Add canonicalize, canonicalizef, canonicalizel.

TS 18661-1 defines canonicalize functions to produce a canonical
version of a floating-point representation.  This patch implements
these functions for glibc.

As with the iscanonical macro, these functions are oriented to the
decimal floating-point case, where some values have both canonical and
noncanonical representations.  However, the functions have a return
value that says whether they succeeded in storing a canonical result;
thus, they can fail for the case of an invalid representation (while
still not making any particular choice from among multiple equally
canonical valid representations of the same value).  Since no
floating-point formats in glibc actually have noncanonical valid
representations, a type-generic implementation of these functions can
be used that expects iscanonical to return 0 only for invalid
representations.  Now that iscanonical is used within libm.so,
libm_hidden_proto / libm_hidden_def are added for __iscanonicall.

The definition of these functions is intended to correspond to a
convertFormat operation to the same floating-point format.  Thus, they
convert signaling NaNs to quiet NaNs, raising the "invalid" exception.
Such a conversion "should" produce "the canonical version of that
signaling NaN made quiet".

libm-test.inc is made to check NaN payloads for the output of these
functions, a new feature (at some point manipulation functions such as
fabs and copysign should have tests added that verify payload
preservation for them).  As however some architectures may not follow
the recommended practice of preserving NaN payloads when converting a
signaling NaN to quiet, a new math-tests.h macro
SNAN_TESTS_PRESERVE_PAYLOAD is added, and defined to 0 for non-NAN2008
MIPS; any other architectures seeing test failures for lack of payload
preservation in this case should also define this macro to 0.  (If any
cases arise where the sign isn't preserved either, those should have a
similar macro added.)

The ldbl-96 and ldbl-128ibm tests of iscanonical are renamed and
adapted to test canonicalizel as well on the same representations.

Tested for x86_64, x86, mips64 and powerpc.

	* math/bits/mathcalls.h [__GLIBC_USE (IEC_60559_BFP_EXT)]
	(canonicalize): New declaration.
	* math/Versions (canonicalize): New libm symbol at version
	GLIBC_2.25.
	(canonicalizef): Likewise.
	(canonicalizel): Likewise.
	* math/Makefile (gen-libm-calls): Add s_canonicalizeF.
	* math/s_canonicalize_template.c: New file.
	* math/libm-test.inc: Update comment on functions tested and
	testing of NaN payloads.
	(TEST_NAN_PAYLOAD): New macro.
	(NO_TEST_INLINE): Update value.
	(XFAIL_TEST): Likewise.
	(ERRNO_UNCHANGED): Likewise.
	(ERRNO_EDOM): Likewise.
	(ERRNO_ERANGE): Likewise.
	(IGNORE_RESULT): Likewise.
	(NON_FINITE): Likewise.
	(TEST_SNAN): Likewise.
	(NO_TEST_MATHVEC): Likewise.
	(TEST_NAN_PAYLOAD_CANONICALIZE): New macro.
	(check_float_internal): Check NaN payloads if TEST_NAN_PAYLOAD.
	(struct test_Ffp_b1_data): New type.
	(RUN_TEST_Ffp_b1): New macro.
	(RUN_TEST_LOOP_Ffp_b1): Likewise.
	(canonicalize_test_data): New array.
	(canonicalize_test): New function.
	(main): Call canonicalize_test.
	* manual/arith.texi (FP Bit Twiddling): Document canonicalize,
	canonicalizef and canonicalizel.
	* manual/libm-err-tab.pl: Update comment on interfaces without
	ulps tabulated.
	* sysdeps/ieee754/ldbl-opt/nldbl-canonicalize.c: New file.
	* sysdeps/ieee754/ldbl-opt/s_canonicalizel.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/Makefile (libnldbl-calls): Add
	canonicalize.
	(CFLAGS-nldbl-canonicalize.c): New variable.
	* sysdeps/ieee754/ldbl-128ibm/test-iscanonical-ldbl-128ibm.c: Move
	to ...
	* sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c:
	... here.
	(do_test): Also test canonicalizel.
	* sysdeps/ieee754/ldbl-128ibm/Makefile (tests): Change
	test-iscanonical-ldbl-128ibm to test-canonical-ldbl-128ibm.
	* sysdeps/ieee754/ldbl-128ibm/include/bits/iscanonical.h: New
	file.
	* sysdeps/ieee754/ldbl-128ibm/s_iscanonicall.c (__iscanonicall):
	Use libm_hidden_def.
	* sysdeps/ieee754/ldbl-96/test-iscanonical-ldbl-96.c: Move to ...
	* sysdeps/ieee754/ldbl-96/test-canonical-ldbl-96.c: ... here.
	(do_test): Also test canonicalizel.
	* sysdeps/ieee754/ldbl-96/Makefile (tests): Change
	test-iscanonical-ldbl-96 to test-canonical-ldbl-96.
	* sysdeps/ieee754/ldbl-96/include/bits/iscanonical.h: New file.
	* sysdeps/ieee754/ldbl-96/s_iscanonicall.c (__iscanonicall): Use
	libm_hidden_def.
	* sysdeps/generic/math-tests.h (SNAN_TESTS_PRESERVE_PAYLOAD): New
	macro.
	* sysdeps/mips/math-tests.h [__mips_hard_float && !__mips_nan2008]
	(SNAN_TESTS_PRESERVE_PAYLOAD): Likewise.
	* 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.

