# [Numpy-discussion] Numpy float precision vs Python list float issue

Charles R Harris charlesr.harris@gmail....
Mon Apr 20 11:03:39 CDT 2009

```On Mon, Apr 20, 2009 at 9:49 AM, Rob Clewley <rob.clewley@gmail.com> wrote:

> On Mon, Apr 20, 2009 at 10:48 AM, David Cournapeau
> <david@ar.media.kyoto-u.ac.jp> wrote:
> > Rob Clewley wrote:
> >> David,
> >>
> >> you'd ever get non-zero error after the forward and inverse transform,
> >> but why his implementation using lists gives zero error but using
> >> arrays he gets something of order 1e-15.
> >>
> >
> > That's more likely just an accident. Forward + inverse = id is the
> > surprising thing, actually. In any numerical package, if you do
> > ifft(fft(a)), you will not recover a exactly for any non trivial size.
> > For example, with floating point numbers, the order in which you do
> > operations matters, so:
> <SNIP ARITHMETIC>
> > Will give you different values for d and c, even if you "on paper",
> > those are exactly the same. For those reasons, it is virtually
> > impossible to have exactly the same values for two different
> > implementations of the same algorithm. As long as the difference is
> > small (if the reconstruction error falls in the 1e-15 range, it is
> > mostly likely the case), it should not matter,
>
> I understand the numerical mathematics behind this very well but my
> point is that his two algorithms appear to be identical (same
> operations, same order), he simply uses lists in one and arrays in the
> other. It's not like he used vectorization or other array-related
> operations - he uses for loops in both cases. Of course I agree that
> 1e-15 error should be acceptable, but that's not the point. I think
> there is legitimate curiosity in wondering why there is any difference
> between using the two data types in exactly the same algorithm.
>

Well, without an example it is hard to tell. Maybe the print formats are
different precisions and the list values are just getting rounded.

Chuck

<snip>
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