Lib/test/test_buffer.py

#
# The ndarray object from _testbuffer.c is a complete implementation of
# a PEP-3118 buffer provider. It is independent from NumPy's ndarray
# and the tests don't require NumPy.
#
# If NumPy is present, some tests check both ndarray implementations
# against each other.
#
# Most ndarray tests also check that memoryview(ndarray) behaves in
# the same way as the original. Thus, a substantial part of the
# memoryview tests is now in this module.
#

import contextlib
import unittest
from test import support
from itertools import permutations, product
from random import randrange, sample, choice
import warnings
import sys, array, io, os
from decimal import Decimal
from fractions import Fraction

try:
    from _testbuffer import *
except ImportError:
    ndarray = None

try:
    import struct
except ImportError:
    struct = None

try:
    import ctypes
except ImportError:
    ctypes = None

try:
    with support.EnvironmentVarGuard() as os.environ, \
         warnings.catch_warnings():
        from numpy import ndarray as numpy_array
except ImportError:
    numpy_array = None


SHORT_TEST = True


# ======================================================================
#                    Random lists by format specifier
# ======================================================================

# Native format chars and their ranges.
NATIVE = {
    '?':0, 'c':0, 'b':0, 'B':0,
    'h':0, 'H':0, 'i':0, 'I':0,
    'l':0, 'L':0, 'n':0, 'N':0,
    'f':0, 'd':0, 'P':0
}

# NumPy does not have 'n' or 'N':
if numpy_array:
    del NATIVE['n']
    del NATIVE['N']

if struct:
    try:
        # Add "qQ" if present in native mode.
        struct.pack('Q', 2**64-1)
        NATIVE['q'] = 0
        NATIVE['Q'] = 0
    except struct.error:
        pass

# Standard format chars and their ranges.
STANDARD = {
    '?':(0, 2),            'c':(0, 1<<8),
    'b':(-(1<<7), 1<<7),   'B':(0, 1<<8),
    'h':(-(1<<15), 1<<15), 'H':(0, 1<<16),
    'i':(-(1<<31), 1<<31), 'I':(0, 1<<32),
    'l':(-(1<<31), 1<<31), 'L':(0, 1<<32),
    'q':(-(1<<63), 1<<63), 'Q':(0, 1<<64),
    'f':(-(1<<63), 1<<63), 'd':(-(1<<1023), 1<<1023)
}

def native_type_range(fmt):
    """Return range of a native type."""
    if fmt == 'c':
        lh = (0, 256)
    elif fmt == '?':
        lh = (0, 2)
    elif fmt == 'f':
        lh = (-(1<<63), 1<<63)
    elif fmt == 'd':
        lh = (-(1<<1023), 1<<1023)
    else:
        for exp in (128, 127, 64, 63, 32, 31, 16, 15, 8, 7):
            try:
                struct.pack(fmt, (1<<exp)-1)
                break
            except struct.error:
                pass
        lh = (-(1<<exp), 1<<exp) if exp & 1 else (0, 1<<exp)
    return lh

fmtdict = {
    '':NATIVE,
    '@':NATIVE,
    '<':STANDARD,
    '>':STANDARD,
    '=':STANDARD,
    '!':STANDARD
}

if struct:
    for fmt in fmtdict['@']:
        fmtdict['@'][fmt] = native_type_range(fmt)

MEMORYVIEW = NATIVE.copy()
ARRAY = NATIVE.copy()
for k in NATIVE:
    if not k in "bBhHiIlLfd":
        del ARRAY[k]

BYTEFMT = NATIVE.copy()
for k in NATIVE:
    if not k in "Bbc":
        del BYTEFMT[k]

fmtdict['m']  = MEMORYVIEW
fmtdict['@m'] = MEMORYVIEW
fmtdict['a']  = ARRAY
fmtdict['b']  = BYTEFMT
fmtdict['@b']  = BYTEFMT

