diff --git a/NEWS b/NEWS
index 6ffc7df286..0f01b751f9 100644
--- a/NEWS
+++ b/NEWS
@@ -17,6 +17,10 @@ Major new features:
   arguments to support expressions with a comma inside a compound
   literal initializer not surrounded by parentheses.
 
+* The C23 typedef names long_double_t, _Float32_t, _Float64_t, and (on
+  platforms supporting _Float128) _Float128_t, introduced in TS
+  18661-3:2015, have been added to <math.h>.
+
 Deprecated and removed features, and other changes affecting compatibility:
 
 * Support for dumped heaps has been removed - malloc_set_state() now always
diff --git a/math/math.h b/math/math.h
index b0d99cff8e..61a4338ce3 100644
--- a/math/math.h
+++ b/math/math.h
@@ -162,34 +162,201 @@ __BEGIN_DECLS
 		to evaluate `float' expressions
     double_t	floating-point type at least as wide as `double' used
 		to evaluate `double' expressions
+
+   TS 18661-3 and C23 additionally define long_double_t and _FloatN_t.
 */
-# if __GLIBC_FLT_EVAL_METHOD == 0 || __GLIBC_FLT_EVAL_METHOD == 16
+# if __GLIBC_FLT_EVAL_METHOD == 0
 typedef float float_t;
 typedef double double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+typedef long double long_double_t;
+#   if __HAVE_FLOAT16
+typedef float _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef _Float32 _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float64 _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
 # elif __GLIBC_FLT_EVAL_METHOD == 1
 typedef double float_t;
 typedef double double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+typedef long double long_double_t;
+#   if __HAVE_FLOAT16
+typedef double _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef double _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float64 _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
 # elif __GLIBC_FLT_EVAL_METHOD == 2
 typedef long double float_t;
 typedef long double double_t;
-# elif __GLIBC_FLT_EVAL_METHOD == 32
-typedef _Float32 float_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+typedef long double long_double_t;
+#   if __HAVE_FLOAT16
+typedef long double _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef long double _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+#    ifdef __NO_LONG_DOUBLE_MATH
+typedef _Float64 _Float64_t;
+#    else
+typedef long double _Float64_t;
+#    endif
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
+# elif __GLIBC_FLT_EVAL_METHOD == 16
+typedef float float_t;
 typedef double double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+typedef long double long_double_t;
+#   if __HAVE_FLOAT16
+typedef _Float16 _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef _Float32 _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float64 _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
+# elif __GLIBC_FLT_EVAL_METHOD == 32
+typedef float float_t;
+typedef double double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+typedef long double long_double_t;
+#   if __HAVE_FLOAT16
+typedef _Float32 _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef _Float32 _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float64 _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
 # elif __GLIBC_FLT_EVAL_METHOD == 33
 typedef _Float32x float_t;
-typedef _Float32x double_t;
+typedef double double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+typedef long double long_double_t;
+#   if __HAVE_FLOAT16
+typedef _Float32x _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef _Float32x _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float64 _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
 # elif __GLIBC_FLT_EVAL_METHOD == 64
 typedef _Float64 float_t;
-typedef _Float64 double_t;
+typedef double double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+typedef long double long_double_t;
+#   if __HAVE_FLOAT16
+typedef _Float64 _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef _Float64 _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float64 _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
 # elif __GLIBC_FLT_EVAL_METHOD == 65
 typedef _Float64x float_t;
 typedef _Float64x double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+typedef long double long_double_t;
+#   if __HAVE_FLOAT16
+typedef _Float64x _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef _Float64x _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float64x _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
 # elif __GLIBC_FLT_EVAL_METHOD == 128
 typedef _Float128 float_t;
 typedef _Float128 double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#   if __HAVE_FLOAT128_UNLIKE_LDBL && __LDBL_MANT_DIG__ != 106
+typedef _Float128 long_double_t;
+#   else
+typedef long double long_double_t;
+#   endif
+#   if __HAVE_FLOAT16
+typedef _Float128 _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef _Float128 _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float128 _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128 _Float128_t;
+#   endif
+#  endif
 # elif __GLIBC_FLT_EVAL_METHOD == 129
 typedef _Float128x float_t;
 typedef _Float128x double_t;
+#  if __GLIBC_USE (IEC_60559_TYPES_EXT)
+#   if __LDBL_MANT_DIG__ != 106
+typedef _Float128x long_double_t;
+#   else
+typedef long double long_double_t;
+#   endif
+#   if __HAVE_FLOAT16
+typedef _Float128x _Float16_t;
+#   endif
+#   if __HAVE_FLOAT32
+typedef _Float128x _Float32_t;
+#   endif
+#   if __HAVE_FLOAT64
+typedef _Float128x _Float64_t;
+#   endif
+#   if __HAVE_FLOAT128
+typedef _Float128x _Float128_t;
+#   endif
+#  endif
 # else
 #  error "Unknown __GLIBC_FLT_EVAL_METHOD"
 # endif
diff --git a/math/test-flt-eval-method.c b/math/test-flt-eval-method.c
index 6fb3e86c15..2996d3de02 100644
--- a/math/test-flt-eval-method.c
+++ b/math/test-flt-eval-method.c
@@ -16,6 +16,7 @@
    License along with the GNU C Library; if not, see
    <https://www.gnu.org/licenses/>.  */
 
