diff --git a/sysdeps/generic/math_ldbl.h b/sysdeps/generic/math_ldbl.h
index f0b97ef8f9..4e7ee7912e 100644
--- a/sysdeps/generic/math_ldbl.h
+++ b/sysdeps/generic/math_ldbl.h
@@ -1,5 +1,7 @@
-#ifndef _MATH_PRIVATE_H_
-#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
-#endif
+#ifndef _MATH_LDBL_H_
+#define _MATH_LDBL_H_ 1
 
-/* This is empty.  Any machine using long double type will override this header.  */
+/* Any machine with a 'long double' distinct from 'double' must
+   override this header.  */
+
+#endif
diff --git a/sysdeps/generic/math_private.h b/sysdeps/generic/math_private.h
index c0d4e3dbcd..be65b9487b 100644
--- a/sysdeps/generic/math_private.h
+++ b/sysdeps/generic/math_private.h
@@ -37,7 +37,7 @@
 /* A union which permits us to convert between a double and two 32 bit
    ints.  */
 
-#if __FLOAT_WORD_ORDER == BIG_ENDIAN
+#if __FLOAT_WORD_ORDER == __BIG_ENDIAN
 
 typedef union
 {
@@ -52,7 +52,7 @@ typedef union
 
 #endif
 
-#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN
+#if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN
 
 typedef union
 {
diff --git a/sysdeps/ia64/fpu/math_ldbl.h b/sysdeps/ia64/fpu/math_ldbl.h
index 475ca795fa..748e9aff5a 100644
--- a/sysdeps/ia64/fpu/math_ldbl.h
+++ b/sysdeps/ia64/fpu/math_ldbl.h
@@ -1,11 +1,13 @@
-#ifndef _MATH_PRIVATE_H_
-#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
-#endif
+#ifndef _MATH_LDBL_H_
+#define _MATH_LDBL_H_ 1
+
+#include <stdint.h>
+#include <endian.h>
 
 /* A union which permits us to convert between a long double and
    three 32 bit ints.  */
 
-#if __FLOAT_WORD_ORDER == BIG_ENDIAN
+#if __FLOAT_WORD_ORDER == __BIG_ENDIAN
 
 typedef union
 {
@@ -15,22 +17,22 @@ typedef union
     unsigned int empty0:32;
     int sign_exponent:16;
     unsigned int empty1:16;
-    u_int32_t msw;
-    u_int32_t lsw;
+    uint32_t msw;
+    uint32_t lsw;
   } parts;
 } ieee_long_double_shape_type;
 
 #endif
 
-#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN
+#if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN
 
 typedef union
 {
   long double value;
   struct
   {
-    u_int32_t lsw;
-    u_int32_t msw;
+    uint32_t lsw;
+    uint32_t msw;
     int sign_exponent:16;
     unsigned int empty1:16;
     unsigned int empty0:32;
@@ -98,3 +100,5 @@ do {								\
   se_u.parts.sign_exponent = (exp);				\
   (d) = se_u.value;						\
 } while (0)
+
+#endif /* math_ldbl.h */
diff --git a/sysdeps/ieee754/ldbl-128/math_ldbl.h b/sysdeps/ieee754/ldbl-128/math_ldbl.h
index c1980c9401..6ea2c385df 100644
--- a/sysdeps/ieee754/ldbl-128/math_ldbl.h
+++ b/sysdeps/ieee754/ldbl-128/math_ldbl.h
@@ -1,41 +1,43 @@
-#ifndef _MATH_PRIVATE_H_
-#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
-#endif
+#ifndef _MATH_LDBL_H_
+#define _MATH_LDBL_H_ 1
+
+#include <stdint.h>
+#include <endian.h>
 
 /* A union which permits us to convert between a long double and
    four 32 bit ints or two 64 bit ints.  */
 
-#if __FLOAT_WORD_ORDER == BIG_ENDIAN
+#if __FLOAT_WORD_ORDER == __BIG_ENDIAN
 
 typedef union
 {
   long double value;
   struct
   {
-    u_int64_t msw;
-    u_int64_t lsw;
+    uint64_t msw;
+    uint64_t lsw;
   } parts64;
   struct
   {
-    u_int32_t w0, w1, w2, w3;
+    uint32_t w0, w1, w2, w3;
   } parts32;
 } ieee854_long_double_shape_type;
 
