Seven-sided dice from five-sided dice
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
(Given an equal-probability generator of one of the integers 1 to 5
as dice5), create dice7 that generates a pseudo-random integer from
1 to 7 in equal probability using only dice5 as a source of random
numbers, and check the distribution for at least one million calls using the function created in Simple Random Distribution Checker.
Implementation suggestion:
dice7 might call dice5 twice, re-call if four of the 25
combinations are given, otherwise split the other 21 combinations
into 7 groups of three, and return the group index from the rolls.
(Task adapted from an answer here)
11l
<lang 11l>F dice5()
R random:(1..5)
F dice7() -> Int
V r = dice5() + dice5() * 5 - 6
R I r < 21 {(r % 7) + 1} E dice7()
F distcheck(func, repeats, delta)
V bin = DefaultDict[Int, Int]()
L 1..repeats
bin[func()]++
V target = repeats I/ bin.len
V deltacount = Int(delta / 100.0 * target)
assert(all(bin.values().map(count -> abs(@target - count) < @deltacount)), ‘Bin distribution skewed from #. +/- #.: #.’.format(target, deltacount, sorted(bin.items()).map((key, count) -> (key, @target - count))))
print(bin)
distcheck(dice5, 1000000, 1) distcheck(dice7, 1000000, 1)</lang>
- Output:
DefaultDict([1 = 199586, 2 = 200094, 3 = 198933, 4 = 200824, 5 = 200563]) DefaultDict([1 = 142478, 2 = 142846, 3 = 143056, 4 = 142894, 5 = 143052, 6 = 143147, 7 = 142527])
Ada
The specification of a package Random_57: <lang Ada>package Random_57 is
type Mod_7 is mod 7;
function Random7 return Mod_7;
-- a "fast" implementation, minimazing the calls to the Random5 generator
function Simple_Random7 return Mod_7;
-- a simple implementation
end Random_57;</lang> Implementation of Random_57: <lang Ada> with Ada.Numerics.Discrete_Random;
package body Random_57 is
type M5 is mod 5;
package Rand_5 is new Ada.Numerics.Discrete_Random(M5);
Gen: Rand_5.Generator;
function Random7 return Mod_7 is
N: Natural;
begin
loop
N := Integer(Rand_5.Random(Gen))* 5 + Integer(Rand_5.Random(Gen));
-- N is uniformly distributed in 0 .. 24
if N < 21 then
return Mod_7(N/3);
else -- (N-21) is in 0 .. 3
N := (N-21) * 5 + Integer(Rand_5.Random(Gen)); -- N is in 0 .. 19
if N < 14 then
return Mod_7(N / 2);
else -- (N-14) is in 0 .. 5
N := (N-14) * 5 + Integer(Rand_5.Random(Gen)); -- N is in 0 .. 29
if N < 28 then
return Mod_7(N/4);
else -- (N-28) is in 0 .. 1
N := (N-28) * 5 + Integer(Rand_5.Random(Gen)); -- 0 .. 9
if N < 7 then
return Mod_7(N);
else -- (N-7) is in 0, 1, 2
N := (N-7)* 5 + Integer(Rand_5.Random(Gen)); -- 0 .. 14
if N < 14 then
return Mod_7(N/2);
else -- (N-14) is 0. This is not useful for us!
null;
end if;
end if;
end if;
end if;
end if;
end loop;
end Random7;
function Simple_Random7 return Mod_7 is
N: Natural :=
Integer(Rand_5.Random(Gen))* 5 + Integer(Rand_5.Random(Gen));
-- N is uniformly distributed in 0 .. 24
begin
while N > 20 loop
N := Integer(Rand_5.Random(Gen))* 5 + Integer(Rand_5.Random(Gen));
end loop; -- Now I <= 20
return Mod_7(N / 3);
end Simple_Random7;
begin
Rand_5.Reset(Gen);
end Random_57;</lang> A main program, using the Random_57 package: <lang Ada>with Ada.Text_IO, Random_57;
procedure R57 is
use Random_57;
type Fun is access function return Mod_7;
function Rand return Mod_7 renames Random_57.Random7; -- change this to "... renames Random_57.Simple_Random;" if you like
procedure Test(Sample_Size: Positive; Rand: Fun; Precision: Float := 0.3) is
Counter: array(Mod_7) of Natural := (others => 0);
Expected: Natural := Sample_Size/7;
Small: Mod_7 := Mod_7'First;
Large: Mod_7 := Mod_7'First;
Result: Mod_7;
begin
Ada.Text_IO.New_Line;
Ada.Text_IO.Put_Line("Sample Size: " & Integer'Image(Sample_Size));
Ada.Text_IO.Put( " Bins:");
for I in 1 .. Sample_Size loop
Result := Rand.all;
Counter(Result) := Counter(Result) + 1;
end loop;
for J in Mod_7 loop
Ada.Text_IO.Put(Integer'Image(Counter(J)));
if Counter(J) < Counter(Small) then Small := J; end if;
if Counter(J) > Counter(Large) then Large := J; end if;
end loop;
Ada.Text_IO.New_Line;
Ada.Text_IO.Put_Line(" Small Bin:" & Integer'Image(Counter(Small)));
Ada.Text_IO.Put_Line(" Large Bin: " & Integer'Image(Counter(Large)));
if Float(Counter(Small)*7) * (1.0+Precision) < Float(Sample_Size) then
Ada.Text_IO.Put_Line("Failed! Small too small!");
elsif Float(Counter(Large)*7) * (1.0-Precision) > Float(Sample_Size) then
Ada.Text_IO.Put_Line("Failed! Large too large!");
else
Ada.Text_IO.Put_Line("Passed");
end if;
end Test;
begin
Test( 10_000, Rand'Access, 0.08); Test( 100_000, Rand'Access, 0.04); Test( 1_000_000, Rand'Access, 0.02); Test(10_000_000, Rand'Access, 0.01);
end R57;</lang>
- Output:
Sample Size: 10000 Bins: 1368 1404 1435 1491 1483 1440 1379 Small Bin: 1368 Large Bin: 1491 Passed Sample Size: 100000 Bins: 14385 14110 14362 14404 14362 14206 14171 Small Bin: 14110 Large Bin: 14404 Passed Sample Size: 1000000 Bins: 143765 142384 142958 142684 142799 142956 142454 Small Bin: 142384 Large Bin: 143765 Passed Sample Size: 10000000 Bins: 1429266 1428214 1428753 1427032 1428418 1428699 1429618 Small Bin: 1427032 Large Bin: 1429618 Passed
ALGOL 68
- note: This specimen retains the original C coding style.
C's version using no multiplications, divisions, or mod operators: <lang algol68>PROC dice5 = INT:
1 + ENTIER (5*random);
PROC mulby5 = (INT n)INT:
ABS (BIN n SHL 2) + n;
PROC dice7 = INT: (
INT d55 := 0; INT m := 1; WHILE m := ABS ((2r1 AND BIN m) SHL 2) + ABS (BIN m SHR 1); # repeats 4 - 2 - 1 # d55 := mulby5(mulby5(d55)) + mulby5(dice5) + dice5 - 6;
- WHILE # d55 < m DO SKIP OD;
m := 1; WHILE d55>0 DO d55 +:= m; m := ABS (BIN d55 AND 2r111); # modulas by 8 # d55 := ABS (BIN d55 SHR 3) # divide by 8 # OD; m
);
PROC distcheck = (PROC INT dice, INT count, upb)VOID: (
[upb]INT sum; FOR i TO UPB sum DO sum[i] := 0 OD;
FOR i TO count DO sum[dice]+:=1 OD;
FOR i TO UPB sum WHILE print(whole(sum[i],0)); i /= UPB sum DO print(", ") OD;
print(new line)
);
main: (
distcheck(dice5, 1000000, 5); distcheck(dice7, 1000000, 7)
)</lang>
- Output:
200598, 199852, 199939, 200602, 199009 143529, 142688, 142816, 142747, 142958, 142802, 142460
AutoHotkey
<lang AutoHotkey>dice5() { Random, v, 1, 5
Return, v
}
dice7() { Loop
{ v := 5 * dice5() + dice5() - 6
IfLess v, 21, Return, (v // 3) + 1
}
}</lang>
Distribution check: Total elements = 10000 Margin = 3% --> Lbound = 1386, Ubound = 1471 Bucket 1 contains 1450 elements. Bucket 2 contains 1374 elements. Skewed. Bucket 3 contains 1412 elements. Bucket 4 contains 1465 elements. Bucket 5 contains 1370 elements. Skewed. Bucket 6 contains 1485 elements. Skewed. Bucket 7 contains 1444 elements.
