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From: Terry Reedy <tjreedy@udel.edu>
Subject: Re: Division and multiplication have a different behavior in the overflow case
Date: Sat, 27 Jul 2013 16:56:48 -0400
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Xref: csiph.com comp.lang.python:51373

On 7/27/2013 1:48 PM, Marco wrote:
> In Python 3, when we hava a division and both the result and at least
> one operand are too large to convert to float, we get an exception:
>
>      >>> 2**1028 / 2**-2

int/float gets converted to float/float and the int to float conversion 
is not possible. The result is irrelevant since it never gets calculated.

>      Traceback (most recent call last):
>        File "<input>", line 1, in <module>
>      OverflowError: long int too large to convert to float
>
> When the result is inside the limits, we get the right value:
>
>      >>> 2 ** 1025 / 2**10
>      3.511119404027961e+305

This must be doing integer division and then converting the result to 
float, which it can.

> Why the behavior is different in the case of the multiplication?
>
>      >>> 2 ** 1025 * 2**-10

Mathematically this is the same thing, but computationally, it is not 
and you cannot expect to get the same answer. Like the first example, 
2**-10 is a float, so 2**1025 must be converted to float to do float 
multiplication. But that is not possible.

>      Traceback (most recent call last):
>        File "<input>", line 1, in <module>
>      OverflowError: long int too large to convert to float
>
> I think the multiplication should have the same behavior than the
> division:
>
> * `inf` or `-inf` when the operands are inside the limits,
>    but the result is not
> * `OverflowError`  when the result, and at least one operand,
>    are out of range.

-- 
Terry Jan Reedy