# Capabilities of the test objects:
MODE = 0
MULT = 1
cap = {         # format chars                  # multiplier
  'ndarray':    (['', '@', '<', '>', '=', '!'], ['', '1', '2', '3']),
  'array':      (['a'],                         ['']),
  'numpy':      ([''],                          ['']),
  'memoryview': (['@m', 'm'],                   ['']),
  'bytefmt':    (['@b', 'b'],                   ['']),
}

def randrange_fmt(mode, char, obj):
    """Return random item for a type specified by a mode and a single
       format character."""
    x = randrange(*fmtdict[mode][char])
    if char == 'c':
        x = bytes([x])
        if obj == 'numpy' and x == b'\x00':
            # http://projects.scipy.org/numpy/ticket/1925
            x = b'\x01'
    if char == '?':
        x = bool(x)
    if char == 'f' or char == 'd':
        x = struct.pack(char, x)
        x = struct.unpack(char, x)[0]
    return x

def gen_item(fmt, obj):
    """Return single random item."""
    mode, chars = fmt.split('#')
    x = []
    for c in chars:
        x.append(randrange_fmt(mode, c, obj))
    return x[0] if len(x) == 1 else tuple(x)

def gen_items(n, fmt, obj):
    """Return a list of random items (or a scalar)."""
    if n == 0:
        return gen_item(fmt, obj)
    lst = [0] * n
    for i in range(n):
        lst[i] = gen_item(fmt, obj)
    return lst

def struct_items(n, obj):
    mode = choice(cap[obj][MODE])
    xfmt = mode + '#'
    fmt = mode.strip('amb')
    nmemb = randrange(2, 10) # number of struct members
    for _ in range(nmemb):
        char = choice(tuple(fmtdict[mode]))
        multiplier = choice(cap[obj][MULT])
        xfmt += (char * int(multiplier if multiplier else 1))
        fmt += (multiplier + char)
    items = gen_items(n, xfmt, obj)
    item = gen_item(xfmt, obj)
    return fmt, items, item

def randitems(n, obj='ndarray', mode=None, char=None):
    """Return random format, items, item."""
    if mode is None:
        mode = choice(cap[obj][MODE])
    if char is None:
        char = choice(tuple(fmtdict[mode]))
    multiplier = choice(cap[obj][MULT])
    fmt = mode + '#' + char * int(multiplier if multiplier else 1)
    items = gen_items(n, fmt, obj)
    item = gen_item(fmt, obj)
    fmt = mode.strip('amb') + multiplier + char
    return fmt, items, item

def iter_mode(n, obj='ndarray'):
    """Iterate through supported mode/char combinations."""
    for mode in cap[obj][MODE]:
        for char in fmtdict[mode]:
            yield randitems(n, obj, mode, char)

def iter_format(nitems, testobj='ndarray'):
    """Yield (format, items, item) for all possible modes and format
       characters plus one random compound format string."""
    for t in iter_mode(nitems, testobj):
        yield t
    if testobj != 'ndarray':
        return
    yield struct_items(nitems, testobj)


def is_byte_format(fmt):
    return 'c' in fmt or 'b' in fmt or 'B' in fmt

def is_memoryview_format(fmt):
    """format suitable for memoryview"""
    x = len(fmt)
    return ((x == 1 or (x == 2 and fmt[0] == '@')) and
            fmt[x-1] in MEMORYVIEW)

NON_BYTE_FORMAT = [c for c in fmtdict['@'] if not is_byte_format(c)]


# ======================================================================
#       Multi-dimensional tolist(), slicing and slice assignments
# ======================================================================

def atomp(lst):
    """Tuple items (representing structs) are regarded as atoms."""
    return not isinstance(lst, list)

def listp(lst):
    return isinstance(lst, list)

def prod(lst):
    """Product of list elements."""
    if len(lst) == 0:
        return 0
    x = lst[0]
    for v in lst[1:]:
        x *= v
    return x

def strides_from_shape(ndim, shape, itemsize, layout):
    """Calculate strides of a contiguous array. Layout is 'C' or
       'F' (Fortran)."""
    if ndim == 0:
        return ()
    if layout == 'C':
        strides = list(shape[1:]) + [itemsize]
        for i in range(ndim-2, -1, -1):
            strides[i] *= strides[i+1]
    else:
        strides = [itemsize] + list(shape[:-1])
        for i in range(1, ndim):
            strides[i] *= strides[i-1]
    return strides

def _ca(items, s):
    """Convert flat item list to the nested list representation of a
       multidimensional C array with shape 's'."""
    if atomp(items):
        return items
    if len(s) == 0:
        return items[0]
    lst = [0] * s[0]
    stride = len(items) // s[0] if s[0] else 0
    for i in range(s[0]):
        start = i*stride
        lst[i] = _ca(items[start:start+stride], s[1:])
    return lst

