Add iscanonical.

TS 18661-1 adds an iscanonical classification macro to <math.h>.

The motivation for this is decimal floating-point, where some values
have both canonical and noncanonical encodings.  For IEEE binary
interchange formats, all encodings are canonical.  For x86/m68k
ldbl-96, and for ldbl-128ibm, there are encodings that do not
represent any valid value of the type; although formally iscanonical
does not need to handle trap representations (and so could just always
return 1), it seems useful, and in line with the description in the TS
of "representations that are extraneous to the floating-point model"
as being non-canonical (as well as "redundant representations of some
or all of its values"), for it to detect those representations and
return 0 for them.

This patch adds iscanonical to glibc.  It goes in a header
<bits/iscanonical.h>, included under appropriate conditions in
<math.h>.  The default header version just evaluates the argument
(converted to its semantic type, though current GCC will probably
discard that conversion and any exceptions resulting from it) and
returns 1.  ldbl-96 and ldbl-128ibm then have versions of the header
that call a function __iscanonicall for long double (the sizeof-based
tests will of course need updating for float128 support, like other
such type-generic macro implementations).  The ldbl-96 version of
__iscanonicall has appropriate conditionals to reflect the differences
in the m68k version of that format (where the high mantissa bit may be
either 0 or 1 when the exponent is 0 or 0x7fff).  Corresponding tests
for those formats are added as well.  Other architectures do not have
any new functions added because just returning 1 is correct for all
their floating-point formats.

Tested for x86_64, x86, mips64 (to test the default macro version) and
powerpc.

	* math/math.h [__GLIBC_USE (IEC_60559_BFP_EXT)]: Include
	<bits/iscanonical.h>.
	* bits/iscanonical.h: New file.
	* math/s_iscanonicall.c: Likewise.
	* math/Versions (__iscanonicall): New libm symbol at version
	GLIBC_2.25.
	* math/libm-test.inc (iscanonical_test_data): New array.
	(iscanonical_test): New function.
	(main): Call iscanonical_test.
	* math/Makefile (headers): Add bits/iscanonical.h.
	(type-ldouble-routines): Add s_iscanonicall.
	* manual/arith.texi (Floating Point Classes): Document
	iscanonical.
	* manual/libm-err-tab.pl: Update comment on interfaces without
	ulps tabulated.
	* sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h: New file.
	* sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/test-iscanonical-ldbl-128ibm.c:
	Likewise.
	* sysdeps/ieee754/ldbl-128ibm/Makefile (tests): Add
	test-iscanonical-ldbl-128ibm.
	* sysdeps/ieee754/ldbl-96/bits/iscanonical.h: New file.
	* sysdeps/ieee754/ldbl-96/s_iscanonicall.c: Likewise.
	* sysdeps/ieee754/ldbl-96/test-iscanonical-ldbl-96.c: Likewise.
	* sysdeps/ieee754/ldbl-96/Makefile: Likewise.
	* sysdeps/unix/sysv/linux/i386/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/ia64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/m68k/m680x0/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/powerpc/powerpc32/nofpu/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/powerpc/powerpc64/libm-le.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/powerpc/powerpc64/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/x86_64/64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/x86_64/x32/libm.abilist: Likewise.

8 files changed, 511 insertions, 1 deletions

diff --git a/sysdeps/ieee754/ldbl-128ibm/Makefile b/sysdeps/ieee754/ldbl-128ibm/Makefile
index 6242edda41..56bebf8391 100644
--- a/sysdeps/ieee754/ldbl-128ibm/Makefile
+++ b/sysdeps/ieee754/ldbl-128ibm/Makefile
@@ -11,5 +11,5 @@ endif
 
 ifeq ($(subdir),math)
 tests += test-fmodl-ldbl-128ibm test-remainderl-ldbl-128ibm \
-	 test-remquol-ldbl-128ibm
+	 test-remquol-ldbl-128ibm test-iscanonical-ldbl-128ibm
 endif
diff --git a/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h b/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h
new file mode 100644
index 0000000000..cbc79ae8da
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/bits/iscanonical.h
@@ -0,0 +1,35 @@
+/* Define iscanonical macro.  ldbl-128ibm version.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#ifndef _MATH_H
+# error "Never use <bits/iscanonical.h> directly; include <math.h> instead."
