diff --git a/ChangeLog b/ChangeLog
index d9682a5ea..6c2f783cd 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -27,6 +27,8 @@ Bugfix
      Found by redplait #590
    * Add MBEDTLS_MPI_CHK to check for error value of mbedtls_mpi_fill_random.
      Reported and fix suggested by guidovranken in #740
+   * Fix conditional preprocessor directives in bignum.h to enable 64-bit
+     compilation when using ARM Compiler 6.
 
 Changes
    * Removed mutexes from ECP hardware accelerator code. Now all hardware
diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index 1a5b4b675..ac89069dc 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -106,33 +106,47 @@
  * 32-bit integers can be forced on 64-bit arches (eg. for testing purposes)
  * by defining MBEDTLS_HAVE_INT32 and undefining MBEDTLS_HAVE_ASM
  */
-#if ( ! defined(MBEDTLS_HAVE_INT32) && \
-        defined(_MSC_VER) && defined(_M_AMD64) )
-  #define MBEDTLS_HAVE_INT64
-  typedef  int64_t mbedtls_mpi_sint;
-  typedef uint64_t mbedtls_mpi_uint;
-#else
-  #if ( ! defined(MBEDTLS_HAVE_INT32) &&               \
-        defined(__GNUC__) && (                          \
-        defined(__amd64__) || defined(__x86_64__)    || \
-        defined(__ppc64__) || defined(__powerpc64__) || \
-        defined(__ia64__)  || defined(__alpha__)     || \
-        (defined(__sparc__) && defined(__arch64__))  || \
-        defined(__s390x__) || defined(__mips64) ) )
-     #define MBEDTLS_HAVE_INT64
-     typedef  int64_t mbedtls_mpi_sint;
-     typedef uint64_t mbedtls_mpi_uint;
-     /* mbedtls_t_udbl defined as 128-bit unsigned int */
-     typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
-     #define MBEDTLS_HAVE_UDBL
-  #else
-     #define MBEDTLS_HAVE_INT32
-     typedef  int32_t mbedtls_mpi_sint;
-     typedef uint32_t mbedtls_mpi_uint;
-     typedef uint64_t mbedtls_t_udbl;
-     #define MBEDTLS_HAVE_UDBL
-  #endif /* !MBEDTLS_HAVE_INT32 && __GNUC__ && 64-bit platform */
-#endif /* !MBEDTLS_HAVE_INT32 && _MSC_VER && _M_AMD64 */
+#if !defined(MBEDTLS_HAVE_INT32)
+    #if defined(_MSC_VER) && defined(_M_AMD64)
+        /* Always choose 64-bit when using MSC */
+        #define MBEDTLS_HAVE_INT64
+        typedef  int64_t mbedtls_mpi_sint;
+        typedef uint64_t mbedtls_mpi_uint;
+    #elif defined(__GNUC__) && (                         \
+        defined(__amd64__) || defined(__x86_64__)     || \
+        defined(__ppc64__) || defined(__powerpc64__)  || \
+        defined(__ia64__)  || defined(__alpha__)      || \
+        ( defined(__sparc__) && defined(__arch64__) ) || \
+        defined(__s390x__) || defined(__mips64) )
+        #define MBEDTLS_HAVE_INT64
+        typedef  int64_t mbedtls_mpi_sint;
+        typedef uint64_t mbedtls_mpi_uint;
+        /* mbedtls_t_udbl defined as 128-bit unsigned int */
+        typedef unsigned int mbedtls_t_udbl __attribute__((mode(TI)));
+        #define MBEDTLS_HAVE_UDBL
+    #elif defined(__ARMCC_VERSION) && defined(__aarch64__)
+        /* __ARMCC_VERSION is defined for both armcc and armclang and
+         * __aarch64__ is only defined by armclang when compiling 64-bit code
+         */
+        #define MBEDTLS_HAVE_INT64
+        typedef  int64_t mbedtls_mpi_sint;
+        typedef uint64_t mbedtls_mpi_uint;
+        /* mbedtls_t_udbl defined as 128-bit unsigned int */
+        typedef __uint128_t mbedtls_t_udbl;
+        #define MBEDTLS_HAVE_UDBL
+    #endif
+#endif /* !MBEDTLS_HAVE_INT32 */
+
+#if !defined(MBEDTLS_HAVE_INT64)
+    /* Default to 32-bit compilation */
+    #if !defined(MBEDTLS_HAVE_INT32)
+        #define MBEDTLS_HAVE_INT32
+    #endif /* !MBEDTLS_HAVE_INT32 */
+    typedef  int32_t mbedtls_mpi_sint;
+    typedef uint32_t mbedtls_mpi_uint;
+    typedef uint64_t mbedtls_t_udbl;
+    #define MBEDTLS_HAVE_UDBL
+#endif /* !MBEDTLS_HAVE_INT64 */
 
 #ifdef __cplusplus
 extern "C" {