# Unbias a random generator

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Unbias a random generator
You are encouraged to solve this task according to the task description, using any language you may know.
Given a weighted one-bit generator of random numbers where the probability of a one occurring, $P_1$ , is not the same as $P_0$ , the probability of a zero occurring, the probability of the occurrence of a one followed by a zero is $P_1$ × $P_0$ , assuming independence. This is the same as the probability of a zero followed by a one: $P_0$ × $P_1$ .

• Use your language's random number generator to create a function/method/subroutine/... randN that returns a one or a zero, but with one occurring, on average, 1 out of N times, where N is an integer from the range 3 to 6 inclusive.
• Create a function unbiased that uses only randN as its source of randomness to become an unbiased generator of random ones and zeroes.
• For N over its range, generate and show counts of the outputs of randN and unbiased(randN).

The actual unbiasing should be done by generating two numbers at a time from randN and only returning a 1 or 0 if they are different. As long as you always return the first number or always return the second number, the probabilities discussed above should take over the biased probability of randN.

This task is an implementation of Von Neumann debiasing, first described in a 1951 paper.

## 11l

Translation of: Python
```F randN(n)
‘1,0 random generator factory with 1 appearing 1/n'th of the time’
R () -> random:(@=n) == 0

F unbiased(biased)
‘uses a biased() generator of 1 or 0, to create an unbiased one’
V (this, that) = (biased(), biased())
L this == that
(this, that) = (biased(), biased())
R this

L(n) 3..6
V biased = randN(n)
V v = (0.<1000000).map(x -> @biased())
V (v1, v0) = (v.count(1), v.count(0))
print(‘Biased(#.):  count1=#., count0=#., percent=#.2’.format(n, v1, v0, 100.0 * v1 / (v1 + v0)))

v = (0.<1000000).map(x -> unbiased(@biased))
(v1, v0) = (v.count(1), v.count(0))
print(‘  Unbiased: count1=#., count0=#., percent=#.2’.format(v1, v0, 100.0 * v1 / (v1 + v0)))```
Output:
```Biased(3):  count1=332946, count0=667054, percent=33.29
Unbiased: count1=499751, count0=500249, percent=49.98
Biased(4):  count1=250561, count0=749439, percent=25.06
Unbiased: count1=500576, count0=499424, percent=50.06
Biased(5):  count1=200056, count0=799944, percent=20.01
Unbiased: count1=499975, count0=500025, percent=50.00
Biased(6):  count1=165953, count0=834047, percent=16.60
Unbiased: count1=500104, count0=499896, percent=50.01
```

```with Ada.Text_IO; with Ada.Numerics.Discrete_Random;

procedure Bias_Unbias is

Modulus: constant Integer := 60; -- lcm of {3,4,5,6}
type M is mod Modulus;
Gen: Rand.Generator;

subtype Bit is Integer range 0 .. 1;

function Biased_Bit(Bias_Base: Integer) return Bit is
begin
if (Integer(Rand.Random(Gen))* Bias_Base) / Modulus > 0 then
return 0;
else
return 1;
end if;
end Biased_Bit;

function Unbiased_Bit(Bias_Base: Integer) return Bit is
A, B: Bit := 0;
begin
while A = B loop
A := Biased_Bit(Bias_Base);
B := Biased_Bit(Bias_Base);
end loop;
return A;
end Unbiased_Bit;

Counter_B, Counter_U: Natural;
Number_Of_Samples: constant Natural := 10_000;

begin
Rand.Reset(Gen);
for I in 3 .. 6 loop
Counter_B := 0;
Counter_U := 0;
for J in 1 .. Number_Of_Samples loop
Counter_B := Counter_B + Biased_Bit(I);
Counter_U := Counter_U + Unbiased_Bit(I);
end loop;
FIO.Put(100.0 * Float(Counter_B) / Float(Number_Of_Samples), 5, 2, 0);
FIO.Put(100.0 * Float(Counter_U) / Float(Number_Of_Samples), 5, 2, 0);
end loop;
end Bias_Unbias;
```
Output:
``` I  Biased% UnBiased%
3   32.87   49.80
4   24.49   50.22
5   19.73   50.05
6   16.75   50.19
```

## Aime

Translation of: C
```integer
biased(integer bias)
{
1 ^ min(drand(bias - 1), 1);
}

integer
unbiased(integer bias)
{
integer a;

while ((a = biased(bias)) == biased(bias)) {
}

a;
}

integer
main(void)
{
integer b, n, cb, cu, i;

n = 10000;
b = 3;
while (b <= 6) {
i = cb = cu = 0;
while ((i += 1) <= n) {
cb += biased(b);
cu += unbiased(b);
}

o_form("bias ~: /d2p2/%% vs /d2p2/%%\n", b, 100r * cb / n,
100r * cu / n);

b += 1;
}

0;
}```
Output:
```bias 3: 33.51% vs 50.27%
bias 4: 24.97% vs 49.99%
bias 5: 19.93% vs 49.92%
bias 6: 16.32% vs 49.36%```

## AutoHotkey

 This example does not show the output mentioned in the task description on this page (or a page linked to from here). Please ensure that it meets all task requirements and remove this message. Note that phrases in task descriptions such as "print and display" and "print and show" for example, indicate that (reasonable length) output be a part of a language's solution.

```Biased(){
Random, q, 0, 4
return q=4
}
Unbiased(){
Loop
If ((a := Biased()) != biased())
return a
}
Loop 1000
t .= biased(), t2 .= unbiased()
StringReplace, junk, t2, 1, , UseErrorLevel
MsgBox % "Unbiased probability of a 1 occurring: " Errorlevel/1000
StringReplace, junk, t, 1, , UseErrorLevel
MsgBox % "biased probability of a 1 occurring: " Errorlevel/1000
```

## BASIC

### BASIC256

Translation of: FreeBASIC
```function randN (n)
if int(rand * n) + 1 <> 1 then return 0 else return 1
end function

function unbiased (n)
do
a = randN (n)
b = randN (n)
until a <> b
return a
end function

numveces = 100000

for n = 3 to 6
dim b_numveces(n) fill 0
dim u_numveces(n) fill 0
for m = 1 to numveces
x = randN (n)
b_numveces[x] += 1
x = unbiased (n)
u_numveces[x] += 1
next m
print "N = "; n
print "  Biased =>", "#0="; (b_numveces); "   #1="; (b_numveces); "   ratio = "; (b_numveces/numveces*100); "%"
print "Unbiased =>", "#0="; (u_numveces); "   #1="; (u_numveces); "   ratio = "; (u_numveces/numveces*100); "%"
next n
end```
Output:
```Resultados de números aleatorios sesgados e imparciales

N = 3
Biased =>   #0=66625   #1=33375   ratio = 33.375%
Unbiased =>   #0=50026   #1=49974   ratio = 49.974%
N = 4
Biased =>   #0=74988   #1=25012   ratio = 25.012%
Unbiased =>   #0=49809   #1=50191   ratio = 50.191%
N = 5
Biased =>   #0=79893   #1=20107   ratio = 20.107%
Unbiased =>   #0=50102   #1=49898   ratio = 49.898%
N = 6
Biased =>   #0=83432   #1=16568   ratio = 16.568%
Unbiased =>   #0=50091   #1=49909   ratio = 49.909%
```

## BBC BASIC

```      FOR N% = 3 TO 6
biased% = 0
unbiased% = 0
FOR I% = 1 TO 10000
IF FNrandN(N%) biased% += 1
IF FNunbiased(N%) unbiased% += 1
NEXT
PRINT "N = ";N% " : biased = "; biased%/100 "%, unbiased = "; unbiased%/100 "%"
NEXT
END

DEF FNunbiased(N%)
LOCAL A%,B%
REPEAT
A% = FNrandN(N%)
B% = FNrandN(N%)
UNTIL A%<>B%
= A%

DEF FNrandN(N%) = -(RND(N%) = 1)
```

Output:

```N = 3 : biased = 33.57%, unbiased = 49.94%
N = 4 : biased = 25.34%, unbiased = 50.76%
N = 5 : biased = 20.06%, unbiased = 50.04%
N = 6 : biased = 16.25%, unbiased = 50.13%
```