+#endif
+
+extern int __iscanonicall (long double __x)
+     __THROW __attribute__ ((__const__));
+
+/* Return nonzero value if X is canonical.  In IEEE interchange binary
+   formats, all values are canonical, but the argument must still be
+   converted to its semantic type for any exceptions arising from the
+   conversion, before being discarded; in IBM long double, there are
+   encodings that are not consistently handled as corresponding to any
+   particular value of the type, and we return 0 for those.  */
+#define iscanonical(x)				\
+  (sizeof (x) == sizeof (long double)		\
+   ? __iscanonicall (x)				\
+   : ((void) (__typeof (x)) (x), 1))
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c b/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c
new file mode 100644
index 0000000000..100b4014e1
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c
@@ -0,0 +1,59 @@
+/* Test whether long double value is canonical.  ldbl-128ibm version.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <math.h>
+#include <math_private.h>
+#include <stdint.h>
+
+int
+__iscanonicall (long double x)
+{
+  double xhi, xlo;
+  uint64_t hx, lx;
+
+  ldbl_unpack (x, &xhi, &xlo);
+  EXTRACT_WORDS64 (hx, xhi);
+  EXTRACT_WORDS64 (lx, xlo);
+  int64_t ix = hx & 0x7fffffffffffffffULL;
+  int64_t iy = lx & 0x7fffffffffffffffULL;
+  int hexp = (ix & 0x7ff0000000000000LL) >> 52;
+  int lexp = (iy & 0x7ff0000000000000LL) >> 52;
+
+  if (iy == 0)
+    /* Low part 0 is always OK.  */
+    return 1;
+
+  if (hexp == 0x7ff)
+    /* If a NaN, the low part does not matter.  If an infinity, the
+       low part must be 0, in which case we have already returned.  */
+    return ix != 0x7ff0000000000000LL;
+
+  /* The high part is finite and the low part is nonzero.  There must
+     be sufficient difference between the exponents.  */
+  bool low_p2;
+  if (lexp == 0)
+    {
+      /* Adjust the exponent for subnormal low part.  */
+      lexp = 12 - __builtin_clzll (iy);
+      low_p2 = iy == (1LL << (51 + lexp));
+    }
+  else
+    low_p2 = (iy & 0xfffffffffffffLL) == 0;
+  int expdiff = hexp - lexp;
+  return expdiff > 53 || (expdiff == 53 && low_p2 && (ix & 1) == 0);
+}
diff --git a/sysdeps/ieee754/ldbl-128ibm/test-iscanonical-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/test-iscanonical-ldbl-128ibm.c
new file mode 100644
index 0000000000..fc16250f5c
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/test-iscanonical-ldbl-128ibm.c
@@ -0,0 +1,203 @@
+/* Test iscanonical for ldbl-128ibm.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <float.h>
+#include <math.h>
+#include <math_private.h>
+#include <stdbool.h>
+#include <stdio.h>
+
+struct test
+{
+  double hi, lo;
+  bool canonical;
+};
+
+static const struct test tests[] =
+  {
+    { __builtin_nan (""), 0.0, true },
+    { __builtin_nan (""), DBL_MAX, true },
+    { __builtin_nan (""), __builtin_inf (), true },
+    { __builtin_nan (""), __builtin_nan (""), true },
+    { __builtin_nan (""), __builtin_nans (""), true },
+    { __builtin_nans (""), 0.0, true },
+    { __builtin_nans (""), DBL_MAX, true },
+    { __builtin_nans (""), __builtin_inf (), true },
