Sorting algorithms/Radix sort

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< Sorting algorithms(Redirected from Radix sort)
Task
Sorting algorithms/Radix sort
You are encouraged to solve this task according to the task description, using any language you may know.


Task

Sort an integer array with the   radix sort algorithm.

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

11l[edit]

Translation of: Python
F flatten(some_list)
   [Int] new_list
   L(sub_list) some_list
      new_list [+]= sub_list
   R new_list

F radix_sort(l, =p = -1, =s = -1)
   I s == -1
      s = String(max(l)).len
   I p == -1
      p = s

   V i = s - p
   I i >= s
      R l

   V bins = [[Int]()] * 10

   L(e) l
      bins[Int(String(e).zfill(s)[i])] [+]= e

   R flatten(bins.map(b -> radix_sort(b, @p - 1, @s)))

V arr = [7, 6, 5, 9, 8, 4, 3, 1, 2, 0]
print(radix_sort(arr))
Output:
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

AArch64 Assembly[edit]

Works with: as version Raspberry Pi 3B version Buster 64 bits
/* ARM assembly AARCH64 Raspberry PI 3B */
/*  program radixSort64.s  */
 
/*******************************************/
/* Constantes file                         */
/*******************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeConstantesARM64.inc"

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"
 
.align 4
TableNumber:      .quad   12485,301,16,25,5006,9,-154389710,26,4400,71,115
#TableNumber:     .quad   10,9,8,7,6,-5,4,3,2,1
                 .equ NBELEMENTS, (. - TableNumber) / 8 
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:       .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                                              // entry of program 
    ldr x0,qAdrTableNumber                         // address number table
    mov x1,0                                       // first element
    mov x2,NBELEMENTS                              // number of élements 
    bl radixSort
    ldr x0,qAdrTableNumber                         // address number table
    bl displayTable
 
    ldr x0,qAdrTableNumber                         // address number table
    mov x1,NBELEMENTS                              // number of élements 
    bl isSorted                                    // control sort
    cmp x0,1                                       // sorted ?
    beq 1f                                    
    ldr x0,qAdrszMessSortNok                       // no !! error sort
    bl affichageMess
    b 100f
1:                                                 // yes
    ldr x0,qAdrszMessSortOk
    bl affichageMess
100:                                               // standard end of the program 
    mov x0,0                                       // return code
    mov x8,EXIT                                    // request to exit program
    svc 0                                          // perform the system call
 
qAdrsZoneConv:            .quad sZoneConv
qAdrszCarriageReturn:     .quad szCarriageReturn
qAdrsMessResult:          .quad sMessResult
qAdrTableNumber:          .quad TableNumber
qAdrszMessSortOk:         .quad szMessSortOk
qAdrszMessSortNok:        .quad szMessSortNok
/******************************************************************/
/*     control sorted table                                   */ 
/******************************************************************/
/* x0 contains the address of table */
/* x1 contains the number of elements  > 0  */
/* x0 return 0  if not sorted   1  if sorted */
isSorted:
    stp x2,lr,[sp,-16]!             // save  registers
    stp x3,x4,[sp,-16]!             // save  registers
    mov x2,0
    ldr x4,[x0,x2,lsl 3]
1:
    add x2,x2,1
    cmp x2,x1
    bge 99f
    ldr x3,[x0,x2, lsl 3]
    cmp x3,x4
    blt 98f
    mov x4,x3
    b 1b
98:
    mov x0,0                       // not sorted
    b 100f
99:
    mov x0,1                       // sorted
100:
    ldp x3,x4,[sp],16              // restaur  2 registers
    ldp x2,lr,[sp],16              // restaur  2 registers
    ret                            // return to address lr x30
    
/******************************************************************/
/*         radix sort                                             */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the first element    */
/* r2 contains the number of element */
/* no registers save                 */
radixSort:
    str lr,[sp,-16]!                      // save  1 register
    mov x7,0b1111                         // mask one digit hexa
    mov x10,0                             // digit counter
1:
    add x3,x1,1                           // start index i
2:                                        // start loop
    ldr x4,[x0,x3,lsl 3]                  // load value A[i]
    and x8,x4,x7                          // and mask
    sub x5,x3,1                           // index j
3:
    ldr x6,[x0,x5,lsl 3]                  // load value A[j]
    and x9,x6,x7                          // and mask
    cmp x9,x8                             // compare one digit hexa
    ble 4f
    add x5,x5,1                           // increment index j
    str x6,[x0,x5,lsl 3]                  // store value A[j+1]
    sub x5,x5,2                           // j = j - 1
    cmp x5,x1
    bge 3b                                // loop if j >= first item
4:
    add x5,x5,1                           // increment index j
    str x4,[x0,x5,lsl 3]                  // store value A[i] in A[j+1]
    add x3,x3,1                           // increment index i
    cmp x3,x2                             // end ?
    blt 2b                                // no -> loop
    
    //bl displayTable
    lsl x7,x7,4                           // shift mask 4 bits left
    add x10,x10,1                         // increment counter
    cmp x10,16                            // 16 digits ?
    blt 1b                                // no loop 
100:

    ldr lr,[sp],16                        // restaur  1 registers
    ret                                   // return to address lr x30
 
/******************************************************************/
/*      Display table elements                                */ 
/******************************************************************/
/* x0 contains the address of table */
displayTable:
    stp x1,lr,[sp,-16]!              // save  registers
    stp x2,x3,[sp,-16]!              // save  registers
    mov x2,x0                        // table address
    mov x3,0
1:                                   // loop display table
    ldr x0,[x2,x3,lsl 3]
    ldr x1,qAdrsZoneConv
    bl conversion10S                  // décimal conversion
    ldr x0,qAdrsMessResult
    ldr x1,qAdrsZoneConv
    bl strInsertAtCharInc            // insert result at // character
    bl affichageMess                 // display message
    add x3,x3,1
    cmp x3,NBELEMENTS - 1
    ble 1b
    ldr x0,qAdrszCarriageReturn
    bl affichageMess
    mov x0,x2
100:
    ldp x2,x3,[sp],16               // restaur  2 registers
    ldp x1,lr,[sp],16               // restaur  2 registers
    ret                             // return to address lr x30
/********************************************************/
/*        File Include fonctions                        */
/********************************************************/
/* for this file see task include a file in language AArch64 assembly */
.include "../includeARM64.inc"
Value  : -154389710
Value  : +9
Value  : +16
Value  : +25
Value  : +26
Value  : +71
Value  : +115
Value  : +301
Value  : +4400
Value  : +5006
Value  : +12485

Table sorted.

