -> #

[170, 45, 75, 91, 90, 92, 802, 24, 2, 66] -> radixsort@{base:10} -> !OUT::write
'
' -> !OUT::write
[-170, -45, -91, -90, -92, -802, -24, -2, -76] -> radixsort@{base:10} -> !OUT::write
'
' -> !OUT::write
[170, 45, 75, -91, -90, -92, -802, 24, 2, 66] -> radixsort@{base:10} -> !OUT::write
'
' -> !OUT::write
[170, 45, 75, -91, -90, -92, -802, 24, 2, 66] -> radixsort@{base:3} -> !OUT::write

```

{{out}}

```txt

[2, 24, 45, 66, 75, 90, 91, 92, 170, 802]
[-802, -170, -92, -91, -90, -76, -45, -24, -2]
[-802, -92, -91, -90, 2, 24, 45, 66, 75, 170]
[-802, -92, -91, -90, 2, 24, 45, 66, 75, 170]

```

## Tcl

{{trans|Python}}

```tcl
package require Tcl 8.5
proc 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 list
proc 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:

```tcl
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:

```txt

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.

```zkl
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
}
```

```zkl
radixSort(T(170, 45, 75, 90, 802, 2, 24, 66)).println();
radixSort(T(170, 45, 75, -90, -802, 24, 2, 66)).println();
```

{{out}}

```txt

L(2,24,45,66,75,90,170,802)
L(-802,-90,2,24,45,66,75,170)

```

{{omit from|GUISS}}

```