[Python-Dev] [Tutor] nice() (original) (raw)

Josiah Carlson jcarlson at uci.edu
Mon Feb 13 01:14:50 CET 2006

"Alan Gauld" <alan.gauld at freenet.co.uk> wrote:

However I do dislike the name nice() - there is already a nice() in the os module with a fairly well understood function. But I'm sure some time with a thesaurus can overcome that single mild objection. :-)

Presumably it would be located somewhere like the math module.

Alan G Author of the learn to program web tutor http://www.freenetpages.co.uk/hp/alan.gauld

----- Original Message ----- From: "Smith" <smiles at worksmail.net> To: <tutor at python.org> Cc: <edu-sig at python.org>; <python-dev at python.org> Sent: Sunday, February 12, 2006 6:44 PM Subject: [Tutor] nice() I've been thinking about a function that was recently proposed at python-dev named 'areclose'. It is a function that is meant to tell whether two (or possible more) numbers are close to each other. It is a function similar to one that exists in Numeric. One such implementation is def areclose(x,y,abstol=1e-8,reltol=1e-5): diff = abs(x-y) return diff <= anstol or diff <= reltol*max(abs(x),abs(y))_ _(This is the form given by Scott Daniels on python-dev.)_ _Anyway, one of the rationales for including such a function was:_ _When teaching some programming to total newbies, a common frustration_ _is how to explain why a==b is False when a and b are floats computed_ _by different routes which should'' give the same results (if_ _arithmetic had infinite precision). Decimals can help, but another_ _approach I've found useful is embodied in Numeric.allclose(a,b) --_ _which returns True if all items of the arrays are close'' (equal to_ _within certain absolute and relative tolerances)_ _The problem with the above function, however, is that it *itself* has a_ _comparison between floats and it will give undesired result for something_ _like the following test:_ _###_ _>>> print areclose(2, 2.1, .1, 0) #see if 2 and 2.1 are within 0.1 of each >>> other False >>> ### Here is an alternative that might be a nice companion to the repr() and round() functions: nice(). It is a combination of Tim Peter's delightful 'case closed' presentation in the thread, "Rounding to n significant digits?" [1] and the hidden magic of "prints" simplification of floating point numbers when being asked to show them. It's default behavior is to return a number in the form that the number would have when being printed. An optional argument, however, allows the user to specify the number of digits to round the number to as counted from the most significant digit. (An alternative name, then, could be 'lround' but I think there is less baggage for the new user to think about if the name is something like nice()--a function that makes the floating point numbers "play nice." And I also think the name...sounds nice.) Here it is in action: ### >>> 3*1.1==3.3 False >>> nice(3*1.1)==nice(3.3) True >>> x=3.21/0.65; print x 4.93846153846 >>> print nice(x,2) 4.9 >>> x=x*1e5; print nice(x,2) 490000.0 ### Here's the function: ### def nice(x,leadingDigits=0): """Return x either as 'print' would show it (the default) or rounded to the specified digit as counted from the leftmost non-zero digit of the number, e.g. nice(0.00326,2) --> 0.0033""" assert leadingDigits>=0 if leadingDigits==0: return float(str(x)) #just give it back like 'print' would give it leadingDigits=int(leadingDigits) return float('%.*e' % (leadingDigits,x)) #give it back as rounded by the %e format ### Might something like this be useful? For new users, no arguments are needed other than x and floating points suddenly seem to behave in tests made using nice() values. It's also useful for those computing who want to show a physically meaningful value that has been rounded to the appropriate digit as counted from the most significant digit rather than from the decimal point. Some time back I had worked on the significant digit problem and had several math calls to figure out what the exponent was. The beauty of Tim's solution is that you just use built in string formatting to do the work. Nice. /c [1] http://mail.python.org/pipermail/tutor/2004-July/030324.html

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