## C

```#include <stdio.h>
#include <stdlib.h>

int biased(int bias)
{
/* balance out the bins, being pedantic */
int r, rand_max = RAND_MAX - (RAND_MAX % bias);
while ((r = rand()) > rand_max);
return r < rand_max / bias;
}

int unbiased(int bias)
{
int a;
while ((a = biased(bias)) == biased(bias));
return a;
}

int main()
{
int b, n = 10000, cb, cu, i;
for (b = 3; b <= 6; b++) {
for (i = cb = cu = 0; i < n; i++) {
cb += biased(b);
cu += unbiased(b);
}
printf("bias %d: %5.3f%% vs %5.3f%%\n", b,
100. * cb / n, 100. * cu / n);
}

return 0;
}
```

output

```bias 3: 33.090% vs 49.710%
bias 4: 25.130% vs 49.430%
bias 5: 19.760% vs 49.650%
bias 6: 16.740% vs 50.030%```

## C++

Translation of: C#
```#include <iostream>
#include <random>

std::default_random_engine generator;
bool biased(int n) {
std::uniform_int_distribution<int> distribution(1, n);
return distribution(generator) == 1;
}

bool unbiased(int n) {
bool flip1, flip2;

/* Flip twice, and check if the values are the same.
* If so, flip again. Otherwise, return the value of the first flip. */

do {
flip1 = biased(n);
flip2 = biased(n);
} while (flip1 == flip2);

return flip1;
}

int main() {
for (size_t n = 3; n <= 6; n++) {
int biasedZero = 0;
int biasedOne = 0;
int unbiasedZero = 0;
int unbiasedOne = 0;

for (size_t i = 0; i < 100000; i++) {
if (biased(n)) {
biasedOne++;
} else {
biasedZero++;
}
if (unbiased(n)) {
unbiasedOne++;
} else {
unbiasedZero++;
}
}

std::cout << "(N = " << n << ")\n";
std::cout << "Biased:\n";
std::cout << "   0 = " << biasedZero << "; " << biasedZero / 1000.0 << "%\n";
std::cout << "   1 = " << biasedOne << "; " << biasedOne / 1000.0 << "%\n";
std::cout << "Unbiased:\n";
std::cout << "   0 = " << unbiasedZero << "; " << unbiasedZero / 1000.0 << "%\n";
std::cout << "   1 = " << unbiasedOne << "; " << unbiasedOne / 1000.0 << "%\n";
std::cout << '\n';
}
return 0;
}
```
Output:
```(N = 3)
Biased:
0 = 66614; 66.614%
1 = 33386; 33.386%
Unbiased:
0 = 49965; 49.965%
1 = 50035; 50.035%

(N = 4)
Biased:
0 = 75032; 75.032%
1 = 24968; 24.968%
Unbiased:
0 = 50030; 50.03%
1 = 49970; 49.97%

(N = 5)
Biased:
0 = 80178; 80.178%
1 = 19822; 19.822%
Unbiased:
0 = 49878; 49.878%
1 = 50122; 50.122%

(N = 6)
Biased:
0 = 83494; 83.494%
1 = 16506; 16.506%
Unbiased:
0 = 50085; 50.085%
1 = 49915; 49.915%```

## C#

```using System;

namespace Unbias
{
internal class Program
{
private static void Main(string[] args)
{
// Demonstrate.
for (int n = 3; n <= 6; n++)
{
int biasedZero = 0, biasedOne = 0, unbiasedZero = 0, unbiasedOne = 0;
for (int i = 0; i < 100000; i++)
{
if (randN(n))
biasedOne++;
else
biasedZero++;
if (Unbiased(n))
unbiasedOne++;
else
unbiasedZero++;
}

Console.WriteLine("(N = {0}):".PadRight(17) + "# of 0\t# of 1\t% of 0\t% of 1", n);
biasedZero, biasedOne,
biasedZero/1000, biasedOne/1000);
unbiasedZero, unbiasedOne,
unbiasedZero/1000, unbiasedOne/1000);
}
}

private static bool Unbiased(int n)
{
bool flip1, flip2;

/* Flip twice, and check if the values are the same.
* If so, flip again. Otherwise, return the value of the first flip. */

do
{
flip1 = randN(n);
flip2 = randN(n);
} while (flip1 == flip2);

return flip1;
}

private static readonly Random random = new Random();

private static bool randN(int n)
{
// Has an 1/n chance of returning 1. Otherwise it returns 0.
return random.Next(0, n) == 0;
}
}
}
```

Sample Output

```(N = 3):       # of 0   # of 1  % of 0  % of 1
Biased:        66867    33133   66      33
Unbiased:      49843    50157   49      50
(N = 4):       # of 0   # of 1  % of 0  % of 1
Biased:        74942    25058   74      25
Unbiased:      50192    49808   50      49
(N = 5):       # of 0   # of 1  % of 0  % of 1
Biased:        80203    19797   80      19
Unbiased:      49928    50072   49      50
(N = 6):       # of 0   # of 1  % of 0  % of 1
Biased:        83205    16795   83      16
Unbiased:      49744    50256   49      50
```

## Clojure

```(defn biased [n]
(if (< (rand 2) (/ n)) 0 1))

(defn unbiased [n]
(loop [a 0 b 0]
(if (= a b)
(recur (biased n) (biased n))
a)))

(for [n (range 3 7)]
[n
(double (/ (apply + (take 50000 (repeatedly #(biased n)))) 50000))
(double (/ (apply + (take 50000 (repeatedly #(unbiased n)))) 50000))])
([3 0.83292 0.50422]
[4 0.87684 0.5023]
[5 0.90122 0.49728]
[6 0.91526 0.5])
```

## CoffeeScript

```biased_rand_function = (n) ->
# return a function that returns 0/1  with
# 1 appearing only 1/Nth of the time
cap = 1/n
->
if Math.random() < cap
1
else
0

unbiased_function = (f) ->
->
while true
[n1, n2] = [f(), f()]
return n1 if n1 + n2 == 1

stats = (label, f) ->
cnt = 0
sample_size = 10000000
for i in [1...sample_size]
cnt += 1 if f() == 1
console.log "ratio of 1s: #{cnt / sample_size} [#{label}]"

for n in [3..6]
console.log "\n---------- n = #{n}"
f_biased = biased_rand_function(n)
f_unbiased = unbiased_function f_biased
stats "biased", f_biased
stats "unbiased", f_unbiased
```

output

```> coffee unbiased.coffee

---------- n = 3
ratio of 1s: 0.3333343 [biased]
ratio of 1s: 0.4999514 [unbiased]

---------- n = 4
ratio of 1s: 0.2499751 [biased]
ratio of 1s: 0.4998067 [unbiased]

---------- n = 5
ratio of 1s: 0.199729 [biased]
ratio of 1s: 0.5003183 [unbiased]

---------- n = 6
ratio of 1s: 0.1664843 [biased]
ratio of 1s: 0.4997813 [unbiased]
```

## Common Lisp

```(defun biased (n) (if (zerop (random n)) 0 1))

(defun unbiased (n)
(loop with x do
(if (/= (setf x (biased n)) (biased n))
(return x))))

(loop for n from 3 to 6 do
(let ((u (loop repeat 10000 collect (unbiased n)))
(b (loop repeat 10000 collect (biased n))))
(format t "~a: unbiased ~d biased ~d~%" n (count 0 u) (count 0 b))))
```

output

```3: unbiased 4992 biased 3361
4: unbiased 4988 biased 2472
5: unbiased 5019 biased 1987
6: unbiased 4913 biased 1658```

## D

```import std.stdio, std.random, std.algorithm, std.range, std.functional;

enum biased = (in int n) /*nothrow*/ => uniform01 < (1.0 / n);

int unbiased(in int bias) /*nothrow*/ {
int a;
while ((a = bias.biased) == bias.biased) {}
return a;
}

void main() {
enum M = 500_000;
foreach (immutable n; 3 .. 7)
writefln("%d: %2.3f%%  %2.3f%%", n,
M.iota.map!(_=> n.biased).sum * 100.0 / M,
M.iota.map!(_=> n.unbiased).sum * 100.0 / M);
}
```
Output:
```3: 33.441%  49.964%
4: 24.953%  49.910%
5: 19.958%  49.987%
6: 16.660%  49.890%```

## Elena

Translation of: C#

ELENA 4.x :

```import extensions;

extension op : IntNumber
{
bool randN()
= randomGenerator.nextInt(self) == 0;

get bool Unbiased()
{
bool flip1 := self.randN();
bool flip2 := self.randN();

while (flip1 == flip2)
{
flip1 := self.randN();
flip2 := self.randN()
};

^ flip1
}
}

public program()
{
for(int n := 3, n <= 6, n += 1)
{
int biasedZero := 0;
int biasedOne := 0;
int unbiasedZero := 0;
int unbiasedOne := 0;

for(int i := 0, i < 100000, i += 1)
{
if(n.randN()) { biasedOne += 1 } else { biasedZero += 1 };
if(n.Unbiased) { unbiasedOne += 1 } else { unbiasedZero += 1 }
};

console
.printLineFormatted("(N = {0}):".padRight(17) + "# of 0"\$9"# of 1"\$9"% of 0"\$9"% of 1", n)
biasedZero, biasedOne, biasedZero / 1000, biasedOne / 1000)
unbiasedZero, unbiasedOne, unbiasedZero / 1000, unbiasedOne / 1000)
}
}```
Output:
```(N = 3):       # of 0	# of 1	% of 0	% of 1
Biased:        66793	33207	66	33
Unbiased:      49965	50035	49	50
(N = 4):       # of 0	# of 1	% of 0	% of 1
Biased:        75233	24767	75	24
Unbiased:      50106	49894	50	49
(N = 5):       # of 0	# of 1	% of 0	% of 1
Biased:        80209	19791	80	19
Unbiased:      50080	49920	50	49
(N = 6):       # of 0	# of 1	% of 0	% of 1
Biased:        83349	16651	83	16
Unbiased:      49699	50301	49	50
```

## Elixir

