"Alan Gauld" <[EMAIL PROTECTED]> 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. - Josiah > Alan G > Author of the learn to program web tutor > http://www.freenetpages.co.uk/hp/alan.gauld > > > > ----- Original Message ----- > From: "Smith" <[EMAIL PROTECTED]> > To: <tutor@python.org> > Cc: <edu-sig@python.org>; <python-dev@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,abs_tol=1e-8,rel_tol=1e-5): > diff = abs(x-y) > return diff <= ans_tol or diff <= rel_tol*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 > > _______________________________________________ > Python-Dev mailing list > Python-Dev@python.org > http://mail.python.org/mailman/listinfo/python-dev > Unsubscribe: > http://mail.python.org/mailman/options/python-dev/jcarlson%40uci.edu _______________________________________________ Python-Dev mailing list Python-Dev@python.org http://mail.python.org/mailman/listinfo/python-dev Unsubscribe: http://mail.python.org/mailman/options/python-dev/archive%40mail-archive.com
