Add totalorder, totalorderf, totalorderl.

TS 18661-1 defines totalorder functions implementing the totalOrder
comparison operation from IEEE 754-2008.  This patch implements these
functions for glibc, including the type-generic macro in <tgmath.h>.
(The totalordermag functions will be added in a separate patch.)

The description of the totalOrder operation is complicated.  However,
for IEEE interchange binary formats and the preferred quiet NaN
convention, what that complicated description means is that you
interpret the representation as a sign-magnitude integer (with -0
coming before +0) and do a <= comparison on that interpretation.  For
finite values and infinities the ordering of the sign-magnitude
integers is just the same as the ordering of floating-point values, so
this extends that to all representations.  (Different representations
of the same floating-point value - which includes same quantum in the
decimal case - must still be considered equal by this operation, but
that issue doesn't arise for IEEE interchange binary formats.)  So the
complications are:

* When MIPS quiet NaN conventions are in use, the representation of
  NaNs needs adjusting before making such an integer comparison.  This
  patch does this adjustment only when both arguments are NaNs, as
  there's no need for it if only one is a NaN, and as long as both are
  NaNs you can just flip the relevant bits without any problems from
  this turning a NaN into an infinity.

* For the m68k version of ldbl-96, where the high mantissa bit is
  "don't care" for infinities and NaNs, representations where it
  differs must compare the same.  Note: although the testcase for this
  compiles, I have not actually tested on m68k.

* For ldbl-128ibm, the low part must be ignored when the high part is
  NaN, and low parts of +0 and -0 must be considered the same whatever
  the high part.

The new tests in libm-test.inc are the first tests there specifying
particular payloads for input NaNs.  Separate tests are also added for
the ldbl-96 and ldbl-128ibm special cases where there are different
representations of the same value that must compare equal (which can't
be covered in libm-test.inc as that only specifies values, not
representations).

Tested for x86_64, x86, mips64 and powerpc.

	* math/bits/mathcalls.h [__GLIBC_USE (IEC_60559_BFP_EXT)]
	(totalorder): New declaration.
	* math/tgmath.h [__GLIBC_USE (IEC_60559_BFP_EXT)] (totalorder):
	New macro.
	* math/Versions (totalorder): New libm symbol at version
	GLIBC_2.25.
	(totalorderf): Likewise.
	(totalorderl): Likewise.
	* math/Makefile (libm-calls): Add s_totalorderF.
	* math/gen-libm-test.pl (parse_args): Escape quotes in test name
	string.
	* math/libm-test.inc (PAYLOAD_DIG): New macro.
	(qnan_value_pl): Likewise.
	(snan_value_pl): Likewise.
	(qnan_value): Define using qnan_value_pl.
	(snan_value): Define using snan_value_pl.
	(struct test_ff_i_data): Add comment about which tests use this
	structure.
	(RUN_TEST_ff_b): New macro.
	(RUN_TEST_LOOP_ff_b): Likewise.
	(totalorder_test_data): New array.
	(totalorder_test): New function.
	(main): Call totalorder_test.
	* math/test-tgmath.c (NCALLS): Increase to 122.
	(F(compile_test)): Call totalorder.
	(F(totalorder)): New function.
	* manual/arith.texi (FP Comparison Functions): Document
	totalorder, totalorderf and totalorderl.
	* manual/libm-err-tab.pl: Update comment on interfaces without
	ulps tabulated.
	* sysdeps/ieee754/dbl-64/s_totalorder.c: New file.
	* sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c: Likewise.
	* sysdeps/ieee754/flt-32/s_totalorderf.c: Likewise.
	* sysdeps/ieee754/ldbl-128/s_totalorderl.c: Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c: Likewise.
	* sysdeps/ieee754/ldbl-96/s_totalorderl.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/nldbl-totalorder.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/Makefile (libnldbl-calls): Add
	totalorder.
	(CFLAGS-nldbl-totalorder.c): New variable.
	* sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c: New
	file.
	* sysdeps/ieee754/ldbl-128ibm/Makefile [$(subdir) = math] (tests):
	Add test-totalorderl-ldbl-128ibm.
	* sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c: New file.
	* sysdeps/ieee754/ldbl-96/Makefile [$(subdir) = math] (tests): Add
	test-totalorderl-ldbl-96.
	* sysdeps/nacl/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/aarch64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/alpha/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/arm/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/hppa/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/i386/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/ia64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/m68k/coldfire/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/m68k/m680x0/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/microblaze/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/mips/mips32/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/mips/mips64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/nios2/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/s390/s390-32/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/s390/s390-64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/sh/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/sparc/sparc32/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/sparc/sparc64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/tile/tilegx/tilegx32/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/tile/tilegx/tilegx64/libm.abilist:
	Likewise.
	* sysdeps/unix/sysv/linux/tile/tilepro/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/x86_64/64/libm.abilist: Likewise.
	* sysdeps/unix/sysv/linux/x86_64/x32/libm.abilist: Likewise.

