Re: [boost] boost interval arithmetic

Subject: Re: [boost] boost interval arithmetic
From: Павел Кудан (coodan_at_[hidden])
Date: 2015-01-15 12:58:46

>>> Now see:
>>>
>>> [-1.0, 1.0] / .0
>>>
>>> What is the correct result? Of course, [-inf, inf]
>>
>> The way I understand interval arithmetics, the result is the set
>> {x / 0 for all x in [-1, 1]}.
>>
>> Now, x/0 is undefined for all x in [-1, 1], so returning an empty set seems 
>> logical to me.
>
>For IEEE double, 1./0 is well defined as +inf, and -1./0 as -inf, so I 
>agree that returning an empty set (apparently creating an empty set 
>throws, with the default policy) is questionable, it depends on your 
>application whether you want empty or [-inf,+inf]. I did not check if 
>boost provides a policy to change that behavior.

The problem is 0 between -1 and 1. For IEEE floats, .0 / .0 is NaN. If not this special 0, the result could be [-inf, inf]. That was my mistake.

But IEEE Interval Arithmetic Working Group also propose empty set as only possible result of / [0, 0] operation. So, full accordance here.

Some conflict is possible with .0 / .0 is NaN C++ conception (as if it were main idea, result interval would be NaN), but it seems to be standard mathematical practice to set this to empty.