BBC BASIC
<lang bbcbasic> MAXRND = 7
FOR r% = 2 TO 5
check% = FNdistcheck(FNdice7, 10^r%, 0.1)
PRINT "Over "; 10^r% " runs dice7 ";
IF check% THEN
PRINT "failed distribution check with "; check% " bin(s) out of range"
ELSE
PRINT "passed distribution check"
ENDIF
NEXT
END
DEF FNdice7
LOCAL x% : x% = FNdice5 + 5*FNdice5
IF x%>26 THEN = FNdice7 ELSE = (x%+1) MOD 7 + 1
DEF FNdice5 = RND(5)
DEF FNdistcheck(RETURN func%, repet%, delta)
LOCAL i%, m%, r%, s%, bins%()
DIM bins%(MAXRND)
FOR i% = 1 TO repet%
r% = FN(^func%)
bins%(r%) += 1
IF r%>m% m% = r%
NEXT
FOR i% = 1 TO m%
IF bins%(i%)/(repet%/m%) > 1+delta s% += 1
IF bins%(i%)/(repet%/m%) < 1-delta s% += 1
NEXT
= s%</lang>
- Output:
Over 100 runs dice7 failed distribution check with 4 bin(s) out of range Over 1000 runs dice7 failed distribution check with 2 bin(s) out of range Over 10000 runs dice7 passed distribution check Over 100000 runs dice7 passed distribution check
C
<lang c>int rand5() { int r, rand_max = RAND_MAX - (RAND_MAX % 5); while ((r = rand()) >= rand_max); return r / (rand_max / 5) + 1; }
int rand5_7() { int r; while ((r = rand5() * 5 + rand5()) >= 27); return r / 3 - 1; }
int main() { printf(check(rand5, 5, 1000000, .05) ? "flat\n" : "not flat\n"); printf(check(rand7, 7, 1000000, .05) ? "flat\n" : "not flat\n"); return 0; }</lang>
- Output:
flat flat
C#
<lang csharp> using System;
public class SevenSidedDice {
Random random = new Random();
static void Main(string[] args)
{ SevenSidedDice sevenDice = new SevenSidedDice(); Console.WriteLine("Random number from 1 to 7: "+ sevenDice.seven());
Console.Read();
}
int seven() { int v=21; while(v>20) v=five()+five()*5-6; return 1+v%7; }
int five() {
return 1 + random.Next(5);
} }</lang>
C++
This solution tries to minimize calls to the underlying d5 by reusing information from earlier calls. <lang cpp>template<typename F> class fivetoseven { public:
fivetoseven(F f): d5(f), rem(0), max(1) {}
int operator()();
private:
F d5; int rem, max;
};
template<typename F>
int fivetoseven<F>::operator()()
{
while (rem/7 == max/7)
{
while (max < 7)
{
int rand5 = d5()-1;
max *= 5;
rem = 5*rem + rand5;
}
int groups = max / 7;
if (rem >= 7*groups)
{
rem -= 7*groups;
max -= 7*groups;
}
}
int result = rem % 7; rem /= 7; max /= 7; return result+1;
}
int d5() {
return 5.0*std::rand()/(RAND_MAX + 1.0) + 1;
}
fivetoseven<int(*)()> d7(d5);
int main() {
srand(time(0)); test_distribution(d5, 1000000, 0.001); test_distribution(d7, 1000000, 0.001);
}</lang>
Clojure
Uses the verify function defined in Verify distribution uniformity/Naive#Clojure <lang Clojure>(def dice5 #(rand-int 5))
(defn dice7 []
(quot (->> dice5 ; do the following to dice5
(repeatedly 2) ; call it twice
(apply #(+ %1 (* 5 %2))) ; d1 + 5*d2 => 0..24
#() ; wrap that up in a function
repeatedly ; make infinite sequence of the above
(drop-while #(> % 20)) ; throw away anything > 20
first) ; grab first acceptable element
3)) ; divide by three rounding down
(doseq [n [100 1000 10000] [num count okay?] (verify dice7 n)]
(println "Saw" num count "times:"
(if okay? "that's" " not") "acceptable"))</lang>
Saw 0 10 times: not acceptable Saw 1 19 times: not acceptable Saw 2 12 times: not acceptable Saw 3 15 times: that's acceptable Saw 4 11 times: not acceptable Saw 5 11 times: not acceptable Saw 6 22 times: not acceptable Saw 0 142 times: that's acceptable Saw 1 158 times: not acceptable Saw 2 151 times: that's acceptable Saw 3 153 times: that's acceptable Saw 4 118 times: not acceptable Saw 5 139 times: that's acceptable Saw 6 139 times: that's acceptable Saw 0 1498 times: that's acceptable Saw 1 1411 times: that's acceptable Saw 2 1436 times: that's acceptable Saw 3 1434 times: that's acceptable Saw 4 1414 times: that's acceptable Saw 5 1408 times: that's acceptable Saw 6 1399 times: that's acceptable
Common Lisp
<lang lisp>(defun d5 ()
(1+ (random 5)))
(defun d7 ()
(loop for d55 = (+ (* 5 (d5)) (d5) -6)
until (< d55 21)
finally (return (1+ (mod d55 7)))))</lang>
> (check-distribution 'd7 1000)
Distribution potentially skewed for 1: expected around 1000/7 got 153.
Distribution potentially skewed for 2: expected around 1000/7 got 119.
Distribution potentially skewed for 3: expected around 1000/7 got 125.
Distribution potentially skewed for 7: expected around 1000/7 got 156.
T
#<EQL Hash Table{7} 200B5A53>
> (check-distribution 'd7 10000)
NIL
#<EQL Hash Table{7} 200CB5BB>
D
<lang d>import std.random; import verify_distribution_uniformity_naive: distCheck;
/// Generates a random number in [1, 5]. int dice5() /*pure nothrow*/ @safe {
return uniform(1, 6);
}
/// Naive, generates a random number in [1, 7] using dice5. int fiveToSevenNaive() /*pure nothrow*/ @safe {
immutable int r = dice5() + dice5() * 5 - 6; return (r < 21) ? (r % 7) + 1 : fiveToSevenNaive();
}
/** Generates a random number in [1, 7] using dice5, minimizing calls to dice5.
- /
int fiveToSevenSmart() @safe {
static int rem = 0, max = 1;
while (rem / 7 == max / 7) {
while (max < 7) {
immutable int rand5 = dice5() - 1;
max *= 5;
rem = 5 * rem + rand5;
}
immutable int groups = max / 7;
if (rem >= 7 * groups) {
rem -= 7 * groups;
max -= 7 * groups;
}
}
immutable int result = rem % 7; rem /= 7; max /= 7; return result + 1;
}
void main() /*@safe*/ {
enum int N = 400_000; distCheck(&dice5, N, 1); distCheck(&fiveToSevenNaive, N, 1); distCheck(&fiveToSevenSmart, N, 1);
}</lang>
- Output:
1 80365 2 79941 3 80065 4 79784 5 79845 1 57186 2 57201 3 57180 4 57231 5 57124 6 56832 7 57246 1 57367 2 56869 3 57644 4 57111 5 57157 6 56809 7 57043
E
<lang e>def dice5() {
return entropy.nextInt(5) + 1
}
def dice7() {
var d55 := null
while ((d55 := 5 * dice5() + dice5() - 6) >= 21) {}
return d55 %% 7 + 1
}</lang> <lang e>def bins := ([0] * 7).diverge() for x in 1..1000 {
bins[dice7() - 1] += 1
} println(bins.snapshot())</lang>
Elixir
<lang elixir>defmodule Dice do
def dice5, do: :rand.uniform( 5 )
def dice7 do
dice7_from_dice5
end
defp dice7_from_dice5 do
d55 = 5*dice5 + dice5 - 6 # 0..24
if d55 < 21, do: rem( d55, 7 ) + 1,
else: dice7_from_dice5
end
end
fun5 = fn -> Dice.dice5 end IO.inspect VerifyDistribution.naive( fun5, 1000000, 3 ) fun7 = fn -> Dice.dice7 end IO.inspect VerifyDistribution.naive( fun7, 1000000, 3 )</lang>
- Output:
:ok :ok
Erlang
<lang Erlang> -module( dice ).