12 files changed, 483 insertions, 3 deletions

diff --git a/sysdeps/ieee754/dbl-64/s_totalorder.c b/sysdeps/ieee754/dbl-64/s_totalorder.c
new file mode 100644
index 0000000000..73ac32f78b
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/s_totalorder.c
@@ -0,0 +1,53 @@
+/* Total order operation.  dbl-64 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
+totalorder (double x, double y)
+{
+  int32_t hx, hy;
+  uint32_t lx, ly;
+  EXTRACT_WORDS (hx, lx, x);
+  EXTRACT_WORDS (hy, ly, y);
+#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+  uint32_t uhx = hx & 0x7fffffff, uhy = hy & 0x7fffffff;
+  /* For the preferred quiet NaN convention, this operation is a
+     comparison of the representations of the arguments interpreted as
+     sign-magnitude integers.  If both arguments are NaNs, invert the
+     quiet/signaling bit so comparing that way works.  */
+  if ((uhx > 0x7ff00000 || (uhx == 0x7ff00000 && lx != 0))
+      && (uhy > 0x7ff00000 || (uhy == 0x7ff00000 && ly != 0)))
+    {
+      hx ^= 0x00080000;
+      hy ^= 0x00080000;
+    }
+#endif
+  uint32_t hx_sign = hx >> 31;
+  uint32_t hy_sign = hy >> 31;
+  hx ^= hx_sign >> 1;
+  lx ^= hx_sign;
+  hy ^= hy_sign >> 1;
+  ly ^= hy_sign;
+  return hx < hy || (hx == hy && lx <= ly);
+}
+#ifdef NO_LONG_DOUBLE
+weak_alias (totalorder, totalorderl)
+#endif
diff --git a/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c b/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c
new file mode 100644
index 0000000000..02cd799cf6
--- /dev/null
+++ b/sysdeps/ieee754/dbl-64/wordsize-64/s_totalorder.c
@@ -0,0 +1,49 @@
+/* Total order operation.  dbl-64/wordsize-64 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
+totalorder (double x, double y)
+{
+  int64_t ix, iy;
+  EXTRACT_WORDS64 (ix, x);
+  EXTRACT_WORDS64 (iy, y);
+#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+  /* For the preferred quiet NaN convention, this operation is a
+     comparison of the representations of the arguments interpreted as
+     sign-magnitude integers.  If both arguments are NaNs, invert the
+     quiet/signaling bit so comparing that way works.  */
+  if ((ix & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL
+      && (iy & 0x7fffffffffffffffULL) > 0x7ff0000000000000ULL)
+    {
+      ix ^= 0x0008000000000000ULL;
+      iy ^= 0x0008000000000000ULL;
+    }
+#endif
+  uint64_t ix_sign = ix >> 63;
+  uint64_t iy_sign = iy >> 63;
+  ix ^= ix_sign >> 1;
+  iy ^= iy_sign >> 1;
+  return ix <= iy;
+}
+#ifdef NO_LONG_DOUBLE
+weak_alias (totalorder, totalorderl)
+#endif
