Re: Strawmans prime sieve/filter

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Message-ID	<10475868.RPHzNtd8jb@PointedEars.de> (permalink)
From	Thomas 'PointedEars' Lahn <PointedEars@web.de>
Reply-To	Thomas 'PointedEars' Lahn <cljs@PointedEars.de>
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Date	Fri, 13 Sep 2013 02:27:08 +0200
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Subject	Re: Strawmans prime sieve/filter
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Dr J R Stockton wrote:

> Thomas 'PointedEars' Lahn posted:
>> Stefan Weiss wrote:
>>> […] I just calculated the [prime] numbers up to 200M. There are 11078937
>>> of them, which would require ~44MB of storage (using 4 bytes to store a
>>> number). If I went the full 2B, the necessary disk storage would still
>>> be less than half a gig. […]
>>
>> The relevant ECMAScript implementations support only one numeric data
>> type, Number, which is an implementation of IEEE-754 double-precision
>> floating-point values.  Each such value requires 64 bits of storage (1
>> sign bit, 11 exponent bits, and 52 mantissa bits), or _8_ bytes whereas
>> each byte consists of 8 bits.
> 
> But perhaps it has not occurred to you that, /in extremis/, one can
> store nearly 64 bits in an ECMAScript IEEE-754 Double.

I believe I have just said that.

> IIRC, of the 2^64 bit patterns in an 8 byte Double, two represent the
> infinities, and about 2^53 represent NaN, which ECMAScript cannot
> "resolve".

True, but:

> One can very easily store 32 bits in a Number, using the integer values
> 0 to 2^32-1.

I do not see how that could reduce the memory footprint without some form of 
(potentially expensive) compression.  The 0-bits of the IEEE-754 value must 
*also* be stored in memory.

Another problem is the limited number of elements in an Array (2³²−2).  This 
means that there comes a point where it is no longer possible to simply push 
to an array like Stefan did, and you have to use, e. g., an Object instance 
whose properties you set (you could also use an Array instance, but there is 
no obvious advantage, and a clear disadvantage: potentially an even greater 
memory footprint), as Ben suggested.  IOW, Ben’s approach scales better than 
both Stefan‘s and the OP’s.

-- 
PointedEars

Twitter: @PointedEars2
Please do not Cc: me. / Bitte keine Kopien per E-Mail.

Thread

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

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