On Fri, Jul 15, 2016, at 12:32, Steven D'Aprano wrote:
> I can take the geometric mean of:
>
> [2.0**900, 2.0**920, 2.0**960, 2.0**980, 2.0**990]
>
> and get to within a relative error of 1e-14 of the correct answer,
> 2**950:
>
> py> geometric_mean([2.0**900, 2.0**920, 2.0**960, 2.0**980, 2.0**990])
> 9.516908214257811e+285
> py> 2.0**950
> 9.516908214257812e+285
>
> Here's one that's exact:
>
> py> geometric_mean([2e300, 4e300, 8e300, 16e300, 32e300])
> 8e+300
My own attempt gave an exact result for both test cases.
from math import frexp as _frexp, ldexp
def frexp(x):
if type(x) is tuple:
m, e1 = x
m, e2 = _frexp(m)
return m, e1 + e2
else:
return _frexp(x)
def _mul(a, b):
ma, ea = frexp(a)
mb, eb = frexp(b)
return frexp((ma * mb, ea + eb))
def _product(values):
return reduce(_mul, values)
def geometric_mean(values):
n = len(values)
pm, pe = _product(values)
me, re = divmod(pe, n)
pm = ldexp(pm, re)
return ldexp(pm**(1./n), me)
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