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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:
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
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