```defmodule Random do
def randN(n) do
if :rand.uniform(n) == 1, do: 1, else: 0
end
def unbiased(n) do
{x, y} = {randN(n), randN(n)}
if x != y, do: x, else: unbiased(n)
end
end

IO.puts "N  biased  unbiased"
m = 10000
for n <- 3..6 do
xs = for _ <- 1..m, do: Random.randN(n)
ys = for _ <- 1..m, do: Random.unbiased(n)
IO.puts "#{n}  #{Enum.sum(xs) / m}  #{Enum.sum(ys) / m}"
end
```
Output:
```N  biased  unbiased
3  0.3356  0.5043
4  0.2523  0.4996
5  0.2027  0.5041
6  0.1647  0.4912
```

## ERRE

```PROGRAM UNBIAS

FUNCTION RANDN(N)
RANDN=INT(1+N*RND(1))=1
END FUNCTION

PROCEDURE UNBIASED(N->RIS)
LOCAL A,B
REPEAT
A=RANDN(N)
B=RANDN(N)
UNTIL A<>B
RIS=A
END PROCEDURE

BEGIN
PRINT(CHR\$(12);) ! CLS
RANDOMIZE(TIMER)

FOR N=3 TO 6 DO
BIASED=0
UNBIASED=0
FOR I=1 TO 10000 DO
IF RANDN(N) THEN biased+=1
UNBIASED(N->RIS)
IF RIS THEN unbiased+=+1
END FOR
PRINT("N =";N;" : biased =";biased/100;", unbiased =";unbiased/100)
END FOR
END PROGRAM```
Output:
```N = 3  : biased = 32.66 , unbiased = 49.14
N = 4  : biased = 25.49 , unbiased = 49.92
N = 5  : biased = 20.53 , unbiased = 50
N = 6  : biased = 17.43 , unbiased = 50.43
```

## Euphoria

```function randN(integer N)
return rand(N) = 1
end function

function unbiased(integer N)
integer a
while 1 do
a = randN(N)
if a != randN(N) then
return a
end if
end while
end function

constant n = 10000
integer cb, cu
for b = 3 to 6 do
cb = 0
cu = 0
for i = 1 to n do
cb += randN(b)
cu += unbiased(b)
end for
printf(1, "%d: %5.2f%%  %5.2f%%\n", {b, 100 * cb / n, 100 * cu / n})
end for```

Output:

```3: 33.68%  49.94%
4: 24.93%  50.48%
5: 20.32%  49.97%
6: 16.98%  50.05%
```

## F#

```open System

let random = Random()

let randN = random.Next >> (=)0 >> Convert.ToInt32

let rec unbiased n =
let a = randN n
if a <> randN n then a else unbiased n

[<EntryPoint>]
let main argv =
let n = if argv.Length > 0 then UInt32.Parse(argv.) |> int else 100000
for b = 3 to 6 do
let cb = ref 0
let cu = ref 0
for i = 1 to n do
cb := !cb + randN b
cu := !cu + unbiased b
printfn "%d: %5.2f%%  %5.2f%%"
b (100. * float !cb / float n) (100. * float !cu / float n)
0
```
Output:
```3: 33.26%  49.97%
4: 25.02%  50.22%
5: 19.98%  50.00%
6: 16.64%  49.69%```

## Factor

```USING: formatting kernel math math.ranges random sequences ;
IN: rosetta-code.unbias

: randN ( n -- m ) random zero? 1 0 ? ;

: unbiased ( n -- m )
dup [ randN ] dup bi 2dup = not
[ drop nip ] [ 2drop unbiased ] if ;

: test-generator ( quot -- x )
[ 1,000,000 dup ] dip replicate sum 100 * swap / ; inline

: main ( -- )
3 6 [a,b] [
dup [ randN ] [ unbiased ] bi-curry
[ test-generator ] bi@ "%d: %.2f%%  %.2f%%\n" printf
] each ;

MAIN: main
```
Output:
```3: 33.25%  50.03%
4: 24.98%  50.02%
5: 20.03%  50.04%
6: 16.66%  49.99%
```

## Fortran

Works with: Fortran version 90 and later
```program Bias_Unbias
implicit none

integer, parameter :: samples = 1000000
integer :: i, j
integer :: c1, c2, rand

do i = 3, 6
c1 = 0
c2 = 0
do j = 1, samples
rand = bias(i)
if (rand == 1) c1 = c1 + 1
rand = unbias(i)
if (rand == 1) c2 = c2 + 1
end do
write(*, "(i2,a,f8.3,a,f8.3,a)") i, ":", real(c1) * 100.0 / real(samples), &
"%", real(c2) * 100.0 / real(samples), "%"
end do

contains

function bias(n)
integer :: bias
integer, intent(in) :: n
real :: r

call random_number(r)
if (r > 1 / real(n)) then
bias = 0
else
bias = 1
end if
end function

function unbias(n)
integer :: unbias
integer, intent(in) :: n
integer :: a, b

do
a = bias(n)
b = bias(n)
if (a /= b) exit
end do
unbias = a
end function

end program
```

Output:

```3:  33.337%  49.971%
4:  24.945%  49.944%
5:  19.971%  49.987%
6:  16.688%  50.097%```

## FreeBASIC

Translation of: PureBasic
```Function randN (n As Ubyte) As Ubyte
If Int(Rnd * n) + 1 <> 1 Then Return 0 Else Return 1
End Function

Function unbiased (n As Ubyte) As Ubyte
Dim As Ubyte a, b
Do
a = randN (n)
b = randN (n)
Loop Until a <> b
Return a
End Function

Const count = 100000

Dim x As Ubyte

Randomize Timer

For n As Ubyte = 3 To 6
Dim As Integer b_count(1)
Dim As Integer u_count(1)
For m As Integer = 1 To count
x = randN (n)
b_count(x) += 1
x = unbiased (n)
u_count(x) += 1
Next m
Print "N ="; n
Print "  Biased =>", "#0="; Str(b_count(0)), "#1="; Str(b_count(1)),
Print Using "ratio = ##.##%"; (b_count(1) / count * 100)
Print "Unbiased =>", "#0="; Str(u_count(0)), "#1="; Str(u_count(1)),
Print Using "ratio = ##.##%"; (u_count(1) / count * 100)
Next n
Sleep
```
Output:
```Resultados de números aleatorios sesgados e imparciales

N = 3
Biased =>   #0=66633      #1=33367      ratio = 33.37%
Unbiased =>   #0=50029      #1=49971      ratio = 49.97%
N = 4
Biased =>   #0=75068      #1=24932      ratio = 24.93%
Unbiased =>   #0=50107      #1=49893      ratio = 49.89%
N = 5
Biased =>   #0=79998      #1=20002      ratio = 20.00%
Unbiased =>   #0=50049      #1=49951      ratio = 49.95%
N = 6
Biased =>   #0=83195      #1=16805      ratio = 16.81%
Unbiased =>   #0=50026      #1=49974      ratio = 49.97%
```

## Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

## GAP

```RandNGen := function(n)
local v, rand;
v := [1 .. n - 1]*0;
rand := function()
return Random(v);
end;
return rand;
end;

UnbiasedGen := function(rand)
local unbiased;
unbiased := function()
local a, b;
while true do
a := rand();
b := rand();
if a <> b then
break;
fi;
od;
return a;
end;
return unbiased;
end;

range := [2 .. 6];
v := List(range, RandNGen);
w := List(v, UnbiasedGen);
apply := gen -> Sum([1 .. 1000000], n -> gen());

# Some tests (2 is added as a witness, since in this case RandN is already unbiased)
PrintArray(TransposedMat([range, List(v, apply), List(w, apply)]));
# [ [       2,  499991,  499041 ],
#   [       3,  333310,  500044 ],
#   [       4,  249851,  500663 ],
#   [       5,  200532,  500448 ],
#   [       6,  166746,  499859 ] ]
```

## Go

