[vtk-developers] vtkMath::Ceil() and vtkMath::Floor()

[Philippe Pébay]

Hello David,

Thanks for the explanation. Also, sorry for the typo, I meant "double cast" (not "double truncation").

My question was with the != comparison between x and static_cast<double>( static_cast<int>( x ) ).

So, as I understand your answer, the intent is effectively to give a definition of what it means
to be an integer, and in this case, it means that static_cast<double>( static_cast<int>( x ) ) is the same as x.

What I don't understand here is what happens to the trailing bits, which are still significant with respect to machine 
epsilon. What will happen when casting x to int?

Thanks
Philippe


On 06/02/2011 03:01 PM, David Gobbi wrote:
> Hi Philippe,
>
> There is only one truncation, not two.  For Floor() the explanation is:
>
> x is input (a double, or maybe extended precision in FPU register)
>
> // step 1: truncate to integer
> int r = static_cast<int>(x);
>
> // step 2: check if x can be represented exactly as an int,
> // put the boolean result "1" or "0" in variable "n"
> int n = ( x != static_cast<double>(r) );
>
> We know that the integer "r" can be represented exactly by
> a double, and so the above checks if "x" can, in turn, be
> represented exactly by an int.
>
> // step 3: check if x is above/below zero, put the boolean
> // result "1" or "0" in variable "g"
> int g = ( x<  0 );
>
> // step 4: subtract 1 from the result if steps 2 and 3 are true
> return r - ( n&  g );
>
>
> The idea behind this is the following: when "x" is>= 0, doing
> static_cast<int>(x) is exactly the same as floor(x).  But if "x"
> is less than zero (step 3) we need to subtract one unless "x"
> can be represented exactly by an int (step 2).
>
> The purpose of step 4 is to avoid any branching in the code,
> as compared to doing the same logic with "if" statements.
>
>   - David
>
>
>
> On Thu, Jun 2, 2011 at 3:25 PM, Philippe Pébay<pppebay at sandia.gov>  wrote:
>> Hello David,
>>
>> Thanks for the prompt answer.
>>
>> I still don't understand the double truncation for Floor() and Ceil(): why
>> cast the readings to int first, and then to double again? I am not sure I
>> understand what "exact results" mean in this contest, as the cast itself
>> changes the nature of the representation, and a double cast does not, as far
>> as I know at least, amount to an identity operation.
>>
>> Or does it? Are you saying that static_cast<double>( static_cast<int>( x ) )
>> has always the exact same FP representation than x?
>>
>> Thanks
>> Philippe
>>
>> On 06/02/2011 02:20 PM, David Gobbi wrote:
>>>
>>> Hi Philippe,
>>>
>>> I wrote the Floor() and Ceil() functions a few months ago.  They are
>>> written specifically for speed.  For double values that are within the
>>> int range, they give exact results.
>>>
>>> The vtkMath::Round() is fast, too, but the operation that it performs
>>> does not conform to any of the IEEE 754 standard rounding modes.
>>>
>>>   - David
>>>
>>> On Thu, Jun 2, 2011 at 3:09 PM, Philippe Pébay<pppebay at sandia.gov>    wrote:
>>>>
>>>> ... a clarification of what I asked earlier...
>>>>
>>>> By "different intent" I was referring to the fact that vtkMath's Floor()
>>>> and
>>>> Ceil() perform something which I find a little intriguing, namely,
>>>> casting a
>>>> double to an int, and then re-casting the latter to a double to perform a
>>>> double-double equality comparison, which, I would venture to say, should
>>>> be
>>>> avoided whenever possible.
>>>>
>>>> On the other hand, Round() does not do this double casting but directly
>>>> performs double-double inequality comparison, and a single cast to an int
>>>> at
>>>> the end. This seems much better to me.
>>>>
>>>> Thanks
>>>> Philippe
>>>>
>>>> On 06/02/2011 02:04 PM, Philippe Pébay wrote:
>>>>>
>>>>> Hello,
>>>>>
>>>>> I was contemplating using vtkMath::Ceil() and vtkMath::Floor() in some
>>>>> of my code, instead of the standard ceil() and floor(). However they
>>>>> appear to be written with a slightly different intent than
>>>>> vtkMath::Round(). Can someone comment on that?
>>>>>
>>>>> Thanks
>>>>> Philippe
>>>>
>>>>
>>>> --
>>>> Philippe Pébay
>>>> Sandia National Laboratories
>>>>
>>>>
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>>>
>>
>>
>> --
>> Philippe Pébay
>> Sandia National Laboratories
>>
>>
>>
>


-- 
Philippe Pébay
Sandia National Laboratories