Eratosthene test algorithm
Implemented in all programming languages
The Eratosten variety is a simple algorithm created by a mathematician of ancient Greek antiquity to search for primes up to a given integer. The algorithm is often used to compare the syntax of programming languages and the speed of compilers, or interpreters.
Algorithm:
Construire une liste de tous les entiers supérieurs à 1 et inférieurs ou égal à n. Supprimer les multiples de tous les premiers inférieurs ou égal à la racine carrée de n, ensuite, les nombres qui restent sont premiers.
The algorithms below calculate all primes, but they all do not exactly implement Eratoshen's algorithm.
Ada Awk Basic Bash C C P Prolog Python Rebol Rexx Ruby Rust Scala Scribtol Scalltalk Swift Tcl WLangage
Hell
procedure Eratosthenes(Result : out Integer) is
size : constant := 8190;
k, prime : Natural;
count : Integer;
type Ftype is array (0 .. Size) of Boolean;
Flags : Ftype;
begin
for Iter in 1 .. 10 loop
count := 0;
for i in 0 .. size loop
Flags (i) := True;
end loop;
for i in 0 .. size loop
if Flags (i) then
prime := i + i + 3;
k := i + prime;
while k <= size loop
Flags (k) := False;
k := k + prime;
end loop;
count := count + 1;
end if;
end loop;
end loop;
Result := count;
end Eratosthenes;
Awk
BEGIN {
top = 50;
n = (ARGV[1] < 1) ? 1 : ARGV[1];
while (n--)
{
for(i=2; i <= top; flags[i++]=1);
for (i=2; i <= top; i++)
{
if (flags[i])
{
for (k = i + i; k <= top; k += i)
{
flags[k] = 0;
}
}
}
}
exit;
}
Basic
QuickBasic, manuel de référence pour Apple Macintosh, by Microsoft.
defint a-z
size=50
dim flags(50)
for i=2 to size
flags(i)=-1
next
for i=2 to sqr(size)
if flags(i) then
for k=i*i to size step i
flags(k)=0
next
end if
next
for i=0 to size
if flags(i) then print i;
next
print
En Basic plus ancien:
1010 REM Quite BASIC Math Project 2000 CLS 2030 LET L = 50 2050 ARRAY N 2070 FOR I = 1 TO L 2080 LET N[I] = I 2090 NEXT I 2110 LET P = 2 2120 PRINT P 2140 FOR I = P TO L STEP P 2150 LET N[I] = 0 2160 NEXT I 2180 LET P = P + 1 2190 IF P = L THEN END 2200 IF N[P] <> 0 THEN GOTO 2120 ELSE GOTO 2180
Bash
#!/bin/bash
# Sieve of Eratosthenes from the bash scripting guide
UPPER_LIMIT=$1
let SPLIT=UPPER_LIMIT/2
Primes=( '' $(seq $UPPER_LIMIT) )
i=1
until (( ( i += 1 ) > SPLIT ))
do
if [[ -n $Primes[i] ]]
then
t=$i
until (( ( t += i ) > UPPER_LIMIT ))
do
Primes[t]=
done
fi
done
echo ${Primes[*]}
exit 0
C
/* Sieve Of Erathosthenes by Denis Sureau */ #include <stdlib.h>#include <stdio.h> void eratosthenes(int top){ int all[10000]; int idx = 0; int prime = 3; int x, j; printf("1 "); while(prime <= top){ for(x = 0; x < top; x++){ if(all[x] == prime) goto skip; } printf("%d ", prime); j = prime; while(j <= (top / prime)) { all[idx++] = prime * j; j += 1; } skip: prime+=2; } puts(""); return; } int main(int argc, char **argv) { if(argc == 2) eratosthenes(atoi(argv[1])); else eratosthenes(50); return 0; }
Une autre version sans goto proposée par un utilisateur:
#include <stdio.h>
#include <stdlib.h>
/* Sieve by Baavgai */
void sieve(int size) {
int i,j;
char *sieve = (char *) calloc(size, 1);
for (i=2; i*i <= size; i++) {
if (!sieve[i]) {
for(j = i+i; j < size; j+=i) { sieve[j] = 1; }
}
}
for (i=2; i<size; i++) {
if (!sieve[i]) { printf("%d ", i); }
}
printf("\n");
free(sieve);
