diff --git a/Doc/library/stdtypes.rst b/Doc/library/stdtypes.rst
index 8adbabe..34d6f89 100644
--- a/Doc/library/stdtypes.rst
+++ b/Doc/library/stdtypes.rst
@@ -2405,6 +2405,52 @@
 
    :class:`memoryview` has several methods:
 
+   .. method:: __eq__(exporter)
+
+      A memoryview and a :pep:`3118` exporter are equal if their shapes are
+      equivalent and if all corresponding values are equal when the operands'
+      respective format codes are interpreted using :mod:`struct` syntax.
+
+      For the subset of :mod:`struct` format strings currently supported by
+      :meth:`tolist`, ``v`` and ``w`` are equal if ``v.tolist() == w.tolist()``::
+
+         >>> import array
+         >>> a = array.array('I', [1, 2, 3, 4, 5])
+         >>> b = array.array('d', [1.0, 2.0, 3.0, 4.0, 5.0])
+         >>> c = array.array('b', [5, 3, 1])
+         >>> x = memoryview(a)
+         >>> y = memoryview(b)
+         >>> x == a == y == b
+         True
+         >>> x.tolist() == a.tolist() == y.tolist() == b.tolist()
+         True
+         >>> z = y[::-2]
+         >>> z == c
+         True
+         >>> z.tolist() == c.tolist()
+         True
+
+      If either format string is not supported by the :mod:`struct` module,
+      then the objects will always compare as unequal (even if the format
+      strings and buffer contents are identical)::
+
+         >>> from ctypes import BigEndianStructure, c_long
+         >>> class BEPoint(BigEndianStructure):
+         ...     _fields_ = [("x", c_long), ("y", c_long)]
+         ...
+         >>> point = BEPoint(100, 200)
+         >>> a = memoryview(point)
+         >>> b = memoryview(point)
+         >>> a == point
+         False
+         >>> a == b
+         False
+
+      Note that, as with floating point numbers, ``v is w`` does *not* imply
+      ``v == w`` for memoryview objects.
+
+      .. versionchanged:: 3.3
+
    .. method:: tobytes()
 
       Return the data in the buffer as a bytestring.  This is equivalent to
@@ -2417,7 +2463,9 @@
          b'abc'
 
       For non-contiguous arrays the result is equal to the flattened list
-      representation with all elements converted to bytes.
+      representation with all elements converted to bytes. :meth:`tobytes`
+      supports all format strings, including those that are not in
+      :mod:`struct` module syntax.
 
    .. method:: tolist()
 
@@ -2431,6 +2479,9 @@
          >>> m.tolist()
          [1.1, 2.2, 3.3]
 
+      :meth:`tolist` is currently restricted to single character native formats
+      in :mod:`struct` module syntax.
+
    .. method:: release()
 
       Release the underlying buffer exposed by the memoryview object.  Many
@@ -2470,7 +2521,10 @@
       ``[byte_length//new_itemsize]``, which means that the result view
       will be one-dimensional. The return value is a new memoryview, but
       the buffer itself is not copied. Supported casts are 1D -> C-contiguous
-      and C-contiguous -> 1D. One of the formats must be a byte format
+      and C-contiguous -> 1D.
+
+      Both formats are restricted to single element native formats in
+      :mod:`struct` syntax. One of the formats must be a byte format
       ('B', 'b' or 'c'). The byte length of the result must be the same
       as the original length.
 
@@ -2608,25 +2662,7 @@
       A string containing the format (in :mod:`struct` module style) for each
       element in the view. A memoryview can be created from exporters with
       arbitrary format strings, but some methods (e.g. :meth:`tolist`) are
-      restricted to native single element formats. Special care must be taken
-      when comparing memoryviews. Since comparisons are required to return a
-      value for ``==`` and ``!=``, two memoryviews referencing the same
-      exporter can compare as not-equal if the exporter's format is not
-      understood::
-
-         >>> from ctypes import BigEndianStructure, c_long
-         >>> class BEPoint(BigEndianStructure):
-         ...     _fields_ = [("x", c_long), ("y", c_long)]
-         ...
-         >>> point = BEPoint(100, 200)
-         >>> a = memoryview(point)
-         >>> b = memoryview(point)
-         >>> a == b
-         False
-         >>> a.tolist()
-         Traceback (most recent call last):
-           File "<stdin>", line 1, in <module>
-         NotImplementedError: memoryview: unsupported format T{>l:x:>l:y:}
+      restricted to native single element formats.
 
    .. attribute:: itemsize
 
diff --git a/Doc/whatsnew/3.3.rst b/Doc/whatsnew/3.3.rst
index 968e788..27bf12d 100644
--- a/Doc/whatsnew/3.3.rst
+++ b/Doc/whatsnew/3.3.rst
@@ -162,7 +162,6 @@
   and the view is read-only. (Contributed by Antoine Pitrou in
   :issue:`13411`)
 
-
 * Arbitrary slicing of any 1-D arrays type is supported. For example, it
   is now possible to reverse a memoryview in O(1) by using a negative step.
 
@@ -178,6 +177,12 @@
   now returns an integer (in accordance with the struct module syntax).
   For returning a bytes object the view must be cast to 'c' first.
 
+* memoryview comparisons now use the logical structure of the operands
+  and compare all array elements by value. All format strings in struct
+  module syntax are supported. Views with unrecognised format strings
+  are still permitted, but will always compare as unequal, regardless
+  of view contents.
+
 * For further changes see `Build and C API Changes`_ and `Porting C code`_ .
 
