Seven-sided dice from five-sided dice
(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.
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
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)
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++
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>
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>
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
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: ${if (allAcceptable) "Yes" else "No"}")
}
fun main(args: Array<String>) {
checkDist(::dice7, 1_400_000)
}</lang>
Sample output:
Repetitions = 1400000, Expected = 200000 Tolerance = 0.5%, Max Error = 1000 Integer Occurrences Error Acceptable 1 199285 715 Yes 2 200247 247 Yes 3 199709 291 Yes 4 199983 17 Yes 5 199990 10 Yes 6 200664 664 Yes 7 200122 122 Yes Acceptable overall: Yes
Liberty BASIC
<lang lb> n=1000000 '1000000 would take several minutes print "Testing ";n;" times" if not(check(n, 0.05)) then print "Test failed" else print "Test passed" end
'function check(n, delta) is defined at 'http://rosettacode.org/wiki/Verify_distribution_uniformity/Naive#Liberty_BASIC
function GENERATOR()
'GENERATOR = int(rnd(0)*10) '0..9 'GENERATOR = 1+int(rnd(0)*5) '1..5: dice5
'dice7()
do
temp =dice5() *5 +dice5() -6
loop until temp <21
GENERATOR =( temp mod 7) +1
end function
function dice5()
dice5=1+int(rnd(0)*5) '1..5: dice5
end function </lang>
- Output:
Testing 1000000 times minVal Expected maxVal 135714 142857 150000 Bucket Counter pass/fail 1 143310 2 143500 3 143040 4 145185 5 140998 6 142610 7 141357 Test passed
Lua
<lang lua>dice5 = function() return math.random(5) end
function dice7()
x = dice5() * 5 + dice5() - 6 if x > 20 then return dice7() end return x%7 + 1
end</lang>
Mathematica
<lang Mathematica>sevenFrom5Dice := (tmp$ = 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"
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%
Perl 6
Since rakudo is still pretty slow, we've done some interesting bits of optimization. We factor out the range object construction so that it doesn't have to be recreated each time, and we sneakily subtract the 1's from the 5's, which takes us back to 0 based without having to subtract 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;
}</lang>
Here's the test. We use a C-style for loop, except it's named loop, because it's currently faster than the other loops--and, er, doesn't segfault the GC on a million iterations...
<lang perl6>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 142835 -0.02% 2 143021 +0.11% 3 142771 -0.06% 4 142706 -0.11% 5 143258 +0.28% 6 142485 -0.26% 7 142924 +0.05%
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}
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>
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>
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.*/
/* [↑] 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(#, 4) " " 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 142990 occurrences difference from expected: 133
side 2 had 142811 occurrences difference from expected: -46
side 3 had 143348 occurrences difference from expected: 491
side 4 had 143219 occurrences difference from expected: 362
side 5 had 142717 occurrences difference from expected: -140
side 6 had 141951 occurrences difference from expected: -906
side 7 had 142964 occurrences difference from expected: 107
─────────────────trial: 2 1000000 samples, expect=142857──────────────────
side 1 had 142707 occurrences difference from expected: -150
side 2 had 142512 occurrences difference from expected: -345
side 3 had 143038 occurrences difference from expected: 181
side 4 had 143268 occurrences difference from expected: 411
side 5 had 142629 occurrences difference from expected: -228
side 6 had 142902 occurrences difference from expected: 45
side 7 had 142944 occurrences difference from expected: 87
─────────────────trial: 3 1000000 samples, expect=142857──────────────────
side 1 had 142743 occurrences difference from expected: -114
side 2 had 142674 occurrences difference from expected: -183
side 3 had 142834 occurrences difference from expected: -23
side 4 had 142668 occurrences difference from expected: -189
side 5 had 143108 occurrences difference from expected: 251
side 6 had 142727 occurrences difference from expected: -130
side 7 had 143246 occurrences difference from expected: 389
