On Tue, 14 Feb 2023 11:17:20 +0000, Oscar Benjamin wrote: > On Tue, 14 Feb 2023 at 07:12, Stephen Tucker <stephen_tuc...@sil.org> wrote: [snip] >> I have just produced the following log in IDLE (admittedly, in Python >> 2.7.10 and, yes I know that it has been superseded). >> >> It appears to show a precision tail-off as the supplied float gets bigger. [snip] >> >> For your information, the first 20 significant figures of the cube root in >> question are: >> 49793385921817447440 >> >> Stephen Tucker. >> ---------------------------------------------- >> >>> 123.456789 ** (1.0 / 3.0) >> 4.979338592181744 >> >>> 123456789000000000000000000000000000000000. ** (1.0 / 3.0) >> 49793385921817.36 > > You need to be aware that 1.0/3.0 is a float that is not exactly equal > to 1/3 ... [snip] > SymPy again: > > In [37]: a, x = symbols('a, x') > > In [38]: print(series(a**x, x, Rational(1, 3), 2)) > a**(1/3) + a**(1/3)*(x - 1/3)*log(a) + O((x - 1/3)**2, (x, 1/3)) > > You can see that the leading relative error term from x being not > quite equal to 1/3 is proportional to the log of the base. You should > expect this difference to grow approximately linearly as you keep > adding more zeros in the base.
Marvelous. Thank you. -- To email me, substitute nowhere->runbox, invalid->com. -- https://mail.python.org/mailman/listinfo/python-list