 .. _pep-393:
diff --git a/Lib/test/test_buffer.py b/Lib/test/test_buffer.py
index fb85dae..26cd9be 100644
--- a/Lib/test/test_buffer.py
+++ b/Lib/test/test_buffer.py
@@ -32,6 +32,11 @@
     struct = None
 
 try:
+    import ctypes
+except ImportError:
+    ctypes = None
+
+try:
     with warnings.catch_warnings():
         from numpy import ndarray as numpy_array
 except ImportError:
@@ -835,8 +840,6 @@
                 # test tobytes()
                 self.assertEqual(result.tobytes(), b)
 
-            if not buf_err and is_memoryview_format(fmt):
-
                 # lst := expected multi-dimensional logical representation
                 # flatten(lst) := elements in C-order
                 ff = fmt if fmt else 'B'
@@ -877,8 +880,10 @@
                     # To 'C'
                     contig = py_buffer_to_contiguous(result, 'C', PyBUF_FULL_RO)
                     self.assertEqual(len(contig), nmemb * itemsize)
-                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)[0]
+                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)
                                for n in range(nmemb)]
+                    if len(initlst[0]) == 1:
+                        initlst = [v[0] for v in initlst]
 
                     y = ndarray(initlst, shape=shape, flags=ro, format=fmt)
                     self.assertEqual(memoryview(y), memoryview(result))
@@ -886,8 +891,10 @@
                     # To 'F'
                     contig = py_buffer_to_contiguous(result, 'F', PyBUF_FULL_RO)
                     self.assertEqual(len(contig), nmemb * itemsize)
-                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)[0]
+                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)
                                for n in range(nmemb)]
+                    if len(initlst[0]) == 1:
+                        initlst = [v[0] for v in initlst]
 
                     y = ndarray(initlst, shape=shape, flags=ro|ND_FORTRAN,
                                 format=fmt)
@@ -896,8 +903,10 @@
                     # To 'A'
                     contig = py_buffer_to_contiguous(result, 'A', PyBUF_FULL_RO)
                     self.assertEqual(len(contig), nmemb * itemsize)
-                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)[0]
+                    initlst = [struct.unpack_from(fmt, contig, n*itemsize)
                                for n in range(nmemb)]
+                    if len(initlst[0]) == 1:
+                        initlst = [v[0] for v in initlst]
 
                     f = ND_FORTRAN if is_contiguous(result, 'F') else 0
                     y = ndarray(initlst, shape=shape, flags=f|ro, format=fmt)
@@ -3025,7 +3034,7 @@
                             self.assertEqual(m.tobytes(), a.tobytes())
                             cmptest(self, a, b, m, singleitem)
 
-    def test_memoryview_compare(self):
+    def test_memoryview_compare_special_cases(self):
 
         a = array.array('L', [1, 2, 3])
         b = array.array('L', [1, 2, 7])
@@ -3054,43 +3063,32 @@
         v = memoryview(a)
         self.assertNotEqual(v, [1, 2, 3])
 
-        # Different formats:
-        c = array.array('l', [1, 2, 3])
-        v = memoryview(a)
-        self.assertNotEqual(v, c)
-        self.assertNotEqual(c, v)
+        # NaNs
+        nd = ndarray([(0, 0)], shape=[1], format='l x d x', flags=ND_WRITABLE)
+        nd[0] = (-1, float('nan'))
+        self.assertNotEqual(memoryview(nd), nd)
 
-        # Not implemented formats. Ugly, but inevitable. This is the same as
-        # issue #2531: equality is also used for membership testing and must
-        # return a result.
-        a = ndarray([(1, 1.5), (2, 2.7)], shape=[2], format='ld')
+        # Depends on issue #15625: the struct module does not understand 'u'.
+        a = array.array('u', 'xyz')
         v = memoryview(a)
-        self.assertNotEqual(v, a)
         self.assertNotEqual(a, v)
-
-        a = ndarray([b'12345'], shape=[1], format="s")
-        v = memoryview(a)
         self.assertNotEqual(v, a)
-        self.assertNotEqual(a, v)
 
-        nd = ndarray([(1,1,1), (2,2,2), (3,3,3)], shape=[3], format='iii')
-        v = memoryview(nd)
-        self.assertNotEqual(v, nd)
-        self.assertNotEqual(nd, v)
+        # Some ctypes format strings are unknown to the struct module.
+        if ctypes:
+            # format: "T{>l:x:>l:y:}"
+            class BEPoint(ctypes.BigEndianStructure):
+                _fields_ = [("x", ctypes.c_long), ("y", ctypes.c_long)]
+            point = BEPoint(100, 200)
+            a = memoryview(point)
+            b = memoryview(point)
+            self.assertNotEqual(a, b)
+            self.assertNotEqual(a, point)
+            self.assertNotEqual(point, a)
+            self.assertRaises(NotImplementedError, a.tolist)
 
-        # '@' prefix can be dropped:
-        nd1 = ndarray([1,2,3], shape=[3], format='@i')
-        nd2 = ndarray([1,2,3], shape=[3], format='i')
-        v = memoryview(nd1)
-        w = memoryview(nd2)
-        self.assertEqual(v, w)
-        self.assertEqual(w, v)
-        self.assertEqual(v, nd2)
-        self.assertEqual(nd2, v)
-        self.assertEqual(w, nd1)
-        self.assertEqual(nd1, w)
+    def test_memoryview_compare_ndim_zero(self):
 
-        # ndim = 0
         nd1 = ndarray(1729, shape=[], format='@L')
         nd2 = ndarray(1729, shape=[], format='L', flags=ND_WRITABLE)
         v = memoryview(nd1)
@@ -3124,7 +3122,37 @@
         m[9] = 100
         self.assertNotEqual(m, nd)
 
-        # ndim = 1: contiguous
+        # struct module: equal
+        nd1 = ndarray((1729, 1.2, b'12345'), shape=[], format='Lf5s')
+        nd2 = ndarray((1729, 1.2, b'12345'), shape=[], format='hf5s',
+                      flags=ND_WRITABLE)
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+        self.assertEqual(v, w)
+        self.assertEqual(w, v)
+        self.assertEqual(v, nd2)
+        self.assertEqual(nd2, v)
+        self.assertEqual(w, nd1)
+        self.assertEqual(nd1, w)
+
+        # struct module: not equal
+        nd1 = ndarray((1729, 1.2, b'12345'), shape=[], format='Lf5s')
+        nd2 = ndarray((-1729, 1.2, b'12345'), shape=[], format='hf5s',
+                      flags=ND_WRITABLE)
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+        self.assertNotEqual(v, w)
+        self.assertNotEqual(w, v)
+        self.assertNotEqual(v, nd2)
+        self.assertNotEqual(nd2, v)
+        self.assertNotEqual(w, nd1)
+        self.assertNotEqual(nd1, w)
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+
+    def test_memoryview_compare_ndim_one(self):
+
+        # contiguous
         nd1 = ndarray([-529, 576, -625, 676, -729], shape=[5], format='@h')
         nd2 = ndarray([-529, 576, -625, 676, 729], shape=[5], format='@h')
         v = memoryview(nd1)
@@ -3136,7 +3164,19 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # ndim = 1: non-contiguous
+        # contiguous, struct module
+        nd1 = ndarray([-529, 576, -625, 676, -729], shape=[5], format='<i')
+        nd2 = ndarray([-529, 576, -625, 676, 729], shape=[5], format='>h')
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertNotEqual(v, nd2)
+        self.assertNotEqual(w, nd1)
+        self.assertNotEqual(v, w)
+
+        # non-contiguous
         nd1 = ndarray([-529, -625, -729], shape=[3], format='@h')
         nd2 = ndarray([-529, 576, -625, 676, -729], shape=[5], format='@h')
         v = memoryview(nd1)
@@ -3147,7 +3187,18 @@
         self.assertEqual(v, w[::2])
         self.assertEqual(v[::-1], w[::-2])
 