```package main

import (
"fmt"
"math/rand"
)

const samples = 1e6

func main() {
fmt.Println("Generator  1 count  0 count  % 1 count")
for n := 3; n <= 6; n++ {
// function randN, per task description
randN := func() int {
if rand.Intn(n) == 0 {
return 1
}
return 0
}
var b int
for x := 0; x < samples; x++ {
b[randN()]++
}
fmt.Printf("randN(%d)   %7d  %7d    %5.2f%%\n",
n, b, b, float64(b)*100/samples)

// function unbiased, per task description
unbiased := func() (b int) {
for b = randN(); b == randN(); b = randN() {
}
return
}
var u int
for x := 0; x < samples; x++ {
u[unbiased()]++
}
fmt.Printf("unbiased   %7d  %7d    %5.2f%%\n",
u, u, float64(u)*100/samples)
}
}
```

Output:

```Generator  1 count  0 count  % 1 count
randN(3)    332711   667289    33.27%
unbiased    499649   500351    49.96%
randN(4)    249742   750258    24.97%
unbiased    499434   500566    49.94%
randN(5)    200318   799682    20.03%
unbiased    499100   500900    49.91%
randN(6)    166900   833100    16.69%
unbiased    499973   500027    50.00%
```

```import Control.Monad.Random
import Text.Printf

randN :: MonadRandom m => Int -> m Int
randN n = fromList [(0, fromIntegral n-1), (1, 1)]
```

Examples of use:

```λ> replicateM 20 (randN 2)
[0,0,1,0,0,1,0,1,1,0,0,1,1,1,1,0,1,1,0,0]
λ> replicateM 20 (randN 5)
[0,1,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,1,0]```

The second task. Returns the unbiased generator for any given random generator.

```unbiased :: (MonadRandom m, Eq x) => m x -> m x
unbiased g = do x <- g
y <- g
if x /= y then return y else unbiased g
```

Examples of use:

```λ> replicateM 20 (unbiased (randN 5))
[0,0,1,0,1,1,1,0,0,0,1,1,1,0,1,1,0,0,1,0]
λ> replicateM 20 (unbiased (fromList [(True,10),(False,1)]))
[True,True,False,True,True,True,False,True,False,True,True,False,False,True,False,True,True,False,False,True]```

```main = forM_ [3..6] showCounts
where
showCounts b = do
r1 <- counts (randN b)
r2 <- counts (unbiased (randN b))
printf "n = %d  biased: %d%%  unbiased: %d%%\n" b r1 r2

counts g = (`div` 100) . length . filter (== 1) <\$> replicateM 10000 g
```

Output:

```n = 3  biased: 33%  unbiased: 49%
n = 4  biased: 24%  unbiased: 50%
n = 5  biased: 19%  unbiased: 50%
n = 6  biased: 16%  unbiased: 49%
```

## Icon and Unicon

This solution works in both languages. Both randN and unbiased are generators in the Icon/Unicon sense.

```procedure main(A)
iters := \A | 10000
write("ratios of 0 to 1 from ",iters," trials:")
every n := 3 to 6 do {
results_randN := table(0)
results_unbiased := table(0)
every 1 to iters do {
results_randN[randN(n)] +:= 1
results_unbiased[unbiased(n)] +:= 1
}
showResults(n, "randN", results_randN)
showResults(n, "unbiased", results_unbiased)
}
end

procedure showResults(n, s, t)
write(n," ",left(s,9),":",t,"/",t," = ",t/real(t))
end

procedure unbiased(n)
repeat {
n1 := randN(n)
n2 := randN(n)
if n1 ~= n2 then suspend n1
}
end

procedure randN(n)
repeat suspend if 1 = ?n then 1 else 0
end
```

and a sample run:

```->ubrn 100000
ratios of 0 to 1 from 100000 trials:
3 randN    :66804/33196 = 2.012411133871551
3 unbiased :49812/50188 = 0.9925081692834941
4 randN    :75017/24983 = 3.002721850858584
4 unbiased :50000/50000 = 1.0
5 randN    :79990/20010 = 3.997501249375312
5 unbiased :50073/49927 = 1.002924269433373
6 randN    :83305/16695 = 4.989817310572027
6 unbiased :49911/50089 = 0.9964463255405378
->```

## J

```randN=: 0 = ?
unbiased=: i.@# { ::\$: 2 | 0 3 -.~ _2 #.\ 4&* randN@# ]
```

Example use:

```   randN 10#6
1 0 0 0 1 0 0 0 0 0
unbiased 10#6
1 0 0 1 0 0 1 0 1 1
```

Some example counts (these are counts of the number of 1s which appear in a test involving 100 random numbers):

```   +/randN 100#3
30
+/randN 100#4
20
+/randN 100#5
18
+/randN 100#6
18
+/unbiased 100#3
49
+/unbiased 100#4
46
+/unbiased 100#5
49
+/unbiased 100#6
47
```

Note that these results are arbitrary. For example, a re-run of `+/randN 100#5` gave 25 as its result, and a re-run of `+/unbiased 100#5` gave 52 as its result.

## Java

```public class Bias {
public static boolean biased(int n) {
return Math.random() < 1.0 / n;
}

public static boolean unbiased(int n) {
boolean a, b;
do {
a = biased(n);
b = biased(n);
} while (a == b);
return a;
}

public static void main(String[] args) {
final int M = 50000;
for (int n = 3; n < 7; n++) {
int c1 = 0, c2 = 0;
for (int i = 0; i < M; i++) {
c1 += biased(n) ? 1 : 0;
c2 += unbiased(n) ? 1 : 0;
}
System.out.format("%d: %2.2f%%  %2.2f%%\n",
n, 100.0*c1/M, 100.0*c2/M);
}
}
}
```

Output:

```3: 33,11%  50,23%
4: 24.97%  49.78%
5: 20.05%  50.00%
6: 17.00%  49.88%```

## jq

Works with: jq

Also works with gojq, the Go implementation of jq

In this entry, /dev/random is used as a source of entropy, and so a suitable invocation would be:

```< /dev/random tr -cd '0-9' | fold -w 1 | jq -Mcnr -f unbias.jq
```

unbias.jq

```### Utility Functions
# Output: a PRN in range(0;\$n) where \$n is .
def prn:
if . == 1 then 0
else . as \$n
| ((\$n-1)|tostring|length) as \$w
| [limit(\$w; inputs)] | join("") | tonumber
| if . < \$n then . else (\$n | prn) end
end;

def round: ((. * 100) | floor) / 100;

# input: n
# output: boolean, such that P(true) == 1/n
def biased:
prn == 1 | debug;

def unbiased:
. as \$n
| {}
| until( .a != .b; {a: (\$n|biased), b: (\$n|biased)})
| .a;

def f(x;y;z): "\(x): \(y|round)%  \(z|round)%";

range(3;7) as \$n
| reduce range(0; \$m) as \$i ( {c1:0, c2:0};
if (\$n|biased)   then .c1 += 1 else . end
| if (\$n|unbiased) then .c2 += 1 else . end)
| f(\$n; 100 * .c1 / \$m; 100 * .c2 / \$m);

Output:
```3: 33.61%  50.09%
4: 25.48%  50.21%
5: 20.32%  50.47%
6: 16.35%  49.72%
```

## Julia

```using Printf

randN(N) = () -> rand(1:N) == 1 ? 1 : 0
function unbiased(biased::Function)
this, that = biased(), biased()
while this == that this, that = biased(), biased() end
return this
end

@printf "%2s | %10s | %5s | %5s | %8s" "N" "bias./unb." "1s" "0s" "pct ratio"
const nrep = 10000
for N in 3:6
biased = randN(N)

v = collect(biased() for __ in 1:nrep)
v1, v0 = count(v .== 1), count(v .== 0)
@printf("%2i | %10s | %5i | %5i | %5.2f%%\n", N, "biased", v1, v0, 100 * v1 / nrep)

v = collect(unbiased(biased) for __ in 1:nrep)
v1, v0 = count(v .== 1), count(v .== 0)
@printf("%2i | %10s | %5i | %5i | %5.2f%%\n", N, "unbiased", v1, v0, 100 * v1 / nrep)
end
```
Output:
``` N | bias./unb. |    1s |    0s | pct ratio
3 |     biased |  3286 |  6714 | 32.86%
3 |   unbiased |  4986 |  5014 | 49.86%
4 |     biased |  2473 |  7527 | 24.73%
4 |   unbiased |  4986 |  5014 | 49.86%
5 |     biased |  1992 |  8008 | 19.92%
5 |   unbiased |  5121 |  4879 | 51.21%
6 |     biased |  1663 |  8337 | 16.63%
6 |   unbiased |  5040 |  4960 | 50.40%```

## Kotlin

Translation of: Java
```// version 1.1.2

fun biased(n: Int) = Math.random() < 1.0 / n

fun unbiased(n: Int): Boolean {
var a: Boolean
var b: Boolean
do {
a = biased(n)
b = biased(n)
}
while (a == b)
return a
}

fun main(args: Array<String>) {
val m = 50_000
val f = "%d: %2.2f%%  %2.2f%%"
for (n in 3..6) {
var c1 = 0
var c2 = 0
for (i in 0 until m) {
if (biased(n)) c1++
if (unbiased(n)) c2++
}
println(f.format(n, 100.0 * c1 / m, 100.0 * c2 / m))
}
}
```

Sample output:

