[src/beta.c] Added comments and some corrections (incomplete) for the

case "z or w is 0".

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@11372 280ebfd0-de03-0410-8827-d642c229c3f4

1 files changed, 25 insertions, 8 deletions

diff --git a/src/beta.c b/src/beta.c
index b2f4154bc..2ab00c16e 100644
--- a/src/beta.c
+++ b/src/beta.c
@@ -121,21 +121,38 @@ mpfr_beta (mpfr_ptr r, mpfr_srcptr z, mpfr_srcptr w, mpfr_rnd_t rnd_mode)
         }
       else /* z or w is 0 */
         {
-          if (mpfr_cmp_ui (z, 0) != 0) /* then w = +0 or -0 */
+          /* If x is not a nonpositive integer, Gamma(x) is regular, so that
+             when y -> 0 with either y >= 0 or y <= 0,
+               Beta(x,y) ~ Gamma(y) / Gamma(x)
+             Gamma(y) tends to an infinity of the same sign as y.
+             Thus Beta(x,y) should be an infinity whose sign is the product
+             of the signs of y and Gamma(x). */
+          if (mpfr_cmp_ui (z, 0) != 0) /* then w is +0 or -0 and z > 0 */
             {
-              /* beta(z,+0) = +Inf, beta(z,-0) = -Inf */
+              /* beta(z,+0) = +Inf, beta(z,-0) = -Inf (see above) */
               MPFR_SET_INF(r);
               MPFR_SET_SAME_SIGN(r,w);
               MPFR_SET_DIVBY0 ();
               MPFR_RET(0);
             }
-          else if (mpfr_cmp_ui (w, 0) != 0)
+          else if (mpfr_cmp_ui (w, 0) != 0) /* then z is +0 or -0 and w < 0 */
             {
-              /* beta(+0,w) = +Inf, beta(-0,w) = -Inf */
-              MPFR_SET_INF(r);
-              MPFR_SET_SAME_SIGN(r,z);
-              MPFR_SET_DIVBY0 ();
-              MPFR_RET(0);
+              if (mpfr_integer_p (w))
+                {
+                  /* When y -> w, |Gamma(y)| -> +Inf but Gamma(y) takes
+                     opposite signs for y < w and y > w, so that the
+                     result is NaN. */
+                  MPFR_SET_NAN(r);
+                  MPFR_RET_NAN;
+                }
+              else
+                {
+                  /* FIXME concerning the sign (see above) */
+                  MPFR_SET_INF(r);
+                  MPFR_SET_SAME_SIGN(r,z);
+                  MPFR_SET_DIVBY0 ();
+                  MPFR_RET(0);
+                }
             }
           else /* w = z = 0:
                   beta(+0,+0) = +Inf