}
int main() {
sieve(100);
return 0;
}
C++
/* Sieve Of Erathosthenes by Denis Sureau */ #include <stdlib.h>#include <stdio.h> #include <iostream> #include <vector> void eratosthenes(int top) { std::vector <int> all = { top }; int idx = 0; std::cout << "1 "; for(int prime = 3; prime <= top; prime += 2) { bool flag = false; for(int x = 0; x < top; x++) { if(all[x] == prime) { flag = true; break; } } if(flag == false) { std::cout << prime << " "; int j = prime; while(j <= (top / prime)) { all[idx++] = prime * j; j += 1; } } } std::cout << std::endl; return; } int main(int argc, char **argv) { if(argc == 2) eratosthenes(atoi(argv[1])); else eratosthenes(50); return 0; }
C# (C Sharp)
using System;
class App
{
public static int Main(String[] args)
{
int num;
bool[] flags = new bool[51];
long i, k;
int count = 0;
num = System.Convert.ToInt32(args[0]);
if(num < 1) num = 1;
while(num-- > 0)
{
count = 0;
for(i = 2; i <= 50; i++)
{
flags[i] = true;
}
for(i = 2; i <= 50; i++)
{
if(flags[i])
{
for(k = i + i; k <= 50; k += i)
{
flags[k] = false;
}
count++;
}
}
}
Console.WriteLine("Count: " + count.ToString());
return(0);
}
}
D
import std.stdio;
bool[8191] flags;
int main()
{
int i, count, prime, k, iter;
writeln("10 iterations");
for (iter = 1; iter <= 10; iter++)
{
count = 0;
flags[] = 1;
for (i = 0; i < flags.length; i++)
{
if (flags[i])
{
prime = i + i + 3;
k = i + prime;
while (k < flags.length)
{
flags[k] = 0;
k += prime;
}
count += 1;
}
}
}
writefln("%d primes", count);
return 0;
}
Source: D language Documentation.
Eiffel
class FIBONACCI
feature
fib (k: INTEGER): INTEGER is
require
pre_fib: k >= 0 do
if k = 0 then
Result := 0
else
if k = 1 then
Result := 1
else
Result := fib (k-2) + fib (k-1) end
end;
Euphoria
-- Sieve Of Erathosthenes by Derek Parnell
-- Language: Euphoria v3.1.1 (www.rapideuphoria.com)
include get.e
procedure eratosthenes(integer target)
sequence sieve
integer next_prime
integer limit
sieve = repeat(0, target)
limit = floor(power(target, 0.5))
sieve[1] = 1
next_prime = 2
while next_prime <= target and next_prime != 0 do
if next_prime <= limit then
for i = next_prime + next_prime to target by next_prime do
sieve[i] = 1
end for
end if
printf(1, "%d ", next_prime)
next_prime = find_from(0, sieve, next_prime+1)
end while
return
end procedure
procedure main(sequence argv)
integer n
n = 50
if length(argv) >= 3 then
argv = value(argv[3])
n = argv[2]
end if
eratosthenes(n)
end procedure
main( command_line() )
F# (F Sharp)
let is_prime n =
let max = int_of_float (Math.Sqrt( float_of_int n ))
not ({ 2 .. max } |> Seq.filter ( fun d -> n%d = 0) |> Seq.nonempty)
let primes = [0 .. top] |> List.filter is_prime
Forth
7919 2/ constant maxp
: primes ( -- n )
here maxp 1 FILL
1 ( count, including 2 )
maxp 0 DO
I here + C@ IF
I 2* 3 + ( dup .) DUP I + ( prime current )
begin DUP maxp U<
while 0 over here + C!
over +
repeat
2drop 1+
then
loop ;
primes . \ 1000
Fortran
* Sieve of Eratosthenes by Chuck Bouldin
top = 50
logical*2 flags(top)
integer*2 i,j,k,count,iter,prime
n = long(362)
do 92 iter = 1,10
count=0
i=0
do 10 i = 1,top
10 flags(i) = .true.
do 91 i = 1,top
if (.not. flags(i)) go to 91
prime = i + i + 3
count = count + 1
k = i + prime
if (k .gt. top) go to 91
do 60 j = k, top, prime
60 flags(j) = .false.