-        # ndim = 1: non-contiguous, suboffsets
+        # non-contiguous, struct module
+        nd1 = ndarray([-529, -625, -729], shape=[3], format='!h')
+        nd2 = ndarray([-529, 576, -625, 676, -729], shape=[5], format='<l')
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd2[::2])
+        self.assertEqual(w[::2], nd1)
+        self.assertEqual(v, w[::2])
+        self.assertEqual(v[::-1], w[::-2])
+
+        # non-contiguous, suboffsets
         nd1 = ndarray([-529, -625, -729], shape=[3], format='@h')
         nd2 = ndarray([-529, 576, -625, 676, -729], shape=[5], format='@h',
                       flags=ND_PIL)
@@ -3159,7 +3210,21 @@
         self.assertEqual(v, w[::2])
         self.assertEqual(v[::-1], w[::-2])
 
-        # ndim = 1: zeros in shape
+        # non-contiguous, suboffsets, struct module
+        nd1 = ndarray([-529, -625, -729], shape=[3], format='h  0c')
+        nd2 = ndarray([-529, 576, -625, 676, -729], shape=[5], format='>  h',
+                      flags=ND_PIL)
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd2[::2])
+        self.assertEqual(w[::2], nd1)
+        self.assertEqual(v, w[::2])
+        self.assertEqual(v[::-1], w[::-2])
+
+    def test_memoryview_compare_zero_shape(self):
+
+        # zeros in shape
         nd1 = ndarray([900, 961], shape=[0], format='@h')
         nd2 = ndarray([-900, -961], shape=[0], format='@h')
         v = memoryview(nd1)
@@ -3171,7 +3236,21 @@
         self.assertEqual(w, nd1)
         self.assertEqual(v, w)
 
-        # ndim = 1: zero strides
+        # zeros in shape, struct module
+        nd1 = ndarray([900, 961], shape=[0], format='= h0c')
+        nd2 = ndarray([-900, -961], shape=[0], format='@   i')
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, nd2)
+        self.assertEqual(w, nd1)
+        self.assertEqual(v, w)
+
+    def test_memoryview_compare_zero_strides(self):
+
+        # zero strides
         nd1 = ndarray([900, 900, 900, 900], shape=[4], format='@L')
         nd2 = ndarray([900], shape=[4], strides=[0], format='L')
         v = memoryview(nd1)
@@ -3183,6 +3262,21 @@
         self.assertEqual(w, nd1)
         self.assertEqual(v, w)
 
+        # zero strides, struct module
+        nd1 = ndarray([(900, 900)]*4, shape=[4], format='@ Li')
+        nd2 = ndarray([(900, 900)], shape=[4], strides=[0], format='!L  h')
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, nd2)
+        self.assertEqual(w, nd1)
+        self.assertEqual(v, w)
+
+    def test_memoryview_compare_random_formats(self):
+
+        # random single character native formats
         n = 10
         for char in fmtdict['@m']:
             fmt, items, singleitem = randitems(n, 'memoryview', '@', char)
@@ -3195,8 +3289,22 @@
                 m = memoryview(nd)
                 self.assertEqual(m, nd)
 
-        ##### ndim > 1: C-contiguous
-        # different values
+        # random formats
+        n = 10
+        for _ in range(100):
+            fmt, items, singleitem = randitems(n)
+            for flags in (0, ND_PIL):
+                nd = ndarray(items, shape=[n], format=fmt, flags=flags)
+                m = memoryview(nd)
+                self.assertEqual(m, nd)
+
+                nd = nd[::-3]
+                m = memoryview(nd)
+                self.assertEqual(m, nd)
+
+    def test_memoryview_compare_multidim_c(self):
+
+        # C-contiguous, different values
         nd1 = ndarray(list(range(-15, 15)), shape=[3, 2, 5], format='@h')
         nd2 = ndarray(list(range(0, 30)), shape=[3, 2, 5], format='@h')
         v = memoryview(nd1)
@@ -3208,7 +3316,19 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # different shape
+        # C-contiguous, different values, struct module
+        nd1 = ndarray([(0, 1, 2)]*30, shape=[3, 2, 5], format='=f q xxL')
+        nd2 = ndarray([(-1.2, 1, 2)]*30, shape=[3, 2, 5], format='< f 2Q')
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertNotEqual(v, nd2)
+        self.assertNotEqual(w, nd1)
+        self.assertNotEqual(v, w)
+
+        # C-contiguous, different shape
         nd1 = ndarray(list(range(30)), shape=[2, 3, 5], format='L')
         nd2 = ndarray(list(range(30)), shape=[3, 2, 5], format='L')
         v = memoryview(nd1)
@@ -3220,9 +3340,9 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # different format
-        nd1 = ndarray(list(range(30)), shape=[2, 3, 5], format='L')
-        nd2 = ndarray(list(range(30)), shape=[2, 3, 5], format='l')
+        # C-contiguous, different shape, struct module
+        nd1 = ndarray([(0, 1, 2)]*21, shape=[3, 7], format='! b B xL')
+        nd2 = ndarray([(0, 1, 2)]*21, shape=[7, 3], format='= Qx l xxL')
         v = memoryview(nd1)
         w = memoryview(nd2)
 