+    { __builtin_nans (""), __builtin_nan (""), true },
+    { __builtin_nans (""), __builtin_nans (""), true },
+    { __builtin_inf (), 0.0, true },
+    { __builtin_inf (), -0.0, true },
+    { -__builtin_inf (), 0.0, true },
+    { -__builtin_inf (), -0.0, true },
+    { __builtin_inf (), DBL_TRUE_MIN, false },
+    { __builtin_inf (), -DBL_TRUE_MIN, false },
+    { -__builtin_inf (), DBL_TRUE_MIN, false },
+    { -__builtin_inf (), -DBL_TRUE_MIN, false },
+    { __builtin_inf (), DBL_MIN, false },
+    { __builtin_inf (), -DBL_MIN, false },
+    { -__builtin_inf (), DBL_MIN, false },
+    { -__builtin_inf (), -DBL_MIN, false },
+    { __builtin_inf (), __builtin_inf (), false },
+    { __builtin_inf (), -__builtin_inf (), false },
+    { -__builtin_inf (), __builtin_inf (), false },
+    { -__builtin_inf (), -__builtin_inf (), false },
+    { __builtin_inf (), __builtin_nan (""), false },
+    { __builtin_inf (), -__builtin_nan (""), false },
+    { -__builtin_inf (), __builtin_nan (""), false },
+    { -__builtin_inf (), -__builtin_nan (""), false },
+    { 0.0, 0.0, true },
+    { 0.0, -0.0, true },
+    { -0.0, 0.0, true },
+    { -0.0, -0.0, true },
+    { 0.0, DBL_TRUE_MIN, false },
+    { 0.0, -DBL_TRUE_MIN, false },
+    { -0.0, DBL_TRUE_MIN, false },
+    { -0.0, -DBL_TRUE_MIN, false },
+    { 0.0, DBL_MAX, false },
+    { 0.0, -DBL_MAX, false },
+    { -0.0, DBL_MAX, false },
+    { -0.0, -DBL_MAX, false },
+    { 0.0, __builtin_inf (), false },
+    { 0.0, -__builtin_inf (), false },
+    { -0.0, __builtin_inf (), false },
+    { -0.0, -__builtin_inf (), false },
+    { 0.0, __builtin_nan (""), false },
+    { 0.0, -__builtin_nan (""), false },
+    { -0.0, __builtin_nan (""), false },
+    { -0.0, -__builtin_nan (""), false },
+    { 1.0, 0.0, true },
+    { 1.0, -0.0, true },
+    { -1.0, 0.0, true },
+    { -1.0, -0.0, true },
+    { 1.0, DBL_TRUE_MIN, true },
+    { 1.0, -DBL_TRUE_MIN, true },
+    { -1.0, DBL_TRUE_MIN, true },
+    { -1.0, -DBL_TRUE_MIN, true },
+    { 1.0, DBL_MAX, false },
+    { 1.0, -DBL_MAX, false },
+    { -1.0, DBL_MAX, false },
+    { -1.0, -DBL_MAX, false },
+    { 1.0, __builtin_inf (), false },
+    { 1.0, -__builtin_inf (), false },
+    { -1.0, __builtin_inf (), false },
+    { -1.0, -__builtin_inf (), false },
+    { 1.0, __builtin_nan (""), false },
+    { 1.0, -__builtin_nan (""), false },
+    { -1.0, __builtin_nan (""), false },
+    { -1.0, -__builtin_nan (""), false },
+    { 0x1p1023, 0x1.1p969, true },
+    { 0x1p1023, -0x1.1p969, true },
+    { -0x1p1023, 0x1.1p969, true },
+    { -0x1p1023, -0x1.1p969, true },
+    { 0x1p1023, 0x1.1p970, false },
+    { 0x1p1023, -0x1.1p970, false },
+    { -0x1p1023, 0x1.1p970, false },
+    { -0x1p1023, -0x1.1p970, false },
+    { 0x1p1023, 0x1p970, true },
+    { 0x1p1023, -0x1p970, true },
+    { -0x1p1023, 0x1p970, true },
+    { -0x1p1023, -0x1p970, true },
+    { 0x1.0000000000001p1023, 0x1p970, false },
+    { 0x1.0000000000001p1023, -0x1p970, false },
+    { -0x1.0000000000001p1023, 0x1p970, false },
+    { -0x1.0000000000001p1023, -0x1p970, false },
+    { 0x1p-969, 0x1.1p-1023, true },
+    { 0x1p-969, -0x1.1p-1023, true },
+    { -0x1p-969, 0x1.1p-1023, true },
