[Numpy-discussion] Precision difference between dot and sum

[Charles R Harris]

On Mon, Nov 1, 2010 at 7:49 PM, Robert Kern <robert.kern at gmail.com> wrote:

> On Mon, Nov 1, 2010 at 20:21, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
> >
> > On Mon, Nov 1, 2010 at 5:30 PM, Joon <groups.and.lists at gmail.com> wrote:
> >>
> >> Hi,
> >>
> >> I just found that using dot instead of sum in numpy gives me better
> >> results in terms of precision loss. For example, I optimized a function
> with
> >> scipy.optimize.fmin_bfgs. For the return value for the function, I tried
> the
> >> following two things:
> >>
> >> sum(Xb) - sum(denominator)
> >>
> >> and
> >>
> >> dot(ones(Xb.shape), Xb) - dot(ones(denominator.shape), denominator)
> >>
> >> Both of them are supposed to yield the same thing. But the first one
> gave
> >> me -589112.30492110562 and the second one gave me -589112.30492110678.
> >>
> >> In addition, with the routine using sum, the optimizer gave me "Warning:
> >> Desired error not necessarily achieved due to precision loss." With the
> >> routine with dot, the optimizer gave me "Optimization terminated
> >> successfully."
> >>
> >> I checked the gradient value as well (I provided analytical gradient)
> and
> >> gradient was smaller in the dot case as well. (Of course, the the
> magnitude
> >> was e-5 to e-6, but still)
> >>
> >> I was wondering if this is well-known fact and I'm supposed to use dot
> >> instead of sum whenever possible.
> >>
> >> It would be great if someone could let me know why this happens.
> >
> > Are you running on 32 bits or 64 bits? I ask because there are different
> > floating point precisions on the 32 bit platform and the results can
> depend
> > on how the compiler does things.
>
> Eh, what? Are you talking about the sometimes-differing intermediate
> precisions? I wasn't aware that was constrained to 32-bit processors.
>
>
It seems to be more of a problem on 32 bits, what with the variety of sse*.
OTOH, all 64 bit systems have at least sse2 available together with more sse
registers and I believe the x87 instruction set is not available when
running in 64 bit mode. I may be wrong about that, these nasty details are
hard to verify, but that has also been my experience.

Chuck
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