def _fa(items, s):
    """Convert flat item list to the nested list representation of a
       multidimensional Fortran array with shape 's'."""
    if atomp(items):
        return items
    if len(s) == 0:
        return items[0]
    lst = [0] * s[0]
    stride = s[0]
    for i in range(s[0]):
        lst[i] = _fa(items[i::stride], s[1:])
    return lst

def carray(items, shape):
    if listp(items) and not 0 in shape and prod(shape) != len(items):
        raise ValueError("prod(shape) != len(items)")
    return _ca(items, shape)

def farray(items, shape):
    if listp(items) and not 0 in shape and prod(shape) != len(items):
        raise ValueError("prod(shape) != len(items)")
    return _fa(items, shape)

def indices(shape):
    """Generate all possible tuples of indices."""
    iterables = [range(v) for v in shape]
    return product(*iterables)

def getindex(ndim, ind, strides):
    """Convert multi-dimensional index to the position in the flat list."""
    ret = 0
    for i in range(ndim):
        ret += strides[i] * ind[i]
    return ret

def transpose(src, shape):
    """Transpose flat item list that is regarded as a multi-dimensional
       matrix defined by shape: dest...[k][j][i] = src[i][j][k]...  """
    if not shape:
        return src
    ndim = len(shape)
    sstrides = strides_from_shape(ndim, shape, 1, 'C')
    dstrides = strides_from_shape(ndim, shape[::-1], 1, 'C')
    dest = [0] * len(src)
    for ind in indices(shape):
        fr = getindex(ndim, ind, sstrides)
        to = getindex(ndim, ind[::-1], dstrides)
        dest[to] = src[fr]
    return dest

def _flatten(lst):
    """flatten list"""
    if lst == []:
        return lst
    if atomp(lst):
        return [lst]
    return _flatten(lst[0]) + _flatten(lst[1:])

def flatten(lst):
    """flatten list or return scalar"""
    if atomp(lst): # scalar
        return lst
    return _flatten(lst)

def slice_shape(lst, slices):
    """Get the shape of lst after slicing: slices is a list of slice
       objects."""
    if atomp(lst):
        return []
    return [len(lst[slices[0]])] + slice_shape(lst[0], slices[1:])

def multislice(lst, slices):
    """Multi-dimensional slicing: slices is a list of slice objects."""
    if atomp(lst):
        return lst
    return [multislice(sublst, slices[1:]) for sublst in lst[slices[0]]]

def m_assign(llst, rlst, lslices, rslices):
    """Multi-dimensional slice assignment: llst and rlst are the operands,
       lslices and rslices are lists of slice objects. llst and rlst must
       have the same structure.

       For a two-dimensional example, this is not implemented in Python:

         llst[0:3:2, 0:3:2] = rlst[1:3:1, 1:3:1]

       Instead we write:

         lslices = [slice(0,3,2), slice(0,3,2)]
         rslices = [slice(1,3,1), slice(1,3,1)]
         multislice_assign(llst, rlst, lslices, rslices)
    """
    if atomp(rlst):
        return rlst
    rlst = [m_assign(l, r, lslices[1:], rslices[1:])
            for l, r in zip(llst[lslices[0]], rlst[rslices[0]])]
    llst[lslices[0]] = rlst
    return llst

def cmp_structure(llst, rlst, lslices, rslices):
    """Compare the structure of llst[lslices] and rlst[rslices]."""
    lshape = slice_shape(llst, lslices)
    rshape = slice_shape(rlst, rslices)
    if (len(lshape) != len(rshape)):
        return -1
    for i in range(len(lshape)):
        if lshape[i] != rshape[i]:
            return -1
        if lshape[i] == 0:
            return 0
    return 0

def multislice_assign(llst, rlst, lslices, rslices):
    """Return llst after assigning: llst[lslices] = rlst[rslices]"""
    if cmp_structure(llst, rlst, lslices, rslices) < 0:
        raise ValueError("lvalue and rvalue have different structures")
    return m_assign(llst, rlst, lslices, rslices)


# ======================================================================
#                          Random structures
# ======================================================================