@@ -3232,8 +3352,21 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        ##### ndim > 1: Fortran contiguous
-        # different values
+        # C-contiguous, different format, struct module
+        nd1 = ndarray(list(range(30)), shape=[2, 3, 5], format='L')
+        nd2 = ndarray(list(range(30)), shape=[2, 3, 5], format='l')
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, nd2)
+        self.assertEqual(w, nd1)
+        self.assertEqual(v, w)
+
+    def test_memoryview_compare_multidim_fortran(self):
+
+        # Fortran-contiguous, different values
         nd1 = ndarray(list(range(-15, 15)), shape=[5, 2, 3], format='@h',
                       flags=ND_FORTRAN)
         nd2 = ndarray(list(range(0, 30)), shape=[5, 2, 3], format='@h',
@@ -3247,7 +3380,21 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # different shape
+        # Fortran-contiguous, different values, struct module
+        nd1 = ndarray([(2**64-1, -1)]*6, shape=[2, 3], format='=Qq',
+                      flags=ND_FORTRAN)
+        nd2 = ndarray([(-1, 2**64-1)]*6, shape=[2, 3], format='=qQ',
+                      flags=ND_FORTRAN)
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertNotEqual(v, nd2)
+        self.assertNotEqual(w, nd1)
+        self.assertNotEqual(v, w)
+
+        # Fortran-contiguous, different shape
         nd1 = ndarray(list(range(-15, 15)), shape=[2, 3, 5], format='l',
                       flags=ND_FORTRAN)
         nd2 = ndarray(list(range(-15, 15)), shape=[3, 2, 5], format='l',
@@ -3261,10 +3408,10 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # different format
-        nd1 = ndarray(list(range(30)), shape=[5, 2, 3], format='@h',
+        # Fortran-contiguous, different shape, struct module
+        nd1 = ndarray(list(range(-15, 15)), shape=[2, 3, 5], format='0ll',
                       flags=ND_FORTRAN)
-        nd2 = ndarray(list(range(30)), shape=[5, 2, 3], format='@b',
+        nd2 = ndarray(list(range(-15, 15)), shape=[3, 2, 5], format='l',
                       flags=ND_FORTRAN)
         v = memoryview(nd1)
         w = memoryview(nd2)
@@ -3275,7 +3422,23 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        ##### ndim > 1: mixed C/Fortran contiguous
+        # Fortran-contiguous, different format, struct module
+        nd1 = ndarray(list(range(30)), shape=[5, 2, 3], format='@h',
+                      flags=ND_FORTRAN)
+        nd2 = ndarray(list(range(30)), shape=[5, 2, 3], format='@b',
+                      flags=ND_FORTRAN)
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, nd2)
+        self.assertEqual(w, nd1)
+        self.assertEqual(v, w)
+
+    def test_memoryview_compare_multidim_mixed(self):
+
+        # mixed C/Fortran contiguous
         lst1 = list(range(-15, 15))
         lst2 = transpose(lst1, [3, 2, 5])
         nd1 = ndarray(lst1, shape=[3, 2, 5], format='@l')
@@ -3287,8 +3450,20 @@
         self.assertEqual(w, nd2)
         self.assertEqual(v, w)
 
-        ##### ndim > 1: non-contiguous
-        # different values
+        # mixed C/Fortran contiguous, struct module
+        lst1 = [(-3.3, -22, b'x')]*30
+        lst1[5] = (-2.2, -22, b'x')
+        lst2 = transpose(lst1, [3, 2, 5])
+        nd1 = ndarray(lst1, shape=[3, 2, 5], format='d b c')
+        nd2 = ndarray(lst2, shape=[3, 2, 5], format='d h c', flags=ND_FORTRAN)
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, w)
+
+        # different values, non-contiguous
         ex1 = ndarray(list(range(40)), shape=[5, 8], format='@I')
         nd1 = ex1[3:1:-1, ::-2]
         ex2 = ndarray(list(range(40)), shape=[5, 8], format='I')
@@ -3302,6 +3477,20 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
+        # same values, non-contiguous, struct module
+        ex1 = ndarray([(2**31-1, -2**31)]*22, shape=[11, 2], format='=ii')
+        nd1 = ex1[3:1:-1, ::-2]
+        ex2 = ndarray([(2**31-1, -2**31)]*22, shape=[11, 2], format='>ii')
+        nd2 = ex2[1:3:1, ::-2]
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, nd2)
+        self.assertEqual(w, nd1)
+        self.assertEqual(v, w)
+
         # different shape
         ex1 = ndarray(list(range(30)), shape=[2, 3, 5], format='b')
         nd1 = ex1[1:3:, ::-2]
@@ -3316,10 +3505,10 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # different format
-        ex1 = ndarray(list(range(30)), shape=[5, 3, 2], format='i')
+        # different shape, struct module
+        ex1 = ndarray(list(range(30)), shape=[2, 3, 5], format='B')
         nd1 = ex1[1:3:, ::-2]
-        nd2 = ndarray(list(range(30)), shape=[5, 3, 2], format='@I')
+        nd2 = ndarray(list(range(30)), shape=[3, 2, 5], format='b')
         nd2 = ex2[1:3:, ::-2]
         v = memoryview(nd1)
         w = memoryview(nd2)
@@ -3330,7 +3519,23 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        ##### ndim > 1: zeros in shape
+        # different format, struct module
+        ex1 = ndarray([(2, b'123')]*30, shape=[5, 3, 2], format='b3s')
+        nd1 = ex1[1:3:, ::-2]
+        nd2 = ndarray([(2, b'123')]*30, shape=[5, 3, 2], format='i3s')
+        nd2 = ex2[1:3:, ::-2]
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertNotEqual(v, nd2)
+        self.assertNotEqual(w, nd1)
+        self.assertNotEqual(v, w)
+
+    def test_memoryview_compare_multidim_zero_shape(self):
+
+        # zeros in shape
         nd1 = ndarray(list(range(30)), shape=[0, 3, 2], format='i')
         nd2 = ndarray(list(range(30)), shape=[5, 0, 2], format='@i')
         v = memoryview(nd1)
@@ -3342,7 +3547,21 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # ndim > 1: zero strides
+        # zeros in shape, struct module
+        nd1 = ndarray(list(range(30)), shape=[0, 3, 2], format='i')
+        nd2 = ndarray(list(range(30)), shape=[5, 0, 2], format='@i')
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertNotEqual(v, nd2)
+        self.assertNotEqual(w, nd1)
+        self.assertNotEqual(v, w)
+
+    def test_memoryview_compare_multidim_zero_strides(self):
+
+        # zero strides
         nd1 = ndarray([900]*80, shape=[4, 5, 4], format='@L')
         nd2 = ndarray([900], shape=[4, 5, 4], strides=[0, 0, 0], format='L')
         v = memoryview(nd1)
@@ -3355,7 +3574,21 @@
         self.assertEqual(v, w)
         self.assertEqual(v.tolist(), w.tolist())
 
