exp.c: completed a comment, describing how rigorous underflow/overflow

detection can be done.

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@5461 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 16 insertions, 3 deletions

diff --git a/exp.c b/exp.c
index 8a718d7c9..95badbdc8 100644
--- a/exp.c
+++ b/exp.c
@@ -60,9 +60,22 @@ mpfr_exp (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
 
   /* First, let's detect the underflow and overflow. */
   /* FIXME: This is still incorrect for the underflow since MPFR chose
-     underflow after rounding (the result is correct, though). Some
-     overflow cases may not be detected (it would probably too difficult
-     to detect them), but is this sufficient for the generic algorithms? */
+     underflow after rounding (the result is correct, though, only the
+     underflow flag may not). Some overflow cases may not be detected
+     (it would probably too difficult to detect them here), but is this
+     sufficient for the generic algorithms?
+     - After a simple modification to do like in the generic case of
+       mpfr_pow, exp_2.c can really detect exceptions rigorously: the
+       final mpfr_mul_2si must be done after MPFR_CAN_ROUND and the
+       rounding.
+     - The exp3.c routine computes a lower bound on the result, thus
+       detects overflows rigorously. Concerning the underflow, this
+       can be detected by a scaling. As the last operation is a square
+       (z^2), the scaling is needed (and very easy to do) only if an
+       underflow is generated by this operation.
+     As a consequence, we won't need a rigorous underflow/overflow
+     detection test here in exp.c (only the main cases of underflow
+     and overflow). */
   {
     mpfr_t elo, ehi, bound;
     int slo, shi;