On Sat, Apr 26, 2014 at 8:05 PM, <josef.p...@gmail.com> wrote: > > > > On Sat, Apr 26, 2014 at 6:37 PM, Matthew Brett <matthew.br...@gmail.com>wrote: > >> Hi, >> >> On Wed, Apr 23, 2014 at 11:59 AM, Matthew Brett <matthew.br...@gmail.com> >> wrote: >> > Hi, >> > >> > On Wed, Apr 23, 2014 at 1:43 AM, Nathaniel Smith <n...@pobox.com> wrote: >> >> On Wed, Apr 23, 2014 at 6:22 AM, Matthew Brett < >> matthew.br...@gmail.com> wrote: >> >>> Hi, >> >>> >> >>> I'm exploring Mingw-w64 for numpy building, and I've found it gives a >> >>> slightly different answer for 'exp' than - say - gcc on OSX. >> >>> >> >>> The difference is of the order of the eps value for the output number >> >>> (2 * eps for a result of ~2.0). >> >>> >> >>> Is accuracy somewhere specified for C functions like exp? Or is >> >>> accuracy left as an implementation detail for the C library author? >> >> >> >> C99 says (sec 5.2.4.2.2) that "The accuracy of the floating point >> >> operations ... and of the library functions in <math.h> and >> >> <complex.h> that return floating point results is implemenetation >> >> defined. The implementation may state that the accuracy is unknown." >> >> (This last sentence is basically saying that with regard to some >> >> higher up clauses that required all conforming implementations to >> >> document this stuff, saying "eh, who knows" counts as documenting it. >> >> Hooray for standards!) >> >> >> >> Presumably the accuracy in this case is a function of the C library >> >> anyway, not the compiler? >> > >> > Mingw-w64 implementation is in assembly: >> > >> > >> http://sourceforge.net/p/mingw-w64/code/HEAD/tree/trunk/mingw-w64-crt/math/exp.def.h >> > >> >> Numpy has its own implementations for a >> >> bunch of the math functions, and it's been unclear in the past whether >> >> numpy or the libc implementations were better in any particular case. >> > >> > I only investigated this particular value, in which case it looked as >> > though the OSX value was closer to the exact value (via sympy.mpmath) >> > - by ~1 unit-at-the-last-place. This was causing a divergence in the >> > powell optimization path and therefore a single scipy test failure. I >> > haven't investigated further - was wondering what investigation I >> > should do, more than running the numpy / scipy test suites. >> >> Investigating further, with this script: >> >> https://gist.github.com/matthew-brett/11301221 >> >> The following are tests of np.exp accuracy for input values between 0 >> and 10, for numpy 1.8.1. >> >> If np.exp(x) performs perfectly, it will return the nearest floating >> point value to the exact value of exp(x). If it does, this scores a >> zero for error in the tables below. If 'proportion of zeros' is 1 - >> then np.exp performs perfectly for all tested values of exp (as is the >> case for linux here). >> >> OSX 10.9 >> >> Proportion of zeros: 0.99789 >> Sum of error: 2.15021267458e-09 >> Sum of squared error: 2.47149370032e-14 >> Max / min error: 5.96046447754e-08 -2.98023223877e-08 >> Sum of squared relative error: 5.22456992025e-30 >> Max / min relative error: 2.19700100681e-16 -2.2098803255e-16 >> eps: 2.22044604925e-16 >> Proportion of relative err >= eps: 0.0 >> >> Debian Jessie / Sid >> >> Proportion of zeros: 1.0 >> Sum of error: 0.0 >> Sum of squared error: 0.0 >> Max / min error: 0.0 0.0 >> Sum of squared relative error: 0.0 >> Max / min relative error: 0.0 0.0 >> eps: 2.22044604925e-16 >> Proportion of relative err >= eps: 0.0 >> >> Mingw-w64 Windows 7 >> >> Proportion of zeros: 0.82089 >> Sum of error: 8.08415331122e-07 >> Sum of squared error: 2.90045099615e-12 >> Max / min error: 5.96046447754e-08 -5.96046447754e-08 >> Sum of squared relative error: 4.18466468175e-28 >> Max / min relative error: 2.22041308226e-16 -2.22042100773e-16 >> eps: 2.22044604925e-16 >> Proportion of relative err >= eps: 0.0 >> >> Take-home : exp implementation for mingw-w64 is exactly (floating >> point) correct 82% of the time, and one unit-at-the-last-place off for >> the rest [1]. OSX is off by 1 ULP only 0.2% of the time. >> > > > Windows 64 with MKL > > \WinPython-64bit-3.3.2.2\python-3.3.2.amd64>python > "E:\Josef\eclipsegworkspace\statsmodels-git\local_scripts\local_scripts\try_exp_error.py" > Proportion of zeros: 0.99793 > Sum of error: -2.10546855506e-07 > Sum of squared error: 3.33304327526e-14 > Max / min error: 5.96046447754e-08 -5.96046447754e-08 > Sum of squared relative error: 4.98420694339e-30 > Max / min relative error: 2.20881302691e-16 -2.18321571939e-16 > eps: 2.22044604925e-16 > Proportion of relative err >= eps: 0.0 > > > Windows 32 bit python with official MingW binaries > > Python 2.7.1 (r271:86832, Nov 27 2010, 18:30:46) [MSC v.1500 32 bit > (Intel)] on win32 > > Proportion of zeros: 0.99464 > Sum of error: -3.91621083118e-07 > Sum of squared error: 9.2239247812e-14 > Max / min error: 5.96046447754e-08 -5.96046447754e-08 > Sum of squared relative error: 1.3334972729e-29 > Max / min relative error: 2.21593462148e-16 -2.2098803255e-16 > eps: 2.22044604925e-16 > Proportion of relative err >= eps: 0.0 > > > >> >> Is mingw-w64 accurate enough? Do we have any policy on this? >> > > I wouldn't worry about a missing or an extra eps in our applications, but > the competition is more accurate. >
Just for comparison, I increased `until` to 300 the proportion of zeros and relative error stays about the same for both MKL and your wheels absolute error are huge, the following is MKL Sum of error: -3.78802736366e+112 Sum of squared error: 1.51136754049e+225 Max / min error: 4.80981520952e+111 -3.84785216762e+112 (I looked a lot at the behavior of exp in the hundreds recently :( As illustration why I don't care about one **relative** eps >>> np.finfo(np.double).eps + 10 == 10 True https://github.com/scipy/scipy/pull/3547 and many others Josef > > Josef > > >> >> Cheers, >> >> Matthew >> >> [1] http://matthew-brett.github.io/pydagogue/floating_error.html >> _______________________________________________ >> NumPy-Discussion mailing list >> NumPy-Discussion@scipy.org >> http://mail.scipy.org/mailman/listinfo/numpy-discussion >> > >
_______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion