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Groups > comp.lang.javascript > #21215 > unrolled thread

Strawmans prime sieve/filter

Started byjonas.thornvall@gmail.com
First post2013-09-08 19:09 -0700
Last post2014-05-02 15:54 -0700
Articles 9 on this page of 49 — 6 participants

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  Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-08 19:09 -0700
    Re: Strawmans prime sieve/filter Stefan Weiss <krewecherl@gmail.com> - 2013-09-09 05:57 +0200
      Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-08 21:22 -0700
      Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-08 21:50 -0700
        Re: Strawmans prime sieve/filter Stefan Weiss <krewecherl@gmail.com> - 2013-09-09 13:45 +0200
          Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-09 06:33 -0700
          Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-09 06:41 -0700
            Re: Strawmans prime sieve/filter Stefan Weiss <krewecherl@gmail.com> - 2013-09-09 18:37 +0200
            Re: Strawmans prime sieve/filter Stefan Weiss <krewecherl@gmail.com> - 2013-09-09 19:54 +0200
              Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-09 12:46 -0700
                Re: Strawmans prime sieve/filter Stefan Weiss <krewecherl@gmail.com> - 2013-09-09 23:25 +0200
                  Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-09 14:58 -0700
          Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-11 10:39 +0200
            Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-11 02:54 -0700
            Re: Strawmans prime sieve/filter Stefan Weiss <krewecherl@gmail.com> - 2013-09-11 12:59 +0200
            Re: Strawmans prime sieve/filter Dr J R Stockton <reply1300@merlyn.demon.co.uk.invalid> - 2013-09-12 20:17 +0100
              Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-13 02:27 +0200
                Re: Strawmans prime sieve/filter Stefan Weiss <krewecherl@gmail.com> - 2013-09-13 04:03 +0200
                  Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-12 19:30 -0700
                  Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-13 05:15 +0200
                    Re: Strawmans prime sieve/filter Stefan Weiss <krewecherl@gmail.com> - 2013-09-13 05:27 +0200
                      Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-13 08:26 -0700
                  Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-13 08:15 -0700
                  Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-13 19:13 +0200
                    Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-13 17:15 -0700
                    Re: Strawmans prime sieve/filter Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-09-14 01:55 +0100
                      Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-14 04:20 +0200
                        Re: Strawmans prime sieve/filter Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-09-14 06:16 +0100
                          Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-14 12:10 +0200
                            Re: Strawmans prime sieve/filter Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-09-14 12:49 +0100
                              Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-14 15:23 +0200
                                Re: Strawmans prime sieve/filter Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-09-14 21:51 +0100
                                  Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-15 03:32 +0200
                                    Re: Strawmans prime sieve/filter Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-09-15 04:07 +0100
                                      Re: Strawmans prime sieve/filter Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2013-09-15 18:57 +0200
                                        Re: Strawmans prime sieve/filter Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-09-15 19:24 +0100
                                  Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-14 20:37 -0700
                  Re: Strawmans prime sieve/filter Dr J R Stockton <reply1300@merlyn.demon.co.uk.invalid> - 2013-09-14 19:38 +0100
      Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-08 22:26 -0700
        Re: Strawmans prime sieve/filter Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-09-10 22:48 +0100
          Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-11 00:36 -0700
            Re: Strawmans prime sieve/filter Ben Bacarisse <ben.usenet@bsb.me.uk> - 2013-09-11 14:47 +0100
      Re: Strawmans prime sieve/filter jonas.thornvall@gmail.com - 2013-09-08 22:33 -0700
        Re: Strawmans prime sieve/filter "Chris M. Thomasson" <no@spam.invalid> - 2013-09-09 21:08 -0700
          Re: Strawmans prime sieve/filter "Chris M. Thomasson" <no@spam.invalid> - 2013-09-10 08:52 -0700
    Re: Strawmans prime sieve/filter Dr J R Stockton <reply1300@merlyn.demon.co.uk.invalid> - 2013-09-10 19:08 +0100
    Re: Strawmans prime sieve/filter "Chris M. Thomasson" <no@spam.invalid> - 2014-04-10 22:02 -0700
      Re: Strawmans prime sieve/filter "Chris M. Thomasson" <no@spam.invalid> - 2014-05-02 15:39 -0700
        Re: Strawmans prime sieve/filter "Chris M. Thomasson" <no@spam.invalid> - 2014-05-02 15:54 -0700

Page 3 of 3 — ← Prev page 1 2 [3]

