Add test infrastructure for narrowing libm functions.

This patch continues preparations for adding TS 18661-1 narrowing libm
functions by adding the required testsuite infrastructure to test such
functions through the libm-test infrastructure.

That infrastructure is based around testing for a single type, FLOAT.
For the narrowing functions, FLOAT, the "main" type for testing, is
the function return type; the argument type is ARG_FLOAT.  This is
consistent with how the code built once for each type,
libm-test-support.c, depends on FLOAT for such things as calculating
ulps errors in results but can already handle different argument types
(pointers, integers, long double for nexttoward).

Makefile machinery is added to handle building tests for all pairs of
types for which there are narrowing functions (as with non-narrowing
functions, aliases are tested just the same as the functions they
alias).  gen-auto-libm-tests gains a --narrow option for building
outputs for narrowing functions (so narrowing sqrt and fma will share
the same inputs as non-narrowing, but gen-auto-libm-tests will be run
with and without that option to generate different output files).  In
the narrowing case, the auto-libm-test-out-narrow-* files include
annotations for each test about what properties ARG_FLOAT must have to
be able to represent all the inputs for that test; those annotations
result in calls to the TEST_COND_arg_fmt macro.

gen-libm-test.pl has some minor updates to handle narrowing tests (for
example, arguments in such tests must be surrounded by ARG_LIT calls
instead of LIT calls).  Various new macros are added to the C test
support code (for example, sNaN initializers need to be properly
typed, so arg_snan_value is added; other such arg_* macros are added
as it seems cleanest to do so, though some are not strictly required).
Special-casing of the ibm128 format to allow for its limitations is
adjusted to handle it as the argument format as well as as the result
format; thus, the tests of the new functions allow nonzero ulps only
in the case where ibm128 is the argument format, as otherwise the
functions correspond to fully-defined IEEE operations.  The ulps in
question appear as e.g. 'Function: "add_ldouble"' in libm-test-ulps
(with 1ulp errors then listed for double and float for that function
in powerpc); no support is added to generate corresponding faddl /
daddl ulps listings in the ulps table in the manual.

For the previous patch, I noted the need to avoid spurious macro
expansions of identifiers such as "add".  A test test-narrow-macros.c
is added to verify such macro expansions are successfully avoided, and
there is also a -mlong-double-64 version of that test for ldbl-opt.
This test is set up to cover the full set of relevant identifiers from
the start rather than adding functions one at a time as each function
group is added.

Tested for x86_64 (this patch in isolation, as well as testing for
various configurations in conjunction with the actual addition of
"add" functions).

	* math/Makefile (test-type-pairs): New variable.
	(test-type-pairs-f64xf128-yes): Likewise.
	(tests): Add test-narrow-macros.
	(libm-test-funcs-narrow): New variable.
	(libm-test-c-narrow): Likewise.
	(generated): Add $(libm-test-c-narrow).
	(libm-tests-base-narrow): New variable.
	(libm-tests-narrow): Likewise.
	(libm-tests): Add $(libm-tests-narrow).
	(libm-tests-for-type): Handle $(libm-tests-narrow).
	(libm-test-c-narrow-obj): New variable.
	($(libm-test-c-narrow-obj)): New rule.
	($(foreach t,$(libm-tests-narrow),$(objpfx)$(t).c)): Likewise.
	($(foreach f,$(libm-test-funcs-narrow),$(objpfx)$(o)-$(f).o)): Use
	$(o-iterator) to set dependencies and CFLAGS.
	* math/gen-auto-libm-tests.c: Document use for narrowing
	functions.
	(output_for_one_input_case): Take argument NARROW.
	(generate_output): Likewise.  Update call to
	output_for_one_input_case.
	(main): Take --narrow option.  Update call to generate_output.
	* math/gen-libm-test.pl (_apply_lit): Take macro name as argument.
	(apply_lit): Update call to _apply_lit.
	(apply_arglit): New function.
	(parse_args): Handle "a" arguments.
	(parse_auto_input): Handle format names using ":".
	* math/README.libm-test: Document "a" parameter type.
	* math/libm-test-support.h (ARG_TYPE_MIN): New macro.
	(ARG_TYPE_TRUE_MIN): Likewise.
	(ARG_TYPE_MAX): Likwise.
	(ARG_MIN_EXP): Likewise.
	(ARG_MAX_EXP): Likewise.
	(ARG_MANT_DIG): Likewise.
	(TEST_COND_arg_ibm128): Likewise.
	(TEST_COND_ibm128_libgcc): Define conditional on [ARG_FLOAT].
	(TEST_COND_arg_fmt): New macro.
	(init_max_error): Update prototype.
	* math/libm-test-support.c (test_ibm128): New variable.
	(init_max_error): Take argument testing_ibm128 and set test_ibm128
	instead of using [TEST_COND_ibm128] conditional.
	(test_exceptions): Use test_ibm128 instead of TEST_COND_ibm128.
	* math/libm-test-driver.c (STR_ARG_FLOAT): New macro.
	[TEST_NARROW] (TEST_MSG): New definition.
	(arg_plus_zero): New macro.
	(arg_minus_zero): Likewise.
	(arg_plus_infty): Likewise.
	(arg_minus_infty): Likewise.
	(arg_qnan_value_pl): Likewise.
	(arg_qnan_value): Likewise.
	(arg_snan_value_pl): Likewise.
	(arg_snan_value): Likewise.
	(arg_max_value): Likewise.
	(arg_min_value): Likewise.
	(arg_min_subnorm_value): Likewise.
	[ARG_FLOAT] (struct test_aa_f_data): New struct type.
	(RUN_TEST_LOOP_aa_f): New macro.
	(TEST_SUFF): New macro.
	(TEST_SUFF_STR): Likewise.
	[!TEST_MATHVEC] (VEC_SUFF): Don't define.
	(TEST_COND_any_ibm128): New macro.
	(START): Use TEST_SUFF and TEST_SUFF_STR in initializer for
	this_func.  Update call to init_max_error.
	* math/test-double.h (FUNC_NARROW_PREFIX): New macro.
	* math/test-float.h (FUNC_NARROW_PREFIX): Likewise.
	* math/test-float128.h (FUNC_NARROW_PREFIX): Likewise.
	* math/test-float32.h (FUNC_NARROW_PREFIX): Likewise.
	* math/test-float32x.h (FUNC_NARROW_PREFIX): Likewise.
	* math/test-float64.h (FUNC_NARROW_PREFIX): Likewise.
	* math/test-float64x.h (FUNC_NARROW_PREFIX): Likewise.
	* math/test-math-scalar.h (TEST_NARROW): Likewise.
	* math/test-math-vector.h (TEST_NARROW): Likewise.
	* math/test-arg-double.h: New file.
	* math/test-arg-float128.h: Likewise.
	* math/test-arg-float32x.h: Likewise.
	* math/test-arg-float64.h: Likewise.
	* math/test-arg-float64x.h: Likewise.
	* math/test-arg-ldouble.h: Likewise.
	* math/test-math-narrow.h: Likewise.
	* math/test-narrow-macros.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/test-narrow-macros-ldbl-64.c: Likewise.
	* sysdeps/ieee754/ldbl-opt/Makefile (tests): Add
	test-narrow-macros-ldbl-64.
	(CFLAGS-test-narrow-macros-ldbl-64.c): New variable.

