[src/zeta.c] Updated FIXME: also suggest a scaling.

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@10810 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 7 insertions, 1 deletions

diff --git a/src/zeta.c b/src/zeta.c
index 962e9f2bc..c7aca97e6 100644
--- a/src/zeta.c
+++ b/src/zeta.c
@@ -432,7 +432,13 @@ mpfr_zeta (mpfr_t z, mpfr_srcptr s, mpfr_rnd_t rnd_mode)
             {
               /* FIXME: An overflow in gamma(s1) does not imply that
                  Zeta(s) will overflow. In this branch, compute the
-                 log to avoid intermediate overflows? */
+                 log to avoid intermediate overflows? To avoid a
+                 problem at the overflow boundary, a scaling can
+                 also be done without any cost here since the log(2)
+                 already appears in the expression: compute
+                 log(...) - log(2), then the exponential, round
+                 correctly, then multiply by 2 (exact, with possible
+                 overflow generation). */
               mpfr_div_2ui (s1, s, 2, MPFR_RNDN); /* s/4, exact */
               mpfr_frac (s1, s1, MPFR_RNDN); /* exact, -1 < s1 < 0 */
               overflow = (mpfr_cmp_si_2exp (s1, -1, -1) > 0) ? -1 : 1;