#
# PEP-3118 is very permissive with respect to the contents of a
# Py_buffer. In particular:
#
#   - shape can be zero
#   - strides can be any integer, including zero
#   - offset can point to any location in the underlying
#     memory block, provided that it is a multiple of
#     itemsize.
#
# The functions in this section test and verify random structures
# in full generality. A structure is valid iff it fits in the
# underlying memory block.
#
# The structure 't' (short for 'tuple') is fully defined by:
#
#   t = (memlen, itemsize, ndim, shape, strides, offset)
#

def verify_structure(memlen, itemsize, ndim, shape, strides, offset):
    """Verify that the parameters represent a valid array within
       the bounds of the allocated memory:
           char *mem: start of the physical memory block
           memlen: length of the physical memory block
           offset: (char *)buf - mem
    """
    if offset % itemsize:
        return False
    if offset < 0 or offset+itemsize > memlen:
        return False
    if any(v % itemsize for v in strides):
        return False

    if ndim <= 0:
        return ndim == 0 and not shape and not strides
    if 0 in shape:
        return True

    imin = sum(strides[j]*(shape[j]-1) for j in range(ndim)
               if strides[j] <= 0)
    imax = sum(strides[j]*(shape[j]-1) for j in range(ndim)
               if strides[j] > 0)

    return 0 <= offset+imin and offset+imax+itemsize <= memlen

def get_item(lst, indices):
    for i in indices:
        lst = lst[i]
    return lst

def memory_index(indices, t):
    """Location of an item in the underlying memory."""
    memlen, itemsize, ndim, shape, strides, offset = t
    p = offset
    for i in range(ndim):
        p += strides[i]*indices[i]
    return p

def is_overlapping(t):
    """The structure 't' is overlapping if at least one memory location
       is visited twice while iterating through all possible tuples of
       indices."""
    memlen, itemsize, ndim, shape, strides, offset = t
    visited = 1<<memlen
    for ind in indices(shape):
        i = memory_index(ind, t)
        bit = 1<<i
        if visited & bit:
            return True
        visited |= bit
    return False

def rand_structure(itemsize, valid, maxdim=5, maxshape=16, shape=()):
    """Return random structure:
           (memlen, itemsize, ndim, shape, strides, offset)
       If 'valid' is true, the returned structure is valid, otherwise invalid.
       If 'shape' is given, use that instead of creating a random shape.
    """
    if not shape:
        ndim = randrange(maxdim+1)
        if (ndim == 0):
            if valid:
                return itemsize, itemsize, ndim, (), (), 0
            else:
                nitems = randrange(1, 16+1)
                memlen = nitems * itemsize
                offset = -itemsize if randrange(2) == 0 else memlen
                return memlen, itemsize, ndim, (), (), offset

        minshape = 2
        n = randrange(100)
        if n >= 95 and valid:
            minshape = 0
        elif n >= 90:
            minshape = 1
        shape = [0] * ndim

        for i in range(ndim):
            shape[i] = randrange(minshape, maxshape+1)
    else:
        ndim = len(shape)

    maxstride = 5
    n = randrange(100)
    zero_stride = True if n >= 95 and n & 1 else False

    strides = [0] * ndim
    strides[ndim-1] = itemsize * randrange(-maxstride, maxstride+1)
    if not zero_stride and strides[ndim-1] == 0:
        strides[ndim-1] = itemsize

    for i in range(ndim-2, -1, -1):
        maxstride *= shape[i+1] if shape[i+1] else 1
        if zero_stride:
            strides[i] = itemsize * randrange(-maxstride, maxstride+1)
        else:
            strides[i] = ((1,-1)[randrange(2)] *
                          itemsize * randrange(1, maxstride+1))

    imin = imax = 0
    if not 0 in shape:
        imin = sum(strides[j]*(shape[j]-1) for j in range(ndim)
                   if strides[j] <= 0)
        imax = sum(strides[j]*(shape[j]-1) for j in range(ndim)
                   if strides[j] > 0)

    nitems = imax - imin
    if valid:
        offset = -imin * itemsize
        memlen = offset + (imax+1) * itemsize
    else:
        memlen = (-imin + imax) * itemsize
        offset = -imin-itemsize if randrange(2) == 0 else memlen
    return memlen, itemsize, ndim, shape, strides, offset