27 files changed, 668 insertions, 57 deletions

diff --git a/ChangeLog b/ChangeLog
index 7aeb699cc3..4fe83a6b7f 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,89 @@
 2018-02-09  Joseph Myers  <joseph@codesourcery.com>
 
+	* math/Makefile (test-type-pairs): New variable.
+	(test-type-pairs-f64xf128-yes): Likewise.
+	(tests): Add test-narrow-macros.
+	(libm-test-funcs-narrow): New variable.
+	(libm-test-c-narrow): Likewise.
+	(generated): Add $(libm-test-c-narrow).
+	(libm-tests-base-narrow): New variable.
+	(libm-tests-narrow): Likewise.
+	(libm-tests): Add $(libm-tests-narrow).
+	(libm-tests-for-type): Handle $(libm-tests-narrow).
+	(libm-test-c-narrow-obj): New variable.
+	($(libm-test-c-narrow-obj)): New rule.
+	($(foreach t,$(libm-tests-narrow),$(objpfx)$(t).c)): Likewise.
+	($(foreach f,$(libm-test-funcs-narrow),$(objpfx)$(o)-$(f).o)): Use
+	$(o-iterator) to set dependencies and CFLAGS.
+	* math/gen-auto-libm-tests.c: Document use for narrowing
+	functions.
+	(output_for_one_input_case): Take argument NARROW.
+	(generate_output): Likewise.  Update call to
+	output_for_one_input_case.
+	(main): Take --narrow option.  Update call to generate_output.
+	* math/gen-libm-test.pl (_apply_lit): Take macro name as argument.
+	(apply_lit): Update call to _apply_lit.
+	(apply_arglit): New function.
+	(parse_args): Handle "a" arguments.
+	(parse_auto_input): Handle format names using ":".
+	* math/README.libm-test: Document "a" parameter type.
+	* math/libm-test-support.h (ARG_TYPE_MIN): New macro.
+	(ARG_TYPE_TRUE_MIN): Likewise.
+	(ARG_TYPE_MAX): Likwise.
+	(ARG_MIN_EXP): Likewise.
+	(ARG_MAX_EXP): Likewise.
+	(ARG_MANT_DIG): Likewise.
+	(TEST_COND_arg_ibm128): Likewise.
+	(TEST_COND_ibm128_libgcc): Define conditional on [ARG_FLOAT].
+	(TEST_COND_arg_fmt): New macro.
+	(init_max_error): Update prototype.
+	* math/libm-test-support.c (test_ibm128): New variable.
+	(init_max_error): Take argument testing_ibm128 and set test_ibm128
+	instead of using [TEST_COND_ibm128] conditional.
+	(test_exceptions): Use test_ibm128 instead of TEST_COND_ibm128.
+	* math/libm-test-driver.c (STR_ARG_FLOAT): New macro.
+	[TEST_NARROW] (TEST_MSG): New definition.
+	(arg_plus_zero): New macro.
+	(arg_minus_zero): Likewise.
+	(arg_plus_infty): Likewise.
+	(arg_minus_infty): Likewise.
+	(arg_qnan_value_pl): Likewise.
+	(arg_qnan_value): Likewise.
+	(arg_snan_value_pl): Likewise.
+	(arg_snan_value): Likewise.
+	(arg_max_value): Likewise.
+	(arg_min_value): Likewise.
+	(arg_min_subnorm_value): Likewise.
+	[ARG_FLOAT] (struct test_aa_f_data): New struct type.
+	(RUN_TEST_LOOP_aa_f): New macro.
+	(TEST_SUFF): New macro.
+	(TEST_SUFF_STR): Likewise.
+	[!TEST_MATHVEC] (VEC_SUFF): Don't define.
+	(TEST_COND_any_ibm128): New macro.
+	(START): Use TEST_SUFF and TEST_SUFF_STR in initializer for
+	this_func.  Update call to init_max_error.
+	* math/test-double.h (FUNC_NARROW_PREFIX): New macro.
+	* math/test-float.h (FUNC_NARROW_PREFIX): Likewise.
+	* math/test-float128.h (FUNC_NARROW_PREFIX): Likewise.
+	* math/test-float32.h (FUNC_NARROW_PREFIX): Likewise.
+	* math/test-float32x.h (FUNC_NARROW_PREFIX): Likewise.
+	* math/test-float64.h (FUNC_NARROW_PREFIX): Likewise.
+	* math/test-float64x.h (FUNC_NARROW_PREFIX): Likewise.
+	* math/test-math-scalar.h (TEST_NARROW): Likewise.
+	* math/test-math-vector.h (TEST_NARROW): Likewise.
+	* math/test-arg-double.h: New file.
+	* math/test-arg-float128.h: Likewise.
+	* math/test-arg-float32x.h: Likewise.
+	* math/test-arg-float64.h: Likewise.
+	* math/test-arg-float64x.h: Likewise.
+	* math/test-arg-ldouble.h: Likewise.
+	* math/test-math-narrow.h: Likewise.
+	* math/test-narrow-macros.c: Likewise.
+	* sysdeps/ieee754/ldbl-opt/test-narrow-macros-ldbl-64.c: Likewise.
+	* sysdeps/ieee754/ldbl-opt/Makefile (tests): Add
+	test-narrow-macros-ldbl-64.
+	(CFLAGS-test-narrow-macros-ldbl-64.c): New variable.
+
 	* math/bits/mathcalls-narrow.h: New file.
 	* include/bits/mathcalls-narrow.h: Likewise.
 	* math/math-narrow.h: Likewise.
diff --git a/math/Makefile b/math/Makefile
index ee0cd6fce1..42e540cf0e 100644
--- a/math/Makefile
+++ b/math/Makefile
@@ -145,6 +145,21 @@ test-types = $(test-types-basic) $(type-float128-$(float128-fcts)) \
 	     float32 float64 $(type-float128-$(float128-alias-fcts)) \
 	     float32x $(type-float64x-$(float64x-alias-fcts))
 
+# Pairs of types for which narrowing functions should be tested (this
+# variable has more entries than libm-narrow-types because it includes
+# pairs for which the functions sometimes or always alias functions
+# for other types). This definition embeds the assumption that if
+# _Float64x is supported, so is _Float128, and vice versa (they may or
+# may not have the same format).
+test-type-pairs = float-double float-ldouble double-ldouble \
+		  float32-float64 float32-float32x float32x-float64 \
+		  $(test-type-pairs-f64xf128-$(float128-fcts)) \
+		  $(test-type-pairs-f64xf128-$(float128-alias-fcts))
+test-type-pairs-f64xf128-yes = float32-float64x float32-float128 \
+			       float64-float64x float64-float128 \
+			       float32x-float64x float32x-float128 \
+			       float64x-float128
+
 # For each of the basic types (float, double, long double), replace the
 # occurrences of 'F' in arg 1 with the appropriate suffix for the type.
 type-basic-foreach = $(foreach t, $(types-basic), \
@@ -219,7 +234,8 @@ tests = test-matherr-3 test-fenv basic-test \
 	test-femode-traps test-iszero-excess-precision \
 	test-iseqsig-excess-precision test-flt-eval-method \
 	test-fp-ilogb-constants test-fp-llogb-constants \
-	test-fe-snans-always-signal test-finite-macros $(tests-static)
+	test-fe-snans-always-signal test-finite-macros test-narrow-macros \
+	$(tests-static)
 tests-static = test-fpucw-static test-fpucw-ieee-static \
 	       test-signgam-uchar-static test-signgam-uchar-init-static \
 	       test-signgam-uint-static test-signgam-uint-init-static \
@@ -268,14 +284,19 @@ libm-test-funcs-noauto = canonicalize ceil cimag conj copysign cproj creal \
 			 scalbln scalbn setpayload setpayloadsig signbit \
 			 significand totalorder totalordermag trunc ufromfp \
 			 ufromfpx
+libm-test-funcs-narrow =
 libm-test-funcs-all = $(libm-test-funcs-auto) $(libm-test-funcs-noauto)
 libm-test-c-auto = $(foreach f,$(libm-test-funcs-auto),libm-test-$(f).c)
 libm-test-c-noauto = $(foreach f,$(libm-test-funcs-noauto),libm-test-$(f).c)
-generated += libm-test-ulps.h $(libm-test-c-auto) $(libm-test-c-noauto)
+libm-test-c-narrow = $(foreach f,$(libm-test-funcs-narrow),\
+				 libm-test-narrow-$(f).c)
+generated += libm-test-ulps.h $(libm-test-c-auto) $(libm-test-c-noauto) \
+	     $(libm-test-c-narrow)
 
