Am 26.05.15 um 05:11 schrieb Steven D'Aprano:
mismatch after 3 trials
naive: 767.3916150255787
alternate: 767.3916150255789
hypot: 767.3916150255787
which shows that:
(1) It's not hard to find mismatches;
(2) It's not obvious which of the three methods is more accurate.
The main problem is not necessarily precision. A square root is a very
precise operation in floating point math, the relative precision
*increases* by sqrt. The big problem is overflow. Take e.g. a=3*10^160,
b=4*10^160, then the exact result is c=5*10^160. But:
>>> a=3e160
>>> b=4e160
>>> math.sqrt(a**2+b**2)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
OverflowError: (34, 'Result too large')
>>> math.hypot(a,b)
5e+160
Christian
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