```3: 33.19%  50.19%
4: 25.29%  49.85%
5: 19.91%  50.07%
6: 16.71%  50.14%
```

## Lua

```local function randN(n)
return function()
if math.random() < 1/n then return 1 else return 0 end
end
end

local function unbiased(n)
local biased = randN (n)
return function()
local a, b = biased(), biased()
while a==b do
a, b = biased(), biased()
end
return a
end
end

local function demonstrate (samples)
for n = 3, 6 do
biased = randN(n)
unbias = unbiased(n)
local bcounts = {=0,=0}
local ucounts = {=0,=0}
for i=1, samples do
local bnum = biased()
local unum = unbias()
bcounts[bnum] = bcounts[bnum]+1
ucounts[unum] = ucounts[unum]+1
end
print(string.format("N = %d",n),
"# 0", "# 1",
"% 0", "% 1")
print("biased", bcounts, bcounts,
bcounts / samples * 100,
bcounts / samples * 100)
print("unbias", ucounts, ucounts,
ucounts / samples * 100,
ucounts / samples * 100)
end
end

demonstrate(100000)
```

Output:

```N = 3	# 0	# 1	% 0	% 1
biased	66832	33168	66.832	33.168
unbias	50207	49793	50.207	49.793
N = 4	# 0	# 1	% 0	% 1
biased	75098	24902	75.098	24.902
unbias	49872	50128	49.872	50.128
N = 5	# 0	# 1	% 0	% 1
biased	80142	19858	80.142	19.858
unbias	50049	49951	50.049	49.951
N = 6	# 0	# 1	% 0	% 1
biased	83407	16593	83.407	16.593
unbias	49820	50180	49.82	50.18
```

## Mathematica/Wolfram Language

```rand[bias_, n_] := 1 - Unitize@RandomInteger[bias - 1, n]
unbiased[bias_, n_] := DeleteCases[rand[bias, {n, 2}], {a_, a_}][[All, 1]]
count = 1000000;
TableForm[
Table[{n, Total[rand[n, count]]/count // N,
Total[#]/Length[#] &@unbiased[n, count] // N}, {n, 3, 6}],
TableHeadings -> {None, {n, "biased", "unbiased"}}]
```
Output:
```n	biased	unbiased
3	0.33312	0.500074
4	0.24932	0.499883
5	0.1998 	0.498421
6	0.16620	0.49805```

## NetRexx

Translation of: Java
```/* NetRexx */
options replace format comments java crossref symbols binary

runSample(arg)
return

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method biased(n = int) public static returns boolean
return Math.random() < 1.0 / n

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method unbiased(n = int) public static returns boolean
a = boolean
b = boolean
loop until a \= b
a = biased(n)
b = biased(n)
end
return a

-- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
method runSample(arg) private static
parse arg Mx .
if Mx.length <= 0 then Mx = 50000
M = int Mx
loop n = int 3 to 6
c1 = int 0
c2 = int 0
loop for M
if biased(n)   then c1 = c1 + 1
if unbiased(n) then c2 = c2 + 1
end
say Rexx(n).right(3)':' Rexx(100.0 * c1 / M).format(6, 2)'%' Rexx(100.0 * c2 / M).format(6, 2)'%'
end n
return
```

Output:

```  3:     32.78%     49.98%
4:     24.72%     50.31%
5:     19.95%     50.34%
6:     17.20%     50.20%
```

## Nim

Translation of: Python
```import random, sequtils, strformat

type randProc = proc: range[0..1]

randomize()

proc randN(n: Positive): randProc =
result = proc: range[0..1] = ord(rand(n) == 0)

proc unbiased(biased: randProc): range[0..1] =
result = biased()
var that = biased()
while result == that:
result = biased()
that = biased()

for n in 3..6:
var biased = randN(n)
var v = newSeqWith(1_000_000, biased())
var cnt0, cnt1 = 0
for x in v:
if x == 0: inc cnt0 else: inc cnt1
echo &"Biased({n}) → count1 = {cnt1}, count0 = {cnt0}, percent = {100*cnt1 / (cnt1+cnt0):.3f}"

v = newSeqWith(1_000_000, unbiased(biased))
cnt0 = 0
cnt1 = 0
for x in v:
if x == 0: inc cnt0 else: inc cnt1
echo &"Unbiased  → count1 = {cnt1}, count0 = {cnt0}, percent = {100*cnt1 / (cnt1+cnt0):.3f}"
```
Output:
```Biased(3) → count1 = 249654, count0 = 750346, percent = 24.965
Unbiased  → count1 = 498631, count0 = 501369, percent = 49.863
Biased(4) → count1 = 200117, count0 = 799883, percent = 20.012
Unbiased  → count1 = 499425, count0 = 500575, percent = 49.943
Biased(5) → count1 = 167218, count0 = 832782, percent = 16.722
Unbiased  → count1 = 500020, count0 = 499980, percent = 50.002
Biased(6) → count1 = 143388, count0 = 856612, percent = 14.339
Unbiased  → count1 = 500378, count0 = 499622, percent = 50.038```

## OCaml

```let randN n =
if Random.int n = 0 then 1 else 0

let rec unbiased n =
let a = randN n in
if a <> randN n then a else unbiased n

let () =
Random.self_init();
let n = 50_000 in
for b = 3 to 6 do
let cb = ref 0 in
let cu = ref 0 in
for i = 1 to n do
cb := !cb + (randN b);
cu := !cu + (unbiased b);
done;
Printf.printf "%d: %5.2f%%  %5.2f%%\n"
b (100.0 *. float !cb /. float n) (100.0 *. float !cu /. float n)
done
```

Output:

```3: 33.07%  49.90%
4: 25.11%  49.85%
5: 19.82%  50.09%
6: 16.51%  50.51%```

## PARI/GP

GP's random number generation is high-quality, using Brent's XORGEN. Thus this program is slow: the required 400,000 unbiased numbers generated through this bias/unbias scheme take nearly a second. This requires about two million calls to `random`, which in turn generate a total of about three million calls to the underlying random number generator through the rejection strategy. The overall efficiency of the scheme is 0.8% for 32-bit and 0.4% for 64-bit...

```randN(N)=!random(N);
unbiased(N)={
my(a,b);
while(1,
a=randN(N);
b=randN(N);
if(a!=b, return(a))
)
};
for(n=3,6,print(n"\t"sum(k=1,1e5,unbiased(n))"\t"sum(k=1,1e5,randN(n))))```

Output:

```3	49997	33540
4	49988	24714
5	50143	20057
6	49913	16770```

## Perl

```sub randn {
my \$n = shift;
return int(rand(\$n) / (\$n - 1));
}

for my \$n (3 .. 6) {
print "Bias \$n: ";
my (@raw, @fixed);
for (1 .. 10000) {
my \$x = randn(\$n);
\$raw[\$x]++;
\$fixed[\$x]++    if randn(\$n) != \$x
}
print "@raw, ";
printf("%3g+-%.3g%%\tfixed: ", \$raw/100,
100 * sqrt(\$raw * \$raw) / (\$raw + \$raw)**1.5);
print "@fixed, ";
printf("%3g+-%.3g%%\n", 100*\$fixed/(\$fixed + \$fixed),
100 * sqrt(\$fixed * \$fixed) / (\$fixed + \$fixed)**1.5);

}
```

Output:

```Bias 3: 6684 3316, 66.84+-0.471%        fixed: 2188 2228, 49.5471+-0.752%
Bias 4: 7537 2463, 75.37+-0.431%        fixed: 1924 1845, 51.048+-0.814%
Bias 5: 7993 2007, 79.93+-0.401%        fixed: 1564 1597, 49.478+-0.889%
Bias 6: 8309 1691, 83.09+-0.375%        fixed: 1403 1410, 49.8756+-0.943%```

## Phix