+    { -0x1p-969, -0x1.1p-1023, true },
+    { 0x1p-969, 0x1.1p-1022, false },
+    { 0x1p-969, -0x1.1p-1022, false },
+    { -0x1p-969, 0x1.1p-1022, false },
+    { -0x1p-969, -0x1.1p-1022, false },
+    { 0x1p-969, 0x1p-1022, true },
+    { 0x1p-969, -0x1p-1022, true },
+    { -0x1p-969, 0x1p-1022, true },
+    { -0x1p-969, -0x1p-1022, true },
+    { 0x1.0000000000001p-969, 0x1p-1022, false },
+    { 0x1.0000000000001p-969, -0x1p-1022, false },
+    { -0x1.0000000000001p-969, 0x1p-1022, false },
+    { -0x1.0000000000001p-969, -0x1p-1022, false },
+    { 0x1p-970, 0x1.1p-1024, true },
+    { 0x1p-970, -0x1.1p-1024, true },
+    { -0x1p-970, 0x1.1p-1024, true },
+    { -0x1p-970, -0x1.1p-1024, true },
+    { 0x1p-970, 0x1.1p-1023, false },
+    { 0x1p-970, -0x1.1p-1023, false },
+    { -0x1p-970, 0x1.1p-1023, false },
+    { -0x1p-970, -0x1.1p-1023, false },
+    { 0x1p-970, 0x1p-1023, true },
+    { 0x1p-970, -0x1p-1023, true },
+    { -0x1p-970, 0x1p-1023, true },
+    { -0x1p-970, -0x1p-1023, true },
+    { 0x1.0000000000001p-970, 0x1p-1023, false },
+    { 0x1.0000000000001p-970, -0x1p-1023, false },
+    { -0x1.0000000000001p-970, 0x1p-1023, false },
+    { -0x1.0000000000001p-970, -0x1p-1023, false },
+    { 0x1p-1000, 0x1.1p-1054, true },
+    { 0x1p-1000, -0x1.1p-1054, true },
+    { -0x1p-1000, 0x1.1p-1054, true },
+    { -0x1p-1000, -0x1.1p-1054, true },
+    { 0x1p-1000, 0x1.1p-1053, false },
+    { 0x1p-1000, -0x1.1p-1053, false },
+    { -0x1p-1000, 0x1.1p-1053, false },
+    { -0x1p-1000, -0x1.1p-1053, false },
+    { 0x1p-1000, 0x1p-1053, true },
+    { 0x1p-1000, -0x1p-1053, true },
+    { -0x1p-1000, 0x1p-1053, true },
+    { -0x1p-1000, -0x1p-1053, true },
+    { 0x1.0000000000001p-1000, 0x1p-1053, false },
+    { 0x1.0000000000001p-1000, -0x1p-1053, false },
+    { -0x1.0000000000001p-1000, 0x1p-1053, false },
+    { -0x1.0000000000001p-1000, -0x1p-1053, false },
+    { 0x1p-1021, 0x1p-1074, true },
+    { 0x1p-1021, -0x1p-1074, true },
+    { -0x1p-1021, 0x1p-1074, true },
+    { -0x1p-1021, -0x1p-1074, true },
+    { 0x1.0000000000001p-1021, 0x1p-1074, false },
+    { 0x1.0000000000001p-1021, -0x1p-1074, false },
+    { -0x1.0000000000001p-1021, 0x1p-1074, false },
+    { -0x1.0000000000001p-1021, -0x1p-1074, false },
+    { 0x1p-1022, 0x1p-1074, false },
+    { 0x1p-1022, -0x1p-1074, false },
+    { -0x1p-1022, 0x1p-1074, false },
+    { -0x1p-1022, -0x1p-1074, false },
+  };
+
+static int
+do_test (void)
+{
+  int result = 0;
+
+  for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++)
+    {
+      long double ld = ldbl_pack (tests[i].hi, tests[i].lo);
+      bool canonical = iscanonical (ld);
+      if (canonical == tests[i].canonical)
+	printf ("PASS: test %zu\n", i);
+      else
+	{
+	  printf ("FAIL: test %zu\n", i);
+	  result = 1;
+	}
+    }
+
+  return result;
+}
+
+#define TEST_FUNCTION do_test ()
+#include "../test-skeleton.c"
diff --git a/sysdeps/ieee754/ldbl-96/Makefile b/sysdeps/ieee754/ldbl-96/Makefile
new file mode 100644
index 0000000000..bf9676e907
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/Makefile
@@ -0,0 +1,21 @@
+# Makefile for sysdeps/ieee754/ldbl-96.
