Re: sanity check - floating point comparison

From:
Richard Herring <junk@[127.0.0.1]>
Newsgroups:
comp.lang.c++
Date:
Tue, 25 Apr 2006 17:24:49 +0100
Message-ID:
<08WjYIdR1kTEFwXq@baesystems.com>
In message <1145974247.296024.308190@u72g2000cwu.googlegroups.com>,
ma740988 <ma740988@gmail.com> writes

template <class T> inline bool isEqual( const T& a, const T& b,
   const T epsilon = std::numeric_limits<T>::epsilon() )
{
   const T diff = a - b;
   return ( diff <= epsilon ) && ( diff >= -epsilon );
}

int main()
{
 std::deque<double> pt ;
 pt.push_back ( 2.3123 );
 pt.push_back ( 4.3445 );
 pt.push_back ( 1.343 );
 pt.push_back ( 4.3445 );
 pt.push_back ( 4.3445 );
 pt.push_back ( 2.3123 );

 std::deque<double> jt ;
 jt.push_back ( 4.3445 );
 jt.push_back ( 2.3123 );

 std::deque<double> results;
 // results should have - 1, 3, 4, 0, 5

 for ( int idx ( 0 ) ; idx < jt.size(); ++idx )
 {
   for ( int kdx ( 0 ); kdx < pt.size(); ++kdx )
   {
     if ( isEqual<double>( jt [ idx ], pt [ kdx ] ) )
     {
       results.push_back ( kdx );
     }
   }
 }
 std::copy ( results.begin(), results.end(),
                std::ostream_iterator<int> ( std::cout, "\n" ) );
}

My intent. I'll search the pt container for the values in the jt
container. If found, I'll store - in the result container - the
index/location where the value was found in the pt container. For
example: Search pt container for first element in jt container. So I
found 4 at postions 1, 3 and 4. Similarily for 2. 2 was found within
the pt container at 0 and 5.

Result will print, 1, 3, 4, 0, 5. Works.

What makes me nervous though is the floating point comparsion. After
all numeric_limits is not defined on one platform (using gcc 2.96).


?

That said, I was opting to use iterators with - I think std::distance


? Use of iterators versus indexing is a completely different question
from how to compare the stored values.

but I'll end up doing floating point comparison anyways, in which case
my own version ( with my own comparator - isEqual) works best. Correct?


IMO no.

I can't imagine anyone deliberately setting out to produce a compiler on
which the same floating literal 2.3123 etc., wouldn't produce the same
double value internally in each place in the code where it's used, if
you use the same compiler flags. (If you're generating the numbers by
arithmetic it's a different matter, of course.)

Even if the compiler did produce different values for the same literal,
there's no reason to suppose that the results would pass isEqual().
epsilon() has its uses in numerical analysis, but I don't think this is
an appropriate one. In effect it's guaranteed that if X==1.0, (a) X and
X + epsilon() are distinct values and (b) X and X + epsilon()/2 are not,
but for other values of X one of those assertions may not be true.

To specify fuzzy floating-point comparisons correctly you generally need
some knowledge of the domain being modelled, but here you're trying to
second-guess a compiler problem that probably doesn't even exist.

Finally, if you really must use your own comparator, don't call it
isEqual.

--
Richard Herring

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