-        ##### ndim > 1: suboffsets
+        # zero strides, struct module
+        nd1 = ndarray([(1, 2)]*10, shape=[2, 5], format='=lQ')
+        nd2 = ndarray([(1, 2)], shape=[2, 5], strides=[0, 0], format='<lQ')
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, nd2)
+        self.assertEqual(w, nd1)
+        self.assertEqual(v, w)
+
+    def test_memoryview_compare_multidim_suboffsets(self):
+
+        # suboffsets
         ex1 = ndarray(list(range(40)), shape=[5, 8], format='@I')
         nd1 = ex1[3:1:-1, ::-2]
         ex2 = ndarray(list(range(40)), shape=[5, 8], format='I', flags=ND_PIL)
@@ -3369,8 +3602,29 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # different shape
-        ex1 = ndarray(list(range(30)), shape=[2, 3, 5], format='b', flags=ND_PIL)
+        # suboffsets, struct module
+        ex1 = ndarray([(2**64-1, -1)]*40, shape=[5, 8], format='=Qq',
+                      flags=ND_WRITABLE)
+        ex1[2][7] = (1, -2)
+        nd1 = ex1[3:1:-1, ::-2]
+
+        ex2 = ndarray([(2**64-1, -1)]*40, shape=[5, 8], format='>Qq',
+                      flags=ND_PIL|ND_WRITABLE)
+        ex2[2][7] = (1, -2)
+        nd2 = ex2[1:3:1, ::-2]
+
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, nd2)
+        self.assertEqual(w, nd1)
+        self.assertEqual(v, w)
+
+        # suboffsets, different shape
+        ex1 = ndarray(list(range(30)), shape=[2, 3, 5], format='b',
+                      flags=ND_PIL)
         nd1 = ex1[1:3:, ::-2]
         nd2 = ndarray(list(range(30)), shape=[3, 2, 5], format='b')
         nd2 = ex2[1:3:, ::-2]
@@ -3383,16 +3637,53 @@
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
 
-        # different format
+        # suboffsets, different shape, struct module
+        ex1 = ndarray([(2**8-1, -1)]*40, shape=[2, 3, 5], format='Bb',
+                      flags=ND_PIL|ND_WRITABLE)
+        nd1 = ex1[1:2:, ::-2]
+
+        ex2 = ndarray([(2**8-1, -1)]*40, shape=[3, 2, 5], format='Bb')
+        nd2 = ex2[1:2:, ::-2]
+
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertNotEqual(v, nd2)
+        self.assertNotEqual(w, nd1)
+        self.assertNotEqual(v, w)
+
+        # suboffsets, different format
         ex1 = ndarray(list(range(30)), shape=[5, 3, 2], format='i', flags=ND_PIL)
         nd1 = ex1[1:3:, ::-2]
-        nd2 = ndarray(list(range(30)), shape=[5, 3, 2], format='@I', flags=ND_PIL)
+        ex2 = ndarray(list(range(30)), shape=[5, 3, 2], format='@I', flags=ND_PIL)
         nd2 = ex2[1:3:, ::-2]
         v = memoryview(nd1)
         w = memoryview(nd2)
 
         self.assertEqual(v, nd1)
         self.assertEqual(w, nd2)
+        self.assertEqual(v, nd2)
+        self.assertEqual(w, nd1)
+        self.assertEqual(v, w)
+
+        # suboffsets, different format, struct module
+        ex1 = ndarray([(b'hello', b'', 1)]*27, shape=[3, 3, 3], format='5s0sP',
+                      flags=ND_PIL|ND_WRITABLE)
+        ex1[1][2][2] = (b'sushi', b'', 1)
+        nd1 = ex1[1:3:, ::-2]
+
+        ex2 = ndarray([(b'hello', b'', 1)]*27, shape=[3, 3, 3], format='5s0sP',
+                      flags=ND_PIL|ND_WRITABLE)
+        ex1[1][2][2] = (b'sushi', b'', 1)
+        nd2 = ex2[1:3:, ::-2]
+
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
         self.assertNotEqual(v, nd2)
         self.assertNotEqual(w, nd1)
         self.assertNotEqual(v, w)
@@ -3409,6 +3700,50 @@
         self.assertEqual(w, nd2)
         self.assertEqual(v, w)
 
+        # initialize mixed C/Fortran + suboffsets, struct module
+        lst1 = [(b'sashimi', b'sliced', 20.05)]*30
+        lst1[11] = (b'ramen', b'spicy', 9.45)
+        lst2 = transpose(lst1, [3, 2, 5])
+
+        nd1 = ndarray(lst1, shape=[3, 2, 5], format='< 10p 9p d', flags=ND_PIL)
+        nd2 = ndarray(lst2, shape=[3, 2, 5], format='> 10p 9p d',
+                      flags=ND_FORTRAN|ND_PIL)
+        v = memoryview(nd1)
+        w = memoryview(nd2)
+
+        self.assertEqual(v, nd1)
+        self.assertEqual(w, nd2)
+        self.assertEqual(v, w)
+
+    def test_memoryview_compare_not_equal(self):
+
+        # items not equal
+        for byteorder in ['=', '<', '>', '!']:
+            x = ndarray([2**63]*120, shape=[3,5,2,2,2], format=byteorder+'Q')
+            y = ndarray([2**63]*120, shape=[3,5,2,2,2], format=byteorder+'Q',
+                        flags=ND_WRITABLE|ND_FORTRAN)
+            y[2][3][1][1][1] = 1
+            a = memoryview(x)
+            b = memoryview(y)
+            self.assertEqual(a, x)
+            self.assertEqual(b, y)
+            self.assertNotEqual(a, b)
+            self.assertNotEqual(a, y)
+            self.assertNotEqual(b, x)
+
+            x = ndarray([(2**63, 2**31, 2**15)]*120, shape=[3,5,2,2,2],
+                        format=byteorder+'QLH')
+            y = ndarray([(2**63, 2**31, 2**15)]*120, shape=[3,5,2,2,2],
+                        format=byteorder+'QLH', flags=ND_WRITABLE|ND_FORTRAN)
+            y[2][3][1][1][1] = (1, 1, 1)
+            a = memoryview(x)
+            b = memoryview(y)
+            self.assertEqual(a, x)
+            self.assertEqual(b, y)
+            self.assertNotEqual(a, b)
+            self.assertNotEqual(a, y)
+            self.assertNotEqual(b, x)
+
     def test_memoryview_check_released(self):
 
         a = array.array('d', [1.1, 2.2, 3.3])
@@ -3452,11 +3787,38 @@
     def test_memoryview_tobytes(self):
         # Many implicit tests are already in self.verify().
 
