[dmlorenzetti]

Nice example, but to those considering implementing this in their own code, please don't use that convergence test in practice.

First, you really don't want to do that division x/y, which is slow, and which fails if y==0. It's much cheaper and safer to compare "abs(x-y) < 1e-10*y".

Also, you almost always want to compare (x-y) to an absolute convergence limit (in addition to your relative tolerance), in case x and y are very near zero.

Finally, if you really want a generic converge function that can be re-used elsewhere, you might want to allow for non-convergent processes. This requires tracking the number of iterations, and bailing when it gets too large.

By the way, now that your convergence function wants to know (x-y) rather than x and y individually, you might consider rewriting your logic functions to return the predicted change, rather than the final state. This avoids forcing a re-calculation of the change, which typically was already known in the logic function. It also avoids floating-point problems in which the calculated change x-y differs from the predicted change that produced y in the first place.

[tikhonj]

Of course, part of the beauty of his approach is that you can incorporate most of your changes just by editing the converge function and not messing up the rest of the code.

The last point does require changing the main code, but it's still easier to do with an external converge function like this.

[thaumasiotes]

> First, you really don't want to do that division x/y, which is slow, and which fails if y==0. It's much cheaper and safer to compare "abs(x-y) < 1e-10*y".

I might be missing something, but won't your cheaper and safer fragment also fail when y is zero (or negative)?

[dmlorenzetti]

Sorry, I wasn't clear. I meant that performing the test, as originally given, will induce a divide-by-zero error. The modified test is safe against that; however, as you point out, it will still fail to indicate convergence (which is one reason to include an absolute tolerance as well).

And as you point out, you need to take the abs(y) as well, on the right-hand side.

Thanks for adding clarity.