 libm-tests-base-normal = $(foreach t,$(test-types),test-$(t))
 libm-tests-base-finite = $(foreach t,$(test-types),test-$(t)-finite)
 libm-tests-base-inline = $(foreach t,$(test-types),test-i$(t))
+libm-tests-base-narrow = $(foreach t,$(test-type-pairs),test-$(t))
 libm-tests-base = $(libm-tests-base-normal) $(libm-tests-base-finite) \
 		  $(libm-tests-base-inline) $(libm-vec-tests)
 libm-tests-normal = $(foreach t,$(libm-tests-base-normal),\
@@ -287,14 +308,18 @@ libm-tests-finite = $(foreach t,$(libm-tests-base-finite),\
 libm-tests-inline = $(foreach t,$(libm-tests-base-inline),\
 				$(foreach f,$(libm-test-funcs-all),\
 					    $(t)-$(f)))
+libm-tests-narrow = $(foreach t,$(libm-tests-base-narrow),\
+				$(foreach f,$(libm-test-funcs-narrow),\
+					    $(t)-$(f)))
 libm-tests-vector = $(foreach t,$(libmvec-tests),\
 				$(foreach f,$($(t)-funcs),test-$(t)-$(f)))
 libm-tests = $(libm-tests-normal) $(libm-tests-finite) $(libm-tests-inline) \
-	     $(libm-tests-vector)
+	     $(libm-tests-narrow) $(libm-tests-vector)
 libm-tests-for-type = $(foreach f,$(libm-test-funcs-all),\
 				  test-$(1)-$(f) test-$(1)-finite-$(f) \
 				  test-i$(1)-$(f)) \
-		      $(filter test-$(1)-%,$(libm-tests-vector))
+		      $(filter test-$(1)-%,$(libm-tests-vector) \
+					   $(libm-tests-narrow))
 
 libm-tests.o = $(addsuffix .o,$(libm-tests))
 
@@ -304,6 +329,7 @@ generated += $(addsuffix .c,$(libm-tests)) \
 
 libm-test-c-auto-obj = $(addprefix $(objpfx),$(libm-test-c-auto))
 libm-test-c-noauto-obj = $(addprefix $(objpfx),$(libm-test-c-noauto))
+libm-test-c-narrow-obj = $(addprefix $(objpfx),$(libm-test-c-narrow))
 
 $(libm-test-c-noauto-obj): $(objpfx)libm-test%.c: libm-test%.inc \
 						  gen-libm-test.pl
@@ -315,6 +341,12 @@ $(libm-test-c-auto-obj): $(objpfx)libm-test%.c: libm-test%.inc \
 						auto-libm-test-out%
 	$(make-target-directory)
 	$(PERL) gen-libm-test.pl -c $< -a auto-libm-test-out$* -C $@
+
+$(libm-test-c-narrow-obj): $(objpfx)libm-test%.c: libm-test%.inc \
+						  gen-libm-test.pl \
+						  auto-libm-test-out%
+	$(make-target-directory)
+	$(PERL) gen-libm-test.pl -c $< -a auto-libm-test-out$* -C $@
 endif
 
 ifdef PYTHON
@@ -457,6 +489,22 @@ $(foreach t,$(libm-tests-inline),$(objpfx)$(t).c): $(objpfx)test-i%.c:
 	  echo "#include <libm-test-$$func.c>"; \
 	) > $@
 
+$(foreach t,$(libm-tests-narrow),$(objpfx)$(t).c): $(objpfx)test-%.c:
+	type_pair_func=$*; \
+	type_pair=$${type_pair_func%-*}; \
+	func=$${type_pair_func##*-}; \
+	ret_type=$${type_pair%%-*}; \
+	arg_type=$${type_pair#*-}; \
+	( \
+	  echo "#include <test-$$ret_type.h>"; \
+	  echo "#include <test-arg-$$arg_type.h>"; \
+	  echo "#include <test-math-no-finite.h>"; \
+	  echo "#include <test-math-no-inline.h>"; \
+	  echo "#include <test-math-errno.h>"; \
+	  echo "#include <test-math-narrow.h>"; \
+	  echo "#include <libm-test-narrow-$$func.c>"; \
+	) > $@
+
 $(foreach t,$(libm-tests-vector),$(objpfx)$(t).c): $(objpfx)test-%.c:
 	type_func=$*; \
 	type=$${type_func%-*}; \
@@ -486,6 +534,14 @@ object-suffixes-left := $(libm-tests-base)
 include $(o-iterator)
 
 define o-iterator-doit
+$(foreach f,$(libm-test-funcs-narrow),\
+	    $(objpfx)$(o)-$(f).o): $(objpfx)$(o)%.o: \
+				   $(objpfx)libm-test-narrow%.c
+endef
+object-suffixes-left := $(libm-tests-base-narrow)
+include $(o-iterator)
+
+define o-iterator-doit
 $(foreach f,$(libm-test-funcs-all),\
 	    $(objpfx)$(o)-$(f).o): CFLAGS += $(libm-test-no-inline-cflags)
 endef
@@ -507,6 +563,13 @@ object-suffixes-left := $(libm-tests-base-inline)
 include $(o-iterator)
 
 define o-iterator-doit
+$(foreach f,$(libm-test-funcs-narrow),\
+	    $(objpfx)$(o)-$(f).o): CFLAGS += $(libm-test-no-inline-cflags)
+endef
+object-suffixes-left := $(libm-tests-base-narrow)
+include $(o-iterator)
+
+define o-iterator-doit
 $(foreach f,$($(o)-funcs),\
 	    $(objpfx)test-$(o)-$(f).o): CFLAGS += $(libm-test-vec-cflags)
 endef
diff --git a/math/README.libm-test b/math/README.libm-test
index 0271f83f3b..41702c6537 100644
--- a/math/README.libm-test
+++ b/math/README.libm-test
@@ -120,6 +120,7 @@ parameter.
 The accepted parameter types are:
 - "f" for FLOAT
 - "j" for long double.
+- "a" for ARG_FLOAT, the argument type for narrowing functions.
 - "b" for boolean - just tests if the output parameter evaluates to 0
   or 1 (only for output).
 - "c" for complex.  This parameter needs two values, first the real,
diff --git a/math/gen-auto-libm-tests.c b/math/gen-auto-libm-tests.c
index 934c64bc76..442a10d5e6 100644
--- a/math/gen-auto-libm-tests.c
+++ b/math/gen-auto-libm-tests.c
@@ -25,6 +25,15 @@
 
    gen-auto-libm-tests auto-libm-test-in <func> auto-libm-test-out-<func>
 
+   to generate results for normal libm functions, or
+
+   gen-auto-libm-tests --narrow auto-libm-test-in <func> \
+     auto-libm-test-out-narrow-<func>
+
+   to generate results for a function rounding results to a narrower
+   type (in the case of fma and sqrt, both output files are generated
+   from the same test inputs).
+
    The input file auto-libm-test-in contains three kinds of lines:
 