def randslice_from_slicelen(slicelen, listlen):
    """Create a random slice of len slicelen that fits into listlen."""
    maxstart = listlen - slicelen
    start = randrange(maxstart+1)
    maxstep = (listlen - start) // slicelen if slicelen else 1
    step = randrange(1, maxstep+1)
    stop = start + slicelen * step
    s = slice(start, stop, step)
    _, _, _, control = slice_indices(s, listlen)
    if control != slicelen:
        raise RuntimeError
    return s

def randslice_from_shape(ndim, shape):
    """Create two sets of slices for an array x with shape 'shape'
       such that shapeof(x[lslices]) == shapeof(x[rslices])."""
    lslices = [0] * ndim
    rslices = [0] * ndim
    for n in range(ndim):
        l = shape[n]
        slicelen = randrange(1, l+1) if l > 0 else 0
        lslices[n] = randslice_from_slicelen(slicelen, l)
        rslices[n] = randslice_from_slicelen(slicelen, l)
    return tuple(lslices), tuple(rslices)

def rand_aligned_slices(maxdim=5, maxshape=16):
    """Create (lshape, rshape, tuple(lslices), tuple(rslices)) such that
       shapeof(x[lslices]) == shapeof(y[rslices]), where x is an array
       with shape 'lshape' and y is an array with shape 'rshape'."""
    ndim = randrange(1, maxdim+1)
    minshape = 2
    n = randrange(100)
    if n >= 95:
        minshape = 0
    elif n >= 90:
        minshape = 1
    all_random = True if randrange(100) >= 80 else False
    lshape = [0]*ndim; rshape = [0]*ndim
    lslices = [0]*ndim; rslices = [0]*ndim

    for n in range(ndim):
        small = randrange(minshape, maxshape+1)
        big = randrange(minshape, maxshape+1)
        if big < small:
            big, small = small, big

        # Create a slice that fits the smaller value.
        if all_random:
            start = randrange(-small, small+1)
            stop = randrange(-small, small+1)
            step = (1,-1)[randrange(2)] * randrange(1, small+2)
            s_small = slice(start, stop, step)
            _, _, _, slicelen = slice_indices(s_small, small)
        else:
            slicelen = randrange(1, small+1) if small > 0 else 0
            s_small = randslice_from_slicelen(slicelen, small)

        # Create a slice of the same length for the bigger value.
        s_big = randslice_from_slicelen(slicelen, big)
        if randrange(2) == 0:
            rshape[n], lshape[n] = big, small
            rslices[n], lslices[n] = s_big, s_small
        else:
            rshape[n], lshape[n] = small, big
            rslices[n], lslices[n] = s_small, s_big

    return lshape, rshape, tuple(lslices), tuple(rslices)

def randitems_from_structure(fmt, t):
    """Return a list of random items for structure 't' with format
       'fmtchar'."""
    memlen, itemsize, _, _, _, _ = t
    return gen_items(memlen//itemsize, '#'+fmt, 'numpy')

def ndarray_from_structure(items, fmt, t, flags=0):
    """Return ndarray from the tuple returned by rand_structure()"""
    memlen, itemsize, ndim, shape, strides, offset = t
    return ndarray(items, shape=shape, strides=strides, format=fmt,
                   offset=offset, flags=ND_WRITABLE|flags)

def numpy_array_from_structure(items, fmt, t):
    """Return numpy_array from the tuple returned by rand_structure()"""
    memlen, itemsize, ndim, shape, strides, offset = t
    buf = bytearray(memlen)
    for j, v in enumerate(items):
        struct.pack_into(fmt, buf, j*itemsize, v)
    return numpy_array(buffer=buf, shape=shape, strides=strides,
                       dtype=fmt, offset=offset)


# ======================================================================
#                          memoryview casts
# ======================================================================

def cast_items(exporter, fmt, itemsize, shape=None):
    """Interpret the raw memory of 'exporter' as a list of items with
       size 'itemsize'. If shape=None, the new structure is assumed to
       be 1-D with n * itemsize = bytelen. If shape is given, the usual
       constraint for contiguous arrays prod(shape) * itemsize = bytelen
       applies. On success, return (items, shape). If the constraints
       cannot be met, return (None, None). If a chunk of bytes is interpreted
       as NaN as a result of float conversion, return ('nan', None)."""
    bytelen = exporter.nbytes
    if shape:
        if prod(shape) * itemsize != bytelen:
            return None, shape
    elif shape == []:
        if exporter.ndim == 0 or itemsize != bytelen:
            return None, shape
    else:
        n, r = divmod(bytelen, itemsize)
        shape = [n]
        if r != 0:
            return None, shape