-        nd = ndarray([-529, 576, -625, 676, -729], shape=[5], format='@h')
+        t = (-529, 576, -625, 676, -729)
 
+        nd = ndarray(t, shape=[5], format='@h')
         m = memoryview(nd)
+        self.assertEqual(m, nd)
         self.assertEqual(m.tobytes(), nd.tobytes())
 
+        nd = ndarray([t], shape=[1], format='>hQiLl')
+        m = memoryview(nd)
+        self.assertEqual(m, nd)
+        self.assertEqual(m.tobytes(), nd.tobytes())
+
+        nd = ndarray([t for _ in range(12)], shape=[2,2,3], format='=hQiLl')
+        m = memoryview(nd)
+        self.assertEqual(m, nd)
+        self.assertEqual(m.tobytes(), nd.tobytes())
+
+        nd = ndarray([t for _ in range(120)], shape=[5,2,2,3,2],
+                     format='<hQiLl')
+        m = memoryview(nd)
+        self.assertEqual(m, nd)
+        self.assertEqual(m.tobytes(), nd.tobytes())
+
+        # Unknown formats are handled: tobytes() purely depends on itemsize.
+        if ctypes:
+            # format: "T{>l:x:>l:y:}"
+            class BEPoint(ctypes.BigEndianStructure):
+                _fields_ = [("x", ctypes.c_long), ("y", ctypes.c_long)]
+            point = BEPoint(100, 200)
+            a = memoryview(point)
+            self.assertEqual(a.tobytes(), bytes(point))
+
     def test_memoryview_get_contiguous(self):
         # Many implicit tests are already in self.verify().
 
diff --git a/Misc/NEWS b/Misc/NEWS
index 98f3f07..83b3cb7 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -10,6 +10,9 @@
 Core and Builtins
 -----------------
 
+- Issue #15573: memoryview comparisons are now performed by value with full
+  support for any valid struct module format definition.  
+
 - Issue #15316: When an item in the fromlist for __import__ doesn't exist,
   don't raise an error, but if an exception is raised as part of an import do
   let that propagate.
diff --git a/Objects/memoryobject.c b/Objects/memoryobject.c
index 46a8416..f547983 100644
--- a/Objects/memoryobject.c
+++ b/Objects/memoryobject.c
@@ -246,7 +246,7 @@
     (view->suboffsets && view->suboffsets[dest->ndim-1] >= 0)
 
 Py_LOCAL_INLINE(int)
-last_dim_is_contiguous(Py_buffer *dest, Py_buffer *src)
+last_dim_is_contiguous(const Py_buffer *dest, const Py_buffer *src)
 {
     assert(dest->ndim > 0 && src->ndim > 0);
     return (!HAVE_SUBOFFSETS_IN_LAST_DIM(dest) &&
@@ -255,37 +255,63 @@
             src->strides[src->ndim-1] == src->itemsize);
 }
 
-/* Check that the logical structure of the destination and source buffers
-   is identical. */
-static int
-cmp_structure(Py_buffer *dest, Py_buffer *src)
+/* This is not a general function for determining format equivalence.
+   It is used in copy_single() and copy_buffer() to weed out non-matching
+   formats. Skipping the '@' character is specifically used in slice
+   assignments, where the lvalue is already known to have a single character
+   format. This is a performance hack that could be rewritten (if properly
+   benchmarked). */
+Py_LOCAL_INLINE(int)
+equiv_format(const Py_buffer *dest, const Py_buffer *src)
 {
     const char *dfmt, *sfmt;
-    int i;
 
     assert(dest->format && src->format);
     dfmt = dest->format[0] == '@' ? dest->format+1 : dest->format;
     sfmt = src->format[0] == '@' ? src->format+1 : src->format;
 
     if (strcmp(dfmt, sfmt) != 0 ||
-        dest->itemsize != src->itemsize ||
-        dest->ndim != src->ndim) {
-        goto value_error;
+        dest->itemsize != src->itemsize) {
+        return 0;
     }
 
+    return 1;
+}
+
+/* Two shapes are equivalent if they are either equal or identical up
+   to a zero element at the same position. For example, in NumPy arrays
+   the shapes [1, 0, 5] and [1, 0, 7] are equivalent. */
+Py_LOCAL_INLINE(int)
+equiv_shape(const Py_buffer *dest, const Py_buffer *src)
+{
+    int i;
+
+    if (dest->ndim != src->ndim)
+        return 0;
+
     for (i = 0; i < dest->ndim; i++) {
         if (dest->shape[i] != src->shape[i])
-            goto value_error;
+            return 0;
         if (dest->shape[i] == 0)
             break;
     }
 
-    return 0;
+    return 1;
+}
 
-value_error:
-    PyErr_SetString(PyExc_ValueError,
-        "ndarray assignment: lvalue and rvalue have different structures");
-    return -1;
+/* Check that the logical structure of the destination and source buffers
+   is identical. */
+static int
+equiv_structure(const Py_buffer *dest, const Py_buffer *src)
+{
+    if (!equiv_format(dest, src) ||
+        !equiv_shape(dest, src)) {
+        PyErr_SetString(PyExc_ValueError,
+            "ndarray assignment: lvalue and rvalue have different structures");
+        return 0;
+    }
+
+    return 1;
 }
 
 /* Base case for recursive multi-dimensional copying. Contiguous arrays are
@@ -358,7 +384,7 @@
 
     assert(dest->ndim == 1);
 
-    if (cmp_structure(dest, src) < 0)
+    if (!equiv_structure(dest, src))
         return -1;
 
     if (!last_dim_is_contiguous(dest, src)) {
@@ -390,7 +416,7 @@
 
     assert(dest->ndim > 0);
 