    Lines beginning with "#" are comments, and are ignored, as are
@@ -120,7 +129,22 @@
    missing or spurious, or because the calculation of correct results
    indicated it was optional).  Conditions "before-rounding" and
    "after-rounding" indicate tests where expectations for underflow
-   exceptions depend on how the architecture detects tininess.  */
+   exceptions depend on how the architecture detects tininess.
+
+   For functions rounding their results to a narrower type, the format
+   given on an output test line is the result format followed by
+   information about the requirements on the argument format to be
+   able to represent the argument values, in the form
+   "format:arg_fmt(MAX_EXP,NUM_ONES,MIN_EXP,MAX_PREC)".  Instead of
+   separate lines for separate argument formats, an output test line
+   relates to all argument formats that can represent the values.
+   MAX_EXP is the maximum exponent of a nonzero bit in any argument,
+   or 0 if all arguments are zero; NUM_ONES is the maximum number of
+   leading bits with value 1 in an argument with exponent MAX_EXP, or
+   0 if all arguments are zero; MIN_EXP is the minimum exponent of a
+   nonzero bit in any argument, or 0 if all arguments are zero;
+   MAX_PREC is the maximum precision required to represent all
+   arguments, or 0 if all arguments are zero.  */
 
 #define _GNU_SOURCE
 
@@ -1718,12 +1742,13 @@ output_generic_value (FILE *fp, const char *filename, const generic_value *v,
     }
 }
 
-/* Generate test output to FP (name FILENAME) for test function TF,
-   input test IT, choice of input values INPUTS.  */
+/* Generate test output to FP (name FILENAME) for test function TF
+   (rounding results to a narrower type if NARROW), input test IT,
+   choice of input values INPUTS.  */
 
 static void
 output_for_one_input_case (FILE *fp, const char *filename, test_function *tf,
-			   input_test *it, generic_value *inputs)
+			   bool narrow, input_test *it, generic_value *inputs)
 {
   bool long_bits_matters = false;
   bool fits_long32 = true;
@@ -1794,24 +1819,81 @@ output_for_one_input_case (FILE *fp, const char *filename, test_function *tf,
 	  mpfr_t res[rm_num_modes];
 	  unsigned int exc_before[rm_num_modes];
 	  unsigned int exc_after[rm_num_modes];
+	  bool have_fp_arg = false;
+	  int max_exp = 0;
+	  int num_ones = 0;
+	  int min_exp = 0;
+	  int max_prec = 0;
 	  for (size_t i = 0; i < tf->num_args; i++)
 	    {
 	      if (inputs[i].type == gtype_fp)
 		{
-		  round_real (res, exc_before, exc_after, inputs[i].value.f,
-			      f);
-		  if (!mpfr_equal_p (res[rm_tonearest], inputs[i].value.f))
-		    fits = false;
-		  for (rounding_mode m = rm_first_mode; m < rm_num_modes; m++)
-		    mpfr_clear (res[m]);
-		  if (!fits)
-		    break;
+		  if (narrow)
+		    {
+		      if (mpfr_zero_p (inputs[i].value.f))
+			continue;
+		      assert (mpfr_regular_p (inputs[i].value.f));
+		      int this_exp, this_num_ones, this_min_exp, this_prec;
+		      mpz_t tmp;
+		      mpz_init (tmp);
+		      mpfr_exp_t e = mpfr_get_z_2exp (tmp, inputs[i].value.f);
+		      if (mpz_sgn (tmp) < 0)
+			mpz_neg (tmp, tmp);
+		      size_t bits = mpz_sizeinbase (tmp, 2);
+		      mp_bitcnt_t tz = mpz_scan1 (tmp, 0);
+		      this_min_exp = e + tz;
+		      this_prec = bits - tz;
+		      assert (this_prec > 0);
+		      this_exp = this_min_exp + this_prec - 1;
+		      assert (this_exp
+			      == mpfr_get_exp (inputs[i].value.f) - 1);
+		      this_num_ones = 1;
+		      while ((size_t) this_num_ones < bits
+			     && mpz_tstbit (tmp, bits - 1 - this_num_ones))
+			this_num_ones++;
+		      mpz_clear (tmp);
+		      if (have_fp_arg)
+			{
+			  if (this_exp > max_exp
+			      || (this_exp == max_exp
+				  && this_num_ones > num_ones))
+			    {
+			      max_exp = this_exp;
+			      num_ones = this_num_ones;
+			    }
+			  if (this_min_exp < min_exp)
+			    min_exp = this_min_exp;
+			  if (this_prec > max_prec)
+			    max_prec = this_prec;
+			}
+		      else
+			{
+			  max_exp = this_exp;
+			  num_ones = this_num_ones;
+			  min_exp = this_min_exp;
+			  max_prec = this_prec;
+			}
+		      have_fp_arg = true;
+		    }
+		  else
+		    {
+		      round_real (res, exc_before, exc_after,
+				  inputs[i].value.f, f);
+		      if (!mpfr_equal_p (res[rm_tonearest], inputs[i].value.f))
+			fits = false;
+		      for (rounding_mode m = rm_first_mode;
+			   m < rm_num_modes;
+			   m++)
+			mpfr_clear (res[m]);
+		      if (!fits)
+			break;
+		    }
 		}
 	    }
 	  if (!fits)
 	    continue;
-	  /* The inputs fit this type, so compute the ideal outputs
-	     and exceptions.  */
+	  /* The inputs fit this type if required to do so, so compute
+	     the ideal outputs and exceptions.  */
 	  mpfr_t all_res[MAX_NRET][rm_num_modes];
 	  unsigned int all_exc_before[MAX_NRET][rm_num_modes];
 	  unsigned int all_exc_after[MAX_NRET][rm_num_modes];
@@ -1895,10 +1977,21 @@ output_for_one_input_case (FILE *fp, const char *filename, test_function *tf,
 		  assert ((merged_exc_before[m] & (1U << exc_underflow)) != 0);
 		}
 	      unsigned int merged_exc = merged_exc_before[m];
-	      if (fprintf (fp, "= %s %s %s%s", tf->name,
-			   rounding_modes[m].name, fp_formats[f].name,
-			   long_cond) < 0)
-		error (EXIT_FAILURE, errno, "write to '%s'", filename);
+	      if (narrow)
+		{
+		  if (fprintf (fp, "= %s %s %s%s:arg_fmt(%d,%d,%d,%d)",
+			       tf->name, rounding_modes[m].name,
+			       fp_formats[f].name, long_cond, max_exp,
+			       num_ones, min_exp, max_prec) < 0)
+		    error (EXIT_FAILURE, errno, "write to '%s'", filename);
+		}
+	      else
+		{
+		  if (fprintf (fp, "= %s %s %s%s", tf->name,
+			       rounding_modes[m].name, fp_formats[f].name,
+			       long_cond) < 0)
+		    error (EXIT_FAILURE, errno, "write to '%s'", filename);
+		}
 	      /* Print inputs.  */
 	      for (size_t i = 0; i < tf->num_args; i++)
 		output_generic_value (fp, filename, &inputs[i], false,
@@ -2158,10 +2251,12 @@ output_for_one_input_case (FILE *fp, const char *filename, test_function *tf,
     generic_value_free (&generic_outputs[i]);
 }
 
