Ok. I'm wrong on that example. On Wed, Mar 21, 2018, 9:11 PM Tim Peters <tim.pet...@gmail.com> wrote:
> [David Mertz <me...@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 <dicki...@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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