5 files changed, 185 insertions, 13 deletions

diff --git a/math/Makefile b/math/Makefile
index 7cecba5357..f400d7b741 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -51,7 +51,7 @@ gen-libm-calls = cargF conjF cimagF crealF cabsF s_cacosF		  \
 		 k_casinhF s_csinhF k_casinhF s_csinhF s_catanhF s_catanF \
 		 s_ctanF s_ctanhF s_cexpF s_clogF s_cprojF s_csqrtF	  \
 		 s_cpowF s_clog10F s_fdimF s_nextdownF s_fmaxF s_fminF	  \
-		 s_nanF s_iseqsigF
+		 s_nanF s_iseqsigF s_canonicalizeF
 
 libm-calls =								  \
 	e_acosF e_acoshF e_asinF e_atan2F e_atanhF e_coshF e_expF e_fmodF \
diff --git a/math/Versions b/math/Versions
index a2e0d900ad..0cd594b378 100644
--- a/math/Versions
+++ b/math/Versions
@@ -220,5 +220,6 @@ libm {
     totalorder; totalorderf; totalorderl;
     totalordermag; totalordermagf; totalordermagl;
     getpayload; getpayloadf; getpayloadl;
+    canonicalize; canonicalizef; canonicalizel;
   }
 }
diff --git a/math/bits/mathcalls.h b/math/bits/mathcalls.h
index c5853a325f..2fd1d289da 100644
--- a/math/bits/mathcalls.h
+++ b/math/bits/mathcalls.h
@@ -395,6 +395,9 @@ __MATHDECL_1 (int, totalorder,, (_Mdouble_ __x, _Mdouble_ __y))
 __MATHDECL_1 (int, totalordermag,, (_Mdouble_ __x, _Mdouble_ __y))
      __attribute__ ((__const__));
 
+/* Canonicalize floating-point representation.  */
+__MATHDECL_1 (int, canonicalize,, (_Mdouble_ *__cx, const _Mdouble_ *__x));
+
 /* Get NaN payload.  */
 __MATHCALL (getpayload,, (const _Mdouble_ *__x));
 #endif
diff --git a/math/libm-test.inc b/math/libm-test.inc
index 89e0e59638..710633842c 100644
--- a/math/libm-test.inc
+++ b/math/libm-test.inc
@@ -43,7 +43,8 @@
 
 /* This testsuite has currently tests for:
    acos, acosh, asin, asinh, atan, atan2, atanh,
-   cbrt, ceil, copysign, cos, cosh, drem, erf, erfc, exp, exp10, exp2, expm1,
+   canonicalize, cbrt, ceil, copysign, cos, cosh, drem,
+   erf, erfc, exp, exp10, exp2, expm1,
    fabs, fdim, finite, floor, fma, fmax, fmin, fmod, fpclassify,
    frexp, gamma, getpayload, hypot,
    ilogb, iscanonical, isfinite, isinf, isnan, isnormal, issignaling,
@@ -85,8 +86,9 @@
    against.  These implemented tests should check all cases that are
    specified in ISO C99.
 
-   NaN values: The payload of NaNs is not examined, but is set in
-   inputs for functions where it is significant.
+   NaN values: The payload of NaNs is set in inputs for functions
+   where it is significant, and is examined in the outputs of some
+   functions.
 