Ada[edit]

radix_sort.adb:

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[edit]

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

ARM Assembly[edit]

Works with: as version Raspberry Pi
/* ARM assembly Raspberry PI  */
/*  program radixSort1.s  */
 
 /* REMARK 1 : this program use routines in a include file 
   see task Include a file language arm assembly 
   for the routine affichageMess conversion10 
   see at end of this program the instruction include */
/* for constantes see task include a file in arm assembly */
/************************************/
/* Constantes                       */
/************************************/
.include "../constantes.inc"

/*********************************/
/* Initialized data              */
/*********************************/
.data
szMessSortOk:       .asciz "Table sorted.\n"
szMessSortNok:      .asciz "Table not sorted !!!!!.\n"
sMessResult:        .asciz "Value  : @ \n"
szCarriageReturn:   .asciz "\n"
 
.align 4
TableNumber:      .int   1,110,30,6,201,5004,29,10,1008,4,7,-25000
#TableNumber:       .int   10,9,8,7,6,5,4,3,2,1
                   .equ NBELEMENTS, (. - TableNumber) / 4
/*********************************/
/* UnInitialized data            */
/*********************************/
.bss
sZoneConv:            .skip 24
/*********************************/
/*  code section                 */
/*********************************/
.text
.global main 
main:                               @ entry of program 
 
    ldr r0,iAdrTableNumber          @ address number table
    mov r1,#0                       @ first element
    mov r2,#NBELEMENTS              @ number of élements 
    bl radixSort
    ldr r0,iAdrTableNumber          @ address number table
    bl displayTable
 
    ldr r0,iAdrTableNumber          @ address number table
    mov r1,#NBELEMENTS              @ number of élements 
    bl isSorted                     @ control sort
    cmp r0,#1                       @ sorted ?
    beq 1f
    ldr r0,iAdrszMessSortNok        @ no !! error sort
    bl affichageMess
    b 100f
1:                                  @ yes
    ldr r0,iAdrszMessSortOk
    bl affichageMess
100:                                @ standard end of the program 
    mov r0, #0                      @ return code
    mov r7, #EXIT                   @ request to exit program
    svc #0                          @ perform the system call
 
iAdrszCarriageReturn:     .int szCarriageReturn
iAdrsMessResult:          .int sMessResult
iAdrTableNumber:          .int TableNumber
iAdrszMessSortOk:         .int szMessSortOk
iAdrszMessSortNok:        .int szMessSortNok
/******************************************************************/
/*     control sorted table                                   */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the number of elements  > 0  */
/* r0 return 0  if not sorted   1  if sorted */
isSorted:
    push {r2-r4,lr}          @ save registers
    mov r2,#0
    ldr r4,[r0,r2,lsl #2]
1:
    add r2,#1
    cmp r2,r1
    movge r0,#1
    bge 100f
    ldr r3,[r0,r2, lsl #2]
    cmp r3,r4
    movlt r0,#0
    blt 100f
    mov r4,r3
    b 1b
100:
    pop {r2-r4,lr}
    bx lr                    @ return 
/******************************************************************/
/*         radix sort                                             */ 
/******************************************************************/
/* r0 contains the address of table */
/* r1 contains the first element    */
/* r2 contains the number of element */
radixSort:
    push {r3-r10,lr}                      @ save registers
    mov r7,#0b1111                        @ mask one digit hexa
    mov r10,#0                            @ digit counter
1:
    add r3,r1,#1                          @ start index i
2:                                        @ start loop
    ldr r4,[r0,r3,lsl #2]                 @ load value A[i]
    and r8,r4,r7                          @ and mask
    sub r5,r3,#1                          @ index j
3:
    ldr r6,[r0,r5,lsl #2]                 @ load value A[j]
    and r9,r6,r7                          @ and mask
    cmp r9,r8                             @ compare one digit hexa
    ble 4f
    add r5,#1                             @ increment index j
    str r6,[r0,r5,lsl #2]                 @ store value A[j+1]
    sub r5,#2                             @ j = j - 1
    cmp r5,r1
    bge 3b                                @ loop if j >= first item
4:
    add r5,#1                             @ increment index j
    str r4,[r0,r5,lsl #2]                 @ store value A[i] in A[j+1]
    add r3,#1                             @ increment index i
    cmp r3,r2                             @ end ?
    blt 2b                                @ no -> loop
    
    //bl displayTable
    lsl r7,#4                             @ shift mask 4 bits left
    add r10,r10,#1                        @ increment counter
    cmp r10,#8                            @ 8 digits ?
    blt 1b                                @ no loop 
100:
    pop {r3-r10,lr}
    bx lr                                 @ return 


/******************************************************************/
/*      Display table elements                                */ 
/******************************************************************/
/* r0 contains the address of table */
displayTable:
    push {r0-r3,lr}                                    @ save registers
    mov r2,r0                                          @ table address
    mov r3,#0
1:                                                     @ loop display table
    ldr r0,[r2,r3,lsl #2]
    ldr r1,iAdrsZoneConv                               @ 
    bl conversion10S                                   @ décimal conversion 
    ldr r0,iAdrsMessResult
    ldr r1,iAdrsZoneConv                               @ insert conversion
    bl strInsertAtCharInc
    bl affichageMess                                   @ display message
    add r3,#1
    cmp r3,#NBELEMENTS - 1
    ble 1b
    ldr r0,iAdrszCarriageReturn
    bl affichageMess
    mov r0,r2
100:
    pop {r0-r3,lr}
    bx lr
iAdrsZoneConv:           .int sZoneConv
/***************************************************/
/*      ROUTINES INCLUDE                           */
/***************************************************/
.include "../affichage.inc"
Value  :      -25000
Value  :          +1
Value  :          +4
Value  :          +6
Value  :          +7
Value  :         +10
Value  :         +29
Value  :         +30
Value  :        +110
Value  :        +201
Value  :       +1008
Value  :       +5004

Table sorted.

Arturo[edit]

radixSort: function [items][
    base: 10
    a: new items
    
    rounds: inc floor (ln max a)/ln base
    loop rounds 'i [
        buckets: array.of: 2*base []
        baseI: base ^ i
        loop a 'n [
            digit: last digits n
            if n >= 0 -> digit: digit + base
            buckets\[digit]: buckets\[digit] ++ n
        ]
        a: new flatten buckets
    ]
    return a
]

print radixSort [3 1 2 8 5 7 9 4 6]
Output:
1 2 3 4 5 6 7 8 9

ATS[edit]

(*
  Stable integer-keyed radix sorts for unsigned and signed integers
  of the various typekinds.

