Thread · HN Continuity

Scientific computing can be done only in 2 ways, either with subnormals or by enabling the underflow exception and writing a suitable exception handler for it.

If the use of subnormals is disabled with FTZ/DAZ that is guaranteed to generate big errors and it is completely unpredictable how big the errors will be.

If a computational algorithm generates underflows at some place, there is no way to modify the algorithm so that flushing-to-zero will not make any difference (i.e. no errors).

What is possible, is to modify the algorithm so that underflows will never happen.

This was the traditional way of writing numeric algorithms. Because on early computers underflows would crash the program, the same as overflows, one had to improve the algorithm in order to avoid both underflows and overflows.

Subnormals and infinities have been introduced in the standard precisely for lazier programmers, so that they would be able to avoid the rewriting of algorithms without the risks that underflows and overflows would generate major errors.

Unfortunately, it seems that for some programmers this is still not enough, because they want simultaneously to not be bothered with rewriting the algorithms and to have the program run as fast as with an optimized algorithm.

For this, the solution is very simple and it is not enabling FTZ/DAZ, which unless is done for a game might cause unpredictable financial losses for an unsuspecting customer, who expects that a computer must provide correct results.

The right solution is to not buy Intel CPUs or any other kind of processors whose vendor believes that the correctness of computations does not matter. It should be noted however, that the Intel server CPUs use CPU cores that are obsolete in desktop and laptop CPUs, i.e. the tested Intel CPUs use cores like those in Meteor Lake and Raptor Lake CPUs. I do not know if the more recent Intel CPU cores, from Panther Lake/Arrow Lake S/Arrow Lake H/Lunar Lake, have retained this Intel misfeature, which has characterized the Intel CPUs for much more than a decade.

If someone says that they have enabled FTZ/DAZ and they did not see any significant difference in the results of a program, that is complete B*S*T, because it is impossible to test exhaustively any program that does floating-point computations and the errors are expected to happen only for certain values, which are unlikely to be encountered during testing, but you cannot predict that those values will not be encountered in production.