    Inline functions: Inlining functions should give an improvement in
    speed - but not in precission.  The inlined functions return
@@ -172,17 +174,22 @@
 /* Some special test flags, passed together with exceptions.  */
 #define IGNORE_ZERO_INF_SIGN		0x400
 #define TEST_NAN_SIGN			0x800
-#define NO_TEST_INLINE			0x1000
-#define XFAIL_TEST			0x2000
+#define TEST_NAN_PAYLOAD		0x1000
+#define NO_TEST_INLINE			0x2000
+#define XFAIL_TEST			0x4000
 /* Indicate errno settings required or disallowed.  */
-#define ERRNO_UNCHANGED			0x4000
-#define ERRNO_EDOM			0x8000
-#define ERRNO_ERANGE			0x10000
+#define ERRNO_UNCHANGED			0x8000
+#define ERRNO_EDOM			0x10000
+#define ERRNO_ERANGE			0x20000
 /* Flags generated by gen-libm-test.pl, not entered here manually.  */
-#define IGNORE_RESULT			0x20000
-#define NON_FINITE			0x40000
-#define TEST_SNAN			0x80000
-#define NO_TEST_MATHVEC			0x100000
+#define IGNORE_RESULT			0x40000
+#define NON_FINITE			0x80000
+#define TEST_SNAN			0x100000
+#define NO_TEST_MATHVEC			0x200000
+
+#define TEST_NAN_PAYLOAD_CANONICALIZE	(SNAN_TESTS_PRESERVE_PAYLOAD	\
+					 ? TEST_NAN_PAYLOAD		\
+					 : 0)
 
 #define __CONCATX(a,b) __CONCAT(a,b)
 
@@ -801,6 +808,13 @@ check_float_internal (const char *test_name, FLOAT computed, FLOAT expected,
 	  ok = 0;
 	  printf ("signaling NaN has wrong sign.\n");
 	}
+      else if ((exceptions & TEST_NAN_PAYLOAD) != 0
+	       && (FUNC (getpayload) (&computed)
+		   != FUNC (getpayload) (&expected)))
+	{
+	  ok = 0;
+	  printf ("signaling NaN has wrong payload.\n");
+	}
       else
 	ok = 1;
     }
@@ -814,6 +828,13 @@ check_float_internal (const char *test_name, FLOAT computed, FLOAT expected,
 	  ok = 0;
 	  printf ("quiet NaN has wrong sign.\n");
 	}
+      else if ((exceptions & TEST_NAN_PAYLOAD) != 0
+	       && (FUNC (getpayload) (&computed)
+		   != FUNC (getpayload) (&expected)))
+	{
+	  ok = 0;
+	  printf ("quiet NaN has wrong payload.\n");
+	}
       else
 	ok = 1;
     }
@@ -1277,6 +1298,18 @@ struct test_fFF_11_data
     FLOAT extra2_expected;
   } rd, rn, rz, ru;
 };
+struct test_Ffp_b1_data
+{
+  const char *arg_str;
+  FLOAT arg;
+  struct
+  {
+    int expected;
+    int exceptions;
+    int extra_test;
+    FLOAT extra_expected;
+  } rd, rn, rz, ru;
+};
 
