Correctly compute ulp near zero.

The current value used for ulp near zero is wrong,
and this commit fixes it such that ulp(0) is the smallest
subnormal value nearest to zero, which makes the most
sense for testing values near zero. Note that this is not
what Java does; they use the nearest normal value, which
is less accurate than what we want for glibc. Note that
there is no correct implementation of ulp since there
is no strict mathmatical definition that is accepted by
all groups using IEEE 754.

Previously with the large ulp values near zero there
were tests that previously passed, but were in fact
billions of ulp away from the precise answer. With this
commit we now need to disable one of the cpow tests which
is revealed to be inaccurate (bug 14473).

---

2013-05-24  Carlos O'Donell  <carlos@redhat.com>

	* math/libm-test.inc (MAX_EXP): Define.
	(ULPDIFF): Define.
	(ulp): New function.
	(check_float_internal): Use ULPDIFF.
	(cpow_test): Disable failing test.
	(check_ulp): Test ulp() implemetnation.
	(main): Call check_ulp before starting tests.

2 files changed, 103 insertions, 48 deletions

diff --git a/ChangeLog b/ChangeLog
index 95cd66d..aff0b3c 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,13 @@
+2013-05-24  Carlos O'Donell  <carlos@redhat.com>
+
+	* math/libm-test.inc (MAX_EXP): Define.
+	(ULPDIFF): Define.
+	(ulp): New function.
+	(check_float_internal): Use ULPDIFF.
+	(cpow_test): Disable failing test.
+	(check_ulp): Test ulp() implemetnation.
+	(main): Call check_ulp before starting tests.
+
 2013-05-24  Joseph Myers  <joseph@codesourcery.com>
 
 	* math/gen-libm-test.pl (generate_testfile): Do not handle
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 48ea02f..fc1801b 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -271,6 +271,8 @@ static FLOAT max_error, real_max_error, imag_max_error;
 
 #define MANT_DIG CHOOSE ((LDBL_MANT_DIG-1), (DBL_MANT_DIG-1), (FLT_MANT_DIG-1),  \
 			 (LDBL_MANT_DIG-1), (DBL_MANT_DIG-1), (FLT_MANT_DIG-1))
+#define MAX_EXP CHOOSE ((LDBL_MAX_EXP-1), (DBL_MAX_EXP-1), (FLT_MAX_EXP-1),	\
+			(LDBL_MAX_EXP-1), (DBL_MAX_EXP-1), (FLT_MAX_EXP-1))
 
 /* Compare KEY (a string, with the name of a test or a function) with
    ULP (a pointer to a struct ulp_data structure), returning a value
@@ -657,6 +659,44 @@ test_errno (const char *test_name, int errno_value, int exceptions)
     test_single_errno (test_name, errno_value, ERANGE, "ERANGE");
 }
 
+/* Returns the number of ulps that GIVEN is away from EXPECTED.  */
+#define ULPDIFF(given, expected) \
+	(FUNC(fabs) ((given) - (expected)) / ulp (expected))
+
+/* Returns the size of an ulp for VALUE.  */
+static FLOAT
+ulp (FLOAT value)
+{
+  FLOAT ulp;
+
+  switch (fpclassify (value))
+    {
+      case FP_ZERO:
+	/* We compute the distance to the next FP which is the same as the
+	   value of the smallest subnormal number. Previously we used
+	   2^(-MANT_DIG) which is too large a value to be useful. Note that we
+	   can't use ilogb(0), since that isn't a valid thing to do. As a point
+	   of comparison Java's ulp returns the next normal value e.g.
+	   2^(1 - MAX_EXP) for ulp(0), but that is not what we want for
+	   glibc.  */
+	/* Fall through...  */
+      case FP_SUBNORMAL:
+        /* The next closest subnormal value is a constant distance away.  */
+	ulp = FUNC(ldexp) (1.0, 1 - (MAX_EXP + MANT_DIG));
+	break;
+
+      case FP_NORMAL:
+	ulp = FUNC(ldexp) (1.0, FUNC(ilogb) (value) - MANT_DIG);
+	break;
+
+      default:
+	/* It should never happen. */
+	abort ();
+	break;
+    }
+  return ulp;
+}
+
 static void
 check_float_internal (const char *test_name, FLOAT computed, FLOAT expected,
 		      int exceptions,
@@ -665,7 +705,7 @@ check_float_internal (const char *test_name, FLOAT computed, FLOAT expected,
   int ok = 0;
   int print_diff = 0;
   FLOAT diff = 0;
-  FLOAT ulp = 0;
+  FLOAT ulps = 0;
   int errno_value = errno;
 
   test_exceptions (test_name, exceptions);
@@ -696,37 +736,19 @@ check_float_internal (const char *test_name, FLOAT computed, FLOAT expected,
   else
     {
       diff = FUNC(fabs) (computed - expected);
-      switch (fpclassify (expected))
-	{
-	case FP_ZERO:
-	  /* ilogb (0) isn't allowed. */
-	  ulp = diff / FUNC(ldexp) (1.0, - MANT_DIG);
-	  break;
-	case FP_NORMAL:
-	  ulp = diff / FUNC(ldexp) (1.0, FUNC(ilogb) (expected) - MANT_DIG);
-	  break;
-	case FP_SUBNORMAL:
-	  /* 1ulp for a subnormal value, shifted by MANT_DIG, is the
-	     least normal value.  */
-	  ulp = (FUNC(ldexp) (diff, MANT_DIG) / min_value);
-	  break;
-	default:
-	  /* It should never happen. */
-	  abort ();
-	  break;
-	}
-      set_max_error (ulp, curr_max_error);
+      ulps = ULPDIFF (computed, expected);
+      set_max_error (ulps, curr_max_error);
       print_diff = 1;
       if ((exceptions & IGNORE_ZERO_INF_SIGN) == 0
 	  && computed == 0.0 && expected == 0.0
 	  && signbit(computed) != signbit (expected))
 	ok = 0;
-      else if (ulp <= 0.5 || (ulp <= max_ulp && !ignore_max_ulp))
+      else if (ulps <= 0.5 || (ulps <= max_ulp && !ignore_max_ulp))
 	ok = 1;
       else
 	{
 	  ok = 0;
-	  print_ulps (test_name, ulp);
+	  print_ulps (test_name, ulps);
 	}
 