diff --git a/sysdeps/ieee754/flt-32/s_totalorderf.c b/sysdeps/ieee754/flt-32/s_totalorderf.c
new file mode 100644
index 0000000000..1ed30d8116
--- /dev/null
+++ b/sysdeps/ieee754/flt-32/s_totalorderf.c
@@ -0,0 +1,45 @@
+/* Total order operation.  flt-32 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
+totalorderf (float x, float y)
+{
+  int32_t ix, iy;
+  GET_FLOAT_WORD (ix, x);
+  GET_FLOAT_WORD (iy, y);
+#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+  /* For the preferred quiet NaN convention, this operation is a
+     comparison of the representations of the arguments interpreted as
+     sign-magnitude integers.  If both arguments are NaNs, invert the
+     quiet/signaling bit so comparing that way works.  */
+  if ((ix & 0x7fffffff) > 0x7f800000 && (iy & 0x7fffffff) > 0x7f800000)
+    {
+      ix ^= 0x00400000;
+      iy ^= 0x00400000;
+    }
+#endif
+  uint32_t ix_sign = ix >> 31;
+  uint32_t iy_sign = iy >> 31;
+  ix ^= ix_sign >> 1;
+  iy ^= iy_sign >> 1;
+  return ix <= iy;
+}
diff --git a/sysdeps/ieee754/ldbl-128/s_totalorderl.c b/sysdeps/ieee754/ldbl-128/s_totalorderl.c
new file mode 100644
index 0000000000..dc76ccf204
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128/s_totalorderl.c
@@ -0,0 +1,53 @@
+/* Total order operation.  ldbl-128 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
+totalorderl (_Float128 x, _Float128 y)
+{
+  int64_t hx, hy;
+  uint64_t lx, ly;
+  GET_LDOUBLE_WORDS64 (hx, lx, x);
+  GET_LDOUBLE_WORDS64 (hy, ly, y);
+#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+  uint64_t uhx = hx & 0x7fffffffffffffffULL;
+  uint64_t uhy = hy & 0x7fffffffffffffffULL;
+  /* For the preferred quiet NaN convention, this operation is a
+     comparison of the representations of the arguments interpreted as
+     sign-magnitude integers.  If both arguments are NaNs, invert the
+     quiet/signaling bit so comparing that way works.  */
+  if ((uhx > 0x7fff000000000000ULL || (uhx == 0x7fff000000000000ULL
+				       && lx != 0))
+      && (uhy > 0x7fff000000000000ULL || (uhy == 0x7fff000000000000ULL
+					  && ly != 0)))
+    {
+      hx ^= 0x0000800000000000ULL;
+      hy ^= 0x0000800000000000ULL;
+    }
+#endif
+  uint64_t hx_sign = hx >> 63;
+  uint64_t hy_sign = hy >> 63;
+  hx ^= hx_sign >> 1;
+  lx ^= hx_sign;
+  hy ^= hy_sign >> 1;
+  ly ^= hy_sign;
+  return hx < hy || (hx == hy && lx <= ly);
+}
diff --git a/sysdeps/ieee754/ldbl-128ibm/Makefile b/sysdeps/ieee754/ldbl-128ibm/Makefile
index 56bebf8391..eb625a7234 100644
--- a/sysdeps/ieee754/ldbl-128ibm/Makefile
+++ b/sysdeps/ieee754/ldbl-128ibm/Makefile
@@ -11,5 +11,6 @@ endif
 