 /* Set the rounding mode, or restore the saved value.  */
 #define IF_ROUND_INIT_	/* Empty.  */
@@ -1550,6 +1583,36 @@ struct test_fFF_11_data
 			    (ARRAY)[i].RM_##ROUNDING_MODE.extra_test,	\
 			    (ARRAY)[i].RM_##ROUNDING_MODE.extra_expected); \
   ROUND_RESTORE_ ## ROUNDING_MODE
+#define RUN_TEST_Ffp_b1(ARG_STR, FUNC_NAME, ARG, EXPECTED,		\
+			EXCEPTIONS, EXTRA_VAR, EXTRA_TEST,		\
+			EXTRA_EXPECTED)					\
+  do									\
+    if (enable_test (EXCEPTIONS))					\
+      {									\
+	COMMON_TEST_SETUP (ARG_STR);					\
+	(EXTRA_VAR) = (EXTRA_EXPECTED) == 0 ? 1 : 0;			\
+	check_bool (test_name, FUNC_TEST (FUNC_NAME) (&(EXTRA_VAR),	\
+						      &(ARG)),		\
+		    EXPECTED, EXCEPTIONS);				\
+	EXTRA_OUTPUT_TEST_SETUP (ARG_STR, 1);				\
+	if (EXTRA_TEST)							\
+	  check_float (extra1_name, EXTRA_VAR, EXTRA_EXPECTED,		\
+		       (EXCEPTIONS) & TEST_NAN_PAYLOAD);		\
+	EXTRA_OUTPUT_TEST_CLEANUP (1);					\
+	COMMON_TEST_CLEANUP;						\
+      }									\
+  while (0)
+#define RUN_TEST_LOOP_Ffp_b1(FUNC_NAME, ARRAY, ROUNDING_MODE,		\
+			     EXTRA_VAR)					\
+  IF_ROUND_INIT_ ## ROUNDING_MODE					\
+    for (size_t i = 0; i < sizeof (ARRAY) / sizeof (ARRAY)[0]; i++)	\
+      RUN_TEST_Ffp_b1 ((ARRAY)[i].arg_str, FUNC_NAME, (ARRAY)[i].arg,	\
+		       (ARRAY)[i].RM_##ROUNDING_MODE.expected,		\
+		       (ARRAY)[i].RM_##ROUNDING_MODE.exceptions,	\
+		       EXTRA_VAR,					\
+		       (ARRAY)[i].RM_##ROUNDING_MODE.extra_test,	\
+		       (ARRAY)[i].RM_##ROUNDING_MODE.extra_expected);	\
+  ROUND_RESTORE_ ## ROUNDING_MODE
 #define RUN_TEST_c_c(ARG_STR, FUNC_NAME, ARGR, ARGC, EXPR, EXPC,	\
 		     EXCEPTIONS)					\
   do									\
@@ -3557,6 +3620,71 @@ cacosh_test (void)
 }
 