91 continue
92 continue
write (9,*) count," primes in ",(long(362)-n)/60.0," seconds "
pause
end
Go
(Selon la documentation du language)
func Generate(ch chan<- int) {
for i := 2; ; i++ {
ch <- i
}
}
func Filter(in <-chan int, out chan<- int, prime int) {
for {
i := <-in // Receive value from 'in'.
if i%prime != 0 {
out <- i
}
}
}
func main() {
ch := make(chan in
go Generate(ch)
for i := 0; i < 10; i++ {
prime := <-ch
fmt.Println(prime)
ch1 := make(chan int)
go Filter(ch, ch1, prime)
ch = ch1
}
}
Haskell
primes = sieve [ 2.. ] where sieve (p:x) = p : sieve [ n | n <- x, n `mod` p > 0 ]
Java
public class Eratosthenes
{
public static void main(String[] args)
{
int N = Integer.parseInt(args[0]);
boolean[] isPrime = new boolean[N + 1];
for (int i = 2; i <= N; i++)
isPrime[i] = true;
for (int i = 2; i*i <= N; i++)
{
if (isPrime[i])
{
for (int j = i; i*j <= N; j++)
isPrime[i*j] = false;
}
}
int primes = 0;
for (int i = 2; i <= N; i++)
{
if (isPrime[i])
System.out.println(" " + i);
}
}
}
JavaScript
<script language="JavaScript">
/* Sieve Of Erathosthenes by Denis Sureau */
function Eratosthenes(element, top)
{
var all = new Uint8Array(new ArrayBuffer(top));
var idx = 0;
var prime = 3;
var x, j;
element.innerHTML = "1 ";
while(prime <= top var flag="true;" for x="0;" x top x if all x="=" prime flag="false;" break if flag element.innerHTML="prime" j="prime;" while j="(top" prime all idx="prime" j j="1;" prime="2;" element.innerHTML="<br>" return lt script gt lt div id="primediv" onclick="Eratosthenes(this, 50);" gt Click to start... lt div gt pre>
Julia
# Sieve of Erasthotenes in Julia
# By Denis Sureau 14/2/2014
function eratosthenes(size)
all=ones(Int32, size)
println(1)
println(2)
idx = 1
prime = 3
while prime <= size
if !in(prime, all)
println(prime)
idx += 1
j = prime
while (j <= (size / prime))
all = [all, prime * j]
j += 1
end
end
prime += 2
end
println
end
eratosthenes(50)
Lisp
(define divides (m n) (= (mod n m) 0))
(define seq (m n)
(if (> m n) `()
(cons m (seq (+ 1 m) n))))
(define remove-multiples (n L)
(if (null? L) `()
(if (divides (n (car l))
(remove-multiples n (cdr L))
(cons (car L)
(remove-multiples n (cdr L))))))
Lua
-- By Darren Kirby
x = arg[1]
y = math.floor(math.sqrt(x))
primes = {}
set = {}
for i=2,x do
table.insert(set, i)
end
function isFactor(index, value)
if math.mod(value, checkint) == 0 then
table.remove(set, index)
end
end
while set[1] <= y do
table.insert(primes, set[1])
checkint = set[1]
table.remove(set, 1)
for i,v in ipairs(set) do isFactor(i,v) end
end
for key, value in primes do
io.write(value .. " ")
end
for key, value in set do
io.write(value .. " ")
end
print()
Nim
import math
proc eratosthenes(n): auto =
prime = newSeq[int8](n+1)
prime[0] = 1;
prime[1] = 1
for i in 0 .. int sqrt(float n):
if prime[i] == 0:
for j in countup(i*i, n, i):
prime[j] = 1
discard eratosthenes(1000)
Source: Hookrace/Conversion d'une des nombreuses solutions en Python.
