Since they don't repeat, each subsequent number requires one less bit to store.

If we store each number using the minimal number of bites, we can pack the information into 63 bytes, which is 70% of using a byte per number. (30% savings) 

$ perl -MPOSIX=ceil -e'
   my $acc = 0;
   $acc += ceil(log($_)/log(2)) for 2..90;
   CORE::say $acc;
'
63

[download]

There's still a lot of loss in there. Each number introduces a little bit of loss. By using a variable-base number, we only loss for the whole line.

If you use a variable-base number, we can pack the information into 58 bytes, which is 64% of using a byte per number. (36% savings) 

$ perl -MPOSIX=ceil -MMath::BigInt -MMath::BigRat -e'
   my $acc = Math::BigRat->new(1);
   $acc *= $_ for 2..90;
   CORE::say Math::BigRat->new($acc)->blog(256)->bceil;
'
58

[download]

In reply to Re: Data compression by 50% + : is it possible? by ikegami
in thread Data compression by 50% + : is it possible? by baxy77bax

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.