+#define __STDC_WANT_IEC_60559_TYPES_EXT__
 #include <float.h>
 #include <math.h>
 
@@ -23,33 +24,191 @@
 /* Cannot test.  */
 typedef float_t my_float_t;
 typedef double_t my_double_t;
-#elif FLT_EVAL_METHOD == 0 || FLT_EVAL_METHOD == 16
+typedef long_double_t my_long_double_t;
+# if __HAVE_FLOAT16
+typedef _Float16_t my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float32_t my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float64_t my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128_t my_Float128_t;
+# endif
+#elif FLT_EVAL_METHOD == 0
 typedef float my_float_t;
 typedef double my_double_t;
+typedef long double my_long_double_t;
+# if __HAVE_FLOAT16
+typedef float my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float32 my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float64 my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
 #elif FLT_EVAL_METHOD == 1
 typedef double my_float_t;
 typedef double my_double_t;
+typedef long double my_long_double_t;
+# if __HAVE_FLOAT16
+typedef double my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef double my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float64 my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
 #elif FLT_EVAL_METHOD == 2
 typedef long double my_float_t;
 typedef long double my_double_t;
-#elif FLT_EVAL_METHOD == 32
-typedef _Float32 my_float_t;
+typedef long double my_long_double_t;
+# if __HAVE_FLOAT16
+typedef long double my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef long double my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+#  ifdef __NO_LONG_DOUBLE_MATH
+typedef _Float64 my_Float64_t;
+#  else
+typedef long double my_Float64_t;
+#  endif
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
+#elif FLT_EVAL_METHOD == 16
+typedef float my_float_t;
 typedef double my_double_t;
+typedef long double my_long_double_t;
+# if __HAVE_FLOAT16
+typedef _Float16 my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float32 my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float64 my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
+#elif FLT_EVAL_METHOD == 32
+typedef float my_float_t;
+typedef double my_double_t;
+typedef long double my_long_double_t;
+# if __HAVE_FLOAT16
+typedef _Float32 my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float32 my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float64 my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
 #elif FLT_EVAL_METHOD == 33
 typedef _Float32x my_float_t;
-typedef _Float32x my_double_t;
+typedef double my_double_t;
+typedef long double my_long_double_t;
+# if __HAVE_FLOAT16
+typedef _Float32x my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float32x my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float64 my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
 #elif FLT_EVAL_METHOD == 64
 typedef _Float64 my_float_t;
-typedef _Float64 my_double_t;
+typedef double my_double_t;
+typedef long double my_long_double_t;
+# if __HAVE_FLOAT16
+typedef _Float64 my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float64 my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float64 my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
 #elif FLT_EVAL_METHOD == 65
 typedef _Float64x my_float_t;
 typedef _Float64x my_double_t;
+typedef long double my_long_double_t;
+# if __HAVE_FLOAT16
+typedef _Float64x my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float64x my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float64x my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
 #elif FLT_EVAL_METHOD == 128
 typedef _Float128 my_float_t;
 typedef _Float128 my_double_t;
+# if __HAVE_FLOAT128_UNLIKE_LDBL && __LDBL_MANT_DIG__ != 106
+typedef _Float128 my_long_double_t;
+# else
+typedef long double my_long_double_t;
+# endif
+# if __HAVE_FLOAT16
+typedef _Float128 my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float128 my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float128 my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128 my_Float128_t;
+# endif
 #elif FLT_EVAL_METHOD == 129
 typedef _Float128x my_float_t;
 typedef _Float128x my_double_t;
+# if __LDBL_MANT_DIG__ != 106
+typedef _Float128x my_long_double_t;
+# else
+typedef long double my_long_double_t;
+# endif
+# if __HAVE_FLOAT16
+typedef _Float128x my_Float16_t;
+# endif
+# if __HAVE_FLOAT32
+typedef _Float128x my_Float32_t;
+# endif
+# if __HAVE_FLOAT64
+typedef _Float128x my_Float64_t;
+# endif
+# if __HAVE_FLOAT128
+typedef _Float128x my_Float128_t;
+# endif
 #else
 # error "Unknown FLT_EVAL_METHOD"
 #endif
@@ -60,6 +219,29 @@ extern my_float_t test_float_t;
 extern double_t test_double_t;
 extern my_double_t test_double_t;
 
+extern long_double_t test_long_double_t;
+extern my_long_double_t test_long_double_t;
+
+#if __HAVE_FLOAT16
+extern _Float16_t test_Float16_t;
+extern my_Float16_t test_Float16_t;
+#endif
+
+#if __HAVE_FLOAT32
+extern _Float32_t test_Float32_t;
+extern my_Float32_t test_Float32_t;
+#endif
+
+#if __HAVE_FLOAT64
+extern _Float64_t test_Float64_t;
+extern my_Float64_t test_Float64_t;
+#endif
+
+#if __HAVE_FLOAT128
+extern _Float128_t test_Float128_t;
+extern my_Float128_t test_Float128_t;
+#endif
+
 /* This is a compilation test.  */
 #define TEST_FUNCTION 0
 #include "../test-skeleton.c"