#21259

Fromjonas.thornvall@gmail.com
Date2013-09-11 00:36 -0700
Message-ID<c8df65e0-e61f-4df8-a02f-96ad2f9dfbfd@googlegroups.com>
In reply to#21255
Den tisdagen den 10:e september 2013 kl. 23:48:34 UTC+2 skrev Ben Bacarisse:
> jonas.thornvall@gmail.com writes:
> 
> 
> 
> <snip>
> 
> > So what is wrong with this code?
> 
> 
> 
> It looks over-complex, and it's not a fast as the plain sieve, so I
> 
> don't see the point of the complexity.  Maybe it kicks in for much
> 
> larger primes sets.
> 
> 
> 
> <snip>
> 
> > function sieve(max) {
> 
> > 	var D = [], primes = [];
> 
> > 	for (var q=2; q<max; q++) {
> 
> > 		if (D[q]) {
> 
> > 			for (var i=0; i<D[q].length; i++) {
> 
> > 				 var p = D[q][i];
> 
> > 				 if (D[p+q]) D[p+q].push(p);
> 
> > 				 else D[p+q]=[p];
> 
> > 			}
> 
> > 			delete D[q];
> 
> > 		} else {
> 
> > 			primes.push(q);
> 
> > 			if (q*q<max) D[q*q]=[q];
> 
> > 		}
> 
> > 	}
> 
> > 	return primes;
> 
> >  }
> 
> <snip>
> 
> 
> 
> The plain sieve of Eratosthenes goes like this:
> 
> 
> 
> function sieve(max) {
> 
>     var comp = [], primes = [], cur_prime = 2;
> 
>     while (cur_prime < max) {
> 
>         primes.push(cur_prime);
> 
>         for (var mult = 2 * cur_prime; mult < max; mult += cur_prime)
> 
>             comp[mult] = true;
> 
>         while (comp[++cur_prime]);
> 
>     }
> 
>     return primes;
> 
> }
> 
> 
> 
> On my machine, this runs five times faster for primes up to 20,000,000.
> 
> 
> 
> -- 
> 
> Ben.

Hello Ben nice implementation, i do not know if i remember wrong but is this a new twist on Eratosthenes only storing the truth values? yours indeed was much faster then strawman, and i found an even faster implementation of Eratosthenes.

But i will try to match your speeds by setting just the index like you seem todo, i found your implementation a bit hard to understand could you explain?

Here is the timings from my computer yours, mine and Eratosthenes like i remembered it but it only uses index.

Barcaisse Timing=10779

Thörnvall Timing=29738

Ereastohenes Timing=6348

Code below.

<!DOCTYPE html>
<html>
<head></head>

<script type="text/javascript">

var MAX = 30000000;

function Eratosthenes()
{
   
   // Eratosthenes algorithm to find all primes under n
   var array = [], upperLimit = Math.sqrt(n), output = [];

   // Make an array from 2 to (n - 1)
   for (var i = 0; i < n; i ++ )
   {
      array.push(true);
   }

   // Remove multiples of primes starting from 2, 3, 5, ...
   for (var i = 2; i <= upperLimit; i ++ )
   {
      if (array[i])
      {
         for (var j = i * i; j < n; j += i)
         {
            array[j] = false;
         }
      }
   }

   for (var i = 2; i < n; i ++ )
   {
      if(array[i])
      {
         output.push(i);
      }
   }
     outE = output.toString();
}



function benB()
{
   var comp = [], primes = [], cur_prime = 2;
   while (cur_prime < MAX)
   {
      primes.push(cur_prime);
      for (var mult = 2 * cur_prime; mult < MAX;
      mult += cur_prime)
      comp[mult] = true;
      while (comp[ ++ cur_prime]);

   }
   outB = primes.toString();
   return outB;
}

function jonasT()
{
   var primes = [2];
   n = 3;
   while(n < MAX)
   {
      p = true;
      k = 0;
      test = Math.sqrt(n) + 1;
      test = Math.round(test);
      while (test >= primes[k])
      {
         if  ((n % primes[k]) == 0)
         {
            p = false;
            break;
            document.write("break");
         }
         k ++ ;
      }
      if (p == true)
      {
         t = primes.length;
         primes[t] = n;
      }
      n ++ ;
   }
   outJ = primes.toString();
   return outJ;
}

var start = new Date().getTime();
benB();
var end = new Date().getTime();
var time = end - start;
outB=outB.substring(0,100);
document.write("Barcaisse=", outB, "<BR> Timing=", time, "<BR>");

var start = new Date().getTime();
jonasT();
var end = new Date().getTime();
var time = end - start;
outJ=outJ.substring(0,100);
document.write("<BR>Thörnvall=", outJ, "<BR> Timing=", time, "<BR>");

var start = new Date().getTime();
Eratosthenes(MAX);
var end = new Date().getTime();
var time = end - start;
outE=outE.substring(0,100);
document.write("<BR>Ereastohenes=",outE,"<BR> Timing=", time, "<BR>");

