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

[download]
We realize that we can simplify the first loop if we simply subtract the first element from $original later: 
sub decode2 {
    my $total = shift;
    my $diff;
    $diff += $_ for @_;
    my $original= ($total-$diff)/(@_+1) - $_[0];
    my $value= $original;
    my @results= map { $value += $_ } @_;
    return ($original, @results);
}

[download]
Now we realize we can rearrange the return if we include the $original in the map: 
sub decode2 {
    my $total = shift;
    my $diff;
    $diff += $_ for @_;
    my $original= ($total-$diff)/(@_+1) - $_[0];
    my $next;
    my @results= map { $next += $_ } $original, @_;
    return @results;
}

[download]

This also lets us get rid of the intermediary @results array altogether.

Next we realize that we needn't shift off the total, because rather than summing everything into $diff first and subtracting that from $total later, we can simply turn the addition loop into a subtraction loop. For that, we have to flip the sign on the total. Note that not shifting off the total affects many locations in the code. 
sub decode2 {
    my $dc;
    $_[0] = -$_[0];
    $dc -= $_ for @_; # subtract the sum of all elements from the firs
+t
    my $original= $dc/@_ - $_[1];
    my $next;
    return map { $next += $_ } $original, splice @_, 1;
}

[download]

$dc is an inaccurate name of course.. the DC component for the values is actually $dc/@_ - but oh well.

Some logical cleanup: rather than declaring a new variable and splicing from @_, we can just modify the first value inplace. And thus, a massive cleanup later, we have 
sub decode2 {
    my ($dc, $next);
    $_[0] = -$_[0];
    $dc -= $_ for @_; # subtract the sum of all elements from the firs
+t
    $_[0] = $dc/@_ - $_[1];
    return map { $next += $_ } @_;
}

[download]
____________
Makeshifts last the longest.

In reply to Re: Perl Drag Racing - sum/delta list by Aristotle
in thread Perl Drag Racing - sum/delta list by John M. Dlugosz

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