─────────────────trial: 4 1000000 samples, expect=142857──────────────────
side 1 had 142575 occurrences difference from expected: -282
side 2 had 143139 occurrences difference from expected: 282
side 3 had 142618 occurrences difference from expected: -239
side 4 had 142647 occurrences difference from expected: -210
side 5 had 142204 occurrences difference from expected: -653
side 6 had 143228 occurrences difference from expected: 371
side 7 had 143589 occurrences difference from expected: 732
─────────────────trial: 5 1000000 samples, expect=142857──────────────────
side 1 had 142539 occurrences difference from expected: -318
side 2 had 143490 occurrences difference from expected: 633
side 3 had 142261 occurrences difference from expected: -596
side 4 had 142755 occurrences difference from expected: -102
side 5 had 142976 occurrences difference from expected: 119
side 6 had 143188 occurrences difference from expected: 331
side 7 had 142791 occurrences difference from expected: -66
─────────────────trial: 6 1000000 samples, expect=142857──────────────────
side 1 had 142706 occurrences difference from expected: -151
side 2 had 142344 occurrences difference from expected: -513
side 3 had 143243 occurrences difference from expected: 386
side 4 had 143626 occurrences difference from expected: 769
side 5 had 142555 occurrences difference from expected: -302
side 6 had 142530 occurrences difference from expected: -327
side 7 had 142996 occurrences difference from expected: 139
─────────────────trial: 7 1000000 samples, expect=142857──────────────────
side 1 had 142901 occurrences difference from expected: 44
side 2 had 142950 occurrences difference from expected: 93
side 3 had 143147 occurrences difference from expected: 290
side 4 had 142081 occurrences difference from expected: -776
side 5 had 143423 occurrences difference from expected: 566
side 6 had 141965 occurrences difference from expected: -892
side 7 had 143533 occurrences difference from expected: 676
─────────────────trial: 8 1000000 samples, expect=142857──────────────────
side 1 had 142818 occurrences difference from expected: -39
side 2 had 142681 occurrences difference from expected: -176
side 3 had 142886 occurrences difference from expected: 29
side 4 had 142975 occurrences difference from expected: 118
side 5 had 142987 occurrences difference from expected: 130
side 6 had 142781 occurrences difference from expected: -76
side 7 had 142872 occurrences difference from expected: 15
─────────────────trial: 9 1000000 samples, expect=142857──────────────────
side 1 had 143501 occurrences difference from expected: 644
side 2 had 142404 occurrences difference from expected: -453
side 3 had 142882 occurrences difference from expected: 25
side 4 had 143051 occurrences difference from expected: 194
side 5 had 142479 occurrences difference from expected: -378
side 6 had 142664 occurrences difference from expected: -193
side 7 had 143019 occurrences difference from expected: 162
─────────────────trial: 10 1000000 samples, expect=142857──────────────────
side 1 had 142945 occurrences difference from expected: 88
side 2 had 143142 occurrences difference from expected: 285
side 3 had 142843 occurrences difference from expected: -14
side 4 had 143043 occurrences difference from expected: 186
side 5 had 142558 occurrences difference from expected: -299
side 6 had 142834 occurrences difference from expected: -23
side 7 had 142635 occurrences difference from expected: -222
─────────────────trial: 11 1000000 samples, expect=142857──────────────────
side 1 had 143248 occurrences difference from expected: 391
side 2 had 142878 occurrences difference from expected: 21
side 3 had 142229 occurrences difference from expected: -628
side 4 had 142902 occurrences difference from expected: 45
side 5 had 142685 occurrences difference from expected: -172
side 6 had 143214 occurrences difference from expected: 357
side 7 had 142844 occurrences difference from expected: -13
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
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
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>
/// @Author: Alexandre Felipe (o.alexandre.felipe@gmail.com) /// @Date: 2017-May-10
/////////////////////////////////////////////////////////////////////////////// /// 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 teh 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)
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%")