  The radix is 256.
*)

(*------------------------------------------------------------------*)

#include "share/atspre_staload.hats"
staload UN = "prelude/SATS/unsafe.sats"

(*------------------------------------------------------------------*)

extern fn {a  : vt@ype}
          {tk : tkind}
g0uint_radix_sort
          {n   : int}
          (arr : &array (a, n) >> _,
           n   : size_t n)
    :<!wrt> void

extern fn {a  : vt@ype}
          {tk : tkind}
g0uint_radix_sort$key
          {n   : int}
          {i   : nat | i < n}
          (arr : &RD(array (a, n)),
           i   : size_t i)
    :<> g0uint tk

(*------------------------------------------------------------------*)

extern fn {a        : vt@ype}
          {tki, tku : tkind}
g0int_radix_sort
          {n   : int}
          (arr : &array (a, n) >> _,
           n   : size_t n)
    :<!wrt> void

extern fn {a   : vt@ype}
          {tki : tkind}
g0int_radix_sort$key
          {n   : int}
          {i   : nat | i < n}
          (arr : &RD(array (a, n)),
           i   : size_t i)
    :<> g0int tki

(*------------------------------------------------------------------*)

(* WARNING: Much of the following code does NOT take into account
            the linearity of array entries. But this unsafeness is
            hidden from the user. *)

fn {}
bin_sizes_to_indices
          (bin_indices : &array (size_t, 256) >> _)
    :<!wrt> void =
  let
    fun
    loop {i           : int | i <= 256}
         {accum       : int}
         .<256 - i>.
         (bin_indices : &array (size_t, 256) >> _,
          i           : size_t i,
          accum       : size_t accum)
        :<!wrt> void =
      if i <> i2sz 256 then
        let
          prval () = lemma_g1uint_param i
          val elem = bin_indices[i]
        in
          if elem = i2sz 0 then
            loop (bin_indices, succ i, accum)
          else
            begin
              bin_indices[i] := accum;
              loop (bin_indices, succ i, accum + g1ofg0 elem)
            end
        end
  in
    loop (bin_indices, i2sz 0, i2sz 0)
  end

fn {a  : vt@ype}
   {tk : tkind}
count_entries
          {n            : int}
          {shift        : nat}
          (arr          : &RD(array (a, n)),
           n            : size_t n,
           bin_indices  : &array (size_t?, 256)
                          >> array (size_t, 256),
           all_expended : &bool? >> bool,
           shift        : int shift)
    :<!wrt> void =
  let
    fun
    loop {i : int | i <= n}
         .<n - i>.
         (arr          : &RD(array (a, n)),
          bin_indices  : &array (size_t, 256) >> _,
          all_expended : &bool >> bool,
          i            : size_t i)
        :<!wrt> void =
      if i <> n then
        let
          prval () = lemma_g1uint_param i
          val key : g0uint tk = g0uint_radix_sort$key<a><tk> (arr, i)
          val key_shifted = key >> shift
          val digit = ($UN.cast{uint} key_shifted) land 255U
          val [digit : int] digit = g1ofg0 digit
          extern praxi set_range :
            () -<prf> [0 <= digit; digit <= 255] void
          prval () = set_range ()
          val count = bin_indices[digit]
          val () = bin_indices[digit] := succ count
        in
          all_expended := all_expended * iseqz key_shifted;
          loop (arr, bin_indices, all_expended, succ i)
        end

    prval () = lemma_array_param arr
  in
    array_initize_elt<size_t> (bin_indices, i2sz 256, i2sz 0);
    all_expended := true;
    loop (arr, bin_indices, all_expended, i2sz 0)
  end

fn {a  : vt@ype}
   {tk : tkind}
sort_by_digit
          {n            : int}
          {shift        : nat}
          (arr1         : &RD(array (a, n)),
           arr2         : &array (a, n) >> _,
           n            : size_t n,
           all_expended : &bool? >> bool,
           shift        : int shift)
    :<!wrt> void =
  let
    var bin_indices : array (size_t, 256)
  in
    count_entries<a><tk> (arr1, n, bin_indices, all_expended, shift);
    if all_expended then
      ()
    else
      let
        fun
        rearrange {i : int | i <= n}
                  .<n - i>.
                  (arr1        : &RD(array (a, n)),
                   arr2        : &array (a, n) >> _,
                   bin_indices : &array (size_t, 256) >> _,
                   i           : size_t i)
            :<!wrt> void =
          if i <> n then
            let
              prval () = lemma_g1uint_param i
              val key = g0uint_radix_sort$key<a><tk> (arr1, i)
              val key_shifted = key >> shift
              val digit = ($UN.cast{uint} key_shifted) land 255U
              val [digit : int] digit = g1ofg0 digit
              extern praxi set_range :
                () -<prf> [0 <= digit; digit <= 255] void
              prval () = set_range ()
              val [j : int] j = g1ofg0 bin_indices[digit]

              (* One might wish to get rid of this assertion somehow,
                 to eliminate the branch, should it prove a
                 problem. *)
              val () = $effmask_exn assertloc (j < n)

              val p_dst = ptr_add<a> (addr@ arr2, j)
              and p_src = ptr_add<a> (addr@ arr1, i)
              val _ = $extfcall (ptr, "memcpy", p_dst, p_src,
                                 sizeof<a>)
              val () = bin_indices[digit] := succ (g0ofg1 j)
            in
              rearrange (arr1, arr2, bin_indices, succ i)
            end

        prval () = lemma_array_param arr1
      in
        bin_sizes_to_indices<> bin_indices;
        rearrange (arr1, arr2, bin_indices, i2sz 0)
      end
  end

fn {a  : vt@ype}
   {tk : tkind}
g0uint_sort {n    : pos}
            (arr1 : &array (a, n) >> _,
             arr2 : &array (a, n) >> _,
             n    : size_t n)
    :<!wrt> void =
  let
    fun
    loop {idigit_max, idigit : nat | idigit <= idigit_max}
         .<idigit_max - idigit>.
         (arr1       : &array (a, n) >> _,
          arr2       : &array (a, n) >> _,
          from1to2   : bool,
          idigit_max : int idigit_max,
          idigit     : int idigit)
        :<!wrt> void =
      if idigit = idigit_max then
        begin
          if ~from1to2 then
            let
              val _ =
                $extfcall (ptr, "memcpy", addr@ arr1, addr@ arr2,
                           sizeof<a> * n)
            in
            end
        end
      else if from1to2 then
        let
          var all_expended : bool
        in
          sort_by_digit<a><tk> (arr1, arr2, n, all_expended,
                                8 * idigit);
          if all_expended then
            ()
          else
            loop (arr1, arr2, false, idigit_max, succ idigit)
        end
      else
        let
          var all_expended : bool
        in
          sort_by_digit<a><tk> (arr2, arr1, n, all_expended,
                                8 * idigit);
          if all_expended then
            let
              val _ =
                $extfcall (ptr, "memcpy", addr@ arr1, addr@ arr2,
                           sizeof<a> * n)
            in
            end
          else
            loop (arr1, arr2, true, idigit_max, succ idigit)
        end
  in
    loop (arr1, arr2, true, sz2i sizeof<g1uint tk>, 0)
  end

