use strict;
use warnings;
use Benchmark 'cmpthese';

sub decode
 {
 my $total= shift;
 my $delta= 0;
 my $diff= 0;
 foreach (@_) {
    $delta += $_;
    $diff += $delta;
    }
 my $original= ($total-$diff)/(1+scalar @_);
 my @results;
 my $value= $original;
 foreach (@_) {
    $value += $_;
    push (@results, $value);
    }
 return ($original, @results);
 }

sub decode2
 {
 my $total= shift;
 my $delta= 0;
 my $diff= 0;
 foreach (@_) {
    $delta += $_;
    $diff += $delta;
    }
 my $original= ($total-$diff)/(1+scalar @_);
 my $value= $original;
 my @results= map {
    $value += $_;
    } @_;
 return ($original, @results);
 }

sub decode3 {
    my ($dc, $next);
    $_[0] = -$_[0];
    $dc -= $_ for @_; # subtract the sum of all elements from the firs
+t
    $_[0] = $dc/@_ - $_[1];
    return map { $next += $_ } @_;
}


sub encode
 {
 my $prev= shift;
 my $total= $prev;
 my @results;
 while (my $value= shift) {
    my $delta= $value-$prev;
    push (@results, $delta);
    $prev= $value;
    $total += $value;
    }
 return ($total, @results);
 }

sub test
 {
 print ("original: @_\n");
 my @x= encode (@_);
 print ("encoded: @x\n");
 my @y= decode3 (@x);
 print ("decoded: @y\n");
 die "error- mismatch" unless scalar(@y)==scalar(@_);
 foreach (@_) {
    die "error- mismatch" unless $_ == shift(@y);
    }
 }

 
my @d1= (1000, 1001, 980, 1024, 1023);
test (@d1);

my @d2= (
     8636,
       460, 
    17372, 
      242, 
       305, 
       347, 
       212, 
      102, 
       738, 
   43797, 
     1769, 
       832, 
    16127, 
       481, 
       233, 
       441, 
       188, 
    2812, 
       430, 
       463, 
    24576, 
       829, 
     5078, 
    50620, 
    89922, 
     1536, 
       339, 
       396, 
    66560, 
     5629, 
       106, 
     4404, 
     3172, 
    28672, 
     1496, 
     2370, 
       495, 
     1264, 
       793, 
    5148, 
       95, 
     8192, 
       408, 
     4096, 
       368, 
       456, 
       776, 
    36080, 
   219104, 
   980912, 
   11607, 
    43496, 
       219, 
      570, 
      563, 
   53248, 
   11361, 
     1916, 
       718, 
    20480, 
     3465, 
        32, 
       88, 
        43, 
       100, 
       226, 
    10042, 
       769, 
       262, 
       246, 
     2837, 
       530, 
     2507, 
     1529, 
     2560, 
     1146, 
       457, 
       517, 
    43520, 
     1448, 
       260, 
        75, 
       247, 
       775, 
       927, 
       517, 
    16606, 
       126, 
       832, 
         5, 
       457, 
    94208, 
    52110, 
     2873, 
    1228, 
   94208, 
   56704, 
       480, 
        48, 
       173, 
       28, 
    24576, 
       391, 
       145, 
     1615, 
       239, 
       106, 
      508, 
       704 );

test (@d2);

my @x= encode (@d2);
cmpthese ( 0, {
   'for' => sub { decode (@x); },
   'map' => sub { decode2 (@x); },
   'Aristotle' => sub { decode3 (@x); },
   });
[download]