[Tutor] int(1.99...99) = 1 and can = 2

[boB Stepp]

On Sun, May 1, 2016 at 5:43 AM, Steven D'Aprano <steve at pearwood.info> wrote:
> On Sun, May 01, 2016 at 01:02:50AM -0500, boB Stepp wrote:
>> Life has kept me from Python studies since March, but now I resume.
>> Playing around in the interpreter I tried:
>>
>> py3: 1.9999999999999999
>> 2.0
>> py3: 1.999999999999999
>> 1.999999999999999

[...]

> Starting with Python 2.6, floats have "hex" and "fromhex" methods which
> allow you to convert them to and from base 16, which is more compact
> than the base 2 used internally but otherwise equivalent.
>
> https://docs.python.org/2/library/stdtypes.html#float.hex

I had not read of these methods yet.  Thanks!

[...]


> Given that we only have 64 bits for a float, and some of them are used
> for the exponent and the sign, it is invariable that conversions to and
> from decimal must be inexact. Remember that I mentioned that both
> 1.9999999999999997 and 1.9999999999999998 are treated as the same float?
> That is because a 64-bit binary float does not have enough binary
> decimal places to distinguish them. You would need more than 64 bits to
> tell them apart. And so, following the IEEE-754 standard (the best
> practice for floating point arithmetic), both numbers are rounded to the
> nearest possible float.

Just before bed, I was looking at the Wikipedia article on IEEE-754.
But it was not clear from it which of the "optional" rounding methods
were being used by Python, though the behavior I was observing
suggested rounding to nearest.

[...]

>> It has been many years since I did problems in converting decimal to
>> binary representation (Shades of two's-complement!), but I am under
>> the (apparently mistaken!) impression that in these 0.999...999
>> situations that the floating point representation should not go "up"
>> in value to the next integer representation.
>
> In ancient days, by which I mean the earlier than the 1980s, ...

Heavy sigh!  I last explicitly did binary arithmetic in an Intro to C.
Sc. class in 1975.  So perhaps my incorrect expectation of *not*
rounding up is an artifact of that long ago era.

Thank you Steve, and Eryk, for your excellent explanations!  I really
appreciate the time and depth both of you put into your answers to my
questions.

boB