</script>
<body>
</body>
</html>

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#21263

FromBen Bacarisse <ben.usenet@bsb.me.uk>
Date2013-09-11 14:47 +0100
Message-ID<0.f56f47af16523795dd40.20130911144711BST.87fvtb31y8.fsf@bsb.me.uk>
In reply to#21259
jonas.thornvall@gmail.com writes:

> Den tisdagen den 10:e september 2013 kl. 23:48:34 UTC+2 skrev Ben Bacarisse:
>> jonas.thornvall@gmail.com writes:
>> 
>> 
>> 
>> <snip>
>> 
>> > So what is wrong with this code?
>> 
>> 
>> 
>> It looks over-complex, and it's not a fast as the plain sieve, so I
>> 
>> don't see the point of the complexity.  Maybe it kicks in for much
>> 
>> larger primes sets.
>> 
>> 
>> 
>> <snip>
>> 
>> > function sieve(max) {
>> 
>> > 	var D = [], primes = [];
>> 
>> > 	for (var q=2; q<max; q++) {
>> 
>> > 		if (D[q]) {
>> 
>> > 			for (var i=0; i<D[q].length; i++) {
>> 
>> > 				 var p = D[q][i];
>> 
>> > 				 if (D[p+q]) D[p+q].push(p);
>> 
>> > 				 else D[p+q]=[p];
>> 
>> > 			}
>> 
>> > 			delete D[q];
>> 
>> > 		} else {
>> 
>> > 			primes.push(q);
>> 
>> > 			if (q*q<max) D[q*q]=[q];
>> 
>> > 		}
>> 
>> > 	}
>> 
>> > 	return primes;
>> 
>> >  }
>> 
>> <snip>
>> 
>> 
>> 
>> The plain sieve of Eratosthenes goes like this:
>> 
>> 
>> 
>> function sieve(max) {
>> 
>>     var comp = [], primes = [], cur_prime = 2;
>> 
>>     while (cur_prime < max) {
>> 
>>         primes.push(cur_prime);
>> 
>>         for (var mult = 2 * cur_prime; mult < max; mult += cur_prime)
>> 
>>             comp[mult] = true;
>> 
>>         while (comp[++cur_prime]);
>> 
>>     }
>> 
>>     return primes;
>> 
>> }
>> 
>> 
>> 
>> On my machine, this runs five times faster for primes up to 20,000,000.
>> 
>> 
>> 
>> -- 
>> 
>> Ben.
>
> Hello Ben nice implementation, i do not know if i remember wrong but
> is this a new twist on Eratosthenes only storing the truth values?

No, it's just a bit faster to use the fact that an unset array element
will test false.  This is you reverse the sense of the array, you don't
have to set the elements first.  Do that to the sieve function you found
and it's yet more efficient.

> yours indeed was much faster then strawman, and i found an even faster
> implementation of Eratosthenes.

Yes, that one stops trying to sieve sooner and it starts the sieving at
the square of the current prime, rather than my naive double.  A similar
modification to mine would looks like this:

function sieve(max) {
    var comp = [], primes = [], cur_prime = 2;
    var upperLimit = Math.sqrt(max);
    while (cur_prime < upperLimit) {
        primes.push(cur_prime);
        for (var mult = cur_prime * cur_prime; mult < max; mult += cur_prime)
            comp[mult] = true;
        while (comp[++cur_prime]);
    }
    for (; cur_prime < max; cur_prime++)
        if (!comp[cur_prime])
            primes.push(cur_prime);
    return primes;
}

> But i will try to match your speeds by setting just the index like you
> seem todo, i found your implementation a bit hard to understand could
> you explain?

Just (a) remove the loop that sets 'array' initially, (b) set array[j]
to true rather than false, and (c) flip the two tests from array[i] to
!array[i].  The result is faster still (on my machine).

<snip>
-- 
Ben.

