diff --git a/docs/Modules.rst b/docs/Modules.rst
index 141d3b8..2b1bde2 100644
--- a/docs/Modules.rst
+++ b/docs/Modules.rst
@@ -360,6 +360,7 @@
   Name.framework/
     Modules/module.modulemap  Module map for the framework
     Headers/                  Subdirectory containing framework headers
+    PrivateHeaders/           Subdirectory containing framework private headers
     Frameworks/               Subdirectory containing embedded frameworks
     Resources/                Subdirectory containing additional resources
     Name                      Symbolic link to the shared library for the framework
@@ -842,6 +843,16 @@
 easier to split a library's public and private APIs along header
 boundaries.
 
+When writing a private module as part of a *framework*, it's recommended that:
+
+* Headers for this module are present in the ``PrivateHeaders``
+  framework subdirectory.
+* The private module is defined as a *submodule* of the public framework (if
+  there's one), similar to how ``Foo.Private`` is defined in the example above.
+* The ``explicit`` keyword should be used to guarantee that its content will
+  only be available when the submodule itself is explicitly named (through a
+  ``@import`` for example).
+
 Modularizing a Platform
 =======================
 To get any benefit out of modules, one needs to introduce module maps for software libraries starting at the bottom of the stack. This typically means introducing a module map covering the operating system's headers and the C standard library headers (in ``/usr/include``, for a Unix system). 
diff --git a/lib/Headers/tgmath.h b/lib/Headers/tgmath.h
index 318e118..34e26dc 100644
--- a/lib/Headers/tgmath.h
+++ b/lib/Headers/tgmath.h
@@ -22,12 +22,21 @@
  *
 \*===----------------------------------------------------------------------===*/
 
-#ifndef __TGMATH_H
-#define __TGMATH_H
+#ifndef __CLANG_TGMATH_H
+#define __CLANG_TGMATH_H
 
 /* C99 7.22 Type-generic math <tgmath.h>. */
 #include <math.h>
 
+/*
+ * Allow additional definitions and implementation-defined values on Apple
+ * platforms. This is done after #include <math.h> to avoid depcycle conflicts
+ * between libcxx and darwin in C++ modules builds.
+ */
+#if defined(__APPLE__) && __STDC_HOSTED__ && __has_include_next(<tgmath.h>)
+#  include_next <tgmath.h>
+#else
+
 /* C++ handles type genericity with overloading in math.h. */
 #ifndef __cplusplus
 #include <complex.h>
@@ -1371,4 +1380,5 @@
 #undef _TG_ATTRS
 
 #endif /* __cplusplus */
-#endif /* __TGMATH_H */
+#endif /* __has_include_next */
+#endif /* __CLANG_TGMATH_H */
diff --git a/test/Headers/Inputs/usr/include/math.h b/test/Headers/Inputs/usr/include/math.h
new file mode 100644
index 0000000..4171d4f
--- /dev/null
+++ b/test/Headers/Inputs/usr/include/math.h
@@ -0,0 +1 @@
+// math.h
diff --git a/test/Headers/Inputs/usr/include/tgmath.h b/test/Headers/Inputs/usr/include/tgmath.h
new file mode 100644
index 0000000..897962d
--- /dev/null
+++ b/test/Headers/Inputs/usr/include/tgmath.h
@@ -0,0 +1,4 @@
+#ifndef SYS_TGMATH_H
+#define SYS_TGMATH_H
+
+#endif /* SYS_TGMATH_H */
diff --git a/test/Headers/tgmath-darwin.c b/test/Headers/tgmath-darwin.c
new file mode 100644
index 0000000..916605a
--- /dev/null
+++ b/test/Headers/tgmath-darwin.c
@@ -0,0 +1,12 @@
+// REQUIRES: system-darwin
+// RUN: %clang -target x86_64-apple-darwin10 -fsyntax-only -std=c11 -isysroot %S/Inputs %s
+#include <tgmath.h>
+
+// Test the #include_next of tgmath.h works on Darwin.
+#ifndef SYS_TGMATH_H
+  #error "SYS_TGMATH_H not defined"
+#endif
+
+#ifndef __CLANG_TGMATH_H
+  #error "__CLANG_TGMATH_H not defined"
+#endif