Re^2: Algorithm for cancelling common factors between two lists of multiplicands

in reply to Re: Algorithm for cancelling common factors between two lists of multiplicands
in thread Algorithm for cancelling common factors between two lists of multiplicands

There are better ways to compute factorial quotients without overflow or loss of precision.

So, now I've got my "schoolboy approach" working, care to point me at the methods clever people would use?

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Comment on Re^2: Algorithm for cancelling common factors between two lists of multiplicands

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Re^3: Algorithm for cancelling common factors between two lists of multiplicands by QM (Parson) on Aug 09, 2005 at 15:19 UTC
So, now I've got my "schoolboy approach" working, care to point me at the methods clever people would use? I was too lazy to look before, but now that I have, I was a bit off. On the other hand, I snuck in something similar in step 5 anyway. Here's what I remembered when I said that: In QOTW #2 MJD considers the n_choose_k function that computes: `sub n_choose_k { my ($n, $k) = @_; # f($n) = $n! return f($n)/f($k)/f($n-$k); }` [download] He notes that the intermediate values are very large, even though the final result is not. He submits this replacement: `sub n_choose_k { my ($n, $k) = @_; my $t = 1; for my $i (1 .. $k) { $t = $n - $k + $i; $t /= $i; } return $t; }` [download] and he notes: $t here is always an integer, and never gets bigger than necessary.* For your formula, this only applies to a small portion of the terms. You may be better off just ignoring MJD's improvement and proceeding as I outlined before. -QM -- Quantum Mechanics: The dreams stuff is made of	[reply] [d/l] [select]

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Re^3: Algorithm for cancelling common factors between two lists of multiplicands
by QM (Parson) on Aug 09, 2005 at 15:19 UTC

So, now I've got my "schoolboy approach" working, care to point me at the methods clever people would use?

In QOTW #2 MJD considers the n_choose_k function that computes:

sub n_choose_k {
  my ($n, $k) = @_;
  # f($n) = $n!
  return f($n)/f($k)/f($n-$k);
}
[download]

sub n_choose_k {
  my ($n, $k) = @_;
  my $t = 1;
  for my $i (1 .. $k) {
    $t *= $n - $k + $i;
    $t /= $i;
  }
  return $t;
}
[download]

$t here is always an integer, and never gets bigger than necessary.

-QM
--
Quantum Mechanics: The dreams stuff is made of

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