-    if (cmp_structure(dest, src) < 0)
+    if (!equiv_structure(dest, src))
         return -1;
 
     if (!last_dim_is_contiguous(dest, src)) {
@@ -1828,6 +1854,131 @@
 
 
 /****************************************************************************/
+/*                       unpack using the struct module                     */
+/****************************************************************************/
+
+/* For reasonable performance it is necessary to cache all objects required
+   for unpacking. An unpacker can handle the format passed to unpack_from().
+   Invariant: All pointer fields of the struct should either be NULL or valid
+   pointers. */
+struct unpacker {
+    PyObject *unpack_from; /* Struct.unpack_from(format) */
+    PyObject *mview;       /* cached memoryview */
+    char *item;            /* buffer for mview */
+    Py_ssize_t itemsize;   /* len(item) */
+};
+
+static struct unpacker *
+unpacker_new(void)
+{
+    struct unpacker *x = PyMem_Malloc(sizeof *x);
+
+    if (x == NULL) {
+        PyErr_NoMemory();
+        return NULL;
+    }
+
+    x->unpack_from = NULL;
+    x->mview = NULL;
+    x->item = NULL;
+    x->itemsize = 0;
+
+    return x;
+}
+
+static void
+unpacker_free(struct unpacker *x)
+{
+    if (x) {
+        Py_XDECREF(x->unpack_from);
+        Py_XDECREF(x->mview);
+        PyMem_Free(x->item);
+        PyMem_Free(x);
+    }
+}
+
+/* Return a new unpacker for the given format. */
+static struct unpacker *
+struct_get_unpacker(const char *fmt, Py_ssize_t itemsize)
+{
+    PyObject *structmodule;     /* XXX cache these two */
+    PyObject *Struct = NULL;    /* XXX in globals?     */
+    PyObject *structobj = NULL;
+    PyObject *format = NULL;
+    struct unpacker *x = NULL;
+
+    structmodule = PyImport_ImportModule("struct");
+    if (structmodule == NULL)
+        return NULL;
+
+    Struct = PyObject_GetAttrString(structmodule, "Struct");
+    Py_DECREF(structmodule);
+    if (Struct == NULL)
+        return NULL;
+
+    x = unpacker_new();
+    if (x == NULL)
+        goto error;
+
+    format = PyBytes_FromString(fmt);
+    if (format == NULL)
+        goto error;
+
+    structobj = PyObject_CallFunctionObjArgs(Struct, format, NULL);
+    if (structobj == NULL)
+        goto error;
+
+    x->unpack_from = PyObject_GetAttrString(structobj, "unpack_from");
+    if (x->unpack_from == NULL)
+        goto error;
+
+    x->item = PyMem_Malloc(itemsize);
+    if (x->item == NULL) {
+        PyErr_NoMemory();
+        goto error;
+    }
+    x->itemsize = itemsize;
+
+    x->mview = PyMemoryView_FromMemory(x->item, itemsize, PyBUF_WRITE);
+    if (x->mview == NULL)
+        goto error;
+
+
+out:
+    Py_XDECREF(Struct);
+    Py_XDECREF(format);
+    Py_XDECREF(structobj);
+    return x;
+
+error:
+    unpacker_free(x);
+    x = NULL;
+    goto out;
+}
+
+/* unpack a single item */
+static PyObject *
+struct_unpack_single(const char *ptr, struct unpacker *x)
+{
+    PyObject *v;
+
+    memcpy(x->item, ptr, x->itemsize);
+    v = PyObject_CallFunctionObjArgs(x->unpack_from, x->mview, NULL);
+    if (v == NULL)
+        return NULL;
+
+    if (PyTuple_GET_SIZE(v) == 1) {
+        PyObject *tmp = PyTuple_GET_ITEM(v, 0);
+        Py_INCREF(tmp);
+        Py_DECREF(v);
+        return tmp;
+    }
+
+    return v;
+}
+
+
+/****************************************************************************/
 /*                              Representations                             */
 /****************************************************************************/
 
@@ -2261,6 +2412,58 @@
 /*                             Comparisons                                */
 /**************************************************************************/
 
+#define MV_COMPARE_EX -1       /* exception */
+#define MV_COMPARE_NOT_IMPL -2 /* not implemented */
+
+/* Translate a StructError to "not equal". Preserve other exceptions. */
+static int
+fix_struct_error_int(void)
+{
+    assert(PyErr_Occurred());
+    /* XXX Cannot get at StructError directly? */
+    if (PyErr_ExceptionMatches(PyExc_ImportError) ||
+        PyErr_ExceptionMatches(PyExc_MemoryError)) {
+        return MV_COMPARE_EX;
+    }
+    /* StructError: invalid or unknown format -> not equal */
+    PyErr_Clear();
+    return 0;
+}
+
+/* Unpack and compare single items of p and q using the struct module. */
+static int
+struct_unpack_cmp(const char *p, const char *q,
+                  struct unpacker *unpack_p, struct unpacker *unpack_q)
+{
+    PyObject *v, *w;
+    int ret;
+
+    /* At this point any exception from the struct module should not be
+       StructError, since both formats have been accepted already. */
+    v = struct_unpack_single(p, unpack_p);
+    if (v == NULL)
+        return MV_COMPARE_EX;
+
+    w = struct_unpack_single(q, unpack_q);
+    if (w == NULL) {
+        Py_DECREF(v);
+        return MV_COMPARE_EX;
+    }
+
+    /* MV_COMPARE_EX == -1: exceptions are preserved */
+    ret = PyObject_RichCompareBool(v, w, Py_EQ);
+    Py_DECREF(v);
+    Py_DECREF(w);
+
+    return ret;
+}
+
+/* Unpack and compare single items of p and q. If both p and q have the same
+   single element native format, the comparison uses a fast path (gcc creates
+   a jump table and converts memcpy into simple assignments on x86/x64).
+
+   Otherwise, the comparison is delegated to the struct module, which is
+   30-60x slower. */
 #define CMP_SINGLE(p, q, type) \
     do {                                 \
         type x;                          \
@@ -2271,11 +2474,12 @@
     } while (0)
 
 Py_LOCAL_INLINE(int)
-unpack_cmp(const char *p, const char *q, const char *fmt)
+unpack_cmp(const char *p, const char *q, char fmt,
+           struct unpacker *unpack_p, struct unpacker *unpack_q)
 {
     int equal;
 
-    switch (fmt[0]) {
+    switch (fmt) {
 
     /* signed integers and fast path for 'B' */
     case 'B': return *((unsigned char *)p) == *((unsigned char *)q);
@@ -2317,9 +2521,17 @@
     /* pointer */
     case 'P': CMP_SINGLE(p, q, void *); return equal;
 