-export( [dice5/0, dice7/0, task/0] ).
dice5() -> random:uniform( 5 ).
dice7() -> dice7_small_enough( dice5() * 5 + dice5() - 6 ). % 0 - 24
task() ->
verify_distribution_uniformity:naive( fun dice7/0, 1000000, 1 ).
dice7_small_enough( N ) when N < 21 -> N div 3 + 1; dice7_small_enough( _N ) -> dice7(). </lang>
- Output:
76> dice:task(). ok
Factor
<lang factor>USING: kernel random sequences assocs locals sorting prettyprint
math math.functions math.statistics math.vectors math.ranges ;
IN: rosetta-code.dice7
! Output a random integer 1..5.
- dice5 ( -- x )
5 [1,b] random
! Output a random integer 1..7 using dice5 as randomness source.
- dice7 ( -- x )
0 [ dup 21 < ] [ drop dice5 5 * dice5 + 6 - ] do until 7 rem 1 +
! Roll the die by calling the quotation the given number of times and return ! an array with roll results. ! Sample call: 1000 [ dice7 ] roll
- roll ( times quot: ( -- x ) -- array )
[ call( -- x ) ] curry replicate
! Input array contains outcomes of a number of die throws. Each die result is ! an integer in the range 1..X. Calculate and return the number of each ! of the results in the array so that in the first position of the result ! there is the number of ones in the input array, in the second position ! of the result there is the number of twos in the input array, etc.
- count-dice-outcomes ( X array -- array )
histogram swap [1,b] [ over [ 0 or ] change-at ] each sort-keys values
! Verify distribution uniformity/Naive. Delta is the acceptable deviation ! from the ideal number of items in each bucket, expressed as a fraction of ! the total count. Sides is the number of die sides. Die-func is a word that ! produces a random number on stack in the range [1..sides], times is the ! number of times to call it. ! Sample call: 0.02 7 [ dice7 ] 100000 verify
- verify ( delta sides die-func: ( -- random ) times -- )
sides times die-func roll count-dice-outcomes dup . times sides / :> ideal-count ideal-count v-n vabs times v/n delta [ < ] curry all? [ "Random enough" . ] [ "Not random enough" . ] if
! Call verify with 1, 10, 100, ... 1000000 rolls of 7-sided die.
- verify-all ( -- )
{ 1 10 100 1000 10000 100000 1000000 }
[| times | 0.02 7 [ dice7 ] times verify ] each
- </lang>
- Output:
USE: rosetta-code.dice7 verify-all
{ 0 0 0 1 0 0 0 }
"Not random enough"
{ 0 2 3 1 1 1 2 }
"Not random enough"
{ 17 12 15 11 13 13 19 }
"Not random enough"
{ 140 130 141 148 143 155 143 }
"Random enough"
{ 1457 1373 1427 1433 1443 1382 1485 }
"Random enough"
{ 14225 14320 14216 14326 14415 14084 14414 }
"Random enough"
{ 142599 141910 142524 143029 143353 142696 143889 }
"Random enough"
Forth
<lang forth>require random.fs
- d5 5 random 1+ ;
- discard? 5 = swap 1 > and ;
- d7
begin d5 d5 2dup discard? while 2drop repeat 1- 5 * + 1- 7 mod 1+ ;</lang>
- Output:
cr ' d7 1000000 7 1 check-distribution . lower bound = 141429 upper bound = 144285 1 : 143241 ok 2 : 142397 ok 3 : 143522 ok 4 : 142909 ok 5 : 142001 ok 6 : 142844 ok 7 : 143086 ok -1
Fortran
<lang fortran>module rand_mod
implicit none
contains
function rand5()
integer :: rand5 real :: r
call random_number(r) rand5 = 5*r + 1
end function
function rand7()
integer :: rand7
do
rand7 = 5*rand5() + rand5() - 6
if (rand7 < 21) then
rand7 = rand7 / 3 + 1
return
end if
end do
end function end module
program Randtest
use rand_mod implicit none integer, parameter :: samples = 1000000 call distcheck(rand7, samples, 0.005) write(*,*) call distcheck(rand7, samples, 0.001)
end program</lang>
- Output:
Distribution Uniform Distribution potentially skewed for bucket 1 Expected: 142857 Actual: 143142 Distribution potentially skewed for bucket 2 Expected: 142857 Actual: 143454 Distribution potentially skewed for bucket 3 Expected: 142857 Actual: 143540 Distribution potentially skewed for bucket 4 Expected: 142857 Actual: 142677 Distribution potentially skewed for bucket 5 Expected: 142857 Actual: 142511 Distribution potentially skewed for bucket 6 Expected: 142857 Actual: 142163 Distribution potentially skewed for bucket 7 Expected: 142857 Actual: 142513
FreeBASIC
<lang freebasic> Function dice5() As Integer
Return Int(Rnd * 5) + 1
End Function
Function dice7() As Integer
Dim As Integer temp
Do
temp = dice5() * 5 + dice5() -6
Loop Until temp < 21
Return (temp Mod 7) +1
End Function
Function distCheck(n As Ulongint, delta As Double) As Ulongint
Dim As Ulongint a(n)
Dim As Ulongint maxBucket = 0
Dim As Ulongint minBucket = 1000000
For i As Ulongint = 1 To n
a(i) = dice5()
If a(i) > maxBucket Then maxBucket = a(i)
If a(i) < minBucket Then minBucket = a(i)
Next i
Dim As Ulongint nBuckets = maxBucket + 1
Dim As Ulongint buckets(maxBucket)
For i As Ulongint = 1 To n
buckets(a(i)) += 1
Next i
Dim As Ulongint expected = n / (maxBucket-minBucket+1)
Dim As Ulongint minVal = Int(expected*(1-delta))
Dim As Ulongint maxVal = Int(expected*(1+delta))
expected = Int(expected)
Print "minVal", "Expected", "maxVal"
Print minVal, expected, maxVal
Print "Bucket", "Counter", "pass/fail"
distCheck = true
For i As Ulongint = minBucket To maxBucket
Print i, buckets(i), Iif((minVal > buckets(i)) Or (buckets(i) > maxVal),"fail","")
If (minVal > buckets(i)) Or (buckets(i) > maxVal) Then Return false Else Return True
Next i
End Function
Dim Shared As Ulongint n = 1000000 Print "Testing "; n; " times" If Not(distCheck(n, 0.05)) Then Print "Test failed" Else Print "Test passed" Sleep </lang>
- Output:
Igual que la entrada de Liberty BASIC.