-/* Generate test output data for FUNCTION to FILENAME.  */
+/* Generate test output data for FUNCTION to FILENAME.  The function
+   is interpreted as rounding its results to a narrower type if
+   NARROW.  */
 
 static void
-generate_output (const char *function, const char *filename)
+generate_output (const char *function, bool narrow, const char *filename)
 {
   FILE *fp = fopen (filename, "w");
   if (fp == NULL)
@@ -2177,7 +2272,8 @@ generate_output (const char *function, const char *filename)
 	  if (fputs (it->line, fp) < 0)
 	    error (EXIT_FAILURE, errno, "write to '%s'", filename);
 	  for (size_t k = 0; k < it->num_input_cases; k++)
-	    output_for_one_input_case (fp, filename, tf, it, it->inputs[k]);
+	    output_for_one_input_case (fp, filename, tf, narrow,
+				       it, it->inputs[k]);
 	}
     }
   if (fclose (fp) != 0)
@@ -2187,14 +2283,30 @@ generate_output (const char *function, const char *filename)
 int
 main (int argc, char **argv)
 {
-  if (argc != 4)
+  if (argc != 4
+      && !(argc == 5 && strcmp (argv[1], "--narrow") == 0))
     error (EXIT_FAILURE, 0,
-	   "usage: gen-auto-libm-tests <input> <func> <output>");
+	   "usage: gen-auto-libm-tests [--narrow] <input> <func> <output>");
+  bool narrow;
   const char *input_filename = argv[1];
   const char *function = argv[2];
   const char *output_filename = argv[3];
+  if (argc == 4)
+    {
+      narrow = false;
+      input_filename = argv[1];
+      function = argv[2];
+      output_filename = argv[3];
+    }
+  else
+    {
+      narrow = true;
+      input_filename = argv[2];
+      function = argv[3];
+      output_filename = argv[4];
+    }
   init_fp_formats ();
   read_input (input_filename);
-  generate_output (function, output_filename);
+  generate_output (function, narrow, output_filename);
   exit (EXIT_SUCCESS);
 }
diff --git a/math/gen-libm-test.pl b/math/gen-libm-test.pl
index 3556817c1d..664fba5909 100755
--- a/math/gen-libm-test.pl
+++ b/math/gen-libm-test.pl
@@ -165,10 +165,10 @@ sub show_exceptions {
   }
 }
 
-# Apply the LIT(x) macro to a literal floating point constant
+# Apply the LIT(x) or ARG_LIT(x) macro to a literal floating point constant
 # and strip any existing suffix.
 sub _apply_lit {
-  my ($lit) = @_;
+  my ($macro, $lit) = @_;
   my $exp_re = "([+-])?[[:digit:]]+";
   # Don't wrap something that does not look like a:
   #  * Hexadecimal FP value
@@ -181,7 +181,7 @@ sub _apply_lit {
   # Strip any existing literal suffix.
   $lit =~ s/[lLfF]$//;
 
-  return "LIT (${lit})";
+  return "$macro (${lit})";
 }
 
 # Apply LIT macro to individual tokens within an expression.
@@ -194,7 +194,17 @@ sub apply_lit {
   my ($lit) = @_;
   my @toks = split (/ /, $lit);
   foreach (@toks) {
-    $_ = _apply_lit ($_);
+    $_ = _apply_lit ("LIT", $_);
+  }
+  return join (' ', @toks);
+}
+
+# Likewise, but apply ARG_LIT for arguments to narrowing functions.
+sub apply_arglit {
+  my ($lit) = @_;
+  my @toks = split (/ /, $lit);
+  foreach (@toks) {
+    $_ = _apply_lit ("ARG_LIT", $_);
   }
   return join (' ', @toks);
 }
@@ -228,8 +238,8 @@ sub parse_args {
     if ($current_arg > 1) {
       $comma = ', ';
     }
-    # FLOAT, long double, int, unsigned int, long int, long long int
-    if ($descr[$i] =~ /f|j|i|u|l|L/) {
+    # FLOAT, ARG_FLOAT, long double, int, unsigned int, long int, long long int
+    if ($descr[$i] =~ /f|a|j|i|u|l|L/) {
       $call_args .= $comma . &beautify ($args[$current_arg]);
       ++$current_arg;
       next;
@@ -293,10 +303,12 @@ sub parse_args {
   $cline = "{ \"$call_args\"";
   @descr = split //,$descr_args;
   for ($i=0; $i <= $#descr; $i++) {
-    # FLOAT, int, long int, long long int
-    if ($descr[$i] =~ /f|j|i|u|l|L/) {
+    # FLOAT, ARG_FLOAT, long double, int, unsigned int, long int, long long int
+    if ($descr[$i] =~ /f|a|j|i|u|l|L/) {
       if ($descr[$i] eq "f") {
         $cline .= ", " . &apply_lit ($args[$current_arg]);
+      } elsif ($descr[$i] eq "a") {
+        $cline .= ", " . &apply_arglit ($args[$current_arg]);
       } else {
         $cline .= ", $args[$current_arg]";
       }
@@ -420,7 +432,9 @@ sub convert_condition {
   my (@conds, $ret);
   @conds = split /:/, $cond;
   foreach (@conds) {
-    s/-/_/g;
+    if ($_ !~ /^arg_fmt\(/) {
+      s/-/_/g;
+    }
     s/^/TEST_COND_/;
   }
   $ret = join " && ", @conds;
@@ -822,7 +836,7 @@ sub parse_auto_input {
     chop;
     next if !/^= /;
     s/^= //;
-    if (/^(\S+) (\S+) ([^:]*) : (.*)$/) {
+    if (/^(\S+) (\S+) ([^: ][^ ]* [^:]*) : (.*)$/) {
       $auto_tests{$1}{$2}{$3} = $4;
     } else {
       die ("bad automatic test line: $_\n");
diff --git a/math/libm-test-driver.c b/math/libm-test-driver.c
index b7c0343062..3713e7074f 100644
--- a/math/libm-test-driver.c
+++ b/math/libm-test-driver.c
@@ -30,6 +30,7 @@ const int flag_test_mathvec = TEST_MATHVEC;
 #define STRX(x) #x
 #define STR(x) STRX (x)
 #define STR_FLOAT STR (FLOAT)
+#define STR_ARG_FLOAT STR (ARG_FLOAT)
 #define STR_VEC_LEN STR (VEC_LEN)
 
 /* Informal description of the functions being tested.  */
@@ -39,6 +40,8 @@ const int flag_test_mathvec = TEST_MATHVEC;
 # define TEST_MSG "testing " STR_FLOAT " (inline functions)\n"
 #elif TEST_FINITE
 # define TEST_MSG "testing " STR_FLOAT " (finite-math-only)\n"
+#elif TEST_NARROW
+# define TEST_MSG "testing " STR_FLOAT " (argument " STR_ARG_FLOAT ")\n"
 #else
 # define TEST_MSG "testing " STR_FLOAT " (without inline functions)\n"
 #endif
@@ -108,6 +111,18 @@ const char qtype_str[] = TYPE_STR;
 #define min_value	TYPE_MIN
 #define min_subnorm_value TYPE_TRUE_MIN
 