 ifeq ($(subdir),math)
 tests += test-fmodl-ldbl-128ibm test-remainderl-ldbl-128ibm \
-	 test-remquol-ldbl-128ibm test-iscanonical-ldbl-128ibm
+	 test-remquol-ldbl-128ibm test-iscanonical-ldbl-128ibm \
+	 test-totalorderl-ldbl-128ibm
 endif
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c b/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c
new file mode 100644
index 0000000000..1535b2fb1e
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/s_totalorderl.c
@@ -0,0 +1,61 @@
+/* Total order operation.  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
+totalorderl (long double x, long double y)
+{
+  double xhi, xlo, yhi, ylo;
+  int64_t hx, hy, lx, ly;
+
+  ldbl_unpack (x, &xhi, &xlo);
+  EXTRACT_WORDS64 (hx, xhi);
+  ldbl_unpack (y, &yhi, &ylo);
+  EXTRACT_WORDS64 (hy, yhi);
+#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+# error not implemented
+#endif
+  uint64_t hx_sign = hx >> 63;
+  uint64_t hy_sign = hy >> 63;
+  int64_t hx_adj = hx ^ (hx_sign >> 1);
+  int64_t hy_adj = hy ^ (hy_sign >> 1);
+  if (hx_adj < hy_adj)
+    return 1;
+  else if (hx_adj > hy_adj)
+    return 0;
+
+  /* The high doubles are identical.  If they are NaNs or both the low
+     parts are zero, the low parts are not significant (and if they
+     are infinities, both the low parts must be zero).  */
+  if ((hx & 0x7fffffffffffffffULL) >= 0x7ff0000000000000ULL)
+    return 1;
+  EXTRACT_WORDS64 (lx, xlo);
+  EXTRACT_WORDS64 (ly, ylo);
+  if (((lx | ly) & 0x7fffffffffffffffULL) == 0)
+    return 1;
+
+  /* Otherwise compare the low parts.  */
+  uint64_t lx_sign = lx >> 63;
+  uint64_t ly_sign = ly >> 63;
+  lx ^= lx_sign >> 1;
+  ly ^= ly_sign >> 1;
+  return lx <= ly;
+}
diff --git a/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c
new file mode 100644
index 0000000000..78b162c4fc
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c
@@ -0,0 +1,64 @@
+/* Test totalorderl 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 <math.h>
+#include <math_private.h>
+#include <stdbool.h>
+#include <stdio.h>
+
+struct test
+{
+  double hi, lo1, lo2;
+};
+
+static const struct test tests[] =
+  {
+    { __builtin_nan (""), 1, __builtin_nans ("") },
+    { -__builtin_nan (""), 1, __builtin_nans ("") },
+    { __builtin_nans (""), 1, __builtin_nan ("") },
+    { -__builtin_nans (""), 1, __builtin_nan ("") },
+    { __builtin_inf (), 0.0, -0.0 },
+    { -__builtin_inf (), 0.0, -0.0 },
+    { 1.5, 0.0, -0.0 },
+  };
+
+static int
+do_test (void)
+{
+  int result = 0;
+
+  for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++)
+    {
+      long double ldx = ldbl_pack (tests[i].hi, tests[i].lo1);
+      long double ldy = ldbl_pack (tests[i].hi, tests[i].lo2);
+      bool to1 = totalorderl (ldx, ldy);
+      bool to2 = totalorderl (ldy, ldx);
+      if (to1 && to2)
+	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
index bf9676e907..931976d7b1 100644
--- a/sysdeps/ieee754/ldbl-96/Makefile
+++ b/sysdeps/ieee754/ldbl-96/Makefile
@@ -17,5 +17,5 @@
 # <http://www.gnu.org/licenses/>.
 
