diff -r a4b66e51e0bf Lib/test/test_sysconfig.py
--- a/Lib/test/test_sysconfig.py	Mon Apr 13 22:11:34 2015 +0200
+++ b/Lib/test/test_sysconfig.py	Mon Apr 13 22:44:42 2015 +0200
@@ -389,12 +389,6 @@
         self.assertIsNotNone(vars['SO'])
         self.assertEqual(vars['SO'], vars['EXT_SUFFIX'])
 
-    @unittest.skipUnless(sys.platform == 'linux', 'Linux-specific test')
-    def test_bitness_in_ext_suffix(self):
-        suffix = sysconfig.get_config_var('EXT_SUFFIX')
-        bitness = '-32b' if sys.maxsize < 2**32 else '-64b'
-        self.assertTrue(suffix.endswith(bitness + '.so'), suffix)
-
 
 class MakefileTests(unittest.TestCase):
 
diff -r a4b66e51e0bf Misc/NEWS
--- a/Misc/NEWS	Mon Apr 13 22:11:34 2015 +0200
+++ b/Misc/NEWS	Mon Apr 13 22:44:42 2015 +0200
@@ -10,6 +10,10 @@
 Core and Builtins
 -----------------
 
+- Issue #22980: Under Linux, GNU/KFreeBSD and the Hurd, C extensions now include
+  the architecture triplet in the extension name, to make it easy to test builds
+  for different ABIs in the same working tree.
+
 - Issue #23731: Implement PEP 488: removal of .pyo files.
 
 - Issue #23726: Don't enable GC for user subclasses of non-GC types that
@@ -357,10 +361,6 @@
 Core and Builtins
 -----------------
 
-- Issue #22980: Under Linux, C extensions now include bitness in the file
-  name, to make it easy to test 32-bit and 64-bit builds in the same
-  working tree.
-
 - Issue #23571: PyObject_Call() and PyCFunction_Call() now raise a SystemError
   if a function returns a result and raises an exception. The SystemError is
   chained to the previous exception.
diff -r a4b66e51e0bf configure.ac
--- a/configure.ac	Mon Apr 13 22:11:34 2015 +0200
+++ b/configure.ac	Mon Apr 13 22:44:42 2015 +0200
@@ -425,7 +425,7 @@
 	esac
 	_PYTHON_HOST_PLATFORM="$MACHDEP${_host_cpu:+-$_host_cpu}"
 fi
-	
+
 # Some systems cannot stand _XOPEN_SOURCE being defined at all; they
 # disable features if it is defined, without any means to access these
 # features as extensions. For these systems, we skip the definition of
@@ -667,6 +667,8 @@
 	fi
 fi
 AC_PROG_CC
+AC_PROG_CPP
+AC_PROG_EGREP
 