+# Copyright (C) 2016 Free Software Foundation, Inc.
+# This file is part of the GNU C Library.
+
+# The GNU C Library is free software; you can redistribute it and/or
+# modify it under the terms of the GNU Lesser General Public
+# License as published by the Free Software Foundation; either
+# version 2.1 of the License, or (at your option) any later version.
+
+# The GNU C Library is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+# Lesser General Public License for more details.
+
+# You should have received a copy of the GNU Lesser General Public
+# License along with the GNU C Library; if not, see
+# <http://www.gnu.org/licenses/>.
+
+ifeq ($(subdir),math)
+tests += test-iscanonical-ldbl-96
+endif
diff --git a/sysdeps/ieee754/ldbl-96/bits/iscanonical.h b/sysdeps/ieee754/ldbl-96/bits/iscanonical.h
new file mode 100644
index 0000000000..af0c72cc7f
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/bits/iscanonical.h
@@ -0,0 +1,35 @@
+/* Define iscanonical macro.  ldbl-96 version.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#ifndef _MATH_H
+# error "Never use <bits/iscanonical.h> directly; include <math.h> instead."
+#endif
+
+extern int __iscanonicall (long double __x)
+     __THROW __attribute__ ((__const__));
+
+/* Return nonzero value if X is canonical.  In IEEE interchange binary
+   formats, all values are canonical, but the argument must still be
+   converted to its semantic type for any exceptions arising from the
+   conversion, before being discarded; in extended precision, there
+   are encodings that are not consistently handled as corresponding to
+   any particular value of the type, and we return 0 for those.  */
+#define iscanonical(x)				\
+  (sizeof (x) == sizeof (long double)		\
+   ? __iscanonicall (x)				\
+   : ((void) (__typeof (x)) (x), 1))
diff --git a/sysdeps/ieee754/ldbl-96/s_iscanonicall.c b/sysdeps/ieee754/ldbl-96/s_iscanonicall.c
new file mode 100644
index 0000000000..f820030dc0
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/s_iscanonicall.c
@@ -0,0 +1,43 @@
+/* Test whether long double value is canonical.  ldbl-96 version.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <float.h>
+#include <math.h>
+#include <math_private.h>
+#include <stdbool.h>
+#include <stdint.h>
+
+int
+__iscanonicall (long double x)
+{
+  uint32_t se, i0, i1 __attribute__ ((unused));
+
+  GET_LDOUBLE_WORDS (se, i0, i1, x);
+  int32_t ix = se & 0x7fff;
+  bool mant_high = (i0 & 0x80000000) != 0;
+
+  if (LDBL_MIN_EXP == -16381)
+    /* Intel variant: the high mantissa bit should have a value
+       determined by the exponent.  */
+    return ix > 0 ? mant_high : !mant_high;
+  else
+    /* M68K variant: both values of the high bit are valid for the
+       greatest and smallest exponents, while other exponents require
+       the high bit to be set.  */
+    return ix == 0 || ix == 0x7fff || mant_high;
+}
diff --git a/sysdeps/ieee754/ldbl-96/test-iscanonical-ldbl-96.c b/sysdeps/ieee754/ldbl-96/test-iscanonical-ldbl-96.c
new file mode 100644
index 0000000000..6827aa8108
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/test-iscanonical-ldbl-96.c
@@ -0,0 +1,114 @@
+/* Test iscanonical for ldbl-96.