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#21222

Fromjonas.thornvall@gmail.com
Date2013-09-08 22:33 -0700
Message-ID<5837258c-4fbe-4c8d-a432-b7e8e5b59495@googlegroups.com>
In reply to#21217
Den måndagen den 9:e september 2013 kl. 05:57:27 UTC+2 skrev Stefan Weiss:
> On 2013-09-09 04:09, jonas.thornvall@gmail.com wrote:
> 
> > It writes all 1 270608 primes less then 20 000 004 into an array in
> 
> > 17 seconds by comparing the natural with the value read into the array, but
> 
> > bigger then 20 million there is to many primes to compare with and it
> 
> > gets slow. I only compare the values in prime array upto square of the
> 
> > natural.
> 
> 
> 
> I didn't look very closely, but from what I can see, you're not using
> 
> the sieve at all, you're just doing dumb trial division.
> 
> 
> 
> Read this: http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
> 
> 
> 
> Algorithms aside, is there a point to what you're doing, or is it just
> 
> recreational? No disrespect, I also like mathematical puzzles and tasks,
> 
> but if you actually need the prime numbers for something, you could just
> 
> download them.
> 
> 
> 
> - stefan

I am waiting for you to post a faster sieve of the primes upto 20 millions.
It is extrordinary that what you call trial division is faster the Eratosthenes.

Maybe i got hold of a bad implementation?

<!DOCTYPE html>
<html>
<head></head>

<script type="text/javascript">

function sieve(max) {
        var D = [], primes = [];
        for (var q=2; q<max; q++) {
                if (D[q]) {
                        for (var i=0; i<D[q].length; i++) {
                                 var p = D[q][i];
                                 if (D[p+q]) D[p+q].push(p);
                                 else D[p+q]=[p];
                        }
                        delete D[q];
                } else {
                        primes.push(q);
                        if (q*q<max) D[q*q]=[q];
                }
        }
        return primes;
 }
var start = new Date().getTime();
 sieve(20000000)
var end = new Date().getTime();
var time = end - start;
alert('Execution time: ' + time);
</script>
<body>

</body>
</html>

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#21245

From"Chris M. Thomasson" <no@spam.invalid>
Date2013-09-09 21:08 -0700
Message-ID<l0m5vq$j4m$1@speranza.aioe.org>
In reply to#21222
> wrote in message 
> news:5837258c-4fbe-4c8d-a432-b7e8e5b59495@googlegroups.com...

> Den måndagen den 9:e september 2013 kl. 05:57:27 UTC+2 skrev Stefan Weiss:
> > On 2013-09-09 04:09, jonas.thornvall@gmail.com wrote:
> >
> > > It writes all 1 270608 primes less then 20 000 004 into an array in
> >
> > > 17 seconds by comparing the natural with the value read into the 
> > > array, but
> >
> > > bigger then 20 million there is to many primes to compare with and it
> >
> > > gets slow. I only compare the values in prime array upto square of the
> >
> > > natural.

[...]

> I am waiting for you to post a faster sieve of the primes upto 20 
> millions.
> It is extrordinary that what you call trial division is faster the 
> Eratosthenes.

[...]

FWIW, here is stupid simple code that finds 1,270,607 prime numbers out of
20,000,000 with average time of 12,500 milliseconds on my little notebook
using Firefox:
______________________________________________________________
<!DOCTYPE html>
<html>
    <title>Primes</title>

    <script type="text/javascript">
        function is_prime(n)
        {
            if (isNaN(n) || ! isFinite(n) || n % 1 || n < 2)
                return false;

            if (! (n % 2)) return (n == 2);
            if (! (n % 3)) return (n == 3);

            var m = Math.sqrt(n);

            for (var i = 5; i <= m; i += 6)
            {
                if (! (n % i) || ! (n % (i + 2)))
                    return false;
            }

            return true;
        }


        function count_prime(m)
        {
            var c = 0;

            for (var n = 2; n < m; ++n)
                if (is_prime(n)) ++c;

            return c;
        }


        function main()
        {
            console.time("count_prime");

            var c = count_prime(20000000);

            console.timeEnd("count_prime");

            alert("Found " + c + " Primes.");
        }
    </script>

    <body onload="main();">

    </body>
</html>
______________________________________________________________


I have no idea if this is anywhere near what you are looking for Jonas...