Oberon
MODULE Eratosthenes;
(* Active Oberon Demo *)
IMPORT Streams;
CONST
N = 50;
Terminate = -1;
VAR log: Streams.Stream;
TYPE
Sieve = POINTER TO SieveDesc;
SieveDesc = RECORD (OBJECT)
VAR prime, n: INTEGER; available: BOOLEAN; next: Sieve;
PROCEDURE Set (i: INTEGER);
BEGIN {EXCLUSIVE}
PASSIVATE (~available); n := i; available := TRUE
END Set;
PROCEDURE Change;
BEGIN {EXCLUSIVE} available := FALSE
END Change;
PROCEDURE & Init;
BEGIN prime := 0; available := FALSE; next := NIL
END Init;
BEGIN {PARALLEL(2)}
LOOP
PASSIVATE (available);
IF n = Terminate THEN
IF next # NIL THEN next.Set (n) END;
EXIT
ELSE
IF prime = 0 THEN
log.Int(n); log.Ln;
prime := n; NEW (next)
ELSIF (n MOD prime) # 0 THEN next.Set (n)
END;
Change
END
END
END SieveDesc;
Gen = POINTER TO GenDesc;
GenDesc = RECORD
VAR s: Sieve; i: INTEGER;
BEGIN {PARALLEL(2)}
NEW (s);
FOR i := 2 TO N-1 DO s.Set (i) END;
s.Set (Terminate)
END GenDesc;
PROCEDURE Start*;
VAR g: Gen;
BEGIN
NEW(log, "Eratosthenes", 70);
NEW (g)
END Start;
END Eratosthenes.
Eratosthenes.Start
Ocaml
(* (c) 2003 David Van Horn -
Licensed under the Academic Free License version 2.0 *)
open List
type integer = Int of int
let number_two = Int(2)
let number_zero = Int(0)
let is_less_than_two (Int n) = n < 2
let incr (Int n) = Int(n + 1)
let decr (Int n) = Int(n - 1)
let is_number_zero (Int n) = n = 0
let iota n =
let rec loop curr counter =
if is_less_than_two counter then []
else curr::(loop (incr curr) (decr counter))
in
loop number_two n
let sieve lst =
let rec choose_pivot = function
| [] -> []
| car::cdr when is_number_zero car ->
car::(choose_pivot cdr)
| car::cdr ->
car::(choose_pivot (do_sieve car (decr car) cdr))
and do_sieve step current lst =
match lst with
| [] -> []
| car::cdr ->
if is_number_zero current
then number_zero::(do_sieve step (decr step) cdr)
else car::(do_sieve step (decr current) cdr)
in
choose_pivot lst
let is_prime n =
match rev (sieve (iota n)) with
x::_ -> not (is_number_zero x)
Oz
functor
import System Application
define Args N Flags Start Stop in
[Args] = {Application.getArgs plain}
N = {String.toInt Args}
Start = 2
Top = 50
Flags = {BitArray.new Start Stop}
for I in Start..Top do {BitArray.set Flags I} end
for I in 1..N do
for J in Start..Top do
if {BitArray.test Flags J} then
for K in J+J..Top;J do {BitArray.clear Flags K} end
end
end
end
{System.showInfo "Count: "#{BitArray.card Flags}}
{Application.exit 0}
end
Pascal
program Eratosthenes;
const N=1000;
var a:ARRAY[1..N] of boolean;
i,j,m:word;
begin
for i:=1 TO N do a[i]:=TRUE;
m:=trunc(sqrt(N));
for i:=2 to m do
if a[i] then for j:=2 to N DIV i do a[i*j]:=FALSE;
for i:=1 to N do if a[i] then write(i:4);
end.
Perl
Contribution des utilisateurs.