Go
<lang go>package main
import (
"fmt" "math" "math/rand" "time"
)
// "given" func dice5() int {
return rand.Intn(5) + 1
}
// function specified by task "Seven-sided dice from five-sided dice" func dice7() (i int) {
for {
i = 5*dice5() + dice5()
if i < 27 {
break
}
}
return (i / 3) - 1
}
// function specified by task "Verify distribution uniformity/Naive" // // Parameter "f" is expected to return a random integer in the range 1..n. // (Values out of range will cause an unceremonious crash.) // "Max" is returned as an "indication of distribution achieved." // It is the maximum delta observed from the count representing a perfectly // uniform distribution. // Also returned is a boolean, true if "max" is less than threshold // parameter "delta." func distCheck(f func() int, n int,
repeats int, delta float64) (max float64, flatEnough bool) {
count := make([]int, n)
for i := 0; i < repeats; i++ {
count[f()-1]++
}
expected := float64(repeats) / float64(n)
for _, c := range count {
max = math.Max(max, math.Abs(float64(c)-expected))
}
return max, max < delta
}
// Driver, produces output satisfying both tasks. func main() {
rand.Seed(time.Now().UnixNano())
const calls = 1000000
max, flatEnough := distCheck(dice7, 7, calls, 500)
fmt.Println("Max delta:", max, "Flat enough:", flatEnough)
max, flatEnough = distCheck(dice7, 7, calls, 500)
fmt.Println("Max delta:", max, "Flat enough:", flatEnough)
}</lang>
- Output:
Max delta: 356.1428571428696 Flat enough: true Max delta: 787.8571428571304 Flat enough: false
Groovy
<lang groovy>random = new Random()
int rand5() {
random.nextInt(5) + 1
}
int rand7From5() {
def raw = 25
while (raw > 21) {
raw = 5*(rand5() - 1) + rand5()
}
(raw % 7) + 1
}</lang> Test: <lang groovy>def test = {
(1..6). each {
def counts = [0g, 0g, 0g, 0g, 0g, 0g, 0g]
def target = 10g**it
def popSize = 7*target
(0..<(popSize)).each {
def i = rand7From5() - 1
counts[i] = counts[i] + 1g
}
BigDecimal stdDev = (counts.collect { it - target}.collect { it * it }.sum() / popSize) ** 0.5g
def countMap = (0..<counts.size()).inject([:]) { map, index -> map + [(index+1):counts[index]] }
println """\
counts: ${countMap}
population size: ${popSize}
std dev: ${stdDev.round(new java.math.MathContext(3))}
"""
}
}
4.times {
println """
TRIAL #${it+1} =============="""
test(it)
}</lang>
- Output:
TRIAL #1
==============
counts: [1:16, 2:10, 3:9, 4:7, 5:12, 6:8, 7:8]
population size: 70
std dev: 0.910
counts: [1:85, 2:97, 3:108, 4:110, 5:95, 6:105, 7:100]
population size: 700
std dev: 0.800
counts: [1:990, 2:1008, 3:992, 4:1060, 5:1008, 6:997, 7:945]
population size: 7000
std dev: 0.995
counts: [1:9976, 2:10007, 3:10009, 4:9858, 5:10109, 6:9988, 7:10053]
population size: 70000
std dev: 0.714
counts: [1:100310, 2:99783, 3:99843, 4:100353, 5:99804, 6:99553, 7:100354]
population size: 700000
std dev: 0.968
counts: [1:999320, 2:1000942, 3:1000201, 4:1000878, 5:999181, 6:999632, 7:999846]
population size: 7000000
std dev: 0.654
TRIAL #2
==============
counts: [1:10, 2:8, 3:9, 4:9, 5:14, 6:7, 7:13]
population size: 70
std dev: 0.756
counts: [1:104, 2:101, 3:97, 4:108, 5:100, 6:87, 7:103]
population size: 700
std dev: 0.619
counts: [1:995, 2:970, 3:1001, 4:953, 5:1006, 6:1081, 7:994]
population size: 7000
std dev: 1.18
counts: [1:10013, 2:10063, 3:9843, 4:9984, 5:9986, 6:10059, 7:10052]
population size: 70000
std dev: 0.711
counts: [1:100048, 2:99647, 3:100240, 4:100683, 5:99813, 6:100320, 7:99249]
population size: 700000
std dev: 1.39
counts: [1:1000579, 2:1000541, 3:999497, 4:1000805, 5:999708, 6:999161, 7:999709]
population size: 7000000
std dev: 0.586
TRIAL #3
==============
counts: [1:9, 2:8, 3:11, 4:14, 5:10, 6:11, 7:7]
population size: 70
std dev: 0.676
counts: [1:100, 2:92, 3:105, 4:107, 5:111, 6:91, 7:94]
population size: 700
std dev: 0.733
counts: [1:1010, 2:1053, 3:967, 4:981, 5:1027, 6:959, 7:1003]
population size: 7000
std dev: 0.984
counts: [1:9857, 2:10037, 3:9992, 4:10231, 5:9828, 6:10140, 7:9915]
population size: 70000
std dev: 1.37
counts: [1:99650, 2:99580, 3:99848, 4:100507, 5:99916, 6:100212, 7:100287]
population size: 700000
std dev: 1.01
counts: [1:1001710, 2:999667, 3:1000685, 4:1000411, 5:999369, 6:998469, 7:999689]
population size: 7000000
std dev: 0.965
TRIAL #4
==============
counts: [1:12, 2:7, 3:11, 4:12, 5:7, 6:9, 7:12]
population size: 70
std dev: 0.676
counts: [1:97, 2:96, 3:101, 4:93, 5:96, 6:124, 7:93]
population size: 700
std dev: 1.01
counts: [1:985, 2:1023, 3:1018, 4:1023, 5:995, 6:973, 7:983]
population size: 7000
std dev: 0.615
counts: [1:9948, 2:9968, 3:10131, 4:10050, 5:9990, 6:10039, 7:9874]
population size: 70000
std dev: 0.764
counts: [1:100125, 2:99616, 3:99912, 4:100286, 5:99674, 6:100190, 7:100197]
population size: 700000
std dev: 0.787
counts: [1:1001267, 2:999911, 3:1000602, 4:999483, 5:1000549, 6:998725, 7:999463]
population size: 7000000
std dev: 0.798
Haskell
<lang haskell>import System.Random import Data.List
sevenFrom5Dice = do
d51 <- randomRIO(1,5) :: IO Int
d52 <- randomRIO(1,5) :: IO Int
let d7 = 5*d51+d52-6
if d7 > 20 then sevenFrom5Dice
else return $ 1 + d7 `mod` 7</lang>
- Output:
<lang haskell>*Main> replicateM 10 sevenFrom5Dice [2,3,1,1,6,2,5,6,5,3]</lang> Test: <lang haskell>*Main> mapM_ print .sort =<< distribCheck sevenFrom5Dice 1000000 3 (1,(142759,True)) (2,(143078,True)) (3,(142706,True)) (4,(142403,True)) (5,(142896,True)) (6,(143028,True)) (7,(143130,True))</lang>
Icon and Unicon
Uses verify_uniform from here.
<lang Icon>
$include "distribution-checker.icn"
- return a uniformly distributed number from 1 to 7,
- but only using a random number in range 1 to 5.
procedure die_7 ()
while rnd := 5*?5 + ?5 - 6 do {
if rnd < 21 then suspend rnd % 7 + 1
}
end
procedure main ()
if verify_uniform (create (|die_7()), 1000000, 0.01)
then write ("uniform")
else write ("skewed")
end </lang>
- Output:
5 142870 2 142812 7 142901 4 142960 1 143113 6 142706 3 142638 uniform
J
The first step is to create 7-sided dice rolls from 5-sided dice rolls (rollD5):
<lang j>rollD5=: [: >: ] ?@$ 5: NB. makes a y shape array of 5s, "rolls" the array and increments.
roll2xD5=: [: rollD5 2 ,~ */ NB. rolls D5 twice for each desired D7 roll (y rows, 2 cols)
toBase10=: 5 #. <: NB. decrements and converts rows from base 5 to 10
keepGood=: #~ 21&> NB. compress out values not less than 21
groupin3s=: [: >. >: % 3: NB. increments, divides by 3 and takes ceiling
getD7=: groupin3s@keepGood@toBase10@roll2xD5</lang> Here are a couple of variations on the theme that achieve the same result: <lang j>getD7b=: 0 8 -.~ 3 >.@%~ 5 #. [: <:@rollD5 2 ,~ ] getD7c=: [: (#~ 7&>:) 3 >.@%~ [: 5&#.&.:<:@rollD5 ] , 2:</lang> The trouble is that we probably don't have enough D7 rolls yet because we compressed out any double D5 rolls that evaluated to 21 or more. So we need to accumulate some more D7 rolls until we have enough. J has two types of verb definition - tacit (arguments not referenced) and explicit (more conventional function definitions) illustrated below:
Here's an explicit definition that accumulates rolls from getD7:
<lang j>rollD7x=: monad define
n=. */y NB. product of vector y is total number of D7 rolls required rolls=. NB. initialize empty noun rolls while. n > #rolls do. NB. checks if if enough D7 rolls accumulated rolls=. rolls, getD7 >. 0.75 * n NB. calcs 3/4 of required rolls and accumulates getD7 rolls end. y $ rolls NB. shape the result according to the vector y
)</lang> Here's a tacit definition that does the same thing: <lang j>getNumRolls=: [: >. 0.75 * */@[ NB. calc approx 3/4 of the required rolls accumD7Rolls=: ] , getD7@getNumRolls NB. accumulates getD7 rolls isNotEnough=: */@[ > #@] NB. checks if enough D7 rolls accumulated
rollD7t=: ] $ (accumD7Rolls ^: isNotEnough ^:_)&</lang>
The verb1 ^: verb2 ^:_ construct repeats x verb1 y while x verb2 y is true. It is like saying "Repeat accumD7Rolls while isNotEnough".