+#define arg_plus_zero	ARG_LIT (0.0)
+#define arg_minus_zero	ARG_LIT (-0.0)
+#define arg_plus_infty	ARG_FUNC (__builtin_inf) ()
+#define arg_minus_infty	-(ARG_FUNC (__builtin_inf) ())
+#define arg_qnan_value_pl(S)	ARG_FUNC (__builtin_nan) (S)
+#define arg_qnan_value	arg_qnan_value_pl ("")
+#define arg_snan_value_pl(S)	ARG_FUNC (__builtin_nans) (S)
+#define arg_snan_value	arg_snan_value_pl ("")
+#define arg_max_value	ARG_TYPE_MAX
+#define arg_min_value	ARG_TYPE_MIN
+#define arg_min_subnorm_value ARG_TYPE_TRUE_MIN
+
 /* For nexttoward tests.  */
 #define snan_value_ld	__builtin_nansl ("")
 
@@ -147,6 +162,18 @@ struct test_fj_f_data
     int exceptions;
   } rd, rn, rz, ru;
 };
+#ifdef ARG_FLOAT
+struct test_aa_f_data
+{
+  const char *arg_str;
+  ARG_FLOAT arg1, arg2;
+  struct
+  {
+    FLOAT expected;
+    int exceptions;
+  } rd, rn, rz, ru;
+};
+#endif
 struct test_fi_f_data
 {
   const char *arg_str;
@@ -467,6 +494,7 @@ struct test_Ff_b1_data
 #define RUN_TEST_ff_f RUN_TEST_2_f
 #define RUN_TEST_LOOP_ff_f RUN_TEST_LOOP_2_f
 #define RUN_TEST_LOOP_fj_f RUN_TEST_LOOP_2_f
+#define RUN_TEST_LOOP_aa_f RUN_TEST_LOOP_2_f
 #define RUN_TEST_fi_f RUN_TEST_2_f
 #define RUN_TEST_LOOP_fi_f RUN_TEST_LOOP_2_f
 #define RUN_TEST_fl_f RUN_TEST_2_f
@@ -945,18 +973,32 @@ struct test_Ff_b1_data
 		       (ARRAY)[i].RM_##ROUNDING_MODE.extra2_expected);	\
   ROUND_RESTORE_ ## ROUNDING_MODE
 
-#if !TEST_MATHVEC
-# define VEC_SUFF
+#if TEST_MATHVEC
+# define TEST_SUFF VEC_SUFF
+# define TEST_SUFF_STR
+#elif TEST_NARROW
+# define TEST_SUFF
+# define TEST_SUFF_STR "_" ARG_TYPE_STR
+#else
+# define TEST_SUFF
+# define TEST_SUFF_STR
 #endif
 
 #define STR_CONCAT(a, b, c) __STRING (a##b##c)
 #define STR_CON3(a, b, c) STR_CONCAT (a, b, c)
 
+#if TEST_NARROW
+# define TEST_COND_any_ibm128 (TEST_COND_ibm128 || TEST_COND_arg_ibm128)
+#else
+# define TEST_COND_any_ibm128 TEST_COND_ibm128
+#endif
+
 /* Start and end the tests for a given function.  */
 #define START(FUN, SUFF, EXACT)					\
   CHECK_ARCH_EXT;						\
-  const char *this_func = STR_CON3 (FUN, SUFF, VEC_SUFF);	\
-  init_max_error (this_func, EXACT)
+  const char *this_func						\
+    = STR_CON3 (FUN, SUFF, TEST_SUFF) TEST_SUFF_STR;		\
+  init_max_error (this_func, EXACT, TEST_COND_any_ibm128)
 #define END					\
   print_max_error (this_func)
 #define END_COMPLEX				\
diff --git a/math/libm-test-support.c b/math/libm-test-support.c
index 2e4f9ef926..e59f15b4d9 100644
--- a/math/libm-test-support.c
+++ b/math/libm-test-support.c
@@ -135,6 +135,7 @@ static int verbose;
 static int output_max_error;	/* Should the maximal errors printed?  */
 static int output_points;	/* Should the single function results printed?  */
 static int ignore_max_ulp;	/* Should we ignore max_ulp?  */
+static int test_ibm128;		/* Is argument or result IBM long double?  */
 
 static FLOAT max_error, real_max_error, imag_max_error;
 
@@ -212,11 +213,12 @@ find_ulps (const char *name, const struct ulp_data *data, size_t nmemb)
 }
 
 void
-init_max_error (const char *name, int exact)
+init_max_error (const char *name, int exact, int testing_ibm128)
 {
   max_error = 0;
   real_max_error = 0;
   imag_max_error = 0;
+  test_ibm128 = testing_ibm128;
   prev_max_error = find_ulps (name, func_ulps,
 			      sizeof (func_ulps) / sizeof (func_ulps[0]));
   prev_real_max_error = find_ulps (name, func_real_ulps,
@@ -225,15 +227,14 @@ init_max_error (const char *name, int exact)
   prev_imag_max_error = find_ulps (name, func_imag_ulps,
 				   (sizeof (func_imag_ulps)
 				    / sizeof (func_imag_ulps[0])));
-#if TEST_COND_ibm128
-  /* The documented accuracy of IBM long double division is 3ulp (see
-     libgcc/config/rs6000/ibm-ldouble-format), so do not require
-     better accuracy for libm functions that are exactly defined for
-     other formats.  */
-  max_valid_error = exact ? 3 : 16;
-#else
-  max_valid_error = exact ? 0 : 9;
-#endif
+  if (testing_ibm128)
+    /* The documented accuracy of IBM long double division is 3ulp
+       (see libgcc/config/rs6000/ibm-ldouble-format), so do not
+       require better accuracy for libm functions that are exactly
+       defined for other formats.  */
+    max_valid_error = exact ? 3 : 16;
+  else
+    max_valid_error = exact ? 0 : 9;
   prev_max_error = (prev_max_error <= max_valid_error
 		    ? prev_max_error
 		    : max_valid_error);
@@ -518,14 +519,14 @@ test_exceptions (const char *test_name, int exception)
 	 arithmetic.  */
 #ifdef FE_UNDERFLOW
       if ((exception & UNDERFLOW_EXCEPTION_OK) == 0
-	  && !(TEST_COND_ibm128
+	  && !(test_ibm128
 	       && (exception & UNDERFLOW_EXCEPTION) == 0))
 	test_single_exception (test_name, exception, UNDERFLOW_EXCEPTION,
 			       FE_UNDERFLOW, "Underflow");
 #endif
 #ifdef FE_INEXACT
       if ((exception & (INEXACT_EXCEPTION | NO_INEXACT_EXCEPTION)) != 0
-	  && !(TEST_COND_ibm128
+	  && !(test_ibm128
 	       && (exception & NO_INEXACT_EXCEPTION) != 0))
 	test_single_exception (test_name, exception, INEXACT_EXCEPTION,
 			       FE_INEXACT, "Inexact");
diff --git a/math/libm-test-support.h b/math/libm-test-support.h
index b86c22796a..64206ab7fa 100644
--- a/math/libm-test-support.h
+++ b/math/libm-test-support.h
@@ -81,6 +81,13 @@ extern const char doc[];
 #define MAX_EXP __CONCATX (PREFIX, _MAX_EXP)
 #define MANT_DIG __CONCATX (PREFIX, _MANT_DIG)
 