 AC_SUBST(CXX)
 AC_SUBST(MAINCC)
@@ -724,6 +726,114 @@
 fi
 
 
+MULTIARCH=$($CC --print-multiarch 2>/dev/null)
+AC_SUBST(MULTIARCH)
+
+AC_MSG_CHECKING([for the platform triplet based on compiler characteristics])
+cat >> conftest.c <<EOF
+#undef linux
+#undef i386
+#undef unix
+#if defined(__linux__)
+# if defined(__x86_64__) && defined(__LP64__)
+        x86_64-linux-gnu
+# elif defined(__x86_64__) && defined(__ILP32__)
+        x86_64-linux-gnux32
+# elif defined(__i386__)
+        i386-linux-gnu
+# elif defined(__aarch64__) && defined(__AARCH64EL__)
+        aarch64-linux-gnu
+# elif defined(__alpha__)
+        alpha-linux-gnu
+# elif defined(__ARM_EABI__) && defined(__ARM_PCS_VFP)
+        arm-linux-gnueabihf
+# elif defined(__ARM_EABI__) && !defined(__ARM_PCS_VFP)
+        arm-linux-gnueabi
+# elif defined(__hppa__)
+        hppa-linux-gnu
+# elif defined(__ia64__)
+        ia64-linux-gnu
+# elif defined(__m68k__) && !defined(__mcoldfire__)
+        m68k-linux-gnu
+# elif defined(__mips_hard_float) && defined(_MIPSEL)
+#  if _MIPS_SIM == _ABIO32
+        mipsel-linux-gnu
+#  elif _MIPS_SIM == _ABIN32
+        mips64el-linux-gnuabin32
+#  elif _MIPS_SIM == _ABI64
+        mips64el-linux-gnuabi64
+#  else
+#   error unknown platform triplet
+#  endif
+# elif defined(__mips_hard_float)
+#  if _MIPS_SIM == _ABIO32
+        mips-linux-gnu
+#  elif _MIPS_SIM == _ABIN32
+        mips64-linux-gnuabin32
+#  elif _MIPS_SIM == _ABI64
+        mips64-linux-gnuabi64
+#  else
+#   error unknown platform triplet
+#  endif
+# elif defined(__or1k__)
+        or1k-linux-gnu
+# elif defined(__powerpc__) && defined(__SPE__)
+        powerpc-linux-gnuspe
+# elif defined(__powerpc64__)
+#  if defined(__LITTLE_ENDIAN__)
+        powerpc64le-linux-gnu
+#  else
+        powerpc64-linux-gnu
+#  endif
+# elif defined(__powerpc__)
+        powerpc-linux-gnu
+# elif defined(__s390x__)
+        s390x-linux-gnu
+# elif defined(__s390__)
+        s390-linux-gnu
+# elif defined(__sh__) && defined(__LITTLE_ENDIAN__)
+        sh4-linux-gnu
+# elif defined(__sparc__) && defined(__arch64__)
+        sparc64-linux-gnu
+# elif defined(__sparc__)
+        sparc-linux-gnu
+# else
+#   error unknown platform triplet
+# endif
+#elif defined(__FreeBSD_kernel__)
+# if defined(__LP64__)
+        x86_64-kfreebsd-gnu
+# elif defined(__i386__)
+        i386-kfreebsd-gnu
+# else
+#   error unknown platform triplet
+# endif
+#elif defined(__gnu_hurd__)
+        i386-gnu
+#else
+# error unknown platform triplet
+#endif
+
+EOF
+
+if $CPP conftest.c >conftest.out 2>/dev/null; then
+  PLATFORM_TRIPLET=`grep -v '^#' conftest.out | grep -v '^ *$' | tr -d ' 	'`
+  AC_MSG_RESULT([$PLATFORM_TRIPLET])
+else
+  AC_MSG_RESULT([none])
+fi
+rm -f conftest.c conftest.out
+
+if test x$PLATFORM_TRIPLET != x && test x$MULTIARCH != x; then
+  if test x$PLATFORM_TRIPLET != x$MULTIARCH; then
+    AC_MSG_ERROR([internal configure error for the platform triplet, please file a bug report])
+  fi
+fi 
+PLATDIR=plat-$MACHDEP
+AC_SUBST(PLATDIR)
+AC_SUBST(PLATFORM_TRIPLET)
+
+
 AC_MSG_CHECKING([for -Wl,--no-as-needed])
 save_LDFLAGS="$LDFLAGS"
 LDFLAGS="$LDFLAGS -Wl,--no-as-needed"
@@ -791,10 +901,6 @@
     esac;;
 esac
 
-MULTIARCH=$($CC --print-multiarch 2>/dev/null)
-AC_SUBST(MULTIARCH)
-
-
 AC_SUBST(LIBRARY)
 AC_MSG_CHECKING(LIBRARY)
 if test -z "$LIBRARY"
@@ -4173,15 +4279,7 @@
 AC_MSG_CHECKING(ABIFLAGS)
 AC_MSG_RESULT($ABIFLAGS)
 AC_MSG_CHECKING(SOABI)
-
-case $ac_sys_system in
-    Linux*|GNU*)
-        BITNESS_SUFFIX=-$(($ac_cv_sizeof_void_p * 8))b;;
-    *)
-        BITNESS_SUFFIX=;;
-esac
-SOABI='cpython-'`echo $VERSION | tr -d .`${ABIFLAGS}${BITNESS_SUFFIX}
-
+SOABI='cpython-'`echo $VERSION | tr -d .`${ABIFLAGS}${PLATFORM_TRIPLET:+-$PLATFORM_TRIPLET}
 AC_MSG_RESULT($SOABI)
 
 AC_SUBST(EXT_SUFFIX)