    mem = exporter.tobytes()
    byteitems = [mem[i:i+itemsize] for i in range(0, len(mem), itemsize)]

    items = []
    for v in byteitems:
        item = struct.unpack(fmt, v)[0]
        if item != item:
            return 'nan', shape
        items.append(item)

    return (items, shape) if shape != [] else (items[0], shape)

def gencastshapes():
    """Generate shapes to test casting."""
    for n in range(32):
        yield [n]
    ndim = randrange(4, 6)
    minshape = 1 if randrange(100) > 80 else 2
    yield [randrange(minshape, 5) for _ in range(ndim)]
    ndim = randrange(2, 4)
    minshape = 1 if randrange(100) > 80 else 2
    yield [randrange(minshape, 5) for _ in range(ndim)]


# ======================================================================
#                              Actual tests
# ======================================================================

def genslices(n):
    """Generate all possible slices for a single dimension."""
    return product(range(-n, n+1), range(-n, n+1), range(-n, n+1))

def genslices_ndim(ndim, shape):
    """Generate all possible slice tuples for 'shape'."""
    iterables = [genslices(shape[n]) for n in range(ndim)]
    return product(*iterables)

def rslice(n, allow_empty=False):
    """Generate random slice for a single dimension of length n.
       If zero=True, the slices may be empty, otherwise they will
       be non-empty."""
    minlen = 0 if allow_empty or n == 0 else 1
    slicelen = randrange(minlen, n+1)
    return randslice_from_slicelen(slicelen, n)

def rslices(n, allow_empty=False):
    """Generate random slices for a single dimension."""
    for _ in range(5):
        yield rslice(n, allow_empty)

def rslices_ndim(ndim, shape, iterations=5):
    """Generate random slice tuples for 'shape'."""
    # non-empty slices
    for _ in range(iterations):
        yield tuple(rslice(shape[n]) for n in range(ndim))
    # possibly empty slices
    for _ in range(iterations):
        yield tuple(rslice(shape[n], allow_empty=True) for n in range(ndim))
    # invalid slices
    yield tuple(slice(0,1,0) for _ in range(ndim))

def rpermutation(iterable, r=None):
    pool = tuple(iterable)
    r = len(pool) if r is None else r
    yield tuple(sample(pool, r))

def ndarray_print(nd):
    """Print ndarray for debugging."""
    try:
        x = nd.tolist()
    except (TypeError, NotImplementedError):
        x = nd.tobytes()
    if isinstance(nd, ndarray):
        offset = nd.offset
        flags = nd.flags
    else:
        offset = 'unknown'
        flags = 'unknown'
    print("ndarray(%s, shape=%s, strides=%s, suboffsets=%s, offset=%s, "
          "format='%s', itemsize=%s, flags=%s)" %
          (x, nd.shape, nd.strides, nd.suboffsets, offset,
           nd.format, nd.itemsize, flags))
    sys.stdout.flush()


ITERATIONS = 100
MAXDIM = 5
MAXSHAPE = 10

if SHORT_TEST:
    ITERATIONS = 10
    MAXDIM = 3
    MAXSHAPE = 4
    genslices = rslices
    genslices_ndim = rslices_ndim
    permutations = rpermutation


@unittest.skipUnless(struct, 'struct module required for this test.')
@unittest.skipUnless(ndarray, 'ndarray object required for this test')
class TestBufferProtocol(unittest.TestCase):

    def setUp(self):
        # The suboffsets tests need sizeof(void *).
        self.sizeof_void_p = get_sizeof_void_p()

    def verify(self, result, *, obj,
                     itemsize, fmt, readonly,
                     ndim, shape, strides,
                     lst, sliced=False, cast=False):
        # Verify buffer contents against expected values.
        if shape:
            expected_len = prod(shape)*itemsize
        else:
            if not fmt: # array has been implicitly cast to unsigned bytes
                expected_len = len(lst)
            else: # ndim = 0
                expected_len = itemsize