+#define ARG_TYPE_MIN __CONCATX (ARG_PREFIX, _MIN)
+#define ARG_TYPE_TRUE_MIN __CONCATX (ARG_PREFIX, _TRUE_MIN)
+#define ARG_TYPE_MAX __CONCATX (ARG_PREFIX, _MAX)
+#define ARG_MIN_EXP __CONCATX (ARG_PREFIX, _MIN_EXP)
+#define ARG_MAX_EXP __CONCATX (ARG_PREFIX, _MAX_EXP)
+#define ARG_MANT_DIG __CONCATX (ARG_PREFIX, _MANT_DIG)
+
 /* Format specific test macros.  */
 #define TEST_COND_binary32 (MANT_DIG == 24	\
 			    && MIN_EXP == -125	\
@@ -96,6 +103,8 @@ extern const char doc[];
 
 #define TEST_COND_ibm128 (MANT_DIG == 106)
 
+#define TEST_COND_arg_ibm128 (ARG_MANT_DIG == 106)
+
 #define TEST_COND_intel96 (MANT_DIG == 64	\
 			   && MIN_EXP == -16381	\
 			   && MAX_EXP == 16384)
@@ -108,7 +117,11 @@ extern const char doc[];
    where in principle the glibc code is OK but the tests fail because
    of limitations of the libgcc support for that format (e.g. GCC bug
    59666, in non-default rounding modes).  */
-#define TEST_COND_ibm128_libgcc TEST_COND_ibm128
+#ifdef ARG_FLOAT
+# define TEST_COND_ibm128_libgcc (TEST_COND_ibm128 || TEST_COND_arg_ibm128)
+#else
+# define TEST_COND_ibm128_libgcc TEST_COND_ibm128
+#endif
 
 /* Mark a test as expected to fail for ibm128-libgcc.  This is used
    via XFAIL_ROUNDING_IBM128_LIBGCC, which gen-libm-test.pl transforms
@@ -132,6 +145,16 @@ extern const char doc[];
 # define PAYLOAD_DIG (MANT_DIG - 2)
 #endif
 
+/* For narrowing functions, whether the argument format can represent
+   all the given argument values.  */
+#define TEST_COND_arg_fmt(MAX_EXP, NUM_ONES, MIN_EXP, MAX_PREC) \
+  (((MAX_EXP) < ARG_MAX_EXP)					\
+   && (!TEST_COND_arg_ibm128					\
+       || (MAX_EXP) < ARG_MAX_EXP - 1				\
+       || (NUM_ONES) <= 53)					\
+   && (MIN_EXP) >= ARG_MIN_EXP - ARG_MANT_DIG			\
+   && (MAX_PREC) <= ARG_MANT_DIG)
+
 /* Values underflowing on architectures detecting tininess before
    rounding, but not on those detecting tininess after rounding.  */
 #define UNDERFLOW_EXCEPTION_BEFORE_ROUNDING	(TININESS_AFTER_ROUNDING \
@@ -149,7 +172,7 @@ extern const char doc[];
 #define TEST_COND_after_rounding	TININESS_AFTER_ROUNDING
 
 int enable_test (int);
-void init_max_error (const char *, int);
+void init_max_error (const char *, int, int);
 void print_max_error (const char *);
 void print_complex_max_error (const char *);
 void check_float (const char *, FLOAT, FLOAT, int);
diff --git a/math/test-arg-double.h b/math/test-arg-double.h
new file mode 100644
index 0000000000..4eec144944
--- /dev/null
+++ b/math/test-arg-double.h
@@ -0,0 +1,25 @@
+/* Common definitions for libm tests for double arguments to narrowing
+   functions.
+   Copyright (C) 2018 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/>.  */
+
+#define ARG_FUNC(function) function
+#define ARG_FLOAT double
+#define ARG_PREFIX DBL
+#define ARG_LIT(x) (x)
+#define ARG_TYPE_STR "double"
+#define FUNC_NARROW_SUFFIX
diff --git a/math/test-arg-float128.h b/math/test-arg-float128.h
new file mode 100644
index 0000000000..d2a7ef8e70
--- /dev/null
+++ b/math/test-arg-float128.h
@@ -0,0 +1,32 @@
+/* Common definitions for libm tests for _Float128 arguments to
+   narrowing functions.
+   Copyright (C) 2018 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 <bits/floatn.h>
+#include <float.h>
+
+#define ARG_FUNC(function) function ## f128
+#define ARG_FLOAT _Float128
+#define ARG_PREFIX FLT128
+#define ARG_LIT(x) __f128 (x)
+#if FLT128_MANT_DIG == LDBL_MANT_DIG
+# define ARG_TYPE_STR "ldouble"
+#else
+# define ARG_TYPE_STR "float128"
+#endif
+#define FUNC_NARROW_SUFFIX f128
diff --git a/math/test-arg-float32x.h b/math/test-arg-float32x.h
new file mode 100644
index 0000000000..d036f9cce5
--- /dev/null
+++ b/math/test-arg-float32x.h
@@ -0,0 +1,28 @@
+/* Common definitions for libm tests for _Float32x arguments to
+   narrowing functions.
+   Copyright (C) 2018 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 <bits/floatn.h>
+#include <float.h>
+
+#define ARG_FUNC(function) function ## f32x
+#define ARG_FLOAT _Float32x
+#define ARG_PREFIX FLT32X
+#define ARG_LIT(x) __f32x (x)
+#define ARG_TYPE_STR "double"
+#define FUNC_NARROW_SUFFIX f32x
diff --git a/math/test-arg-float64.h b/math/test-arg-float64.h
new file mode 100644
index 0000000000..346711917c
--- /dev/null
+++ b/math/test-arg-float64.h
@@ -0,0 +1,28 @@
+/* Common definitions for libm tests for _Float64 arguments to
+   narrowing functions.
+   Copyright (C) 2018 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 <bits/floatn.h>
+#include <float.h>
+
+#define ARG_FUNC(function) function ## f64
+#define ARG_FLOAT _Float64
+#define ARG_PREFIX FLT64
+#define ARG_LIT(x) __f64 (x)
+#define ARG_TYPE_STR "double"
+#define FUNC_NARROW_SUFFIX f64
diff --git a/math/test-arg-float64x.h b/math/test-arg-float64x.h
new file mode 100644
index 0000000000..c07d908b54
--- /dev/null
+++ b/math/test-arg-float64x.h
@@ -0,0 +1,32 @@
+/* Common definitions for libm tests for _Float64x arguments to
+   narrowing functions.
+   Copyright (C) 2018 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 <bits/floatn.h>
+#include <float.h>
+
+#define ARG_FUNC(function) function ## f64x
+#define ARG_FLOAT _Float64x
+#define ARG_PREFIX FLT64X
+#define ARG_LIT(x) __f64x (x)
+#if FLT64X_MANT_DIG == LDBL_MANT_DIG
+# define ARG_TYPE_STR "ldouble"
+#else
+# define ARG_TYPE_STR "float128"
+#endif
+#define FUNC_NARROW_SUFFIX f64x
diff --git a/math/test-arg-ldouble.h b/math/test-arg-ldouble.h
new file mode 100644
index 0000000000..41b475eae3
--- /dev/null
+++ b/math/test-arg-ldouble.h
@@ -0,0 +1,31 @@
+/* Common definitions for libm tests for long double arguments to
+   narrowing functions.
+   Copyright (C) 2018 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>
+
+#define ARG_FUNC(function) function ## l
+#define ARG_FLOAT long double
+#define ARG_PREFIX LDBL
+#define ARG_LIT(x) (x ## L)
+#if LDBL_MANT_DIG == DBL_MANT_DIG
+# define ARG_TYPE_STR "double"
+#else
+# define ARG_TYPE_STR "ldouble"
+#endif
+#define FUNC_NARROW_SUFFIX l
diff --git a/math/test-double.h b/math/test-double.h
index 238b086496..0b0fc96bf1 100644
--- a/math/test-double.h
+++ b/math/test-double.h
@@ -29,3 +29,4 @@
 #define FTOSTR strfromd
 #define snan_value_MACRO SNAN
 #define TEST_FLOATN 0
+#define FUNC_NARROW_PREFIX d
diff --git a/math/test-float.h b/math/test-float.h
index 7e301c3c74..dc3646d008 100644
--- a/math/test-float.h
+++ b/math/test-float.h
@@ -30,3 +30,4 @@
 #define FTOSTR strfromf
 #define snan_value_MACRO SNANF
 #define TEST_FLOATN 0
+#define FUNC_NARROW_PREFIX f
diff --git a/math/test-float128.h b/math/test-float128.h
index 7678913ca9..376d3da11e 100644
--- a/math/test-float128.h
+++ b/math/test-float128.h
@@ -41,3 +41,4 @@
 #define LITM(x) x ## f128
 #define FTOSTR strfromf128
 #define snan_value_MACRO SNANF128
+#define FUNC_NARROW_PREFIX f128
diff --git a/math/test-float32.h b/math/test-float32.h
index 2df9909724..f319fe6268 100644
--- a/math/test-float32.h
+++ b/math/test-float32.h
@@ -35,3 +35,4 @@
 #define LITM(x) x ## f32
 #define FTOSTR strfromf32
 #define snan_value_MACRO SNANF32
+#define FUNC_NARROW_PREFIX f32
diff --git a/math/test-float32x.h b/math/test-float32x.h
index ce02e28809..2aadc4a674 100644
--- a/math/test-float32x.h
+++ b/math/test-float32x.h
@@ -35,3 +35,4 @@
 #define LITM(x) x ## f32x
 #define FTOSTR strfromf32x
 #define snan_value_MACRO SNANF32X
+#define FUNC_NARROW_PREFIX f32x
diff --git a/math/test-float64.h b/math/test-float64.h
index d5c7c84e7d..debdf5aaf6 100644
--- a/math/test-float64.h
+++ b/math/test-float64.h
@@ -35,3 +35,4 @@
 #define LITM(x) x ## f64
 #define FTOSTR strfromf64
 #define snan_value_MACRO SNANF64
+#define FUNC_NARROW_PREFIX f64
diff --git a/math/test-float64x.h b/math/test-float64x.h
index 54c931f2bb..bf1b934311 100644
--- a/math/test-float64x.h
+++ b/math/test-float64x.h
@@ -41,3 +41,4 @@
 #define LITM(x) x ## f64x
 #define FTOSTR strfromf64x
 #define snan_value_MACRO SNANF64X
+#define FUNC_NARROW_PREFIX f64x
diff --git a/math/test-math-narrow.h b/math/test-math-narrow.h
new file mode 100644
index 0000000000..1c7fa30e98
--- /dev/null
+++ b/math/test-math-narrow.h
@@ -0,0 +1,26 @@
+/* Common definitions for libm tests for narrowing scalar functions.
+   Copyright (C) 2018 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/>.  */
+
+#define FUNC_TEST(function)						\
+  FUNC_TEST_CONCAT (FUNC_NARROW_PREFIX, function, FUNC_NARROW_SUFFIX)
+#define FUNC_TEST_CONCAT(prefix, function, suffix)	\
+  _FUNC_TEST_CONCAT (prefix, function, suffix)
+#define _FUNC_TEST_CONCAT(prefix, function, suffix)	\
+  prefix ## function ## suffix
+#define TEST_MATHVEC 0
+#define TEST_NARROW 1
diff --git a/math/test-math-scalar.h b/math/test-math-scalar.h
index 764db89f35..8df0d5ddc5 100644
--- a/math/test-math-scalar.h
+++ b/math/test-math-scalar.h
@@ -1,4 +1,4 @@
-/* Common definitions for libm tests for scalar functions.
+/* Common definitions for libm tests for scalar (non-narrowing) functions.
    Copyright (C) 1997-2018 Free Software Foundation, Inc.
    This file is part of the GNU C Library.
 
