[tests/tsqr.c] added a corner underflow case

git-svn-id: svn://scm.gforge.inria.fr/svn/mpfr/trunk@11258 280ebfd0-de03-0410-8827-d642c229c3f4

2 files changed, 37 insertions, 1 deletions

diff --git a/src/sqr.c b/src/sqr.c
index 0be9ba19d..36587cec7 100644
--- a/src/sqr.c
+++ b/src/sqr.c
@@ -65,6 +65,14 @@ mpfr_sqr_1 (mpfr_ptr a, mpfr_srcptr b, mpfr_rnd_t rnd_mode, mpfr_prec_t p)
      a >= 0.111...111[1]*2^(emin-1), there is no underflow. */
   if (MPFR_UNLIKELY(ax < __gmpfr_emin))
     {
+      /* Note: for emin=2*k+1, a >= 0.111...111*2^(emin-1) is not possible,
+         i.e., a >= (1 - 2^(-p))*2^(2k), since we need a = b^2 with EXP(b)=k,
+         and the largest such b is (1 - 2^(-p))*2^k satisfies
+         b^2 < (1 - 2^(-p))*2^(2k).
+         For emin=2*k, it is only possible for some values of p: it is not
+         possible for p=53, because the largest significand is 6369051672525772
+         but its square has only 52 leading ones. For p=24 it is possible,
+         with b = 11863283, whose square has 24 leading ones. */
       if ((ax == __gmpfr_emin - 1) && (ap[0] == ~mask) &&
           ((rnd_mode == MPFR_RNDN && rb) ||
            (MPFR_IS_LIKE_RNDA(rnd_mode, MPFR_IS_NEG (a)) && (rb | sb))))
diff --git a/tests/tsqr.c b/tests/tsqr.c
index c8d0ea340..2d9169747 100644
--- a/tests/tsqr.c
+++ b/tests/tsqr.c
@@ -118,6 +118,33 @@ check_special (void)
   mpfr_clear (x);
 }
 
+/* check ax < __gmpfr_emin with rnd_mode == MPFR_RNDN, rb = 0 and sb <> 0 */
+static void
+test_underflow (void)
+{
+  mpfr_t x, y;
+  mpfr_exp_t emin;
+
+  emin = mpfr_get_emin ();
+  mpfr_set_emin (0);
+
+  mpfr_init2 (x, 24);
+  mpfr_init2 (y, 24);
+
+  mpfr_set_ui_2exp (x, 11863283, -24, MPFR_RNDN);
+  /* x^2 = 0.011111111111111111111111101101100111111010101001*2^(-48)
+     thus we have an underflow */
+  mpfr_clear_underflow ();
+  mpfr_sqr (y, x, MPFR_RNDN);
+  MPFR_ASSERTN(mpfr_cmp_ui_2exp (y, 1, -1) == 0);
+  MPFR_ASSERTN(mpfr_underflow_p ());
+
+  mpfr_clear (y);
+  mpfr_clear (x);
+
+  mpfr_set_emin (emin);
+}
+
 /* Test of a bug seen with GCC 4.5.2 and GMP 5.0.1 on m68k (m68000 target).
      https://sympa.inria.fr/sympa/arc/mpfr/2011-05/msg00003.html
      https://sympa.inria.fr/sympa/arc/mpfr/2011-05/msg00041.html
@@ -161,8 +188,9 @@ main (void)
   tests_start_mpfr ();
 
   check_mpn_sqr ();
-
   check_special ();
+  test_underflow ();
+
   for (p = MPFR_PREC_MIN; p < 200; p++)
     check_random (p);