Example usage: <lang j> rollD7t 10 NB. 10 rolls of D7 6 4 5 1 4 2 4 5 2 5
rollD7t 2 5 NB. 2 by 5 array of D7 rolls
5 1 5 1 3 3 4 3 5 6
rollD7t 2 3 5 NB. 2 by 3 by 5 array of D7 rolls
4 7 7 5 7 3 7 1 4 5 5 4 5 7 6
1 1 7 6 3 4 4 1 4 4 1 1 1 6 5
NB. check results from rollD7x and rollD7t have same shape
($@rollD7x -: $@rollD7t) 10
1
($@rollD7x -: $@rollD7t) 2 3 5
1</lang>
Java
<lang Java>import java.util.Random; public class SevenSidedDice { private static final Random rnd = new Random(); public static void main(String[] args) { SevenSidedDice now=new SevenSidedDice(); System.out.println("Random number from 1 to 7: "+now.seven()); } int seven() { int v=21; while(v>20) v=five()+five()*5-6; return 1+v%7; } int five() { return 1+rnd.nextInt(5); } }</lang>
JavaScript
<lang javascript>function dice5() {
return 1 + Math.floor(5 * Math.random());
}
function dice7() {
while (true)
{
var dice55 = 5 * dice5() + dice5() - 6;
if (dice55 < 21)
return dice55 % 7 + 1;
}
}
distcheck(dice5, 1000000); print(); distcheck(dice7, 1000000);</lang>
- Output:
1 199792 2 200425 3 199243 4 200407 5 200133 1 143617 2 142209 3 143023 4 142990 5 142894 6 142648 7 142619
Julia
<lang Julia>dice5() = rand(1:5)
function dice7()
r = 5*dice5() + dice5() - 6 r < 21 ? (r%7 + 1) : dice7()
end</lang> Distribution check:
julia> hist([dice5() for i=1:10^6]) (0:1:5,[199932,200431,199969,199925,199743]) julia> hist([dice7() for i=1:10^6]) (0:1:7,[142390,143032,142837,142999,142800,142642,143300])
Kotlin
<lang scala>// version 1.1.3
import java.util.Random
val r = Random()
fun dice5() = 1 + r.nextInt(5)
fun dice7(): Int {
while (true) {
val t = (dice5() - 1) * 5 + dice5() - 1
if (t >= 21) continue
return 1 + t / 3
}
}
fun checkDist(gen: () -> Int, nRepeats: Int, tolerance: Double = 0.5) {
val occurs = mutableMapOf<Int, Int>()
for (i in 1..nRepeats) {
val d = gen()
if (occurs.containsKey(d))
occurs[d] = occurs[d]!! + 1
else
occurs.put(d, 1)
}
val expected = (nRepeats.toDouble()/ occurs.size).toInt()
val maxError = (expected * tolerance / 100.0).toInt()
println("Repetitions = $nRepeats, Expected = $expected")
println("Tolerance = $tolerance%, Max Error = $maxError\n")
println("Integer Occurrences Error Acceptable")
val f = " %d %5d %5d %s"
var allAcceptable = true
for ((k,v) in occurs.toSortedMap()) {
val error = Math.abs(v - expected)
val acceptable = if (error <= maxError) "Yes" else "No"
if (acceptable == "No") allAcceptable = false
println(f.format(k, v, error, acceptable))
}
println("\nAcceptable overall: ${if (allAcceptable) "Yes" else "No"}")
}
fun main(args: Array<String>) {
checkDist(::dice7, 1_400_000)
}</lang>
Sample output:
Repetitions = 1400000, Expected = 200000 Tolerance = 0.5%, Max Error = 1000 Integer Occurrences Error Acceptable 1 199285 715 Yes 2 200247 247 Yes 3 199709 291 Yes 4 199983 17 Yes 5 199990 10 Yes 6 200664 664 Yes 7 200122 122 Yes Acceptable overall: Yes
Liberty BASIC
<lang lb> n=1000000 '1000000 would take several minutes print "Testing ";n;" times" if not(check(n, 0.05)) then print "Test failed" else print "Test passed" end
'function check(n, delta) is defined at 'http://rosettacode.org/wiki/Verify_distribution_uniformity/Naive#Liberty_BASIC
function GENERATOR()
'GENERATOR = int(rnd(0)*10) '0..9 'GENERATOR = 1+int(rnd(0)*5) '1..5: dice5
'dice7()
do
temp =dice5() *5 +dice5() -6
loop until temp <21
GENERATOR =( temp mod 7) +1
end function
function dice5()
dice5=1+int(rnd(0)*5) '1..5: dice5
end function </lang>
- Output:
Testing 1000000 times minVal Expected maxVal 135714 142857 150000 Bucket Counter pass/fail 1 143310 2 143500 3 143040 4 145185 5 140998 6 142610 7 141357 Test passed
Lua
<lang lua>dice5 = function() return math.random(5) end
function dice7()
x = dice5() * 5 + dice5() - 6 if x > 20 then return dice7() end return x%7 + 1
end</lang>
M2000 Interpreter
We make a stack object (is reference type) and pass it as a closure to dice7 lambda function. For each dice7 we pop the top value of stack, and we add a fresh dice5 (random(1,5)) as last value of stack, so stack used as FIFO. Each time z has the sum of 7 random values.
We check for uniform numbers using +-5% from expected value. <lang M2000 Interpreter> Module CheckIt {
Def long i, calls, max, min
s=stack:=random(1,5),random(1,5), random(1,5), random(1,5), random(1,5), random(1,5), random(1,5)
z=0: for i=1 to 7 { z+=stackitem(s, i)}
dice7=lambda z, s -> {
=((z-1) mod 7)+1 : stack s {z-=Number : data random(1,5): z+=Stackitem(7)}
}
Dim count(1 to 7)=0& ' long type
calls=700000
p=0.05
IsUniform=lambda max=calls/7*(1+p), min=calls/7*(1-p) (a)->{
if len(a)=0 then =false : exit
=false
m=each(a)
while m
if array(m)<min or array(m)>max then break
end while
=true
}
For i=1 to calls {count(dice7())++}
max=count()#max()
expected=calls div 7
min=count()#min()
for i=1 to 7
document doc$=format$("{0}{1::-7}",i,count(i))+{
}
Next i
doc$=format$("min={0} expected={1} max={2}", min, expected, max)+{
}+format$("Verify Uniform:{0}", if$(IsUniform(count())->"uniform", "skewed"))+{
}
Print
report doc$
clipboard doc$
} CheckIt </lang>
- Output:
1 9865 2 10109 3 9868 4 9961 5 9936 6 9922 7 10339 min=9865 expected=10000 max=10339 Verify Uniform:uniform 1 100214 2 100336 3 100049 4 99505 5 99951 6 99729 7 100216 min=99505 expected=100000 max=100336 Verify Uniform:uniform
Mathematica
<lang Mathematica>sevenFrom5Dice := (tmp$ = 5*RandomInteger[{1, 5}] + RandomInteger[{1, 5}] - 6;
If [tmp$ < 21, 1 + Mod[tmp$ , 7], sevenFrom5Dice])</lang>
CheckDistribution[sevenFrom5Dice, 1000000, 5]
->Expected: 142857., Generated :{142206,142590,142650,142693,142730,143475,143656}
->"Flat"
Nim
We use the distribution checker from task Simple Random Distribution Checker. <lang Nim>import random, tables
proc dice5(): int = rand(1..5)
proc dice7(): int =
while true:
let val = 5 * dice5() + dice5() - 6
if val < 21:
return val div 3 + 1
proc checkDist(f: proc(): int; repeat: Positive; tolerance: float) =
var counts: CountTable[int] for _ in 1..repeat: counts.inc f()
