Re: floating point comparison

[dewar@merv.cs.nyu.edu (Robert Dewar)]

Gerald says

<<Things you call approximate hocus-pocus make life hard if you try to
implement some algortithms wich are exact (in exact arithmetic), but
fail due to rounding erros EVEN ON MODERN IEE MACHINES.

Comparing floating point numbers for equality should be avoided, the
programmer need some deeper insight of the problem.
>>


Nothing "fails" due to rounding errors on modern IEEE machines. What is
wrong here is not some kind of failure in the arithemtic, but the
programmers misuse of it. 

Of course if you expect to be able to take an algorithm which is
"exact" using real arithmetic, it is often completely bogus to
simply encode it using floating point arithmetic, that's exactly what
I mean by "approximate hocus pocus".

If you try to store 1001 numbers in a 1000 array, your program
malfunctions, but you immediately understand that the program is
wrong, you do not blame the array for "failing".

Misuse of IEEE floating-arithmetic is the same as any other bug a
careless programmer introduces into their program.

As to whether equality is what you want, it is a well defined
operation, you use it when and only when you want this operation.
It is certainly not the case that if the real arithmetic algorithm
you are using as an implementation model has an equality that you
should blindly use the equality IEEE operation. But then it is
equally foolish to think that you can blinndly translate an
addition to to a floating-point add. Any kind of blind unthinking
behavior is likely to get you into big trouble.

As (one) example of a case where equality is approrpiate, consider
the problem of computing a square root by Newton Raphson, using
round-towards-zero. In this situation, the estimate will converge
accurately to IEEE equality.

Floating-point code is had stuff, most people who do it shouldn't!