#define SIZE_THRESHOLD 256

extern praxi
unsafe_cast_array
          {a   : vt@ype}
          {b   : vt@ype}
          {n   : int}
          (arr : &array (b, n) >> array (a, n))
    :<prf> void

implement {a} {tk}
g0uint_radix_sort {n} (arr, n) =
  if n <> 0 then
    let
      prval () = lemma_array_param arr

      fn
      sort {n    : pos}
           (arr1 : &array (a, n) >> _,
            arr2 : &array (a, n) >> _,
            n    : size_t n)
          :<!wrt> void =
        g0uint_sort<a><tk> (arr1, arr2, n)
    in
      if n <= SIZE_THRESHOLD then
        let
          var arr2 : array (a, SIZE_THRESHOLD)
          prval @(pf_left, pf_right) =
            array_v_split {a?} {..} {SIZE_THRESHOLD} {n} (view@ arr2)
          prval () = view@ arr2 := pf_left
          prval () = unsafe_cast_array{a} arr2

          val () = sort (arr, arr2, n)

          prval () = unsafe_cast_array{a?} arr2
          prval () = view@ arr2 :=
            array_v_unsplit (view@ arr2, pf_right)
        in
        end
      else
        let
          val @(pf_arr2, pfgc_arr2 | p_arr2) = array_ptr_alloc<a> n
          macdef arr2 = !p_arr2
          prval () = unsafe_cast_array{a} arr2

          val () = sort (arr, arr2, n)

          prval () = unsafe_cast_array{a?} arr2
          val () = array_ptr_free (pf_arr2, pfgc_arr2 | p_arr2)
        in
        end
    end

(*------------------------------------------------------------------*)

fn {a        : vt@ype}
   {tki, tku : tkind}
g0int_sort {n   : int}
           (arr : &array (a, n) >> _,
            n   : size_t n)
    :<!wrt> void =
  let
    macdef get_key = g0int_radix_sort$key<a><tki>
    prval () = lemma_array_param arr
  in
    if n = 0 then
      ()
    else
      let
        val () = $effmask_exn
          assertloc (sizeof<g0int tki> = sizeof<g0uint tku>)

        fn
        find_least_key (arr : &RD(array (a, n)))
            :<> g0int tki =
          let
            fun
            loop {i : int | i <= n}
                 .<n - i>.
                 (arr       : &RD(array (a, n)),
                  least_key : g0int tki,
                  i         : size_t i)
                :<> g0int tki =
              if i <> n then
                let
                  prval () = lemma_g1uint_param i
                  val key = get_key (arr, i)
                in
                  loop (arr, min (least_key, key), succ i)
                end
              else
                least_key
          in
            if n = 0 then
              get_key (arr, i2sz 0)
            else
              let
                val first_key = get_key (arr, i2sz 0)
              in
                loop (arr, first_key, i2sz 1)
              end
          end

        val least_key = find_least_key arr

        (* The offset is the two's complement of the least key. Thus the
           least key is mapped to zero and the order of keys is
           preserved. *)
        val offset = succ (lnot ($UN.cast{g1uint tku} least_key))

        implement
        g0uint_radix_sort$key<a><tku> (arr, i) =
          let
            val keyi = get_key (arr, i)
          in
            g0i2u keyi + offset
          end
      in
        g0uint_radix_sort<a><tku> (arr, n)
      end
  end

implement {a} {tki, tku}
g0int_radix_sort (arr, n) =
  g0int_sort<a><tki, tku> (arr, n)

(*------------------------------------------------------------------*)

implement
main0 () =
  let
    implement
    g0int_radix_sort$key<int><intknd> (arr, i) =
      arr[i]

    var arr : array (int, 10)
    val () =
      array_initize_list<int>
        (arr, 10, $list (1, 2, 1, ~2, 330, 5000, 16, ~20000, 1, 2))
    val () = g0int_radix_sort<int><intknd, uintknd> (arr, i2sz 10)
    val () = println! (list_vt2t (array2list (arr, i2sz 10)))
  in
  end

(*------------------------------------------------------------------*)
Output:
$ patscc -O3 -DATS_MEMALLOC_LIBC radix_sort_task.dats && ./a.out
-20000, -2, 1, 1, 1, 2, 2, 16, 330, 5000

AutoHotkey[edit]

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
MsgBox, 262144, , % Radix_Sort(d)
Outputs:
2,24,45,66,75,90,170,802

B4X[edit]

Sub RadixSort (Old() As Int)
	Dim i, j As Int
	Dim tmp(Old.Length) As Int
	For shift = 31 To 0 Step - 1
		j = 0
		For i = 0 To Old.Length - 1
			Dim move As Boolean = Bit.ShiftLeft(Old(i), shift) >= 0
			If (shift = 0 And move = False) Or (shift <> 0 And move) Then
				Old(i - j) = Old(i)
			Else
				tmp(j) = Old(i)
				j = j + 1
			End If
		Next
		Bit.ArrayCopy(tmp, 0, Old, Old.Length - j, j)
	Next
End Sub

Sub Test
	Dim arr() As Int = Array As Int(34, 23, 54, -123, 543, 123)
	RadixSort(arr)
	For Each i As Int In arr
		Log(i)
	Next
End Sub

Output:

-123
23
34
54
123
543

BBC BASIC[edit]

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[edit]

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#[edit]

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();
        }
    }
}

C++[edit]

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
class radix_test
{
    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
void 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_sort
int 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 

D[edit]

Shorter Version[edit]

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[edit]

import std.array, std.traits;

// considered pure for this program
extern(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]

Original C++ code, modified (unknown license), by Andre Reinald, Paul Harris, Ryan Rohrer, Dirk Jagdmann: http://www.cubic.org/docs/download/radix_ar_2011.cpp