let expected = (repeat / counts.len).toInt # Rounded to nearest. let allowedDelta = (expected.toFloat * tolerance / 100).toInt var maxDelta = 0 for val, count in counts.pairs: let d = abs(count - expected) if d > maxDelta: maxDelta = d
let status = if maxDelta <= allowedDelta: "passed" else: "failed" echo "Checking ", repeat, " values with a tolerance of ", tolerance, "%." echo "Random generator ", status, " the uniformity test." echo "Max delta encountered = ", maxDelta, " Allowed delta = ", allowedDelta
when isMainModule:
import random randomize() checkDist(dice7, 1_000_000, 0.5)</lang>
- Output:
Checking 1000000 values with a tolerance of 0.5%. Random generator passed the uniformity test. Max delta encountered = 552 Allowed delta = 714
OCaml
<lang ocaml>let dice5() = 1 + Random.int 5 ;;
let dice7 =
let rolls2answer = Hashtbl.create 25 in
let n = ref 0 in
for roll1 = 1 to 5 do
for roll2 = 1 to 5 do
Hashtbl.add rolls2answer (roll1,roll2) (!n / 3 +1);
incr n
done;
done;
let rec aux() =
let trial = Hashtbl.find rolls2answer (dice5(),dice5()) in
if trial <= 7 then trial else aux()
in
aux
- </lang>
PARI/GP
<lang parigp>dice5()=random(5)+1;
dice7()={
my(t); while((t=dice5()*5+dice5()) > 21,); (t+2)\3
};</lang>
Perl
Using dice5 twice to generate numbers in the range 0 to 24. If we consider these modulo 8 and re-call if we get zero, we have eliminated 4 cases and created the necessary number in the range from 1 to 7. <lang perl>sub dice5 { 1+int rand(5) }
sub dice7 {
while(1) {
my $d7 = (5*dice5()+dice5()-6) % 8;
return $d7 if $d7;
}
}
my %count7; my $n = 1000000; $count7{dice7()}++ for 1..$n; printf "%s: %5.2f%%\n", $_, 100*($count7{$_}/$n*7-1) for sort keys %count7; </lang>
- Output:
1: 0.05% 2: 0.16% 3: -0.43% 4: 0.11% 5: 0.01% 6: -0.15% 7: 0.24%
Phix
replace rand7() in Verify_distribution_uniformity/Naive#Phix with: <lang Phix>function dice5()
return rand(5)
end function
function dice7()
while true do
integer r = dice5()*5+dice5()-3 -- ( ie 3..27, but )
if r<24 then return floor(r/3) end if -- (only 3..23 useful)
end while
end function</lang>
- Output:
1000000 iterations: flat
PicoLisp
<lang PicoLisp>(de dice5 ()
(rand 1 5) )
(de dice7 ()
(use R
(until (> 21 (setq R (+ (* 5 (dice5)) (dice5) -6))))
(inc (% R 7)) ) )</lang>
- Output:
: (let R NIL (do 1000000 (accu 'R (dice7) 1)) (sort R) ) -> ((1 . 142295) (2 . 142491) (3 . 143448) (4 . 143129) (5 . 142701) (6 . 143142) (7 . 142794))
PureBasic
<lang PureBasic>Procedure dice5()
ProcedureReturn Random(4) + 1
EndProcedure
Procedure dice7()
Protected x x = dice5() * 5 + dice5() - 6 If x > 20 ProcedureReturn dice7() EndIf ProcedureReturn x % 7 + 1
EndProcedure</lang>
Python
<lang python>from random import randint
def dice5():
return randint(1, 5)
def dice7():
r = dice5() + dice5() * 5 - 6 return (r % 7) + 1 if r < 21 else dice7()</lang>
Distribution check using Simple Random Distribution Checker:
>>> distcheck(dice5, 1000000, 1)
{1: 200244, 2: 199831, 3: 199548, 4: 199853, 5: 200524}
>>> distcheck(dice7, 1000000, 1)
{1: 142853, 2: 142576, 3: 143067, 4: 142149, 5: 143189, 6: 143285, 7: 142881}
R
5-sided die. <lang r>dice5 <- function(n=1) sample(5, n, replace=TRUE)</lang> Simple but slow 7-sided die, using a while loop. <lang r>dice7.while <- function(n=1) {
score <- numeric()
while(length(score) < n)
{
total <- sum(c(5,1) * dice5(2)) - 3
if(total < 24) score <- c(score, total %/% 3)
}
score
} system.time(dice7.while(1e6)) # longer than 4 minutes</lang> More complex, but much faster vectorised version. <lang r>dice7.vec <- function(n=1, checkLength=TRUE) {
morethan2n <- 3 * n + 10 + (n %% 2) #need more than 2*n samples, because some are discarded
twoDfive <- matrix(dice5(morethan2n), nrow=2)
total <- colSums(c(5, 1) * twoDfive) - 3
score <- ifelse(total < 24, total %/% 3, NA)
score <- score[!is.na(score)]
#If length is less than n (very unlikely), add some more samples
if(checkLength)
{
while(length(score) < n)
{
score <- c(score, dice7(n, FALSE))
}
score[1:n]
} else score
} system.time(dice7.vec(1e6)) # ~1 sec</lang>
Racket
<lang Racket>
- lang racket
(define (dice5) (add1 (random 5)))
(define (dice7)
(define res (+ (* 5 (dice5)) (dice5) -6)) (if (< res 21) (+ 1 (modulo res 7)) (dice7)))
</lang>
Checking the uniformity using math library:
<lang racket> -> (require math/statistics) -> (samples->hash (for/list ([i 700000]) (dice7))) '#hash((7 . 100392)
(6 . 100285)
(5 . 99774)
(4 . 100000)
(3 . 100000)
(2 . 99927)
(1 . 99622))
</lang>
Raku
(formerly Perl 6)
<lang perl6>my $d5 = 1..5; sub d5() { $d5.roll; } # 1d5
sub d7() {
my $flat = 21; $flat = 5 * d5() - d5() until $flat < 21; $flat % 7 + 1;
}
- Testing
my @dist; my $n = 1_000_000; my $expect = $n / 7;
loop ($_ = $n; $n; --$n) { @dist[d7()]++; }
say "Expect\t",$expect.fmt("%.3f"); for @dist.kv -> $i, $v {
say "$i\t$v\t" ~ (($v - $expect)/$expect*100).fmt("%+.2f%%") if $v;
}</lang>
- Output:
Expect 142857.143 1 143088 +0.16% 2 143598 +0.52% 3 141741 -0.78% 4 142832 -0.02% 5 143040 +0.13% 6 142988 +0.09% 7 142713 -0.10%
REXX
<lang rexx>/*REXX program simulates a 7─sided die based on a 5─sided throw for a number of trials. */ parse arg trials sample seed . /*obtain optional arguments from the CL*/ if trials== | trials="," then trials= 1 /*Not specified? Then use the default.*/ if sample== | sample="," then sample= 1000000 /* " " " " " " */ if datatype(seed,'W') then call random ,,seed /*Integer? Then use it as a RAND seed.*/ L= length(trials) /* [↑] one million samples to be used.*/
do #=1 for trials; die.= 0 /*performs the number of desired trials*/
k= 0
do until k==sample; r= 5 * random(1, 5) + random(1, 5) - 6
if r>20 then iterate
k= k+1; r=r // 7 + 1; die.r= die.r + 1
end /*until*/
say
expect= sample % 7
say center('trial:' right(#, L) " " sample 'samples, expect' expect, 80, "─")
do j=1 for 7
say ' side' j "had " die.j ' occurrences',
' difference from expected:'right(die.j - expect, length(sample) )
end /*j*/
end /*#*/ /*stick a fork in it, we're all done. */</lang>
- output when using the input of: 11
(Shown at five-sixth size.)
