Re: What is acceptable for -ffast-math? A numerical viewpoint

[Jonathan Thornburg <jthorn at galileo dot thp dot univie dot ac dot at>]

In message <url:http://gcc.gnu.org/ml/gcc/2001-08/msg00176.html>,
I wrote
| [[...]] if I grant license to do this by saying
| -ffast-math, I would like very much for the compiler to (eg) convert
| (...)/5.0 into 0.2*(...).  My philosophy is that if I care about
| exact bit-for-bit rounding, then I shouldn't use -ffast-math.
[[...]]
| Having optimization change program results is a trickier case.
| I guess I'd like this to be user-controllable.  [[...]]

In message <url:http://gcc.gnu.org/ml/gcc/2001-08/msg00192.html>,
dewar <dewar at gnat dot com> pointed out
> But *all* the "optimizations" you suggest *do* change program results!

Sorry, I didn't choose my examples carefully enough.

For (binary) IEEE arithmetic, transforming   (...)/2.0  into   (...)*0.5
won't change program results, because 1/2 is an exactly representatable
(binary) IEEE floating point number and IEEE specifies that the result
is the true mathematical result (identical in both cases precisely because
1/2 is exactly representable) rounded to the destination format.  (I think
this argument is still valid even in the presence of +/- 0, +/-infinity,
and NAN.)  So, I would argue that gcc could reasonably leave this
transformation enabled by default.  (We could of course also provide a
"do arithmetic exactly as I wrote it" mode which disables this.)

In contrast, my earlier example of   (...)/5.0  -->  (...)*0.2  *does*
change program results in the last bit or two (because 0.2 can't be exactly
represented in binary floating-point), so we might reasonably require
explict permission from the user (eg -ffast-math) before doint this.
We might also disable this transformation if the user requests "only
optimizations that don't change results".

At least in the absence of cross-compilation, it's quite practical
(with careful programming -- and _this_ programming is an example of
code that requires a "do arithmetic exactly as I wrote it" mode!) to
check at compile-time whether or not a given literal constant can be
exactly represented in a given floating-point format, and thus whether
or not the reciprocal transformation will change program results (slightly).

-- 
-- Jonathan Thornburg <jthorn@thp.univie.ac.at>
   Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut),
   Golm, Germany             http://www.aei.mpg.de/~jthorn/home.html
   "The first strike in the American Colonies was in 1776 in Philadelphia,
    when [...] carpenters demanded a 72-hour week." -- Anatole Beck