Re: Float conversion

[Stephen Leake <stephen_leake@stephe-leake.org>]

Phil Clayton <phil.clayton@lineone.net> writes:

> On Jul 31, 4:12 pm, Stephen Leake <stephen_le...@stephe-leake.org>
> wrote:
>> Clearly to cover all cases, you
>> need A < B, A = B, A > B, A < C, etc.
>
> You make it sound easy...  

It is easy! This is a very small program; exhaustive testing is
appropriate. 

> Generally, how do you justify that tests 'cover all cases' so giving
> you a 100% chance of finding an error?

There are three inputs: A, B, C.

According to the code, there are three important edge cases for each
pair: A < B, A = B, A > B

If we assume the floating point hardware is correct, we don't need to
worry about any other cases.

So that's nine cases to test, total.

> Note that even if I had test cases that exercise all possible
> orderings of A, B and C, I am not guaranteed to find an error in an
> incorrect implementation of Y = min {A, B, C}.  For example, I could
> have chosen positive values for A in every test but the program could
> have contained an extra erroneous condition
>
>   ... and 0 < A
>
> that would have gone undetected.  So the tests need to take account of
> the particular implementation too.

Ok. I agree this is a white box test that is aware of the code. So add
another set of conditions: A < 0, A = 0, A > 0. Still a small finite set
of tests.

>> > Where does the original justification go wrong?  Well, when talking
>> > about 'the smallest' there is an implicit assumption being made that
>> > it is unique.  The justification never considers the case when A or B
>> > is the non-unique smallest.
>>
>> And the same error could be made in a formal specification. "formal"
>> does _not_ mean "complete"!
>
> Although I said "formal methods", I use this example to motivate
> formal verification, not formal specification.  Any specification,
> formal or not, can be a load of rubbish!

What are you verifying, if not a specification?

If the specification is rubbish, what is the point of verifying it?

-- 
-- Stephe