──────────────────trial: 1 1000000 samples, expect 142857──────────────────
side 1 had 142076 occurrences difference from expected: -781
side 2 had 143053 occurrences difference from expected: 196
side 3 had 142342 occurrences difference from expected: -515
side 4 had 142633 occurrences difference from expected: -224
side 5 had 143024 occurrences difference from expected: 167
side 6 had 143827 occurrences difference from expected: 970
side 7 had 143045 occurrences difference from expected: 188
──────────────────trial: 2 1000000 samples, expect 142857──────────────────
side 1 had 143470 occurrences difference from expected: 613
side 2 had 142998 occurrences difference from expected: 141
side 3 had 142654 occurrences difference from expected: -203
side 4 had 142545 occurrences difference from expected: -312
side 5 had 142452 occurrences difference from expected: -405
side 6 had 143144 occurrences difference from expected: 287
side 7 had 142737 occurrences difference from expected: -120
──────────────────trial: 3 1000000 samples, expect 142857──────────────────
side 1 had 142773 occurrences difference from expected: -84
side 2 had 143198 occurrences difference from expected: 341
side 3 had 142296 occurrences difference from expected: -561
side 4 had 142804 occurrences difference from expected: -53
side 5 had 142897 occurrences difference from expected: 40
side 6 had 142382 occurrences difference from expected: -475
side 7 had 143650 occurrences difference from expected: 793
──────────────────trial: 4 1000000 samples, expect 142857──────────────────
side 1 had 143150 occurrences difference from expected: 293
side 2 had 142635 occurrences difference from expected: -222
side 3 had 142763 occurrences difference from expected: -94
side 4 had 142853 occurrences difference from expected: -4
side 5 had 143132 occurrences difference from expected: 275
side 6 had 142403 occurrences difference from expected: -454
side 7 had 143064 occurrences difference from expected: 207
──────────────────trial: 5 1000000 samples, expect 142857──────────────────
side 1 had 143041 occurrences difference from expected: 184
side 2 had 142701 occurrences difference from expected: -156
side 3 had 143416 occurrences difference from expected: 559
side 4 had 142097 occurrences difference from expected: -760
side 5 had 142451 occurrences difference from expected: -406
side 6 had 143332 occurrences difference from expected: 475
side 7 had 142962 occurrences difference from expected: 105
──────────────────trial: 6 1000000 samples, expect 142857──────────────────
side 1 had 142502 occurrences difference from expected: -355
side 2 had 142429 occurrences difference from expected: -428
side 3 had 143146 occurrences difference from expected: 289
side 4 had 142791 occurrences difference from expected: -66
side 5 had 143271 occurrences difference from expected: 414
side 6 had 143415 occurrences difference from expected: 558
side 7 had 142446 occurrences difference from expected: -411
──────────────────trial: 7 1000000 samples, expect 142857──────────────────
side 1 had 142700 occurrences difference from expected: -157
side 2 had 142691 occurrences difference from expected: -166
side 3 had 143067 occurrences difference from expected: 210
side 4 had 141562 occurrences difference from expected: -1295
side 5 had 143316 occurrences difference from expected: 459
side 6 had 143150 occurrences difference from expected: 293
side 7 had 143514 occurrences difference from expected: 657
──────────────────trial: 8 1000000 samples, expect 142857──────────────────
side 1 had 142362 occurrences difference from expected: -495
side 2 had 143298 occurrences difference from expected: 441
side 3 had 142639 occurrences difference from expected: -218
side 4 had 142811 occurrences difference from expected: -46
side 5 had 143275 occurrences difference from expected: 418
side 6 had 142765 occurrences difference from expected: -92
side 7 had 142850 occurrences difference from expected: -7
──────────────────trial: 9 1000000 samples, expect 142857──────────────────
side 1 had 143508 occurrences difference from expected: 651
side 2 had 142650 occurrences difference from expected: -207
side 3 had 142614 occurrences difference from expected: -243
side 4 had 142916 occurrences difference from expected: 59
side 5 had 142944 occurrences difference from expected: 87
side 6 had 143129 occurrences difference from expected: 272
side 7 had 142239 occurrences difference from expected: -618
──────────────────trial: 10 1000000 samples, expect 142857──────────────────
side 1 had 142455 occurrences difference from expected: -402
side 2 had 143112 occurrences difference from expected: 255
side 3 had 143435 occurrences difference from expected: 578
side 4 had 142704 occurrences difference from expected: -153
side 5 had 142376 occurrences difference from expected: -481
side 6 had 142721 occurrences difference from expected: -136
side 7 had 143197 occurrences difference from expected: 340
──────────────────trial: 11 1000000 samples, expect 142857──────────────────
side 1 had 142967 occurrences difference from expected: 110
side 2 had 142204 occurrences difference from expected: -653
side 3 had 142993 occurrences difference from expected: 136
side 4 had 142797 occurrences difference from expected: -60
side 5 had 143081 occurrences difference from expected: 224
side 6 had 142711 occurrences difference from expected: -146
side 7 had 143247 occurrences difference from expected: 390
Ring
<lang ring>
- Project : Seven-sided dice from five-sided dice
for n = 1 to 20
d = dice7()
see "" + d + " "
next see nl
func dice7()
x = dice5() * 5 + dice5() - 6
if x > 20
return dice7()
ok
dc = x % 7 + 1
return dc
func dice5()
rnd = random(4) + 1
return rnd
</lang> Output:
7 6 3 5 2 2 7 1 2 7 3 7 4 4 4 2 3 2 6 1
Ruby
Uses distcheck from here.
<lang ruby>require './distcheck.rb'
def d5
1 + rand(5)
end
def d7
loop do d55 = 5*d5 + d5 - 6 return (d55 % 7 + 1) if d55 < 21 end
end
distcheck(1_000_000) {d5} distcheck(1_000_000) {d7}</lang>
- Output:
1 200227 2 200264 3 199777 4 199387 5 200345 1 143175 2 143031 3 142731 4 142716 5 142931 6 142605 7 142811
Scala
- Output:
Best seen running in your browser either by ScalaFiddle (ES aka JavaScript, non JVM) or Scastie (remote JVM).
<lang Scala>import scala.util.Random
object SevenSidedDice extends App {
private val rnd = new Random
private def seven = {
var v = 21
def five = 1 + rnd.nextInt(5)
while (v > 20) v = five + five * 5 - 6 1 + v % 7 }
println("Random number from 1 to 7: " + seven)
}</lang>
Sidef
<lang ruby>func dice5 { 1 + 5.rand.int }
func dice7 {
loop {
var d7 = ((5*dice5() + dice5() - 6) % 8);
d7 && return d7;
}
}
var count7 = Hash.new;
var n = 1e6; n.times { count7{dice7()} := 0 ++ } count7.keys.sort.each { |k|
printf("%s: %5.2f%%\n", k, 100*(count7{k}/n * 7 - 1));
}</lang>
- Output:
1: -0.00% 2: 0.02% 3: 0.23% 4: 0.42% 5: -0.23% 6: -0.54% 7: 0.10%
Tcl
Any old D&D hand will know these as a D5 and a D7... <lang tcl>proc D5 {} {expr {1 + int(5 * rand())}}
proc D7 {} {
while 1 {
set d55 [expr {5 * [D5] + [D5] - 6}]
if {$d55 < 21} {
return [expr {$d55 % 7 + 1}]
}
}
}</lang> Checking:
% distcheck D5 1000000 1 199893 2 200162 3 200075 4 199630 5 200240 % distcheck D7 1000000 1 143121 2 142383 3 143353 4 142811 5 142172 6 143291 7 142869
VBA
The original StackOverflow page doesn't exist any longer. Luckily archive.org exists. <lang vb>Private Function Test4DiscreteUniformDistribution(ObservationFrequencies() As Variant, Significance As Single) As Boolean
'Returns true if the observed frequencies pass the Pearson Chi-squared test at the required significance level.