EasyLang[edit]

func sort . d[] .
  # radix = 10
  radix = 256
  max = 0
  for di = 1 to len d[]
    if d[di] > max
      max = d[di]
    .
  .
  len buck[][] radix
  pos = 1
  while pos <= max
    for i = 1 to radix
      len buck[i][] 0
    .
    for di = 1 to len d[]
      h = d[di] div pos mod radix + 1
      buck[h][] &= d[di]
    .
    di = 1
    for i = 1 to radix
      for j = 1 to len buck[i][]
        d[di] = buck[i][j]
        di += 1
      .
    .
    pos *= radix
  .
.
data[] = [ 29 4 72 44 55 26 27 77 92 5 ]
call sort data[]
print data[]

Eiffel[edit]

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[edit]

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)
  end
end

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[edit]

      SUBROUTINE VARRADIX(A , Siz)

!
!	No Copyright is exerted due to considerable prior art in the Public Domain.
!       This Fortran version by Peter Kelly ~ peter.kelly@acm.org
!
!	Permission is hereby granted, free of charge, to any person obtaining
!	a copy of this software and associated documentation files (the
!	"Software"), to deal in the Software without restriction, including
!	without limitation the rights to use, copy, modify, merge, publish,
!	distribute, sublicense, and/or sell copies of the Software, and to
!	permit persons to whom the Software is furnished to do so, subject to
!	the following conditions:
!	The above copyright notice and this permission notice shall be
!	included in all copies or substantial portions of the Software.
!	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
!	EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
!	MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
!	IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
!	CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
!	TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
!	SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
!          
!    
!     LSD sort with a configurable RADIX, Using a RADIX of 256 performs well, hence I have defaulted it in. It is snarly fast.
!     It could be optimized by merging the two routines but this way gives greater clarity as to what's going on.
      IMPLICIT NONE
!
! PARAMETER definitions
!
      INTEGER , PARAMETER  ::  BASE = 256 ! whatever base you need, just change this
!
! Dummy arguments
!
      INTEGER  ::  Siz
      INTEGER , DIMENSION(Siz)  ::  A
!
! Local variables
!
      INTEGER , ALLOCATABLE , DIMENSION(:)  ::  b
      INTEGER , ALLOCATABLE , DIMENSION(:)  ::  c
      INTEGER  ::  exps
      INTEGER  ::  maxs
!
      ALLOCATE(b(Siz))
      ALLOCATE(c(BASE))
 
      exps = 1
      maxs = MAXVAL(A)
      DO WHILE ( (maxs/exps)>0 )
         CALL XXCOUNTING_SORT(A , Siz , exps , BASE , b , c)
         exps = exps*BASE
      END DO
      deallocate(C)
      deallocate(B)
      RETURN
      CONTAINS
!
!//b is the base you want
!//exp is the value used for the division
      SUBROUTINE XXCOUNTING_SORT(A , Siz , Exps , Base , B , C)
      IMPLICIT NONE
! I used zero based arrays as it made the calcs infinitely easier :)
!
! Dummy arguments
!
      INTEGER  ::  Base
      INTEGER  ::  Exps
      INTEGER  ::  Siz    ! Size
      INTEGER , DIMENSION(0:)  ::  A
      INTEGER , DIMENSION(0:)  ::  B
      INTEGER , DIMENSION(0:)  ::  C
      INTENT (IN) Base , Exps , Siz
      INTENT (INOUT) A , B , C
!
! Local variables
!
      INTEGER  ::  i
      INTEGER  ::  k
!
      C = 0                             ! Init the arrays
      B = 0
!
      DO i = 0 , Siz - 1 , 1
         k = MOD((A(i)/Exps) , Base)    ! Fill Histo
         C(k) = C(k) + 1
      END DO
! 
      DO i = 1 , Base - 1 , 1
         C(i) = C(i) + C(i - 1)         ! Build cumulative Histo
      END DO
! 
      DO i = Siz - 1 , 0 , -1
         k = MOD(A(i)/Exps , Base)      ! Load the Buffer Array in order
         B(C(k) - 1) = A(i)
         C(k) = C(k) - 1
      END DO
!
      DO i = 0 , Siz - 1 , 1              ! Copy across
         A(i) = B(i)
      END DO
      RETURN
      END SUBROUTINE XXCOUNTING_SORT
    END SUBROUTINE Varradix
!*************************************************************************** 
!                            End of LSD sort with any Radix
!***************************************************************************
      MODULE LEASTSIG
      IMPLICIT NONE
!
!	No Copyright is exerted due to considerable prior art in the Public Domain.
!       This Fortran version by Peter Kelly ~ peter.kelly@acm.org
!
!	Permission is hereby granted, free of charge, to any person obtaining
!	a copy of this software and associated documentation files (the
!	"Software"), to deal in the Software without restriction, including
!	without limitation the rights to use, copy, modify, merge, publish,
!	distribute, sublicense, and/or sell copies of the Software, and to
!	permit persons to whom the Software is furnished to do so, subject to
!	the following conditions:
!	The above copyright notice and this permission notice shall be
!	included in all copies or substantial portions of the Software.
!	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
!	EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
!	MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
!	IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
!	CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
!	TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
!	SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
!          
!     Implementation of a classic Radix Sort LSD style :)
!     Works well, Integers only but it goes faster than a comparison sort
      CONTAINS
 
! Main Radix Sort sort function
      SUBROUTINE LSDRADIXSORT(A , N)
      IMPLICIT NONE
!
! Dummy arguments
!
      INTEGER  ::  N
      INTEGER , target, DIMENSION(0:N - 1)  ::  A           ! All arrays based off zero, one day I'll fix it
      INTENT (IN) N
      INTENT (INOUT) A
!
! Local variables
! 
      INTEGER , DIMENSION(0:9)  ::  counts
      INTEGER  ::  digitplace
      INTEGER  ::  i
      INTEGER  ::  j
      INTEGER  ::  largestnum
      INTEGER, DIMENSION(0:N - 1)  ::  results 
! 
      digitplace = 1                                        ! Count of the keys
      largestnum = MAXVAL(A)
 
      DO WHILE ( (largestnum/digitplace)>0 )
         counts = 0                                         ! Init the count array
        DO i = 0 , N - 1 , 1
            J = (A(i)/digitplace)
            J = MODULO(j , 10) 
            counts(j) = counts(j) + 1
        END DO