 #endif
 
-#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN
+#if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN
 
 typedef union
 {
   long double value;
   struct
   {
-    u_int64_t lsw;
-    u_int64_t msw;
+    uint64_t lsw;
+    uint64_t msw;
   } parts64;
   struct
   {
-    u_int32_t w3, w2, w1, w0;
+    uint32_t w3, w2, w1, w0;
   } parts32;
 } ieee854_long_double_shape_type;
 
@@ -96,3 +98,5 @@ do {								\
 */
 #define _Float128 long double
 #define L(x) x##L
+
+#endif /* math_ldbl.h */
diff --git a/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h b/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h
index 625ce00e13..5420fb27af 100644
--- a/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h
+++ b/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h
@@ -1,6 +1,5 @@
-#ifndef _MATH_PRIVATE_H_
-#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
-#endif
+#ifndef _MATH_LDBL_H_
+#define _MATH_LDBL_H_ 1
 
 #include <ieee754.h>
 #include <stdint.h>
@@ -239,9 +238,14 @@ ldbl_nearbyint (double a)
 static inline void
 ldbl_canonicalize_int (double *a, double *aa)
 {
-  int64_t ax, aax;
-  EXTRACT_WORDS64 (ax, *a);
-  EXTRACT_WORDS64 (aax, *aa);
+  /* We can't use math_private.h macros in this file.  */
+  uint64_t ax, aax;
+  union { double value; uint64_t word; } extractor;
+  extractor.value = *a;
+  ax = extractor.word;
+  extractor.value = *aa;
+  aax = extractor.word;
+
   int expdiff = ((ax >> 52) & 0x7ff) - ((aax >> 52) & 0x7ff);
   if (expdiff <= 53)
     {
@@ -263,3 +267,5 @@ ldbl_canonicalize_int (double *a, double *aa)
 	}
     }
 }
+
+#endif /* math_ldbl.h */
diff --git a/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c
index 8be4499bd5..75735db18e 100644
--- a/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c
+++ b/sysdeps/ieee754/ldbl-128ibm/test-canonical-ldbl-128ibm.c
@@ -18,7 +18,7 @@
 
 #include <float.h>
 #include <math.h>
-#include <math_private.h>
+#include <math_ldbl.h>
 #include <stdbool.h>
 #include <stdio.h>
 
diff --git a/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c b/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c
index 86869aceda..eaada2f848 100644
--- a/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c
+++ b/sysdeps/ieee754/ldbl-128ibm/test-totalorderl-ldbl-128ibm.c
@@ -17,7 +17,7 @@
    <http://www.gnu.org/licenses/>.  */
 
 #include <math.h>
-#include <math_private.h>
+#include <math_ldbl.h>
 #include <stdbool.h>
 #include <stdio.h>
 
diff --git a/sysdeps/ieee754/ldbl-96/math_ldbl.h b/sysdeps/ieee754/ldbl-96/math_ldbl.h
index cca30657ce..74fbad6374 100644
--- a/sysdeps/ieee754/ldbl-96/math_ldbl.h
+++ b/sysdeps/ieee754/ldbl-96/math_ldbl.h
@@ -1,11 +1,13 @@
-#ifndef _MATH_PRIVATE_H_
-#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
-#endif
+#ifndef _MATH_LDBL_H_
+#define _MATH_LDBL_H_ 1
+
+#include <stdint.h>
+#include <endian.h>
 
 /* A union which permits us to convert between a long double and
    three 32 bit ints.  */
 
-#if __FLOAT_WORD_ORDER == BIG_ENDIAN
+#if __FLOAT_WORD_ORDER == __BIG_ENDIAN
 
 typedef union
 {
@@ -14,22 +16,22 @@ typedef union
   {
     int sign_exponent:16;
     unsigned int empty:16;
-    u_int32_t msw;
-    u_int32_t lsw;
+    uint32_t msw;
+    uint32_t lsw;
   } parts;
 } ieee_long_double_shape_type;
 