+   Copyright (C) 2016 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <http://www.gnu.org/licenses/>.  */
+
+#include <float.h>
+#include <math.h>
+#include <math_private.h>
+#include <stdbool.h>
+#include <stdint.h>
+#include <stdio.h>
+
+struct test
+{
+  bool sign;
+  uint16_t exponent;
+  bool high;
+  uint64_t mantissa;
+  bool canonical;
+};
+
+#define M68K_VARIANT (LDBL_MIN_EXP == -16382)
+
+static const struct test tests[] =
+  {
+    { false, 0, true, 0, M68K_VARIANT },
+    { true, 0, true, 0, M68K_VARIANT },
+    { false, 0, true, 1, M68K_VARIANT },
+    { true, 0, true, 1, M68K_VARIANT },
+    { false, 0, true, 0x100000000ULL, M68K_VARIANT },
+    { true, 0, true, 0x100000000ULL, M68K_VARIANT },
+    { false, 0, false, 0, true },
+    { true, 0, false, 0, true },
+    { false, 0, false, 1, true },
+    { true, 0, false, 1, true },
+    { false, 0, false, 0x100000000ULL, true },
+    { true, 0, false, 0x100000000ULL, true },
+    { false, 1, true, 0, true },
+    { true, 1, true, 0, true },
+    { false, 1, true, 1, true },
+    { true, 1, true, 1, true },
+    { false, 1, true, 0x100000000ULL, true },
+    { true, 1, true, 0x100000000ULL, true },
+    { false, 1, false, 0, false },
+    { true, 1, false, 0, false },
+    { false, 1, false, 1, false },
+    { true, 1, false, 1, false },
+    { false, 1, false, 0x100000000ULL, false },
+    { true, 1, false, 0x100000000ULL, false },
+    { false, 0x7ffe, true, 0, true },
+    { true, 0x7ffe, true, 0, true },
+    { false, 0x7ffe, true, 1, true },
+    { true, 0x7ffe, true, 1, true },
+    { false, 0x7ffe, true, 0x100000000ULL, true },
+    { true, 0x7ffe, true, 0x100000000ULL, true },
+    { false, 0x7ffe, false, 0, false },
+    { true, 0x7ffe, false, 0, false },
+    { false, 0x7ffe, false, 1, false },
+    { true, 0x7ffe, false, 1, false },
+    { false, 0x7ffe, false, 0x100000000ULL, false },
+    { true, 0x7ffe, false, 0x100000000ULL, false },
+    { false, 0x7fff, true, 0, true },
+    { true, 0x7fff, true, 0, true },
+    { false, 0x7fff, true, 1, true },
+    { true, 0x7fff, true, 1, true },
+    { false, 0x7fff, true, 0x100000000ULL, true },
+    { true, 0x7fff, true, 0x100000000ULL, true },
+    { false, 0x7fff, false, 0, M68K_VARIANT },
+    { true, 0x7fff, false, 0, M68K_VARIANT },
+    { false, 0x7fff, false, 1, M68K_VARIANT },
+    { true, 0x7fff, false, 1, M68K_VARIANT },
+    { false, 0x7fff, false, 0x100000000ULL, M68K_VARIANT },
+    { true, 0x7fff, false, 0x100000000ULL, M68K_VARIANT },
+  };
+
+static int
+do_test (void)
+{
+  int result = 0;
+
+  for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++)
+    {
+      long double ld;
+      SET_LDOUBLE_WORDS (ld, tests[i].exponent | (tests[i].sign << 15),
+			 (tests[i].mantissa >> 32) | (tests[i].high << 31),
+			 tests[i].mantissa & 0xffffffffULL);
+      bool canonical = iscanonical (ld);
+      if (canonical == tests[i].canonical)
+	printf ("PASS: test %zu\n", i);
+      else
+	{
+	  printf ("FAIL: test %zu\n", i);
+	  result = 1;
+	}
+    }
+
+  return result;
+}
+
+#define TEST_FUNCTION do_test ()
+#include "../test-skeleton.c"