```with javascript_semantics
function randN(integer N)
return rand(N) = 1
end function

function unbiased(integer N)
while true do
integer a = randN(N)
if a!=randN(N) then
return a
end if
end while
end function

constant n = 100000
for b=3 to 6 do
integer cb = 0,
cu = 0
for i=1 to n do
cb += randN(b)
cu += unbiased(b)
end for
printf(1, "%d: biased:%.0f%%  unbiased:%.0f%%\n", {b,(cb/n)*100,(cu/n)*100})
end for
```
Output:

(Rounded to the nearest whole percent, of course)

```3: biased:33%  unbiased:50%
4: biased:25%  unbiased:50%
5: biased:20%  unbiased:50%
6: biased:17%  unbiased:50%
```

## PicoLisp

```(de randN (N)
(if (= 1 (rand 1 N)) 1 0) )

(de unbiased (N)
(use (A B)
(while
(=
(setq A (randN N))
(setq B (randN N)) ) )
A ) )```

Test:

```(for N (range 3 6)
(tab (2 1 7 2 7 2)
N ":"
(format
(let S 0 (do 10000 (inc 'S (randN N))))
2 )
"%"
(format
(let S 0 (do 10000 (inc 'S (unbiased N))))
2 )
"%" ) )```

Output:

``` 3:  33.21 %  50.48 %
4:  25.06 %  49.79 %
5:  20.04 %  49.75 %
6:  16.32 %  49.02 %```

## PL/I

```test: procedure options (main); /* 20 Nov. 2012 */

randN: procedure(N) returns (bit (1));
declare N fixed (1);
declare random builtin;
declare r fixed (2) external initial (-1);
if r >= 0 then do; r = r-1; return ('0'b); end;
r = random()*2*N;
return ('1'b);
end randN;

random: procedure returns (bit(1));
declare (r1, r2) bit (1);
do until (r1 ^= r2);
r1 = randN(N); r2 = randN(N);
end;
return (r1);
end random;

declare (biasedrn, unbiasedrn) (100) bit (1);
declare N fixed (1);

put ('N     Biased  Unbiased (tally of 100 random numbers)');
do N = 3 to 6;
biasedrn = randN(N); unbiasedrn = random;
put skip edit (N, sum(biasedrn), sum(unbiasedrn)) (F(1), 2 F(10));
end;

end test;```

Results:

```N     Biased  Unbiased (tally of 100 random numbers)
3        24        42
4        18        47
5        16        41
6        11        53
```

## PowerShell

Works with: PowerShell version 2
```function randN ( [int]\$N )
{
[int]( ( Get-Random -Maximum \$N ) -eq 0 )
}

function unbiased ( [int]\$N )
{
do  {
\$X = randN \$N
\$Y = randN \$N
}
While ( \$X -eq \$Y )

return \$X
}
```

Note: The [pscustomobject] type accelerator, used to simplify making the test output look pretty, requires version 3.0 or higher.

```\$Tests = 1000
ForEach ( \$N in 3..6 )
{
\$Biased   = 0
\$Unbiased = 0

ForEach ( \$Test in 1..\$Tests )
{
\$Biased   += randN \$N
\$Unbiased += unbiased \$N
}
[pscustomobject]@{ N = \$N
"Biased Ones out of \$Test" = \$Biased
"Unbiased Ones out of \$Test" = \$Unbiased }
}
```
Output:
```N Biased Ones out of 1000 Unbiased Ones out of 1000
- ----------------------- -------------------------
3                     322                       503
4                     273                       518
5                     217                       515
6                     173                       486
```

## PureBasic

```Procedure biased(n)
If Random(n) <> 1
ProcedureReturn 0
EndIf
ProcedureReturn 1
EndProcedure

Procedure unbiased(n)
Protected a, b
Repeat
a = biased(n)
b = biased(n)
Until a <> b
ProcedureReturn a
EndProcedure

#count = 100000

Define n, m, output.s
For n = 3 To 6
Dim b_count(1)
Dim u_count(1)
For m = 1 To #count
x = biased(n)
b_count(x) + 1
x = unbiased(n)
u_count(x) + 1
Next
output + "N = " + Str(n) + #LF\$
output + "  biased =>" + #tab\$ + "#0=" + Str(b_count(0)) + #tab\$ + "#1=" +Str(b_count(1))
output + #tab\$ + " ratio=" + StrF(b_count(1) / #count * 100, 2) + "%" + #LF\$
output + "  unbiased =>" + #tab\$ + "#0=" + Str(u_count(0)) + #tab\$ + "#1=" + Str(u_count(1))
output + #tab\$ + " ratio=" + StrF(u_count(1) / #count * 100, 2) + "%" + #LF\$
Next
MessageRequester("Biased and Unbiased random number results", output)
```

Sample output:

```---------------------------
Biased and Unbiased random number results
---------------------------
N = 3
biased =>	#0=74856	#1=25144	 ratio=25.14%
unbiased =>	#0=50066	#1=49934	 ratio=49.93%
N = 4
biased =>	#0=80003	#1=19997	 ratio=20.00%
unbiased =>	#0=49819	#1=50181	 ratio=50.18%
N = 5
biased =>	#0=83256	#1=16744	 ratio=16.74%
unbiased =>	#0=50268	#1=49732	 ratio=49.73%
N = 6
biased =>	#0=85853	#1=14147	 ratio=14.15%
unbiased =>	#0=49967	#1=50033	 ratio=50.03%```

## Python

```from __future__ import print_function
import random

def randN(N):
" 1,0 random generator factory with 1 appearing 1/N'th of the time"
return lambda: random.randrange(N) == 0

def unbiased(biased):
'uses a biased() generator of 1 or 0, to create an unbiased one'
this, that = biased(), biased()
while this == that: # Loop until 10 or 01
this, that = biased(), biased()
return this         # return the first

if __name__ == '__main__':
from collections import namedtuple

Stats = namedtuple('Stats', 'count1 count0 percent')

for N in range(3, 7):
biased = randN(N)
v = [biased() for x in range(1000000)]
v1, v0 = v.count(1), v.count(0)
print ( "Biased(%i)  = %r" % (N, Stats(v1, v0, 100. * v1/(v1 + v0))) )

v = [unbiased(biased) for x in range(1000000)]
v1, v0 = v.count(1), v.count(0)
print ( "  Unbiased = %r" % (Stats(v1, v0, 100. * v1/(v1 + v0)), ) )
```

Sample output

```Biased(3)  = Stats(count1=331800, count0=668200, percent=33.18)
Unbiased = Stats(count1=499740, count0=500260, percent=49.973999999999997)
Biased(4)  = Stats(count1=249770, count0=750230, percent=24.977)
Unbiased = Stats(count1=499707, count0=500293, percent=49.970700000000001)
Biased(5)  = Stats(count1=199764, count0=800236, percent=19.976400000000002)
Unbiased = Stats(count1=499456, count0=500544, percent=49.945599999999999)
Biased(6)  = Stats(count1=167561, count0=832439, percent=16.7561)
Unbiased = Stats(count1=499963, count0=500037, percent=49.996299999999998)```

## Quackery

```  \$ "bigrat.qky" loadfile

[ random 0 = ]                  is randN      ( n --> n )

[ dup randN
over randN
2dup = iff
2drop again
drop nip ]                    is unbias     ( n --> n )

[ dup echo say " biased   --> "
0
1000000 times
[ over randN if 1+ ]
nip 1000000 6 point\$ echo\$ ]  is showbias   ( n -->   )

[ dup echo say " unbiased --> "
0
1000000 times
[ over unbias if 1+ ]
nip 1000000 6 point\$ echo\$ ]  is showunbias ( n -->   )

' [ 3 4 5 6 ]
witheach
[ dup cr
showbias cr
showunbias cr ]```
Output:
```3 biased   --> 0.333225
3 unbiased --> 0.500147

4 biased   --> 0.249658
4 unbiased --> 0.499851

5 biased   --> 0.200169
5 unbiased --> 0.500073

6 biased   --> 0.166804
6 unbiased --> 0.499045
```

## R

```randN = function(N) sample.int(N, 1) == 1

unbiased = function(f)
{while ((x <- f()) == f()) {}
x}

samples = 10000
print(t(round(d = 2, sapply(3:6, function(N) c(
N = N,
biased = mean(replicate(samples, randN(N))),
unbiased = mean(replicate(samples, unbiased(function() randN(N)))))))))
```

Sample output:

```     N biased unbiased
[1,] 3   0.32     0.50
[2,] 4   0.24     0.50
[3,] 5   0.21     0.49
[4,] 6   0.16     0.51```

## Racket

```#lang racket
;; Using boolean #t/#f instead of 1/0
(define ((randN n)) (zero? (random n)))
(define ((unbiased biased))
(let loop () (let ([r (biased)]) (if (eq? r (biased)) (loop) r))))