!  Change count(i) so that count(i) now contains actual position of this digit in result()
!  Working similar to the counting sort algorithm
         DO i = 1 , 9 , 1
            counts(i) = counts(i) + counts(i - 1)       ! Build up the prefix sum
         END DO
!
         DO i = N - 1 , 0 , -1                          ! Move from left to right
            j = (A(i)/digitplace)
            j = MODULO(j, 10)
            results(counts(j) - 1) = A(i)               ! Need to subtract one as we are zero based but prefix sum is 1 based
            counts(j) = counts(j) - 1
         END DO
!
         DO i = 0 , N - 1 , 1                           ! Copy the semi-sorted data into the input
           A(i) = results(i)
         END DO
!
         digitplace = digitplace*10
      END DO                                             ! While loop
      RETURN
      END SUBROUTINE LSDRADIXSORT
      END MODULE LEASTSIG
!*************************************************************************** 
!                            End of Classic LSD sort with Radix 10
!***************************************************************************
!Superfast FORTRAN LSD sort
! Dataset is input array, Scratch is working array
!
      SUBROUTINE FASTLSDRAD(Dataset , Scratch , Dsize)
!
!	No Copyright is exerted due to considerable prior art in the Public Domain.
!       This Fortran version by Peter Kelly ~ peter.kelly@acm.org
!
!	Permission is hereby granted, free of charge, to any person obtaining
!	a copy of this software and associated documentation files (the
!	"Software"), to deal in the Software without restriction, including
!	without limitation the rights to use, copy, modify, merge, publish,
!	distribute, sublicense, and/or sell copies of the Software, and to
!	permit persons to whom the Software is furnished to do so, subject to
!	the following conditions:
!	The above copyright notice and this permission notice shall be
!	included in all copies or substantial portions of the Software.
!	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
!	EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
!	MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
!	IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
!	CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
!	TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
!	SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
!          
!     This LSD sort is optimized to a base 16,Radix 256 sort which is about as fast as LSD gets. As well as a fast
!     algorithm, it has great cache coherency so performs exceptionally on large data sets,
!     I have optimized out all the divide and modulus functions and replaced them with bit shifts for speed.
!     A further speed optimization is obtained by using pointers to the DATA and TEMP arrays and swapping them each pass of
!     the LSB calculation. In FORTRAN this is a bit clunky but much faster than copying data back and forth between arrays.
!
!     All arrays are zero based as this makes the indexing calculations straightforward without the need for
!     subsequent adds and subtracts to track the correct index
!         .
      IMPLICIT NONE
!
! Dummy arguments
!
      INTEGER  ::  Dsize
      INTEGER , TARGET , DIMENSION(0:Dsize - 1)  ::  Scratch    ! Declared as TARGET as we will manipulate with pointers
      INTEGER , TARGET , DIMENSION(0:Dsize - 1)  ::  Dataset
      INTENT (IN) Dsize
      INTENT (INOUT) Scratch , Dataset
!
! Local variables
!
      INTEGER , POINTER , DIMENSION(:)  ::  a                   ! The pointer to the data
      INTEGER , POINTER , DIMENSION(:)  ::  b                   ! The pointer to the buffer
      INTEGER  ::  i
      INTEGER  ::  j
      INTEGER  ::  m
      INTEGER , DIMENSION(0:255,0:3)  ::  stats_table
      INTEGER  ::  n
      LOGICAL  ::  swap
      INTEGER  ::  u
      
!
      stats_table = 0                                           !   index matrix
      swap = .TRUE.                                             !   For swapping pointers
!
      a => Dataset
      b => Scratch
!
      DO i = 0 , Dsize - 1 , 1                                  ! generate histograms
         u = a(i)
         DO j = 0 , 3 , 1
            n = IAND(u , z'FF')
            u = SHIFTR(u , 8)
            stats_table(n,j) = stats_table(n,j) + 1
         END DO
      END DO
!
      DO i = 0 , 3 , 1                                          ! convert to indices
         m = 0
         DO j = 0 , 255 , 1
            n = stats_table(j , i)
            stats_table(j , i) = m
            m = m + n
         END DO
      END DO
!
      DO j = 0 , 3 , 1                                          ! Radix Sort, sort by LSB
         DO i = 0 , Dsize - 1 , 1
            u = a(i)
            m = IAND(SHIFTR(u,SHIFTL(j,3)) , z'FF')             ! Eliminate the MOD 16 and div with shifts
            b(stats_table(m,j)) = u                             ! Push the data into the buffer
            stats_table(m,j) = stats_table(m,j) + 1
         END DO
!
!        Instead of copying back from the temp values swap the array pointers
!
         IF( swap )THEN
            a => Scratch                                        ! A now points to the b buffer
            b => Dataset                                        ! B now is the data set
         ELSE
            a => Dataset
            b => Scratch
         END IF
         swap = .NOT.swap                                       ! Set to swap back and forth every pass
      END DO
 !
      RETURN
      END SUBROUTINE FASTLSDRAD
!*************************************************************************** 
!                            End of Superfast LSD sort
!***************************************************************************
*=======================================================================
* 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[edit]

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)
        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[edit]

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]

Haskell[edit]

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

Icon and Unicon[edit]

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 A
end

Sample run:

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

J[edit]

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 data
16 radixSortR y
:
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

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:

   radixsort ?.@#~10
4 5 6 6 6 6 6 8 8

Or, for negative number support:

rsort=: (] + radixsort@:-) <./

Example:

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

Java[edit]

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[edit]

# Sort the input array;
# "base" must be an integer greater than 1
def 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[edit]

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
    arr
end

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))
    end
end

testradixsort()
Output:

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

Kotlin[edit]

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/Wolfram Language[edit]

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}

Nim[edit]

Translation of: Kotlin
func radixSort[T](a: openArray[T]): seq[T] =

  result = @a

  ## Loop for every bit in the integers.
  for shift in countdown(63, 0):
    var tmp = newSeq[T](result.len)   # The array to put the partially sorted array into.
    var j = 0                         # The number of 0s.
    for i in 0..result.high:
      # If there is a 1 in the bit we are testing, the number will be negative.
      let move = result[i] shl shift >= 0
      # If this is the last bit, negative numbers are actually lower.
      let toBeMoved = if shift == 0: not move else: move
      if toBeMoved:
        tmp[j] = result[i]
        inc j
      else:
        # It's a 1, so stick it in the result array for now.
        result[i - j] = result[i]
    # Copy over the 1s from the old array.
    for i in j..tmp.high:
      tmp[i] = result[i - j]
    # And now the tmp array gets switched for another round of sorting.
    result.shallowCopy(tmp)


when isMainModule:

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

  for a in arrays:
    echo radixSort(a)
Output:
@[-802, -90, 2, 24, 45, 66, 75, 170]
@[-1837, -990, -26, -4, 5, 58, 331, 331, 990, 2028]

NetRexx[edit]

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

Using the Rexx class[edit]

/* 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[edit]

/* 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[edit]

Radix sort in base 10.

