[Python-Dev] Deprecating float.is_integer()

[David Mertz]

Ok. I'm wrong on that example.

On Wed, Mar 21, 2018, 9:11 PM Tim Peters <tim.peters at gmail.com> wrote:

> [David Mertz <mertz at gnosis.cx>]
> >> For example, this can be true (even without reaching inf):
> >>
> >> >>> x.is_integer()
> >> True
> >> >>> (math.sqrt(x**2)).is_integer()
> >> False
>
> [Mark Dickinson <dickinsm at gmail.com> ]
> > If you have a moment to share it, I'd be interested to know what value of
> > `x` you used to achieve this, and what system you were on. This can't
> happen
> > under IEEE 754 arithmetic.
>
> I expect it might happen under one of the directed rounding modes
> (like "to +infinity").
>
> But under 754 binary round-nearest/even arithmetic, it's been formally
> proved that sqrt(x*x) == x exactly for all non-negative finite x such
> that x*x neither overflows nor underflows (and .as_integer() has
> nothing to do with that very strong result):
>
>     https://hal.inria.fr/hal-01148409/document
>
> OTOH, the paper notes that it's not necessarily true for IEEE decimal
> arithmetic; e.g.,
>
> >>> import decimal
> >>> decimal.getcontext().prec = 4
> >>> (decimal.Decimal("31.66") ** 2).sqrt()  # result is 1 ulp smaller
> Decimal('31.65')
>
> >>> decimal.getcontext().prec = 5
> >>> (decimal.Decimal("31.660") ** 2).sqrt() # result is 1 ulp larger
> Decimal('31.661')
>
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