;; Counts
(define N 1000000)
(for ([n (in-range 3 7)])
(define (try% R) (round (/ (for/sum ([i N]) (if (R) 1 0)) N 1/100)))
(define biased (randN n))
(printf "Count: ~a => Biased: ~a%; Unbiased: ~a%.\n"
n (try% biased) (try% (unbiased biased))))
```
Output:
```Count: 3 => Biased: 33%; Unbiased: 50%.
Count: 4 => Biased: 25%; Unbiased: 50%.
Count: 5 => Biased: 20%; Unbiased: 50%.
Count: 6 => Biased: 17%; Unbiased: 50%.
```

## Raku

(formerly Perl 6)

Translation of: Perl
Works with: Rakudo version 2020.08.1
```sub randN ( \$n where 3..6 ) {
return ( \$n.rand / (\$n - 1) ).Int;
}

sub unbiased ( \$n where 3..6 ) {
my \$n1;
repeat { \$n1 = randN(\$n) } until \$n1 != randN(\$n);
return \$n1;
}

my \$iterations = 1000;
for 3 .. 6 -> \$n {
my ( @raw, @fixed );
for ^\$iterations {
@raw[      randN(\$n) ]++;
@fixed[ unbiased(\$n) ]++;
}
printf "N=%d   randN: %s, %4.1f%%   unbiased: %s, %4.1f%%\n",
\$n, map { .raku, . * 100 / \$iterations }, @raw, @fixed;
}
```
Output:
```N=3   randN: [676, 324], 32.4%   unbiased: [517, 483], 48.3%
N=4   randN: [734, 266], 26.6%   unbiased: [489, 511], 51.1%
N=5   randN: [792, 208], 20.8%   unbiased: [494, 506], 50.6%
N=6   randN: [834, 166], 16.6%   unbiased: [514, 486], 48.6%```

## REXX

```/*REXX program generates  unbiased random numbers  and displays the results to terminal.*/
parse arg # R seed .                             /*obtain optional arguments from the CL*/
if #==''  |  #==","     then #=1000              /*#:  the number of SAMPLES to be used.*/
if R==''  |  R==","     then R=6                 /*R:  the high number for the  range.  */
if datatype(seed, 'W')  then call random ,,seed  /*Specified?  Then use for RANDOM seed.*/
dash='─';    @b="biased";         @ub='un'@b     /*literals for the SAY column headers. */
say left('',5)   ctr("N",5)   ctr(@b)   ctr(@b'%')  ctr(@ub)  ctr(@ub"%")   ctr('samples')
dash=
do N=3  to R;      b=0;                u=0
do j=1  for #;   b=b + randN(N);     u=u + unbiased()
end   /*j*/
say  left('', 5)     ctr(N, 5)     ctr(b)    pct(b)    ctr(u)    pct(u)    ctr(#)
end     /*N*/
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
ctr:       return center( arg(1), word(arg(2) 12, 1), left(dash, 1)) /*show hdr│numbers.*/
pct:       return ctr( format(arg(1) / # * 100, , 2)'%' )            /*2 decimal digits.*/
randN:     parse arg z;            return random(1, z)==z            /*ret 1 if rand==Z.*/
unbiased:  do  until x\==randN(N); x=randN(N);  end;       return x  /* "  unbiased RAND*/
```
output   when using the default inputs:
```      ──N── ───biased─── ──biased%─── ──unbiased── ─unbiased%── ──samples───
3       348         34.80%        541         54.10%        1000
4       259         25.90%        479         47.90%        1000
5       188         18.80%        475         47.50%        1000
6       178         17.80%        488         48.80%        1000
```
output   when using the input of:   10000
```      ──N── ───biased─── ──biased%─── ──unbiased── ─unbiased%── ──samples───
3       3435        34.35%        4995        49.95%       10000
4       2535        25.35%        4957        49.57%       10000
5       2019        20.19%        4958        49.58%       10000
6       1644        16.44%        4982        49.82%       10000
```
output   when using the input of:   100000   30
```      ──N── ───biased─── ──biased%─── ──unbiased── ─unbiased%── ──samples───
3      33301        33.30%       50066        50.07%       100000
4      25359        25.36%       49401        49.40%       100000
5      20026        20.03%       49966        49.97%       100000
6      16579        16.58%       49956        49.96%       100000
7      14294        14.29%       50008        50.01%       100000
8      12402        12.40%       50479        50.48%       100000
9      11138        11.14%       50099        50.10%       100000
10       9973        9.97%        49988        49.99%       100000
11       9062        9.06%        50009        50.01%       100000
12       8270        8.27%        49929        49.93%       100000
13       7704        7.70%        49876        49.88%       100000
14       7223        7.22%        50414        50.41%       100000
15       6725        6.73%        50043        50.04%       100000
16       6348        6.35%        50252        50.25%       100000
17       5900        5.90%        49977        49.98%       100000
18       5583        5.58%        49991        49.99%       100000
19       5139        5.14%        49958        49.96%       100000
20       4913        4.91%        50198        50.20%       100000
21       4714        4.71%        49892        49.89%       100000
22       4517        4.52%        49760        49.76%       100000
23       4226        4.23%        50021        50.02%       100000
24       4174        4.17%        50141        50.14%       100000
25       4005        4.01%        49816        49.82%       100000
26       3890        3.89%        49819        49.82%       100000
27       3705        3.71%        50036        50.04%       100000
28       3567        3.57%        49665        49.67%       100000
29       3481        3.48%        50094        50.09%       100000
30       3355        3.36%        49831        49.83%       100000
```

## Ring

```for n = 3 to 6
biased = 0
unb = 0
for i = 1 to 10000
biased += randN(n)
unb += unbiased(n)
next
see "N = " + n + " : biased = " + biased/100  + "%, unbiased = " + unb/100 + "%" + nl
next

func unbiased nr
while 1
a = randN(nr)
if a != randN(nr) return a ok
end

func randN m
m = (random(m) = 1)
return m```

Output:

```N = 3 : biased = 25.38%, unbiased = 50.12%
N = 4 : biased = 20.34%, unbiased = 49.17%
N = 5 : biased = 16.65%, unbiased = 48.86%
N = 6 : biased = 13.31%, unbiased = 49.96%
```

## RPL

```≪ INV RAND ≥ ≫ ‘RandN’ STO

≪ 0 DUP WHILE DUP2 == REPEAT
DROP2 DUP RandN OVER RandN
END ROT DROP2
≫ ‘Unbiased’ STO

≪ 3 6 FOR n
(0,0) 1 10000 START
n RandN + n Unbiased i * →NUM +
NEXT 10000 / NEXT
≫ ‘SHOW’ STO
```
Input:
```SHOW
```
Output:
```4: (0.3272,0.4976)
3: (0.2504,0.4961)
2: (0.201,0.5008)
1: (0.166,0.4952)
```

## Ruby

```def rand_n(bias)
rand(bias) == 0 ? 1 : 0
end

def unbiased(bias)
a, b = rand_n(bias), rand_n(bias) until a != b #loop until a and b are 0,1 or 1,0
a
end

runs = 1_000_000
keys = %i(bias biased unbiased) #use [:bias,:biased,:unbiased] in Ruby < 2.0
puts keys.join("\t")

(3..6).each do |bias|
counter = Hash.new(0) # counter will respond with 0 when key is not known
runs.times do
counter[:biased] += 1 if rand_n(bias) == 1 #the first time, counter has no key for :biased, so it will respond 0
counter[:unbiased] += 1 if unbiased(bias) == 1
end
counter[:bias] = bias
puts counter.values_at(*keys).join("\t")
end
```
Output:
```bias	biased	unbiased
3	333043	500161
4	249133	499393
5	199767	500354
6	166163	499809
```

## Rust

```#![feature(inclusive_range_syntax)]

extern crate rand;

use rand::Rng;

fn rand_n<R: Rng>(rng: &mut R, n: u32) -> usize {
rng.gen_weighted_bool(n) as usize // maps `false` to 0 and `true` to 1
}

fn unbiased<R: Rng>(rng: &mut R, n: u32) -> usize {
let mut bit = rand_n(rng, n);
while bit == rand_n(rng, n) {
bit = rand_n(rng, n);
}
bit
}

fn main() {
const SAMPLES: usize = 100_000;
let mut rng = rand::weak_rng();

println!(" Bias    rand_n  unbiased");
for n in 3..=6 {
let mut count_biased = 0;
let mut count_unbiased = 0;
for _ in 0..SAMPLES {
count_biased += rand_n(&mut rng, n);
count_unbiased += unbiased(&mut rng, n);
}

let b_percentage = 100.0 * count_biased as f64 / SAMPLES as f64;
let ub_percentage = 100.0 * count_unbiased as f64 / SAMPLES as f64;
println!(
"bias {}:  {:0.2}%   {:0.2}%",
n, b_percentage, ub_percentage
);
}
}
```
Output:
``` Bias    rand_n  unbiased
bias 3:  33.32%   49.80%
bias 4:  25.22%   50.16%
bias 5:  19.91%   50.00%
bias 6:  16.66%   49.95%
```

## Scala

