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. 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
