[Bug middle-end/29335] transcendental functions with constant arguments should be resolved at compile-time

["ghazi at gcc dot gnu dot org" <gcc-bugzilla at gcc dot gnu dot org>]

------- Comment #30 from ghazi at gcc dot gnu dot org  2006-11-02 14:41 -------
(In reply to comment #28)
> (In reply to comment #27)
> > It's likely that I'll end up doing it, so would you please tell me how?
> According to the C rationale (I haven't checked), the sign of gamma(x) is -1 if
> [iff] x < 0 && remainder(floor(x), 2) != 0. But if x is a non-positive integer,
> the sign of gamma(x) isn't defined. Handle these cases first.
> The test x < 0 is easy to do. In MPFR, you can compute floor(x) (or trunc(x))
> with the precision min(PREC(x),max(EXP(x),MPFR_PREC_MIN)), but then, there's no
> direct function to decide whether the result is even or odd (I thought we added
> this, but this isn't the case). The solution can be to divide x by 2 (this is
> exact, except in case of underflow) and call mpfr_frac directly. If the result
> is between -0.5 and 0, then gamma(x) is negative. If the result is between -1
> and -0.5, then gamma(x) is positive. So, a 2-bit precision for mpfr_frac should
> be sufficient (as -0.5 is representable in this precision), but choose a
> directed rounding (not GMP_RNDN) for that. Then you can just do a comparison
> with -0.5; the case of equality with -0.5 depends on the chosen rounding (if
> you obtain -0.5, then it is an inexact result since x is not an integer). For
> instance, if you choose GMP_RNDZ, then a result > -0.5 means that gamma(x) is
> negative, and a result <= -0.5 means that gamma(x) is positive.

Vincent, thank you for the detailed instructions.  I also read your two
possible solutions posted here:
http://sympa.loria.fr/wwsympa/arc/mpfr/2006-10/msg00036.html

I could be satisfied with either solution from that message.  However in the
case of choice 1, I feel the calculation of signgam should be provided from a
function call in the library rather than forcing each user to write a routine
to calculate it.  IMHO, I'd rather leave the math to the mathematicians. :-) 
E.g. you could add a function mpfr_signgam() that figures out the value for the
user and thereby leave the interface for mpfr_lngamma() unchanged.  Choice 2
also solves the issue by providing the int* parameter.

Thanks.


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http://gcc.gnu.org/bugzilla/show_bug.cgi?id=29335