```def biased( n:Int ) = scala.util.Random.nextFloat < 1.0 / n

def unbiased( n:Int ) = { def loop : Boolean = { val a = biased(n); if( a != biased(n) ) a else loop }; loop }

for( i <- (3 until 7) ) println {

val m = 50000
var c1,c2 = 0

(0 until m) foreach { j => if( biased(i) ) c1 += 1; if( unbiased(i) ) c2 += 1 }

"%d: %2.2f%%  %2.2f%%".format(i, 100.0*c1/m, 100.0*c2/m)
}
```
Output:
```3: 33.09%  49.79%
4: 24.92%  49.92%
5: 19.75%  49.92%
6: 16.67%  50.23%```

## Seed7

```\$ include "seed7_05.s7i";
include "float.s7i";

const func integer: randN (in integer: n) is
return ord(rand(1, n) = 1);

const func integer: unbiased (in integer: n) is func
result
var integer: unbiased is 0;
begin
repeat
unbiased := randN(n);
until unbiased <> randN(n);
end func;

const proc: main is func
local
const integer: tests is 50000;
var integer: n is 0;
var integer: sumBiased is 0;
var integer: sumUnbiased is 0;
var integer: count is 0;
begin
for n range 3 to 6 do
sumBiased := 0;
sumUnbiased := 0;
for count range 1 to tests do
sumBiased +:= randN(n);
sumUnbiased +:= unbiased(n);
end for;
writeln(n <& ": " <& flt(100 * sumBiased) / flt(tests) digits 3 lpad 6 <&
"  " <& flt(100 * sumUnbiased) / flt(tests) digits 3 lpad 6);
end for;
end func;```

Output:

```3: 33.004  50.024
4: 25.158  50.278
5: 20.186  49.978
6: 16.570  49.936
```

## Sidef

Translation of: Raku
```func randN (n) {
n.rand / (n-1) -> int
}

func unbiased(n) {
var n1 = nil
do { n1 = randN(n) } while (n1 == randN(n))
return n1
}

var iterations = 1000

for n in (3..6) {
var raw = []
var fixed = []
iterations.times {
raw[    randN(n) ] := 0 ++
fixed[ unbiased(n) ] := 0 ++
}
printf("N=%d   randN: %s, %4.1f%%   unbiased: %s, %4.1f%%\n",
n, [raw, fixed].map {|a| (a.dump, a * 100 / iterations) }...)
}
```
Output:
```N=3   randN: [661, 339], 33.9%   unbiased: [497, 503], 50.3%
N=4   randN: [765, 235], 23.5%   unbiased: [493, 507], 50.7%
N=5   randN: [812, 188], 18.8%   unbiased: [509, 491], 49.1%
N=6   randN: [820, 180], 18.0%   unbiased: [510, 490], 49.0%
```

## Tcl

```# 1,0 random generator factory with 1 appearing 1/N'th of the time
proc randN n {expr {rand()*\$n < 1}}

# uses a biased generator of 1 or 0, to create an unbiased one
proc unbiased {biased} {
while 1 {
if {[set a [eval \$biased]] != [eval \$biased]} {return \$a}
}
}

for {set n 3} {\$n <= 6} {incr n} {
set biased [list randN \$n]
for {set i 0;array set c {0 0 1 0}} {\$i < 1000000} {incr i} {
incr c([eval \$biased])
}
puts [format "  biased %d => #0=%d #1=%d ratio=%.2f%%" \$n \$c(0) \$c(1) \
[expr {100.*\$c(1)/\$i}]]
for {set i 0;array set c {0 0 1 0}} {\$i < 1000000} {incr i} {
incr c([unbiased \$biased])
}
puts [format "unbiased %d => #0=%d #1=%d ratio=%.2f%%" \$n \$c(0) \$c(1) \
[expr {100.*\$c(1)/\$i}]]
}
```

Sample output:

```  biased 3 => #0=667076 #1=332924 ratio=33.29%
unbiased 3 => #0=500263 #1=499737 ratio=49.97%
biased 4 => #0=750470 #1=249530 ratio=24.95%
unbiased 4 => #0=500644 #1=499356 ratio=49.94%
biased 5 => #0=800243 #1=199757 ratio=19.98%
unbiased 5 => #0=500878 #1=499122 ratio=49.91%
biased 6 => #0=833623 #1=166377 ratio=16.64%
unbiased 6 => #0=500518 #1=499482 ratio=49.95%
```

## Visual Basic .NET

Translation of: C#
```Module Module1
Dim random As New Random()

Function RandN(n As Integer) As Boolean
Return random.Next(0, n) = 0
End Function

Function Unbiased(n As Integer) As Boolean
Dim flip1 As Boolean
Dim flip2 As Boolean

Do
flip1 = RandN(n)
flip2 = RandN(n)
Loop While flip1 = flip2

Return flip1
End Function

Sub Main()
For n = 3 To 6
Dim biasedZero = 0
Dim biasedOne = 0
Dim unbiasedZero = 0
Dim unbiasedOne = 0
For i = 1 To 100000
If RandN(n) Then
biasedOne += 1
Else
biasedZero += 1
End If
If Unbiased(n) Then
unbiasedOne += 1
Else
unbiasedZero += 1
End If
Next

Console.WriteLine("(N = {0}):".PadRight(17) + "# of 0" + vbTab + "# of 1" + vbTab + "% of 0" + vbTab + "% of 1", n)
Console.WriteLine("(Biased: {0}):".PadRight(15) + "{0}" + vbTab + "{1}" + vbTab + "{2}" + vbTab + "{3}", biasedZero, biasedOne, biasedZero / 1000, biasedOne / 1000)
Console.WriteLine("(UnBiased: {0}):".PadRight(15) + "{0}" + vbTab + "{1}" + vbTab + "{2}" + vbTab + "{3}", unbiasedZero, unbiasedOne, unbiasedZero / 1000, unbiasedOne / 1000)
Next
End Sub

End Module
```
Output:
```(N = 3):       # of 0   # of 1  % of 0  % of 1
(Biased: 66844): 66844  33156   66.844  33.156
(UnBiased: 50081):50081 49919   50.081  49.919
(N = 4):       # of 0   # of 1  % of 0  % of 1
(Biased: 74827): 74827  25173   74.827  25.173
(UnBiased: 50095):50095 49905   50.095  49.905
(N = 5):       # of 0   # of 1  % of 0  % of 1
(Biased: 79878): 79878  20122   79.878  20.122
(UnBiased: 50544):50544 49456   50.544  49.456
(N = 6):       # of 0   # of 1  % of 0  % of 1
(Biased: 83449): 83449  16551   83.449  16.551
(UnBiased: 49907):49907 50093   49.907  50.093```

## Wren

Translation of: Kotlin
Library: Wren-fmt
```import "random" for Random
import "/fmt" for Fmt

var rand = Random.new()

var biased = Fn.new { |n| rand.float() < 1 / n }

var unbiased = Fn.new { |n|
while (true) {
var a = biased.call(n)
var b = biased.call(n)
if (a != b) return a
}
}

var m = 50000
var f = "\$d: \$2.2f\%  \$2.2f\%"
for (n in 3..6) {
var c1 = 0
var c2 = 0
for (i in 0...m) {
if (biased.call(n)) c1 = c1 + 1
if (unbiased.call(n)) c2 = c2 + 1
}
Fmt.print(f, n, 100 * c1 / m, 100 * c2 / m)
}
```
Output:

Sample output:

```3: 33.36%  49.91%
4: 24.80%  49.89%
5: 20.07%  49.95%
6: 16.64%  50.17%
```

## zkl

```fcn randN(N){ (not (0).random(N)).toInt() }
fcn unbiased(randN){ while((a:=randN())==randN()){} a }```
```const Z=0d100_000;
foreach N in ([3..6]){
"%d: biased: %3.2f%%, unbiased: %3.2f%%".fmt(N,
(0).reduce(Z,'wrap(s,_){ s+randN(N) },0.0)/Z*100,
(0).reduce(Z,'wrap(s,_){ s+unbiased(randN.fp(N)) },0.0)/Z*100)
.println();
}```
Output:
```3: biased: 33.46%, unbiased: 49.80%
4: biased: 24.95%, unbiased: 50.01%
5: biased: 19.89%, unbiased: 50.18%
6: biased: 16.75%, unbiased: 50.22%
```