[Numpy-discussion] Bug in logaddexp2.reduce
Charles R Harris
charlesr.harris@gmail....
Thu Apr 1 09:37:47 CDT 2010
On Thu, Apr 1, 2010 at 12:46 AM, Anne Archibald
<peridot.faceted@gmail.com>wrote:
> On 1 April 2010 02:24, Charles R Harris <charlesr.harris@gmail.com> wrote:
> >
> >
> > On Thu, Apr 1, 2010 at 12:04 AM, Anne Archibald <
> peridot.faceted@gmail.com>
> > wrote:
> >>
> >> On 1 April 2010 01:59, Charles R Harris <charlesr.harris@gmail.com>
> wrote:
> >> >
> >> >
> >> > On Wed, Mar 31, 2010 at 11:46 PM, Anne Archibald
> >> > <peridot.faceted@gmail.com>
> >> > wrote:
> >> >>
> >> >> On 1 April 2010 01:40, Charles R Harris <charlesr.harris@gmail.com>
> >> >> wrote:
> >> >> >
> >> >> >
> >> >> > On Wed, Mar 31, 2010 at 11:25 PM, <josef.pktd@gmail.com> wrote:
> >> >> >>
> >> >> >> On Thu, Apr 1, 2010 at 1:22 AM, <josef.pktd@gmail.com> wrote:
> >> >> >> > On Thu, Apr 1, 2010 at 1:17 AM, Charles R Harris
> >> >> >> > <charlesr.harris@gmail.com> wrote:
> >> >> >> >>
> >> >> >> >>
> >> >> >> >> On Wed, Mar 31, 2010 at 6:08 PM, <josef.pktd@gmail.com> wrote:
> >> >> >> >>>
> >> >> >> >>> On Wed, Mar 31, 2010 at 7:37 PM, Warren Weckesser
> >> >> >> >>> <warren.weckesser@enthought.com> wrote:
> >> >> >> >>> > T J wrote:
> >> >> >> >>> >> On Wed, Mar 31, 2010 at 1:21 PM, Charles R Harris
> >> >> >> >>> >> <charlesr.harris@gmail.com> wrote:
> >> >> >> >>> >>
> >> >> >> >>> >>> Looks like roundoff error.
> >> >> >> >>> >>>
> >> >> >> >>> >>>
> >> >> >> >>> >>
> >> >> >> >>> >> So this is "expected" behavior?
> >> >> >> >>> >>
> >> >> >> >>> >> In [1]: np.logaddexp2(-1.5849625007211563,
> >> >> >> >>> >> -53.584962500721154)
> >> >> >> >>> >> Out[1]: -1.5849625007211561
> >> >> >> >>> >>
> >> >> >> >>> >> In [2]: np.logaddexp2(-0.5849625007211563,
> >> >> >> >>> >> -53.584962500721154)
> >> >> >> >>> >> Out[2]: nan
> >> >> >> >>> >>
> >> >> >> >>> >
> >> >> >> >>> > Is any able to reproduce this? I don't get 'nan' in either
> >> >> >> >>> > 1.4.0
> >> >> >> >>> > or
> >> >> >> >>> > 2.0.0.dev8313 (32 bit Mac OSX). In an earlier email T J
> >> >> >> >>> > reported
> >> >> >> >>> > using
> >> >> >> >>> > 1.5.0.dev8106.
> >> >> >> >>>
> >> >> >> >>>
> >> >> >> >>>
> >> >> >> >>> >>> np.logaddexp2(-0.5849625007211563, -53.584962500721154)
> >> >> >> >>> nan
> >> >> >> >>> >>> np.logaddexp2(-1.5849625007211563, -53.584962500721154)
> >> >> >> >>> -1.5849625007211561
> >> >> >> >>>
> >> >> >> >>> >>> np.version.version
> >> >> >> >>> '1.4.0'
> >> >> >> >>>
> >> >> >> >>> WindowsXP 32
> >> >> >> >>>
> >> >> >> >>
> >> >> >> >> What compiler? Mingw?
> >> >> >> >
> >> >> >> > yes, mingw 3.4.5. , official binaries release 1.4.0 by David
> >> >> >>
> >> >> >> sse2 Pentium M
> >> >> >>
> >> >> >
> >> >> > Can you try the exp2/log2 functions with the problem data and see
> if
> >> >> > something goes wrong?
> >> >>
> >> >> Works fine for me.
> >> >>
> >> >> If it helps clarify things, the difference between the two problem
> >> >> input values is exactly 53 (and that's what logaddexp2 does an exp2
> >> >> of); so I can provide a simpler example:
> >> >>
> >> >> In [23]: np.logaddexp2(0, -53)
> >> >> Out[23]: nan
> >> >>
> >> >> Of course, for me it fails in both orders.
> >> >>
> >> >
> >> > Ah, that's progress then ;) The effective number of bits in a double
> is
> >> > 53
> >> > (52 + implicit bit). That shouldn't cause problems but it sure looks
> >> > suspicious.
> >>
> >> Indeed, that's what led me to the totally wrong suspicion that
> >> denormals have something to do with the problem. More data points:
> >>
> >> In [38]: np.logaddexp2(63.999, 0)
> >> Out[38]: nan
> >>
> >> In [39]: np.logaddexp2(64, 0)
> >> Out[39]: 64.0
> >>
> >> In [42]: np.logaddexp2(52.999, 0)
> >> Out[42]: 52.999000000000002
> >>
> >> In [43]: np.logaddexp2(53, 0)
> >> Out[43]: nan
> >>
> >> It looks to me like perhaps the NaNs are appearing when the smaller
> >> term affects only the "extra" bits provided by the FPU's internal
> >> larger-than-double representation. Some such issue would explain why
> >> the problem seems to be hardware- and compiler-dependent.
> >>
> >
> > Hmm, that 63.999 is kinda strange. Here is a bit of code that might
> confuse
> > a compiler working with different size mantissas:
> >
> > @type@ npy_log2_1p@c@(@type@ x)
> > {
> > @type@ u = 1 + x;
> > if (u == 1) {
> > return LOG2E*x;
> > } else {
> > return npy_log2@c@(u) * x / (u - 1);
> > }
> > }
> >
> > It might be that u != 1 does not imply u-1 != 0.
>
> That does indeed look highly suspicious. I'm not entirely sure how to
> work around it. GSL uses a volatile declaration:
>
> http://www.google.ca/codesearch/p?hl=en#p9nGS4eQGUI/gnu/gsl/gsl-1.8.tar.gz%7C8VCQSLJ5jR8/gsl-1.8/sys/log1p.c&q=log1p
> On the other hand boost declares itself defeated by optimizing
> compilers and uses a Taylor series:
>
> http://www.google.ca/codesearch/p?hl=en#sdP2GRSfgKo/dcplusplus/trunk/boost/boost/math/special_functions/log1p.hpp&q=log1p&sa=N&cd=7&ct=rc
> While R makes no mention of the corrected formula or optimizing
> compilers but takes the same approach, only with Chebyshev series:
>
> http://www.google.ca/codesearch/p?hl=en#gBBSWbwZmuk/src/base/R-2/R-2.3.1.tar.gz%7CVuh8XhRbUi8/R-2.3.1/src/nmath/log1p.c&q=log1p
>
> Since, at least on my machine, ordinary log1p appears to work fine, is
> there any reason not to have log2_1p call it and scale the result? Or
> does the compiler make a hash of our log1p too?
>
>
Calling log1p and scaling looks like the right thing to do here. And our
log1p needs improvement.
Chuck
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