#!/usr/bin/perl
use strict;
use integer;
my $count = 0;
my $top = 50;
my @flags = (0 .. $top);
for my $i (2 .. int(sqrt($top)) + 1)
{
next unless defined $flags[$i];
for (my $k=$i+$i; $k <= $top; $k+=$i)
{
undef $flags[$k];
}
}
print "Here is the list of primes from 1 to $top:\n";
for my $j ( 1 .. $top)
{
print ("$j ") && $count++ if defined
$flags[$j];
}
print "\n";
print "Number of primes found: $count\n";
Code source
PHP
<?php
/* Sieve Of Erathosthenes by Denis Sureau */
function eratosthenes($n)
{
$all=array();
$prime=1;
echo 1," ",2;
$i=3;
while($i<=$n)
{
if(!in_array($i,$all))
{
echo " ",$i;
$prime+=1;
$j=$i;
while($j<=($n/$i))
{
array_push($all,$i*$j);
$j+=1;
}
}
$i+=2;
}
echo "\n";
return;
}
eratosthenes(50);
?>
Prolog
% Sieve of Eratosthene
% Le Huitouze and Ridoux translated by DGS
$ erathostenes :- freeze(L,prime(L)),
list_of_ints(2,L).
$ prime([X|L]) :-
write(X), nl,
freeze(L,sieve(X,L,Canal)),
freeze(Canal,prime(Canal)).
$ sieve(X,[Nb|L],Canal) :-
mod(Nb,X,0), !,
freeze(L,sieve(X,L,Canal)).
$ sieve(X,[Nb|L],[Nb|Canal2]) :-
freeze(L,sieve(X,L,Canal2)).
$ list_of_ints(X,[X|L]) :-
plus(X,1,X1),
list_of_ints(X1,L)..
Python 3
def eratosthenes(n):
all = []
prime = 1
print(1)
print(2)
i = 3
while (i <= n):
if i not in all:
print(i, ",")
prime += 1
j = i
while (j <= (n / i)):
all.append(i * j)
j += 1
i += 2
print("\n")
eratosthenes(1000)
Contribution d'un utilisateur plus conforme à l'algorithme du crible d'Eratosthène:
# Sieve by Baavgai
def eratosthenes(n):
sieve = [ True for i in range(n+1) ]
def markOff(pv):
for i in range(pv+pv, n+1, pv):
sieve[i] = False
markOff(2)
for i in range(3, n+1):
if sieve[i]:
markOff(i)
return [ i for i in range(1, n+1) if sieve[i] ]
print(eratosthenes(100))
Rebol
ctr: to-integer to-string system/script/args
ctr: either ctr < 1 [ 1 ] [ ctr ]
top: 50
while [ ctr > 0 ]
[
flags: copy []
for i 0 top 1
[
insert tail flags 1
]
flags: head flags
for i 2 top 1
[
p: pick flags i
if p = 1
[
k: i + i
while [ k <= top ]
[
change at flags k 0
k: k + i
]
]
]
ctr: ctr - 1
]
Rexx
limit = 50
isPrime. = 1
do n=2 to limit
if isPrime.n then
call anotherPrime n
end
exit 0
anotherPrime
arg prime
say right( prime, length( limit ) )
do multiple=prime by prime to limit
isPrime.multiple = 0
end
return
Ruby
# sieve of Eratosthenes from the ruby distro
top = Integer(ARGV.shift || 100)
sieve = []
for i in 2 .. top
sieve[i] = i
end
for i in 2 .. Math.sqrt(top)
next unless sieve[i]
(i*i).step(top, i) do |j|
sieve[j] = nil
end
end
puts sieve.compact.join " "
Rust
fn sieve(bound: uint) -> ~[uint] {
let mut primes = std::vec::from_fn(bound+1, |num| num == 2 || num & 1 != 0);
for num in count(3u, 2).filter(|&num| primes[num]).take_while(|&num| num * num <= bound) {
for j in range_step_inclusive(num*num, bound, num) {
primes[j] = false;
}
}
primes.move_iter().enumerate().skip(2).filter_map(|(i, p)| if p {Some(i)} else {None}).collect::<~[uint]>()
}
fn main() {
assert_eq!(sieve(20), ~[2, 3, 5, 7, 11, 13, 17, 19]);
}
Source: jsanders sur Github.