@@ -18,3 +18,4 @@
 
 #define FUNC_TEST(function) FUNC (function)
 #define TEST_MATHVEC 0
+#define TEST_NARROW 0
diff --git a/math/test-math-vector.h b/math/test-math-vector.h
index 1592c4a9c3..43d01d064a 100644
--- a/math/test-math-vector.h
+++ b/math/test-math-vector.h
@@ -17,6 +17,7 @@
    <http://www.gnu.org/licenses/>.  */
 
 #define TEST_MATHVEC 1
+#define TEST_NARROW 0
 #define TEST_FINITE 0
 #define TEST_ERRNO 0
 #define TEST_EXCEPTIONS 0
diff --git a/math/test-narrow-macros.c b/math/test-narrow-macros.c
new file mode 100644
index 0000000000..f53c86ae16
--- /dev/null
+++ b/math/test-narrow-macros.c
@@ -0,0 +1,56 @@
+/* Test code declaring narrowing functions does not conflict with user macros.
+   Copyright (C) 2018 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/>.  */
+
+/* The code generating declarations of narrowing functions involves
+   concatenations of fragments of function names that are not
+   themselves reserved; thus, it needs to be arranged so that those
+   fragments are not subject to macro expansion.  Verify that
+   inclusion of <math.h> compiles with such fragments defined as
+   macros.  */
+
+#define f test macro
+#define d test macro
+#define l test macro
+#define f16 test macro
+#define f32 test macro
+#define f64 test macro
+#define f128 test macro
+#define f32x test macro
+#define f64x test macro
+#define f128x test macro
+#define add test macro
+#define sub test macro
+#define mul test macro
+#define div test macro
+#define dadd test macro
+#define dsub test macro
+#define dmul test macro
+#define ddiv test macro
+#define dsqrt test macro
+#define dfma test macro
+
+#include <math.h>
+
+static int
+do_test (void)
+{
+  /* This is a compilation test.  */
+  return 0;
+}
+
+#include <support/test-driver.c>
diff --git a/sysdeps/ieee754/ldbl-opt/Makefile b/sysdeps/ieee754/ldbl-opt/Makefile
index ffc55d1d9a..38afe38ab8 100644
--- a/sysdeps/ieee754/ldbl-opt/Makefile
+++ b/sysdeps/ieee754/ldbl-opt/Makefile
@@ -163,4 +163,7 @@ CFLAGS-nldbl-y0.c = -fno-builtin-y0l
 CFLAGS-nldbl-y1.c = -fno-builtin-y1l
 CFLAGS-nldbl-yn.c = -fno-builtin-ynl
 
+tests += test-narrow-macros-ldbl-64
+CFLAGS-test-narrow-macros-ldbl-64.c += -mlong-double-64
+
 endif
diff --git a/sysdeps/ieee754/ldbl-opt/test-narrow-macros-ldbl-64.c b/sysdeps/ieee754/ldbl-opt/test-narrow-macros-ldbl-64.c
new file mode 100644
index 0000000000..be92325403
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-opt/test-narrow-macros-ldbl-64.c
@@ -0,0 +1 @@
+#include <math/test-narrow-macros.c>