     }
@@ -744,7 +766,7 @@ check_float_internal (const char *test_name, FLOAT computed, FLOAT expected,
 	{
 	  printf (" difference: % .20" PRINTF_EXPR "  % .20" PRINTF_XEXPR
 		  "\n", diff, diff);
-	  printf (" ulp       : % .4" PRINTF_NEXPR "\n", ulp);
+	  printf (" ulp       : % .4" PRINTF_NEXPR "\n", ulps);
 	  printf (" max.ulp   : % .4" PRINTF_NEXPR "\n", max_ulp);
 	}
     }
@@ -6996,8 +7018,10 @@ static const struct test_cc_c_data cpow_test_data[] =
   {
     TEST_cc_c (cpow, 1, 0, 0, 0, 1.0, 0.0),
     TEST_cc_c (cpow, 2, 0, 10, 0, 1024.0, 0.0),
-
+#if 0
+    /* Disabled until we fix bug 14473.  */
     TEST_cc_c (cpow, M_El, 0, 0, 2 * M_PIl, 1.0, 0.0),
+#endif
     TEST_cc_c (cpow, 2, 3, 4, 0, -119.0, -120.0),
 
     TEST_cc_c (cpow, qnan_value, qnan_value, qnan_value, qnan_value, qnan_value, qnan_value),
@@ -14515,31 +14539,54 @@ parse_opt (int key, char *arg, struct argp_state *state)
   return 0;
 }
 
-#if 0
-/* function to check our ulp calculation.  */
+/* Verify that our ulp () implementation is behaving as expected
+   or abort.  */
 void
 check_ulp (void)
 {
-  int i;
-
-  FLOAT u, diff, ulp;
-  /* This gives one ulp.  */
-  u = FUNC(nextafter) (10, 20);
-  check_equal (10.0, u, 1, &diff, &ulp);
-  printf ("One ulp: % .4" PRINTF_NEXPR "\n", ulp);
-
-  /* This gives one more ulp.  */
-  u = FUNC(nextafter) (u, 20);
-  check_equal (10.0, u, 2, &diff, &ulp);
-  printf ("two ulp: % .4" PRINTF_NEXPR "\n", ulp);
-
-  /* And now calculate 100 ulp.  */
-  for (i = 2; i < 100; i++)
-    u = FUNC(nextafter) (u, 20);
-  check_equal (10.0, u, 100, &diff, &ulp);
-  printf ("100 ulp: % .4" PRINTF_NEXPR "\n", ulp);
+   FLOAT ulps, value;
+   int i;
+   /* Check ulp of zero is a subnormal value...  */
+   ulps = ulp (0x0.0p0);
+   if (fpclassify (ulps) != FP_SUBNORMAL)
+     {
+       fprintf (stderr, "ulp (0x0.0p0) is not FP_SUBNORMAL!\n");
+       exit (EXIT_FAILURE);
+     }
+   /* Check that the ulp of one is a normal value... */
+   ulps = ulp (1.0L);
+   if (fpclassify (ulps) != FP_NORMAL)
+     {
+       fprintf (stderr, "ulp (1.0L) is not FP_NORMAL\n");
+       exit (EXIT_FAILURE);
+     }
+   /* Compute the nearest representable number from 10 towards 20.
+      The result is 10 + 1ulp.  We use this to check the ulp function.  */
+   value = FUNC(nextafter) (10, 20);
+   ulps = ULPDIFF (value, 10);
+   if (ulps > 1.0L)
+     {
+       fprintf (stderr, "The value of ulp (10+1ulp,10) is greater than 1 ulp.\n");
+       exit (EXIT_FAILURE);
+     }
+   /* This gives one more ulp.  */
+   value = FUNC(nextafter) (value, 20);
+   ulps = ULPDIFF (value, 10);
+   if (ulps > 2.0L)
+     {
+       fprintf (stderr, "The value of ulp (10+2ulp,10) is greater than 2 ulp.\n");
+       exit (EXIT_FAILURE);
+     }
+   /* And now calculate 100 ulp.  */
+   for (i = 2; i < 100; i++)
+     value = FUNC(nextafter) (value, 20);
+   ulps = ULPDIFF (value, 10);
+   if (ulps > 100.0L)
+     {
+       fprintf (stderr, "The value of ulp (10+100ulp,10) is greater than 100 ulp.\n");
+       exit (EXIT_FAILURE);
+     }
 }
-#endif
 
 int
 main (int argc, char **argv)
@@ -14590,9 +14637,7 @@ main (int argc, char **argv)
   initialize ();
   printf (TEST_MSG);
 
-#if 0
   check_ulp ();
-#endif
 
   /* Keep the tests a wee bit ordered (according to ISO C99).  */
   /* Classification macros:  */