diff --git a/clang/lib/Headers/float.h b/clang/lib/Headers/float.h
--- a/clang/lib/Headers/float.h
+++ b/clang/lib/Headers/float.h
@@ -14,10 +14,11 @@
  * additional definitions provided for Windows.
  * For more details see http://msdn.microsoft.com/en-us/library/y0ybw9fy.aspx
  *
- * Also fall back on Darwin to allow additional definitions and
+ * Also fall back on Darwin and AIX to allow additional definitions and
  * implementation-defined values.
  */
-#if (defined(__APPLE__) || (defined(__MINGW32__) || defined(_MSC_VER))) && \
+#if (defined(__APPLE__) || defined(__MINGW32__) || defined(_MSC_VER) ||        \
+     defined(_AIX)) &&                                                         \
     __STDC_HOSTED__ && __has_include_next(<float.h>)
 
 /* Prior to Apple's 10.7 SDK, float.h SDK header used to apply an extra level
@@ -37,7 +38,9 @@
 #  undef FLT_MANT_DIG
 #  undef DBL_MANT_DIG
 #  undef LDBL_MANT_DIG
-#  if __STDC_VERSION__ >= 199901L || !defined(__STRICT_ANSI__) || __cplusplus >= 201103L
+#  if __STDC_VERSION__ >= 199901L || !defined(__STRICT_ANSI__) ||              \
+      __cplusplus >= 201103L ||                                                \
+      (__STDC_HOSTED__ && defined(_AIX) && defined(_ALL_SOURCE))
 #    undef DECIMAL_DIG
 #  endif
 #  undef FLT_DIG
@@ -64,7 +67,9 @@
 #  undef FLT_MIN
 #  undef DBL_MIN
 #  undef LDBL_MIN
-#  if __STDC_VERSION__ >= 201112L || !defined(__STRICT_ANSI__) || __cplusplus >= 201703L
+#  if __STDC_VERSION__ >= 201112L || !defined(__STRICT_ANSI__) ||              \
+      __cplusplus >= 201703L ||                                                \
+      (__STDC_HOSTED__ && defined(_AIX) && defined(_ALL_SOURCE))
 #    undef FLT_TRUE_MIN
 #    undef DBL_TRUE_MIN
 #    undef LDBL_TRUE_MIN
@@ -87,7 +92,9 @@
 #define DBL_MANT_DIG __DBL_MANT_DIG__
 #define LDBL_MANT_DIG __LDBL_MANT_DIG__
 
-#if __STDC_VERSION__ >= 199901L || !defined(__STRICT_ANSI__) || __cplusplus >= 201103L
+#if __STDC_VERSION__ >= 199901L || !defined(__STRICT_ANSI__) ||                \
+    __cplusplus >= 201103L ||                                                  \
+    (__STDC_HOSTED__ && defined(_AIX) && defined(_ALL_SOURCE))
 #  define DECIMAL_DIG __DECIMAL_DIG__
 #endif
 
@@ -123,7 +130,9 @@
 #define DBL_MIN __DBL_MIN__
 #define LDBL_MIN __LDBL_MIN__
 
-#if __STDC_VERSION__ >= 201112L || !defined(__STRICT_ANSI__) || __cplusplus >= 201703L
+#if __STDC_VERSION__ >= 201112L || !defined(__STRICT_ANSI__) ||                \
+    __cplusplus >= 201703L ||                                                  \
+    (__STDC_HOSTED__ && defined(_AIX) && defined(_ALL_SOURCE))
 #  define FLT_TRUE_MIN __FLT_DENORM_MIN__
 #  define DBL_TRUE_MIN __DBL_DENORM_MIN__
 #  define LDBL_TRUE_MIN __LDBL_DENORM_MIN__
diff --git a/clang/test/Headers/Inputs/include/float.h b/clang/test/Headers/Inputs/include/float.h
new file mode 100644
--- /dev/null
+++ b/clang/test/Headers/Inputs/include/float.h
@@ -0,0 +1,2 @@
+#pragma once
+#define FLOAT_LOCAL_DEF 1
diff --git a/clang/test/Headers/float-aix.c b/clang/test/Headers/float-aix.c
new file mode 100644
--- /dev/null
+++ b/clang/test/Headers/float-aix.c
@@ -0,0 +1,6 @@
+// RUN: %clang_cc1 -triple powerpc-ibm-aix -fsyntax-only -verify -internal-isystem %S/Inputs/include %s
+// expected-no-diagnostics
+
+#include <float.h>
+
+_Static_assert(FLOAT_LOCAL_DEF, "");