On 6/15/18 1:38 PM, Andre Roberge wrote: > I have a suggestion to make inspired by the current discussion about > trigonometric functions in degrees, and the desire to have them show > "exact" values in some special cases. > > I suggest that it would be useful to have operators for performing > **approximate** comparisons. I believe that such operators would be > useful both for students learning using Python as well as experts > doing numerical computations. > > For discussion purpose, I will use ~= as representing an operator > testing for approximate equality. (I will show some sample usage below). > > When teaching students, the availability of both == and ~= would give > the opportunity to discuss the fact that numerical computations using > floats are approximate, while having the possibility to write code > that is readable using the approximate equality operator instead of > the strict equality operator when needed. > > Before I started writing this email, I had noticed that numpy includes > at least two functions (isclose and allclose) whose purpose is to > perform such approximate comparisons. [1] I had completely missed the > fact that Python added the function isclose() in the math module in > version 3.5, as described in PEP 485 [0]. I would suggest that the > possibility of using operators instead of explicit function calls > could make programs easier to write and read, both for beginners and > experts alike. I note that PEP 485 makes no mention of introducing > operators as a possibility. > > In addition to an approximate equality operator, it would be natural > to include two additional operators, greater than or approximately > equal, and lesser than or approximately equal. These could be written > respectively as >~= and <~=. I did consider using some relevant utf-8 > symbol instead of combination of ascii characters, but I think that it > would be easier to write programs if one does not require characters > nor found on any normal keyboard. > > Some time ago, I created a toy module [2] to enable easy experiments > with some syntactic additions to Python. Using this module, I created > a very poor and limited implementation that shows what using these > proposed o[erators might look like [3] ... My current implementation > is slightly different from either Numpy or Python's math.isclose() > function [This may no longer be the case soon as I plan to change it > to use Python's version instead.] . As is the case for isclose(), > there are two paramaters to be set to determine if the values are > close enough to be considered approximately equal: an absolute > tolerance and a relative one. Given that one cannot pass parameters > to an operator, my implementation includes a function which can change > the values of these parameters for a given session. If these new > operators were to be added to Python, such a function would either > have to be added as a builtin or as a special function in the math module. > > Here's a sample session for demonstration purpose... > > $ python -m experimental > experimental console version 0.9.5. [Python version: 3.6.1] > > ~~> 0.1 + 0.2 > 0.30000000000000004 > ~~> 0.1 + 0.2 == 0.3 > False > ~~> from __experimental__ import approx > ~~> 0.1 + 0.2 ~= 0.3 # use approximately equal operator > True > ~~> 0.1 + 0.2 <~= 0.3 > True > ~~> 0.1 + 0.2 >~= 0.3 > True > ~~> 2 ** 0.5 > 1.4142135623730951 > ~~> 2**0.5 ~= 1.414 > False > ~~> set_tols(0.001, 0.001) > ~~> 2**0.5 ~= 1.414 > True > > > André Roberge > > [0] https://www.python.org/dev/peps/pep-0485/ > > [1] See for > example > https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.isclose.html > > [2] https://github.com/aroberge/experimental > > [3] > https://github.com/aroberge/experimental/blob/master/experimental/transformers/readme.md#approxpy > The big issue with 'approximately equals' is that the definition of it is hard to come up with. This is especially true for small values. In particular how small does a number need to be to be ~= 0. You also get inconsistencies, you can have a ~= b, and b ~= c but not a ~= c. You can have a + b ~= c but not a ~= c - b
should 0.0000001 ~= 0.00000011 To properly handle this sort of thing you need that tolerance parameter, but the values you give should be carefully though about for THAT comparison, having a 'global' value is apt to lead to laziness and wrong answers. -- Richard Damon _______________________________________________ Python-ideas mailing list Python-ideas@python.org https://mail.python.org/mailman/listinfo/python-ideas Code of Conduct: http://python.org/psf/codeofconduct/