-    /* Py_NotImplemented */
-    default: return -1;
+    /* use the struct module */
+    case '_':
+        assert(unpack_p);
+        assert(unpack_q);
+        return struct_unpack_cmp(p, q, unpack_p, unpack_q);
     }
+
+    /* NOT REACHED */
+    PyErr_SetString(PyExc_RuntimeError,
+        "memoryview: internal error in richcompare");
+    return MV_COMPARE_EX;
 }
 
 /* Base case for recursive array comparisons. Assumption: ndim == 1. */
@@ -2327,7 +2539,7 @@
 cmp_base(const char *p, const char *q, const Py_ssize_t *shape,
          const Py_ssize_t *pstrides, const Py_ssize_t *psuboffsets,
          const Py_ssize_t *qstrides, const Py_ssize_t *qsuboffsets,
-         const char *fmt)
+         char fmt, struct unpacker *unpack_p, struct unpacker *unpack_q)
 {
     Py_ssize_t i;
     int equal;
@@ -2335,7 +2547,7 @@
     for (i = 0; i < shape[0]; p+=pstrides[0], q+=qstrides[0], i++) {
         const char *xp = ADJUST_PTR(p, psuboffsets);
         const char *xq = ADJUST_PTR(q, qsuboffsets);
-        equal = unpack_cmp(xp, xq, fmt);
+        equal = unpack_cmp(xp, xq, fmt, unpack_p, unpack_q);
         if (equal <= 0)
             return equal;
     }
@@ -2350,7 +2562,7 @@
         Py_ssize_t ndim, const Py_ssize_t *shape,
         const Py_ssize_t *pstrides, const Py_ssize_t *psuboffsets,
         const Py_ssize_t *qstrides, const Py_ssize_t *qsuboffsets,
-        const char *fmt)
+        char fmt, struct unpacker *unpack_p, struct unpacker *unpack_q)
 {
     Py_ssize_t i;
     int equal;
@@ -2364,7 +2576,7 @@
         return cmp_base(p, q, shape,
                         pstrides, psuboffsets,
                         qstrides, qsuboffsets,
-                        fmt);
+                        fmt, unpack_p, unpack_q);
     }
 
     for (i = 0; i < shape[0]; p+=pstrides[0], q+=qstrides[0], i++) {
@@ -2373,7 +2585,7 @@
         equal = cmp_rec(xp, xq, ndim-1, shape+1,
                         pstrides+1, psuboffsets ? psuboffsets+1 : NULL,
                         qstrides+1, qsuboffsets ? qsuboffsets+1 : NULL,
-                        fmt);
+                        fmt, unpack_p, unpack_q);
         if (equal <= 0)
             return equal;
     }
@@ -2385,9 +2597,12 @@
 memory_richcompare(PyObject *v, PyObject *w, int op)
 {
     PyObject *res;
-    Py_buffer wbuf, *vv, *ww = NULL;
-    const char *vfmt, *wfmt;
-    int equal = -1; /* Py_NotImplemented */
+    Py_buffer wbuf, *vv;
+    Py_buffer *ww = NULL;
+    struct unpacker *unpack_v = NULL;
+    struct unpacker *unpack_w = NULL;
+    char vfmt, wfmt;
+    int equal = MV_COMPARE_NOT_IMPL;
 
     if (op != Py_EQ && op != Py_NE)
         goto result; /* Py_NotImplemented */
@@ -2414,38 +2629,59 @@
         ww = &wbuf;
     }
 
-    vfmt = adjust_fmt(vv);
-    wfmt = adjust_fmt(ww);
-    if (vfmt == NULL || wfmt == NULL) {
-        PyErr_Clear();
-        goto result; /* Py_NotImplemented */
-    }
-
-    if (cmp_structure(vv, ww) < 0) {
+    if (!equiv_shape(vv, ww)) {
         PyErr_Clear();
         equal = 0;
         goto result;
     }
 
+    /* Use fast unpacking for identical primitive C type formats. */
+    if (get_native_fmtchar(&vfmt, vv->format) < 0)
+        vfmt = '_';
+    if (get_native_fmtchar(&wfmt, ww->format) < 0)
+        wfmt = '_';
+    if (vfmt == '_' || wfmt == '_' || vfmt != wfmt) {
+        /* Use struct module unpacking. NOTE: Even for equal format strings,
+           memcmp() cannot be used for item comparison since it would give
+           incorrect results in the case of NaNs or uninitialized padding
+           bytes. */
+        vfmt = '_';
+        unpack_v = struct_get_unpacker(vv->format, vv->itemsize);
+        if (unpack_v == NULL) {
+            equal = fix_struct_error_int();
+            goto result;
+        }
+        unpack_w = struct_get_unpacker(ww->format, ww->itemsize);
+        if (unpack_w == NULL) {
+            equal = fix_struct_error_int();
+            goto result;
+        }
+    }
+
     if (vv->ndim == 0) {
-        equal = unpack_cmp(vv->buf, ww->buf, vfmt);
+        equal = unpack_cmp(vv->buf, ww->buf,
+                           vfmt, unpack_v, unpack_w);
     }
     else if (vv->ndim == 1) {
         equal = cmp_base(vv->buf, ww->buf, vv->shape,
                          vv->strides, vv->suboffsets,
                          ww->strides, ww->suboffsets,
-                         vfmt);
+                         vfmt, unpack_v, unpack_w);
     }
     else {
         equal = cmp_rec(vv->buf, ww->buf, vv->ndim, vv->shape,
                         vv->strides, vv->suboffsets,
                         ww->strides, ww->suboffsets,
-                        vfmt);
+                        vfmt, unpack_v, unpack_w);
     }
 
 result:
-    if (equal < 0)
-        res = Py_NotImplemented; 
+    if (equal < 0) {
+        if (equal == MV_COMPARE_NOT_IMPL)
+            res = Py_NotImplemented;
+        else /* exception */
+            res = NULL;
+    }
     else if ((equal && op == Py_EQ) || (!equal && op == Py_NE))
         res = Py_True;
     else
@@ -2453,7 +2689,11 @@
 
     if (ww == &wbuf)
         PyBuffer_Release(ww);
-    Py_INCREF(res);
+
+    unpacker_free(unpack_v);
+    unpacker_free(unpack_w);
+
+    Py_XINCREF(res);
     return res;
 }