[Python-Dev] math.areclose ...?

Sun Feb 5 18:31:48 CET 2006

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):
 >>> (1.0/3.0)==(0.1/0.3)
False
 >>> Numeric.allclose(1.0/3.0, 0.1/0.3)
1
But pulling in the whole of Numeric just to have that one handy 
function is often overkill. So I was wondering if module math (and 
perhaps by symmetry module cmath, too) shouldn't grow a function 
'areclose' (calling it just 'close' seems likely to engender 
confusion, since 'close' is more often used as a verb than as an 
adjective; maybe some other name would work better, e.g. 
'almost_equal') taking two float arguments and optional tolerances 
and using roughly the same specs as Numeric, e.g.:
def areclose(x,y,rtol=1.e-5,atol=1.e-8):
 return abs(x-y)<atol+rtol*abs(y)
What do y'all think...?
Alex