#!/usr/bin/perl
use 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]);
}

Phix[edit]

with javascript_semantics

function radixSortn(sequence s, integer n)
    sequence buckets = repeat({},10),
             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 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
 
function radixSort(sequence s)
    integer mins = min(s),
            passes = max(max(s),abs(mins))
    passes = floor(log10(passes))+1
    if mins<0 then
        sequence buckets = split_by_sign(s)
        s = reverse(sq_uminus(radixSortn(buckets[1],passes)))
          & radixSortn(buckets[2],passes)
    else
        s = radixSortn(s,passes)
    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})
?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[edit]

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[edit]

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
      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
  Next
EndProcedure

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[edit]

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 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
 
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:
        #If the bin is empty it skips the recursive call
        if b == []:
            continue
        # 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[edit]

#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
    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
    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
                            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 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&
        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 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

Quackery[edit]

  [ stack ]                    is digit     (   --> s )

  [ behead swap witheach min ] is smallest  ( [ --> n )

  [ [] over smallest
    rot witheach
      [ over -
        rot swap join swap ]
    swap
    0 digit put
    dup size temp put
    [ ' [ [ ] ] 16 of
      constant
      swap witheach
        [ dup dip
            [ digit share
              >> 15 &
          2dup peek ]
          join
          unrot poke ]
      dup 0 peek size
      temp share != while
      behead swap
      witheach join
      4 digit tally again ]
    behead nip
    temp release
    digit release
    [] unrot
    witheach
      [ over +
        rot swap join swap ]
    drop ]                     is radixsort ( [ --> [ )

  [] 256 times
    [ 1999 random 999 - join ]
  radixsort
  16 times
     [ 16 times
         [ behead
           dup 0 > if sp
           dup abs dup
           10 < if sp
           100 < if sp
           echo sp ] cr ]
  drop
Output:
-992 -984 -982 -962 -957 -952 -921 -907 -906 -906 -903 -874 -870 -864 -861 -858 
-852 -852 -844 -836 -835 -823 -804 -804 -802 -800 -794 -791 -789 -786 -778 -770 
-766 -759 -754 -752 -744 -743 -743 -718 -716 -695 -685 -683 -680 -677 -672 -670 
-669 -644 -643 -640 -639 -639 -623 -603 -601 -589 -588 -575 -572 -567 -565 -557 
-554 -542 -535 -531 -527 -518 -515 -501 -475 -474 -457 -420 -411 -386 -377 -376 
-371 -367 -350 -348 -347 -346 -332 -314 -301 -301 -299 -293 -285 -272 -242 -239 
-237 -234 -230 -225 -225 -196 -188 -163 -147 -146 -145 -143 -125 -121 -119 -116 
-110 -108 -105 -104  -97  -85  -71  -69  -66  -58  -52  -40  -25   -9   -8   14 
  23   44   45   49   67   69   83   87   87  127  138  143  145  159  160  166 
 168  169  178  187  204  218  220  231  231  232  235  237  244  251  255  258 
 264  265  272  285  287  300  314  337  341  348  351  353  359  367  370  372 
 376  398  402  410  415  420  443  464  465  474  479  483  516  519  520  541 
 543  546  552  558  559  561  565  579  596  607  616  637  668  668  679  682 
 698  698  714  720  728  734  736  744  768  768  789  789  797  797  799  802 
 802  814  815  815  819  833  841  844  848  862  868  885  887  890  894  906 
 912  927  930  933  936  946  947  950  955  963  967  968  969  969  989  999 

Racket[edit]

#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

Raku[edit]

(formerly 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

REXX[edit]

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

/*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, w                               /*invoke the  radix sort  subroutine.  */
call show                                        /*display the elements in the  @  array*/
exit 0                                           /*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 @.;  parse arg size,w;   mote= c2d(' ');    #= 1;   !.#._n= size
!.#._b= 1;                     if w==''  then w= 8
!.#._i= 1;  do i=1  for size;  y=@.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= $+1;  iterate
                              end
     L= c2d(L);   H= c2d(H);      ?= ctr._ + low;        top._= ?;          ts= mote
     max= L
                  do k=L  to H;   _= d2c(k, 1);   c= ctr._  /* [↓]  swap 2 item radices.*/
                  if c>ts  then parse value  c k  with  ts max;     ?= ?+c;       top._= ?
                  end   /*k*/
     piv= low                                    /*set PIVot to the low part of the sort*/
             do  while piv<low+n
             it= @.piv
                        do forever;     parse var it  =($)  _  +1;         c= top._ -1
                        if piv>=c  then leave;   top._= c;    ?= @.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;                       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  for size;    if @.i>=0  then iterate;     #= #+1;      @@.#= @.i
        end   /*i*/
        do j=1  for size;   if @.j>=0  then do;  #= #+1;   @@.#= @.j;  end;    @.j= @@.j+0
        end   /*j*/                              /* [↑↑↑]  combine 2 lists into 1 list. */
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
show:  do j=1  for n;   say 'item'   right(j, w)   "after the radix sort:"   right(@.j, w)
       end   /*j*/;     return                   /* [↑]  display sorted items ───► term.*/
output     (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[edit]

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)
  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:

[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}
  end
end

Rust[edit]

fn merge(in1: &[i32], in2: &[i32], out: &mut [i32]) {
    let (left, right) = out.split_at_mut(in1.len());
    left.clone_from_slice(in1);
    right.clone_from_slice(in2);
}

// least significant digit radix sort
fn radix_sort(data: &mut [i32]) {
    for bit in 0..31 {
        // types of small and big is Vec<i32>.
        // It will be infered from the next call of merge function.
        let (small, big): (Vec<_>, Vec<_>) = data.iter().partition(|&&x| (x >> bit) & 1 == 0);
        merge(&small, &big, data);
    }
    // last bit is sign
    let (negative, positive): (Vec<_>, Vec<_>) = data.iter().partition(|&&x| x < 0);
    merge(&negative, &positive, data);
}

fn main() {
    let mut data = [170, 45, 75, -90, -802, 24, 2, 66, -17, 2];
    println!("Before: {:?}", data);
    radix_sort(&mut data);
    println!("After: {:?}", data);
}
Output:
Before: [170, 45, 75, -90, -802, 24, 2, 66, -17, 2]
After: [-802, -90, -17, 2, 2, 24, 45, 66, 75, 170]

Scala[edit]

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(", "))
}

Scheme[edit]

An implementation for non-negative integers only[edit]

Works with: R7RS


;;; An illustrative implementation of the radix-10 example at
;;; https://en.wikipedia.org/w/index.php?title=Radix_sort&oldid=1070890278#Least_significant_digit

