[doc/mpfr.texi] Completed specification:

  * on special numbers (±0, ±Inf);
  * of mpfr_lngamma and mpfr_lgamma on 1 and 2 (result is +0);
  * general rules for special values and on mpfr_lngamma.
[src/lngamma.c] Fixed mpfr_lngamma behavior on nonpositive integers
  and -Inf.
[tests/tlngamma.c] Update. Test the flags for some special values.
See <https://sympa.inria.fr/sympa/arc/mpfr/2013-08/msg00008.html> about
the behavior of mpfr_lngamma on zero and general rule for such limits.
(merged changesets r8629,8632-8633,8841,8847 from the trunk)

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/branches/3.1@9605 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 7 insertions, 6 deletions

diff --git a/src/lngamma.c b/src/lngamma.c
index cd43df615..1a760192b 100644
--- a/src/lngamma.c
+++ b/src/lngamma.c
@@ -603,16 +603,17 @@ mpfr_lngamma (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
       mpfr_get_prec (y), mpfr_log_prec, y, inex));
 
   /* special cases */
-  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x) ||
+                     (MPFR_IS_NEG (x) && mpfr_integer_p (x))))
     {
-      if (MPFR_IS_NAN (x) || MPFR_IS_NEG (x))
+      if (MPFR_IS_NAN (x))
         {
           MPFR_SET_NAN (y);
           MPFR_RET_NAN;
         }
-      else /* lngamma(+Inf) = lngamma(+0) = +Inf */
+      else /* lngamma(+/-Inf) = lngamma(nonpositive integer) = +Inf */
         {
-          if (MPFR_IS_ZERO (x))
+          if (!MPFR_IS_INF (x))
             mpfr_set_divby0 ();
           MPFR_SET_INF (y);
           MPFR_SET_POS (y);
@@ -620,8 +621,8 @@ mpfr_lngamma (mpfr_ptr y, mpfr_srcptr x, mpfr_rnd_t rnd)
         }
     }
 
-  /* if x < 0 and -2k-1 <= x <= -2k, then lngamma(x) = NaN */
-  if (MPFR_IS_NEG (x) && (unit_bit (x) == 0 || mpfr_integer_p (x)))
+  /* if -2k-1 < x < -2k <= 0, then lngamma(x) = NaN */
+  if (MPFR_IS_NEG (x) && unit_bit (x) == 0)
     {
       MPFR_SET_NAN (y);
       MPFR_RET_NAN;