 
+static const struct test_Ffp_b1_data canonicalize_test_data[] =
+  {
+    TEST_Ffp_b1 (canonicalize, plus_infty, 0, plus_infty, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, minus_infty, 0, minus_infty, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, plus_zero, 0, plus_zero, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, minus_zero, 0, minus_zero, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, 1000, 0, 1000, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, max_value, 0, max_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, -max_value, 0, -max_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, min_value, 0, min_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, -min_value, 0, -min_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, min_subnorm_value, 0, min_subnorm_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, -min_subnorm_value, 0, -min_subnorm_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED),
+    TEST_Ffp_b1 (canonicalize, qnan_value, 0, qnan_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, -qnan_value, 0, -qnan_value, NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, snan_value, 0, qnan_value, NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN),
+    TEST_Ffp_b1 (canonicalize, -snan_value, 0, -qnan_value, NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN),
+#if HIGH_ORDER_BIT_IS_SET_FOR_SNAN
+    TEST_Ffp_b1 (canonicalize, snan_value_pl ("0x0"), 0, qnan_value, NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN),
+    TEST_Ffp_b1 (canonicalize, -snan_value_pl ("0x0"), 0, -qnan_value, NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN),
+#else
+    TEST_Ffp_b1 (canonicalize, qnan_value_pl ("0x0"), 0, qnan_value_pl ("0x0"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, -qnan_value_pl ("0x0"), 0, -qnan_value_pl ("0x0"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+#endif
+    TEST_Ffp_b1 (canonicalize, qnan_value_pl ("0x1"), 0, qnan_value_pl ("0x1"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, -qnan_value_pl ("0x1"), 0, -qnan_value_pl ("0x1"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, snan_value_pl ("0x1"), 0, qnan_value_pl ("0x1"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+    TEST_Ffp_b1 (canonicalize, -snan_value_pl ("0x1"), 0, -qnan_value_pl ("0x1"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+    TEST_Ffp_b1 (canonicalize, qnan_value_pl ("0x2"), 0, qnan_value_pl ("0x2"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, -qnan_value_pl ("0x2"), 0, -qnan_value_pl ("0x2"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, snan_value_pl ("0x2"), 0, qnan_value_pl ("0x2"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+    TEST_Ffp_b1 (canonicalize, -snan_value_pl ("0x2"), 0, -qnan_value_pl ("0x2"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+    TEST_Ffp_b1 (canonicalize, qnan_value_pl ("0x3fffff"), 0, qnan_value_pl ("0x3fffff"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, -qnan_value_pl ("0x3fffff"), 0, -qnan_value_pl ("0x3fffff"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, snan_value_pl ("0x3fffff"), 0, qnan_value_pl ("0x3fffff"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+    TEST_Ffp_b1 (canonicalize, -snan_value_pl ("0x3fffff"), 0, -qnan_value_pl ("0x3fffff"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+#if PAYLOAD_DIG >= 51
+    TEST_Ffp_b1 (canonicalize, qnan_value_pl ("0x7ffffffffffff"), 0, qnan_value_pl ("0x7ffffffffffff"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, -qnan_value_pl ("0x7ffffffffffff"), 0, -qnan_value_pl ("0x7ffffffffffff"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, snan_value_pl ("0x7ffffffffffff"), 0, qnan_value_pl ("0x7ffffffffffff"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+    TEST_Ffp_b1 (canonicalize, -snan_value_pl ("0x7ffffffffffff"), 0, -qnan_value_pl ("0x7ffffffffffff"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+#endif
+#if PAYLOAD_DIG >= 62
+    TEST_Ffp_b1 (canonicalize, qnan_value_pl ("0x3fffffffffffffff"), 0, qnan_value_pl ("0x3fffffffffffffff"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, -qnan_value_pl ("0x3fffffffffffffff"), 0, -qnan_value_pl ("0x3fffffffffffffff"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, snan_value_pl ("0x3fffffffffffffff"), 0, qnan_value_pl ("0x3fffffffffffffff"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+    TEST_Ffp_b1 (canonicalize, -snan_value_pl ("0x3fffffffffffffff"), 0, -qnan_value_pl ("0x3fffffffffffffff"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+#endif
+#if PAYLOAD_DIG >= 111
+    TEST_Ffp_b1 (canonicalize, qnan_value_pl ("0x7fffffffffffffffffffffffffff"), 0, qnan_value_pl ("0x7fffffffffffffffffffffffffff"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, -qnan_value_pl ("0x7fffffffffffffffffffffffffff"), 0, -qnan_value_pl ("0x7fffffffffffffffffffffffffff"), NO_INEXACT_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD),
+    TEST_Ffp_b1 (canonicalize, snan_value_pl ("0x7fffffffffffffffffffffffffff"), 0, qnan_value_pl ("0x7fffffffffffffffffffffffffff"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+    TEST_Ffp_b1 (canonicalize, -snan_value_pl ("0x7fffffffffffffffffffffffffff"), 0, -qnan_value_pl ("0x7fffffffffffffffffffffffffff"), NO_INEXACT_EXCEPTION|INVALID_EXCEPTION|ERRNO_UNCHANGED|TEST_NAN_SIGN|TEST_NAN_PAYLOAD_CANONICALIZE),
+#endif
+  };
+
+static void
+canonicalize_test (void)
+{
+  FLOAT x;
+
+  ALL_RM_TEST (canonicalize, 1, canonicalize_test_data, RUN_TEST_LOOP_Ffp_b1, END, x);
+}
+
+
 static const struct test_c_f_data carg_test_data[] =
   {
     /* carg (x + iy) is specified as atan2 (y, x) */
@@ -13511,6 +13639,9 @@ main (int argc, char **argv)
   totalorder_test ();
   totalordermag_test ();
 
+  /* Canonicalize functions:  */
+  canonicalize_test ();
+
   /* NaN functions:  */
   getpayload_test ();
 
diff --git a/math/s_canonicalize_template.c b/math/s_canonicalize_template.c
new file mode 100644
index 0000000000..fa06f5c083
--- /dev/null
+++ b/math/s_canonicalize_template.c
@@ -0,0 +1,37 @@
+/* Canonicalize floating-point representation.
+   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>
+
+int
+M_DECL_FUNC (__canonicalize) (FLOAT *cx, const FLOAT *x)
+{
+  FLOAT val = *x;
+  /* For all binary formats supported by glibc, iscanonical only fails
+     if the representation is not a valid representation of the type,
+     so the only work to do is for signaling NaNs.  */
+  if (!iscanonical (val))
+    return 1;
+  if (issignaling (val))
+    *cx = val + val;
+  else
+    *cx = val;
+  return 0;
+}
+
+declare_mgen_alias (__canonicalize, canonicalize)