(cond-expand
  (r7rs)
  (chicken (import (r7rs))))

(import (scheme base))
(import (scheme write))

(define (sort-by-decimal-digit data power-of-10)
  (define bins (make-vector 10 '()))
  (do ((i (- (vector-length data) 1) (- i 1)))
      ((= i -1))
    (let* ((element (vector-ref data i))
           (digit (truncate-remainder
                   (truncate-quotient element power-of-10)
                   10)))
      (vector-set! bins digit
                   (cons element (vector-ref bins digit)))))
  (let ((non-zero-found
         (let loop ((i 1))
           (cond ((= i (vector-length bins)) #f)
                 ((pair? (vector-ref bins i)) #t)
                 (else (loop (+ i 1)))))))
    (when non-zero-found
      (let ((i 0))
        (do ((j 0 (+ j 1)))
            ((= j (vector-length bins)))
          (do ((p (vector-ref bins j) (cdr p)))
              ((null? p))
            (vector-set! data i (car p))
            (set! i (+ i 1))))))
    (not non-zero-found)))

(define (radix-sort data)
  (let loop ((power-of-10 1))
    (let ((done (sort-by-decimal-digit data power-of-10)))
      (unless done
        (loop (* 10 power-of-10))))))

(define data (vector-copy #(170 45 75 90 2 802 2 66)))
(write data)
(newline)
(radix-sort data)
(write data)
(newline)
Output:
$ gosh radix_sort_task.scm
#(170 45 75 90 2 802 2 66)
#(2 2 45 66 75 90 170 802)

An implementation using lexicographic order to support negative integers[edit]

Works with: R7RS


The following implementation converts signed integers to a lexicographically ordered representation (specifically, unsigned numbers in the correct order). It then sorts the lexicographically ordered representation, and finally converts back to the original representation.

;;; An illustrative implementation of the radix-10 example at
;;; https://en.wikipedia.org/w/index.php?title=Radix_sort&oldid=1070890278#Least_significant_digit

(cond-expand
  (r7rs)
  (chicken (import (r7rs))))

(import (scheme base))
(import (scheme write))

(define (sort-by-decimal-digit data power-of-10)
  (define bins (make-vector 10 '()))
  (do ((i (- (vector-length data) 1) (- i 1)))
      ((= i -1))
    (let* ((element (vector-ref data i))
           (digit (truncate-remainder
                   (truncate-quotient element power-of-10)
                   10)))
      (vector-set! bins digit
                   (cons element (vector-ref bins digit)))))
  (let ((non-zero-found
         (let loop ((i 1))
           (cond ((= i (vector-length bins)) #f)
                 ((pair? (vector-ref bins i)) #t)
                 (else (loop (+ i 1)))))))
    (when non-zero-found
      (let ((i 0))
        (do ((j 0 (+ j 1)))
            ((= j (vector-length bins)))
          (do ((p (vector-ref bins j) (cdr p)))
              ((null? p))
            (vector-set! data i (car p))
            (set! i (+ i 1))))))
    (not non-zero-found)))

(define (radix-sort data)
  (define offset 0)

  (do ((i 0 (+ i 1)))
      ((<= (vector-length data) i))
    (let ((x (vector-ref data i)))
      (when (negative? x)
        (set! offset (max offset (- x))))))

  (do ((i 0 (+ i 1)))
      ((= i (vector-length data)))
    (vector-set! data i (+ (vector-ref data i) offset)))

  (let loop ((power-of-10 1))
    (let ((done (sort-by-decimal-digit data power-of-10)))
      (unless done
        (loop (* 10 power-of-10)))))

  (do ((i 0 (+ i 1)))
      ((= i (vector-length data)))
    (let ((x (vector-ref data i)))
      (vector-set! data i (- (vector-ref data i) offset)))))

(define data (vector-copy #(170 45 75 90 2 802 2 66)))
(write data)
(newline)
(radix-sort data)
(write data)
(newline)

(newline)
(set! data (vector-copy #(170 -45 75 -90 2 -802 2 -66)))
(write data)
(newline)
(radix-sort data)
(write data)
(newline)
Output:
$ chibi radix_sort_task-2.scm
#(170 45 75 90 2 802 2 66)
#(2 2 45 66 75 90 170 802)

#(170 -45 75 -90 2 -802 2 -66)
#(-802 -90 -66 -45 2 2 75 170)

Sidef[edit]

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]

Tailspin[edit]

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

[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
Output:
[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[edit]

Translation of: Python
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:

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

Wren[edit]

This is based on the approach used here which I've adjusted to deal with negative elements.

// counting sort of 'a' according to the digit represented by 'exp'
var countSort = Fn.new { |a, exp|
    var n = a.count
    var output = [0] * n
    var count  = [0] * 10
    for (i in 0...n) {
        var t = (a[i]/exp).truncate % 10
        count[t] = count[t] + 1
    }
    for (i in 1..9) count[i] = count[i] + count[i-1]
    for (i in n-1..0) {
        var t = (a[i]/exp).truncate % 10
        output[count[t] - 1] = a[i]
        count[t] = count[t] - 1
    }
    for (i in 0...n) a[i] = output[i]
}

// sorts 'a' in place
var radixSort = Fn.new { |a|
    // check for negative elements
    var min = a.reduce { |m, i| (i < m) ? i : m }
    // if there are any, increase all elements by -min
    if (min < 0) (0...a.count).each { |i| a[i] = a[i] - min }
    // now get the maximum to know number of digits
    var max = a.reduce { |m, i| (i > m) ? i : m }
    // do counting sort for each digit
    var exp = 1
    while ((max/exp).truncate > 0) {
        countSort.call(a, exp)
        exp = exp * 10
    }
    // if there were negative elements, reduce all elements by -min
    if (min < 0) (0...a.count).each { |i| a[i] = a[i] + min }
}

var aa =  [[4, 65, 2, -31, 0, 99, 2, 83, 782, 1], [170, 45, 75, 90, 2, 24, -802, -66]]
for (a in aa) {
    System.print("Unsorted: %(a)")
    radixSort.call(a)
    System.print("Sorted  : %(a)\n")
}
Output:
Unsorted: [4, 65, 2, -31, 0, 99, 2, 83, 782, 1]
Sorted  : [-31, 0, 1, 2, 2, 4, 65, 83, 99, 782]

Unsorted: [170, 45, 75, 90, 2, 24, -802, -66]
Sorted  : [-802, -66, 2, 24, 45, 75, 90, 170]

zkl[edit]

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)