Dim Total As Long, Ei As Long, i As Integer
Dim ChiSquared As Double, DegreesOfFreedom As Integer, p_value As Double
Debug.Print "[1] ""Data set:"" ";
For i = LBound(ObservationFrequencies) To UBound(ObservationFrequencies)
Total = Total + ObservationFrequencies(i)
Debug.Print ObservationFrequencies(i); " ";
Next i
DegreesOfFreedom = UBound(ObservationFrequencies) - LBound(ObservationFrequencies)
'This is exactly the number of different categories minus 1
Ei = Total / (DegreesOfFreedom + 1)
For i = LBound(ObservationFrequencies) To UBound(ObservationFrequencies)
ChiSquared = ChiSquared + (ObservationFrequencies(i) - Ei) ^ 2 / Ei
Next i
p_value = 1 - WorksheetFunction.ChiSq_Dist(ChiSquared, DegreesOfFreedom, True)
Debug.Print
Debug.Print "Chi-squared test for given frequencies"
Debug.Print "X-squared ="; Format(ChiSquared, "0.0000"); ", ";
Debug.Print "df ="; DegreesOfFreedom; ", ";
Debug.Print "p-value = "; Format(p_value, "0.0000")
Test4DiscreteUniformDistribution = p_value > Significance
End Function Private Function Dice5() As Integer
Dice5 = Int(5 * Rnd + 1)
End Function Private Function Dice7() As Integer
Dim i As Integer
Do
i = 5 * (Dice5 - 1) + Dice5
Loop While i > 21
Dice7 = i Mod 7 + 1
End Function Sub TestDice7()
Dim i As Long, roll As Integer
Dim Bins(1 To 7) As Variant
For i = 1 To 1000000
roll = Dice7
Bins(roll) = Bins(roll) + 1
Next i
Debug.Print "[1] ""Uniform? "; Test4DiscreteUniformDistribution(Bins, 0.05); """"
End Sub</lang>
- Output:
[1] "Data set:" 142418 142898 142940 142573 143030 143139 143002Chi-squared test for given frequencies X-squared =2.8870, df = 6 , p-value = 0.8229 [1] "Uniform? True"
VBScript
<lang vb>Option Explicit
function dice5 dice5 = int(rnd*5) + 1 end function
function dice7 dim j do j = 5 * dice5 + dice5 - 6 loop until j < 21 dice7 = j mod 7 + 1 end function</lang>
Verilog
<lang verilog>
/////////////////////////////////////////////////////////////////////////////// /// seven_sided_dice_tb : (testbench) /// /// Check the distribution of the output of a seven sided dice circuit /// /////////////////////////////////////////////////////////////////////////////// module seven_sided_dice_tb;
reg [31:0] freq[0:6];
reg clk;
wire [2:0] dice_face;
reg req;
wire valid_roll;
integer i;
initial begin
clk <= 0;
forever begin
#1;
clk <= ~clk;
end
end
initial begin
req <= 1'b1;
for(i = 0; i < 7; i = i + 1) begin
freq[i] <= 32'b0;
end
repeat(10) @(posedge clk);
repeat(7000000) begin
@(posedge clk);
while(~valid_roll) begin
@(posedge clk);
end
freq[dice_face] <= freq[dice_face] + 32'b1;
end
$display("********************************************");
$display("*** Seven sided dice distribution: ");
$display(" Theoretical distribution is an uniform ");
$display(" distribution with (1/7)-probability ");
$display(" for each possible outcome, ");
$display(" The experimental distribution is: ");
for(i = 0; i < 7; i = i + 1) begin
if(freq[i] < 32'd1_000_000) begin
$display("%d with probability 1/7 - (%d ppm)", i, (32'd1_000_000 - freq[i])/7);
end
else begin
$display("%d with probability 1/7 + (%d ppm)", i, (freq[i] - 32'd1_000_000)/7);
end
end
$finish;
end
seven_sided_dice DUT( .clk(clk), .req(req), .valid_roll(valid_roll), .dice_face(dice_face) );
endmodule /////////////////////////////////////////////////////////////////////////////// /// seven_sided_dice : /// /// Synthsizeable module that using a 5 sided dice as a black box /// /// is able to reproduce the outcomes if a 7-sided dice /// /////////////////////////////////////////////////////////////////////////////// module seven_sided_dice(
input wire clk, input wire req, output reg valid_roll, output reg [2:0] dice_face
);
wire [2:0] face1;
wire [2:0] face2;
reg [4:0] combination;
reg req_p1;
reg req_p2;
reg req_p3;
always @(posedge clk) begin
req_p1 <= req;
req_p2 <= req_p1;
end
always @(posedge clk) begin
if(req_p1) begin
combination <= face1 + face2 + {face2, 2'b00};
end
if(req_p2) begin
case(combination)
5'd0, 5'd1, 5'd2: {valid_roll, dice_face} <= {1'b1, 3'd0};
5'd3, 5'd4, 5'd5: {valid_roll, dice_face} <= {1'b1, 3'd1};
5'd6, 5'd7, 5'd8: {valid_roll, dice_face} <= {1'b1, 3'd2};
5'd9, 5'd10, 5'd11: {valid_roll, dice_face} <= {1'b1, 3'd3};
5'd12, 5'd13, 5'd14: {valid_roll, dice_face} <= {1'b1, 3'd4};
5'd15, 5'd16, 5'd17: {valid_roll, dice_face} <= {1'b1, 3'd5};
5'd18, 5'd19, 5'd20: {valid_roll, dice_face} <= {1'b1, 3'd6};
default: valid_roll <= 1'b0;
endcase
end
end
five_sided_dice dice1( .clk(clk), .req(req), .dice_face(face1) );
five_sided_dice dice2( .clk(clk), .req(req), .dice_face(face2) );
endmodule
/////////////////////////////////////////////////////////////////////////////// /// five_sided_dice : /// /// A model of the five sided dice component /// /////////////////////////////////////////////////////////////////////////////// module five_sided_dice(
input wire clk, input wire req, output reg [2:0] dice_face
);
always @(posedge clk) begin
if(req) begin
dice_face <= $urandom % 5;
end
end
endmodule </lang>
Compiling with Icarus Verilog
> iverilog seven-sided-dice.v -o seven-sided-dice
Running the test
> vvp seven-sided-dice
********************************************
*** Seven sided dice distribution:
Theoretical distribution is an uniform
distribution with (1/7)-probability
for each possible outcome,
The experimental distribution is:
0 with probability 1/7 + ( 67 ppm)
1 with probability 1/7 - ( 47 ppm)
2 with probability 1/7 + ( 92 ppm)
3 with probability 1/7 - ( 17 ppm)
4 with probability 1/7 - ( 36 ppm)
5 with probability 1/7 + ( 51 ppm)
6 with probability 1/7 - ( 109 ppm)
Wren
<lang ecmascript>import "random" for Random import "/sort" for Sort import "/fmt" for Fmt
var r = Random.new()
var dice5 = Fn.new { r.int(1, 6) }
var dice7 = Fn.new {
while (true) {
var t = (dice5.call() - 1) * 5 + dice5.call() - 1
if (t < 21) return 1 + (t/3).floor
}
}
var checkDist = Fn.new { |gen, nRepeats, tolerance|
var occurs = {}
for (i in 1..nRepeats) {
var d = gen.call()
occurs[d] = occurs.containsKey(d) ? occurs[d] + 1 : 1
}
var expected = (nRepeats/occurs.count).floor
var maxError = (expected * tolerance / 100).floor
System.print("Repetitions = %(nRepeats), Expected = %(expected)")
System.print("Tolerance = %(tolerance)\%, Max Error = %(maxError)\n")
System.print("Integer Occurrences Error Acceptable")
var f = " $d $5d $5d $s"
var allAcceptable = true
var cmp = Fn.new { |me1, me2| (me1.key - me2.key).sign }
occurs = occurs.toList
Sort.insertion(occurs, cmp)
for (me in occurs) {
var k = me.key
var v = me.value
var error = (v - expected).abs
var acceptable = (error <= maxError) ? "Yes" : "No"
if (acceptable == "No") allAcceptable = false
Fmt.print(f, k, v, error, acceptable)
}
System.print("\nAcceptable overall: %(allAcceptable ? "Yes" : "No")")
}
checkDist.call(dice7, 1400000, 0.5)</lang>
- Output:
Repetitions = 1400000, Expected = 200000 Tolerance = 0.5%, Max Error = 1000 Integer Occurrences Error Acceptable 1 199744 256 Yes 2 199678 322 Yes 3 200254 254 Yes 4 199903 97 Yes 5 200080 80 Yes 6 200070 70 Yes 7 200271 271 Yes Acceptable overall: Yes
zkl
<lang zkl>var die5=(1).random.fp(6); // [1..5] fcn die7{ while((r:=5*die5() + die5())>=27){} r/3-1 }
fcn rtest(N){ //test spread over [0..9]
dist:=L(0,0,0,0,0,0,0,0,0,0);
do(N){ dist[die7()]+=1 }
sum:=dist.sum();
dist=dist.apply('wrap(n){ "%.2f%%".fmt(n.toFloat()/sum*100) }).println();
}
println("Looking for ",100.0/7,"%"); rtest(0d1_000_000);</lang>
- Output:
Looking for 14.2857%
L("0.00%","14.28%","14.36%","14.22%","14.26%","14.34%","14.33%","14.21%","0.00%","0.00%")
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