psini,
You may want to look at Finding all Combinations which has several iterator solutions (including mine). In essence, we want to find all possible combinations (powerset) minus the empty set.

Iterating over all combinations is as simple as counting. Think of all values in the array to be calculated as being 0s or 1s. If it is a 1, the value is included and if it is 0, it isn't. For instance:

5  -6  8  10  12  3  10
0  0   0  0   0   0  1 = 10
0  0   0  0   0   1  0 = 3
0  0   0  0   0   1  1 = 3, 10
0  0   0  0   1   0  0 = 12
0  0   0  0   1   0  1 = 12, 10
...
1  1   1  1   1   1  1 = 5, -6, 8, 10, 12, 3, 10
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#!/usr/bin/perl
use strict;
use warnings;
use List::Util 'sum';

my @amount = (5, -6, 8, 10, 12, 3, 10);
my $count = @amount;

for (1 .. 2 ** $count - 1) {
    my @bit = split //, sprintf("%.${count}b", $_);
    my $total = sum( map {$bit[$_] ? $amount[$_] : 0 } 0 .. $#bit);
    print "$total\n";
}
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