Scala
object Sieve
{
def ints(n: Int): Stream[Int] =
Stream.cons(n, ints(n+1))
def primes(nums: Stream[Int]): Stream[Int] =
Stream.cons(nums.head, primes ((nums tail)
filter (x => x % nums.head != 0)) )
def main(args: Array[String]): Unit =
{
val n = Integer.parseInt(args(0))
System.out.println(primes(ints(2)) take n toList)
}
}
Scheme
(define (sieve-of-eratosthenes n)
(let ((table (make-bit-string (- n 2) #t)))
(define (prime? k) (bit-string-ref table (- k 2)))
(define (not-prime! k) (bit-string-clear! table (- k 2)))
(loop ((for k (in-range (from 2) (up-to n))))
(if (prime? k)
(loop ((for i (in-range (from (* 2 k)) (up-to n) (by k))))
(not-prime! i))))
(collect-list (for k (in-range (from 2) (up-to n)))
(if (prime? k))
k)))
# Sieve of Eratosthenes par Denis Sureau
array sieve(int top)
array all = [ top ]
array somelist = [1]
int idx = 0
for int prime in 3 -- top step 2
if prime in all ? continue
somelist.push(prime)
int j = prime
while j <= (top / prime)
all[idx] = prime * j
idx + 1
j + 1
/while
/for
return somelist
array a = sieve(1000)
print a
Smalltalk
" Sieve of Erastosthenes in Smalltalk by Rob Hoelz
Object subclass: #Sieve
instanceVariableNames: 'primes'
classVariableNames: ''
poolDictionaries: ''
category: nil.
!Sieve class methodsFor: 'instance creation'!
new: limit
|r|
r := super new.
r init: limit.
^r
! !
!Sieve methodsFor: 'instance initialization'!
init: limit
primes := Array new: limit.
primes at: 1 put: 0.
2 to: limit do: [:x| primes at: x put: 1]
! !
!Sieve methodsFor: 'prime generation'!
generate
|currPrime|
currPrime := 2.
[((currPrime * currPrime) <= (primes size))]
whileTrue: [self removeMultiples: currPrime. currPrime :=
self nextPrime: currPrime]
! !
!Sieve methodsFor: 'printing'!
printPrimes
|index|
index := 1.
primes do: [:x| (x = 1) ifTrue:
[Transcript show: (index displayString). Transcript show: ' ']. index :=
index + 1].
Transcript cr
! !
!Sieve methodsFor: 'private'!
removeMultiples: currPrime
|index|
index := currPrime * 2.
[(index <= (primes size))]
whileTrue: [primes at: index put: 0. index := index + currPrime]
!
nextPrime: currPrime
|index|
index := currPrime + 1.
[(index <= (primes size))] whileTrue:
[(1 = (primes at: index)) ifTrue: [^index]. index := index + 1].
^(primes size)
! !
|argv limit s|
argv := Smalltalk arguments.
limit := (argv at: 1) asInteger.
s := Sieve new: limit.
s generate.
s printPrimes.
Swift
func eratosthenes(n: Int)-> sieveResult {
var sieve = [Int] 0 ..< n
var i = 1
let top = Int(sqrt(Double(n)))
return sieveResult {
while ++i < n {
if sieve[i] != 0 {
if i <= top {
for notPrime in stride(from: i*i, to: n, by: i) {
sieve[notPrime] = 0
}
}
return i
}
}
return nil
}
}
Tcl
# By Sam Shen
set n 50
narray create sieve $n
sieve status
sieve map {
if ![]
{
inc = @0 + 2;
for (i = @0 + inc; i < @#0; i += inc)
{
[i] = 1;
}
}
}
sieve map
{
if ![]
{
printf("%4d ", @0 + 2);
}
post { printf("\n"); }
}
WLangage
Proposé par l'auteur:
(c) 2010 Jacques De Schryver
Licensed under the Academic Free License.
i, j, k sont entiers = 1
tantque i <= 1000
i += (1 + (i>2))
k = 1
POUR j = 2 A Racine(i)
SI i modulo j = 0 ALORS k = 0
FIN
SI k = 1 ALORS Description_de_l_erreur += i + " ; "
FIN
Voir aussi
- Le programme "Hello world!" (Salut le monde!) dans tous les langages de programmation.
- Histoire et évolution des langages pour ordinateur.
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Les programmes sont du domaine public ou écrit par moi-même ou contribués par les utilisateurs.
Les programmes sont du domaine public ou écrit par moi-même ou contribués par les utilisateurs.