On Thu, Apr 1, 2010 at 8:37 AM, Charles R Harris
<charlesr.har...@gmail.com>wrote:
>
>
> On Thu, Apr 1, 2010 at 12:46 AM, Anne Archibald <peridot.face...@gmail.com
> > wrote:
>
>> On 1 April 2010 02:24, Charles R Harris <charlesr.har...@gmail.com>
>> wrote:
>> >
>> >
>> > On Thu, Apr 1, 2010 at 12:04 AM, Anne Archibald <
>> peridot.face...@gmail.com>
>> > wrote:
>> >>
>> >> On 1 April 2010 01:59, Charles R Harris <charlesr.har...@gmail.com>
>> wrote:
>> >> >
>> >> >
>> >> > On Wed, Mar 31, 2010 at 11:46 PM, Anne Archibald
>> >> > <peridot.face...@gmail.com>
>> >> > wrote:
>> >> >>
>> >> >> On 1 April 2010 01:40, Charles R Harris <charlesr.har...@gmail.com>
>> >> >> wrote:
>> >> >> >
>> >> >> >
>> >> >> > On Wed, Mar 31, 2010 at 11:25 PM, <josef.p...@gmail.com> wrote:
>> >> >> >>
>> >> >> >> On Thu, Apr 1, 2010 at 1:22 AM, <josef.p...@gmail.com> wrote:
>> >> >> >> > On Thu, Apr 1, 2010 at 1:17 AM, Charles R Harris
>> >> >> >> > <charlesr.har...@gmail.com> wrote:
>> >> >> >> >>
>> >> >> >> >>
>> >> >> >> >> On Wed, Mar 31, 2010 at 6:08 PM, <josef.p...@gmail.com>
>> wrote:
>> >> >> >> >>>
>> >> >> >> >>> On Wed, Mar 31, 2010 at 7:37 PM, Warren Weckesser
>> >> >> >> >>> <warren.weckes...@enthought.com> wrote:
>> >> >> >> >>> > T J wrote:
>> >> >> >> >>> >> On Wed, Mar 31, 2010 at 1:21 PM, Charles R Harris
>> >> >> >> >>> >> <charlesr.har...@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...@c@(@type@ x)
>> > {
>> > @type@ u = 1 + x;
>> > if (u == 1) {
>> > return LOG2E*x;
>> > } else {
>> > return npy_l...@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.
>
>
Tinkering a bit, I think we should implement the auxiliary function f(p) =
log((1+p)/(1 - p)), which is antisymmetric and has the expansion 2p*(1 +
p^2/3 + p^4/5 + ...). The series in the parens is increasing, so it is easy
to terminate. Note that for p = +/- 1 it goes over to the harmonic series,
so convergence is slow near the ends, but they can be handled using normal
logs. Given 1 + x = (1+p)/(1-p) and solving for p gives p = x/(2 + x), so
when x ranges from -1/2 -> 1/2, p ranges from -1/3 -> 1/5, hence achieving
double precision should involve no more than about 17 terms. I think this
is better than the expansion in R.
Chuck
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