;^o

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#21252

From"Chris M. Thomasson" <no@spam.invalid>
Date2013-09-10 08:52 -0700
Message-ID<l0nf7q$6sp$1@speranza.aioe.org>
In reply to#21245
"Chris M. Thomasson"  wrote in message 
news:l0m5vq$j4m$1@speranza.aioe.org...
[...]
> FWIW, here is stupid simple code that finds 1,270,607 prime numbers out of
> 20,000,000 with average time of 12,500 milliseconds on my little notebook
> using Firefox:
> ______________________________________________________________
> [...]
>         function count_prime(m)
>         {
>             var c = 0;
>
>             for (var n = 2; n < m; ++n)
>                 if (is_prime(n)) ++c;
>
>             return c;
>         }
> [...]
> ______________________________________________________________

This tiny "optimization" of the function above shaves off a couple seconds
of runtime:
______________________________________________________________
        function count_prime(m)
        {
            var c = 0;

            for (var n = 2; n < m; ++n)
            {
                if (is_prime(n)) ++c;
                if (n > 2) ++n;
            }

            return c;
        }
______________________________________________________________

Might as well skip all of the even numbers greater than two...

;^)

Since no even numbers other than two will ever be passed to the `is_prime()'
function, you can remove one of mod operations. Actually, I don't know why
I used the mod in the first place when, in this case, bitwise AND will do 
the
trick!

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#21256

FromDr J R Stockton <reply1300@merlyn.demon.co.uk.invalid>
Date2013-09-10 19:08 +0100
Message-ID<ypQ6Ba6eA2LSFwOn@invalid.uk.co.demon.merlyn.invalid>
In reply to#21215
In comp.lang.javascript message <6e464d33-47e4-41b8-bfda-19511de92915@go
oglegroups.com>, Sun, 8 Sep 2013 19:09:51, jonas.thornvall@gmail.com
posted:

>It writes all 1 270608 primes less then 20 000 004 into an array in 17 seconds by comparing the natural with the value read into the array, but
>bigger then 20 million there is to many primes to compare with and it gets slow. I only compare the values in prime array upto square of the
>natural.
> ...

(1) That 17 seconds is not very meaningful as you have not said what
your browser is, what your OS is, or what your CPU is.

(2) Have you checked your list of primes against a known-good list?

(3) In Chrome 29, WinXP sp3, P4/3G, I find 1270608 primes in under 4.6
seconds, using straight Eratosthenes as previously cited.

-- 
 (c) John Stockton, near London.                Mail ?.?.Stockton@physics.org
  Web  <http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, and links.

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#23845

From"Chris M. Thomasson" <no@spam.invalid>
Date2014-04-10 22:02 -0700
Message-ID<li7t26$lgr$1@speranza.aioe.org>
In reply to#21215
Hey Jonas, you might be interested in:

https://plus.google.com/104956987891789686401/posts/fwkWtaQKYgY

?

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#24012

From"Chris M. Thomasson" <no@spam.invalid>
Date2014-05-02 15:39 -0700
Message-ID<lk16rt$ur$1@speranza.aioe.org>
In reply to#23845
> "Chris M. Thomasson"  wrote in message 
> news:li7t26$lgr$1@speranza.aioe.org... Hey Jonas, you might be interested 
> in:
> https://plus.google.com/104956987891789686401/posts/fwkWtaQKYgY

FWIW, check the out as well:

http://webpages.charter.net/appcore/prime/prime_map_p0.bmp

(around a 2.86 mb 1000x1000 bmp)

Each intersection between the red and blue
lines are colored white and represent a point
where both x and y are prime.

x and y are unsigned integers. Lattice points
are where the x and y coordinates are prime.

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#24013

From"Chris M. Thomasson" <no@spam.invalid>
Date2014-05-02 15:54 -0700
Message-ID<lk17o4$2ns$1@speranza.aioe.org>
In reply to#24012
> "Chris M. Thomasson"  wrote in message 
> news:lk16rt$ur$1@speranza.aioe.org...
> > "Chris M. Thomasson"  wrote in message 
> > news:li7t26$lgr$1@speranza.aioe.org... Hey Jonas, you might be 
> > interested in:
> > https://plus.google.com/104956987891789686401/posts/fwkWtaQKYgY
> FWIW, check the out as well:
> http://webpages.charter.net/appcore/prime/prime_map_p0.bmp
> (around a 2.86 mb 1000x1000 bmp)
> Each intersection between the red and blue
> lines are colored white and represent a point
> where both x and y are prime.
> x and y are unsigned integers. Lattice points
> are where the x and y coordinates are prime.

I wonder what would happen if I planted DLA
seeds on the lattice points of the graph!?

Humm... I bet it would be pretty!

:^)

Example of DLA planted in a spiral...

https://plus.google.com/101799841244447089430/posts/Pmm7Qsh9W2t

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