 #endif
 
-#if __FLOAT_WORD_ORDER == LITTLE_ENDIAN
+#if __FLOAT_WORD_ORDER == __LITTLE_ENDIAN
 
 typedef union
 {
   long double value;
   struct
   {
-    u_int32_t lsw;
-    u_int32_t msw;
+    uint32_t lsw;
+    uint32_t msw;
     int sign_exponent:16;
     unsigned int empty:16;
   } parts;
@@ -96,3 +98,5 @@ do {								\
   se_u.parts.sign_exponent = (exp);				\
   (d) = se_u.value;						\
 } while (0)
+
+#endif /* math_ldbl.h */
diff --git a/sysdeps/ieee754/ldbl-96/test-canonical-ldbl-96.c b/sysdeps/ieee754/ldbl-96/test-canonical-ldbl-96.c
index db9db04367..3254097754 100644
--- a/sysdeps/ieee754/ldbl-96/test-canonical-ldbl-96.c
+++ b/sysdeps/ieee754/ldbl-96/test-canonical-ldbl-96.c
@@ -18,7 +18,7 @@
 
 #include <float.h>
 #include <math.h>
-#include <math_private.h>
+#include <math_ldbl.h>
 #include <stdbool.h>
 #include <stdint.h>
 #include <stdio.h>
diff --git a/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c b/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c
index eb21956e4f..4e01f15aa9 100644
--- a/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c
+++ b/sysdeps/ieee754/ldbl-96/test-totalorderl-ldbl-96.c
@@ -18,7 +18,7 @@
 
 #include <float.h>
 #include <math.h>
-#include <math_private.h>
+#include <math_ldbl.h>
 #include <stdbool.h>
 #include <stdint.h>
 #include <stdio.h>
diff --git a/sysdeps/powerpc/fpu/math_ldbl.h b/sysdeps/powerpc/fpu/math_ldbl.h
index 36378c0239..597d216a07 100644
--- a/sysdeps/powerpc/fpu/math_ldbl.h
+++ b/sysdeps/powerpc/fpu/math_ldbl.h
@@ -1,6 +1,5 @@
-#ifndef _MATH_PRIVATE_H_
-#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
-#endif
+#ifndef _MATH_LDBL_H_PPC_
+#define _MATH_LDBL_H_PPC_ 1
 
 /* GCC does not optimize the default ldbl_pack code to not spill register
    in the stack. The following optimization tells gcc that pack/unpack
@@ -34,3 +33,5 @@ ldbl_unpack_ppc (long double l, double *a, double *aa)
 #define ldbl_unpack ldbl_unpack_ppc
 
 #include <sysdeps/ieee754/ldbl-128ibm/math_ldbl.h>
+
+#endif /* math_ldbl.h */
diff --git a/sysdeps/x86_64/fpu/math_ldbl.h b/sysdeps/x86_64/fpu/math_ldbl.h
index b9ff8dadaf..cbc47c2935 100644
--- a/sysdeps/x86_64/fpu/math_ldbl.h
+++ b/sysdeps/x86_64/fpu/math_ldbl.h
@@ -1,6 +1,7 @@
-#ifndef _MATH_PRIVATE_H_
-#error "Never use <math_ldbl.h> directly; include <math_private.h> instead."
-#endif
+#ifndef _MATH_LDBL_H_
+#define _MATH_LDBL_H_ 1
+
+#include <stdint.h>
 
 /* A union which permits us to convert between a long double and
    three 32 bit ints.  */
@@ -10,8 +11,8 @@ typedef union
   long double value;
   struct
   {
-    u_int32_t lsw;
-    u_int32_t msw;
+    uint32_t lsw;
+    uint32_t msw;
     int sign_exponent:16;
     unsigned int empty1:16;
     unsigned int empty0:32;
@@ -77,3 +78,5 @@ do {								\
   se_u.parts.sign_exponent = (exp);				\
   (d) = se_u.value;						\
 } while (0)
+
+#endif /* math_ldbl.h */
