Fixing ilogb()

[David Schultz]

On Mon, May 10, 2004, Bruce Evans wrote:
> On Sun, 9 May 2004, I wrote:
> 
> > ...
> > % @@ -43,11 +43,27 @@
> > %  	subl	$4,%esp
> > %
> > %  	fldl	8(%ebp)
> > % +	fxam
> > % +	fnstsw	%ax
> > % +	sahf
> >
> > This is the main runtime overhead.  I think it can mostly be avoided by
> > checking the return value.  ilogb() can only be INT_MIN after overflow
> > or other conversion errors (check this).  There 3 cases:
> > - logb(0) = -Inf; fistpl(-Inf) = INT_MIN + IE
> > - logb(Inf) = Inf; fistpl(-Inf) = INT_MIN + IE
> > - logb(NaN) = same NaN; fistpl(NaN) = INT_MIN + IE
> > After finding one of these rare cases, the exact case still needs to be
> > determined by looking at the original value or the result of fxtract.
> > Then fucom with 0 should be a faster way to do the classification.  A
> > full classification is not needed sice denormals are not special here
> > and unsupported formats are unsupported here too.
> 
> Another thing to decide is whether the exception flags should be set (or
> not) to indicate overflow.  I think they should be.  Checking after doing
> the operation sets them; checking before does not.  The standard is not
> clear.  It says that the result is equivalent to (int)logb() for the
> non-overflowing cases but has special rules with unusual wording for
> the overflowing cases.  It says "If x is zero they [the ilogb functions]
> compute the value FP_ILOGB0. ..."  Computation a constant value is
> different from returning it, so this can be interpreted as saying that
> the exception flags may be set.  I think there's a meta-rule that math
> functions set execption flags where appropriate.

ilogb() isn't part of IEEE-754 and it is poorly specified in C99,
but it is a proposed addition to the next revision of 754, namely
IEEE-754R.  In that proposal, ilogb() signals no exceptions,
except for the automatic invalid exception you get from a
signalling NaN.  See http://754r.ucbtest.org.

(This seems strange, given that logb(0) signals a divide-by-zero
exception, but the proposal is quite specific.)