 ifeq ($(subdir),math)
-tests += test-iscanonical-ldbl-96
+tests += test-iscanonical-ldbl-96 test-totalorderl-ldbl-96
 endif
diff --git a/sysdeps/ieee754/ldbl-96/s_totalorderl.c b/sysdeps/ieee754/ldbl-96/s_totalorderl.c
new file mode 100644
index 0000000000..4f14bafb44
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/s_totalorderl.c
@@ -0,0 +1,56 @@
+/* Total order operation.  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 <stdint.h>
+
+int
+totalorderl (long double x, long double y)
+{
+  int16_t expx, expy;
+  uint32_t hx, hy;
+  uint32_t lx, ly;
+  GET_LDOUBLE_WORDS (expx, hx, lx, x);
+  GET_LDOUBLE_WORDS (expy, hy, ly, y);
+  if (LDBL_MIN_EXP == -16382)
+    {
+      /* M68K variant: for the greatest exponent, the high mantissa
+	 bit is not significant and both values of it are valid, so
+	 set it before comparing.  For the Intel variant, only one
+	 value of the high mantissa bit is valid for each exponent, so
+	 this is not necessary.  */
+      if ((expx & 0x7fff) == 0x7fff)
+	hx |= 0x80000000;
+      if ((expy & 0x7fff) == 0x7fff)
+	hy |= 0x80000000;
+    }
+#ifdef HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+# error not implemented
+#endif
+  uint32_t x_sign = expx >> 15;
+  uint32_t y_sign = expy >> 15;
+  expx ^= x_sign >> 17;
+  hx ^= x_sign;
+  lx ^= x_sign;
+  expy ^= y_sign >> 17;
+  hy ^= y_sign;
+  ly ^= y_sign;
+  return expx < expy || (expx == expy && (hx < hy || (hx == hy && lx <= ly)));
+}
diff --git a/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c b/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c
new file mode 100644
index 0000000000..07fa772414
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c
@@ -0,0 +1,71 @@
+/* Test totalorderl 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>
+
+static const uint64_t tests[] =
+  {
+    0, 1, 0x4000000000000000ULL, 0x4000000000000001ULL,
+    0x7fffffffffffffffULL
+  };
+
+static int
+do_test (void)
+{
+  int result = 0;
+
+  if (LDBL_MIN_EXP == -16382)
+    for (size_t i = 0; i < sizeof (tests) / sizeof (tests[0]); i++)
+      {
+	long double ldx, ldy, ldnx, ldny;
+	/* Verify that the high bit of the mantissa is ignored for
+	   infinities and NaNs for the M68K variant of this
+	   format.  */
+	SET_LDOUBLE_WORDS (ldx, 0x7fff,
+			   tests[i] >> 32, tests[i] & 0xffffffffULL);
+	SET_LDOUBLE_WORDS (ldy, 0x7fff,
+			   (tests[i] >> 32) | 0x80000000,
+			   tests[i] & 0xffffffffULL);
+	SET_LDOUBLE_WORDS (ldnx, 0xffff,
+			   tests[i] >> 32, tests[i] & 0xffffffffULL);
+	SET_LDOUBLE_WORDS (ldny, 0xffff,
+			   (tests[i] >> 32) | 0x80000000,
+			   tests[i] & 0xffffffffULL);
+	bool to1 = totalorderl (ldx, ldy);
+	bool to2 = totalorderl (ldy, ldx);
+	bool to3 = totalorderl (ldnx, ldny);
+	bool to4 = totalorderl (ldny, ldnx);
+	if (to1 && to2 && to3 && to4)
+	  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-opt/Makefile b/sysdeps/ieee754/ldbl-opt/Makefile
index af08209570..12255d6951 100644
--- a/sysdeps/ieee754/ldbl-opt/Makefile
+++ b/sysdeps/ieee754/ldbl-opt/Makefile
@@ -41,7 +41,7 @@ libnldbl-calls = asprintf dprintf fprintf fscanf fwprintf fwscanf iovfscanf \
 		 isoc99_vscanf isoc99_vfscanf isoc99_vsscanf \
 		 isoc99_wscanf isoc99_fwscanf isoc99_swscanf \
 		 isoc99_vwscanf isoc99_vfwscanf isoc99_vswscanf \
-		 nextup nextdown
+		 nextup nextdown totalorder
 libnldbl-routines = $(libnldbl-calls:%=nldbl-%)
 libnldbl-inhibit-o = $(object-suffixes)
 libnldbl-static-only-routines = $(libnldbl-routines)
@@ -142,6 +142,7 @@ CFLAGS-nldbl-sqrt.c = -fno-builtin-sqrtl
 CFLAGS-nldbl-tan.c = -fno-builtin-tanl
 CFLAGS-nldbl-tanh.c = -fno-builtin-tanhl
 CFLAGS-nldbl-tgamma.c = -fno-builtin-tgammal
+CFLAGS-nldbl-totalorder.c = -fno-builtin-totalorderl
 CFLAGS-nldbl-trunc.c = -fno-builtin-truncl
 CFLAGS-nldbl-y0.c = -fno-builtin-y0l
 CFLAGS-nldbl-y1.c = -fno-builtin-y1l
diff --git a/sysdeps/ieee754/ldbl-opt/nldbl-totalorder.c b/sysdeps/ieee754/ldbl-opt/nldbl-totalorder.c
new file mode 100644
index 0000000000..0be5a6d07e
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-opt/nldbl-totalorder.c
@@ -0,0 +1,26 @@
+/* Compatibility routine for IEEE double as long double for totalorder.
+   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 "nldbl-compat.h"
+
+double
+attribute_hidden
+totalorderl (double x, double y)
+{
+  return totalorder (x, y);
+}