        # Reconstruct suboffsets from strides. Support for slicing
        # could be added, but is currently only needed for test_getbuf().
        suboffsets = ()
        if result.suboffsets:
            self.assertGreater(ndim, 0)

            suboffset0 = 0
            for n in range(1, ndim):
                if shape[n] == 0:
                    break
                if strides[n] <= 0:
                    suboffset0 += -strides[n] * (shape[n]-1)

            suboffsets = [suboffset0] + [-1 for v in range(ndim-1)]

            # Not correct if slicing has occurred in the first dimension.
            stride0 = self.sizeof_void_p
            if strides[0] < 0:
                stride0 = -stride0
            strides = [stride0] + list(strides[1:])

        self.assertIs(result.obj, obj)
        self.assertEqual(result.nbytes, expected_len)
        self.assertEqual(result.itemsize, itemsize)
        self.assertEqual(result.format, fmt)
        self.assertIs(result.readonly, readonly)
        self.assertEqual(result.ndim, ndim)
        self.assertEqual(result.shape, tuple(shape))
        if not (sliced and suboffsets):
            self.assertEqual(result.strides, tuple(strides))
        self.assertEqual(result.suboffsets, tuple(suboffsets))

        if isinstance(result, ndarray) or is_memoryview_format(fmt):
            rep = result.tolist() if fmt else result.tobytes()
            self.assertEqual(rep, lst)

        if not fmt: # array has been cast to unsigned bytes,
            return  # the remaining tests won't work.

        # PyBuffer_GetPointer() is the definition how to access an item.
        # If PyBuffer_GetPointer(indices) is correct for all possible
        # combinations of indices, the buffer is correct.
        #
        # Also test tobytes() against the flattened 'lst', with all items
        # packed to bytes.
        if not cast: # casts chop up 'lst' in different ways
            b = bytearray()
            buf_err = None
            for ind in indices(shape):
                try:
                    item1 = get_pointer(result, ind)
                    item2 = get_item(lst, ind)
                    if isinstance(item2, tuple):
                        x = struct.pack(fmt, *item2)
                    else:
                        x = struct.pack(fmt, item2)
                    b.extend(x)
                except BufferError:
                    buf_err = True # re-exporter does not provide full buffer
                    break
                self.assertEqual(item1, item2)

            if not buf_err:
                # test tobytes()
                self.assertEqual(result.tobytes(), b)

                # test hex()
                m = memoryview(result)
                h = "".join("%02x" % c for c in b)
                self.assertEqual(m.hex(), h)

                # lst := expected multi-dimensional logical representation
                # flatten(lst) := elements in C-order
                ff = fmt if fmt else 'B'
                flattened = flatten(lst)

                # Rules for 'A': if the array is already contiguous, return
                # the array unaltered. Otherwise, return a contiguous 'C'
                # representation.
                for order in ['C', 'F', 'A']:
                    expected = result
                    if order == 'F':
                        if not is_contiguous(result, 'A') or \
                           is_contiguous(result, 'C'):
                            # For constructing the ndarray, convert the
                            # flattened logical representation to Fortran order.
                            trans = transpose(flattened, shape)
                            expected = ndarray(trans, shape=shape, format=ff,
                                               flags=ND_FORTRAN)
                    else: # 'C', 'A'
                        if not is_contiguous(result, 'A') or \
                           is_contiguous(result, 'F') and order == 'C':
                            # The flattened list is already in C-order.
                            expected = ndarray(flattened, shape=shape, format=ff)

                    contig = get_contiguous(result, PyBUF_READ, order)
                    self.assertEqual(contig.tobytes(), b)
                    self.assertTrue(cmp_contig(contig, expected))

                    if ndim == 0:
                        continue

                    nmemb = len(flattened)
                    ro = 0 if readonly else ND_WRITABLE

                    ### See comment in test_py_buffer_to_contiguous for an
                    ### explanation why these tests are valid.

                    # 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)
                               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))

                    # 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)
                               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)
                    self.assertEqual(memoryview(y), memoryview(result))

                    # 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)
                               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)
                    self.assertEqual(memoryview(y), memoryview(result))

        if is_memoryview_format(fmt):
            try:
                m = memoryview(result)
            except BufferError: # re-exporter does not provide full information
                return
            ex = result.obj if isinstance(result, memoryview) else result

            def check_memoryview(m, expected_readonly=readonly):
                self.assertIs(m.obj, ex)
                self.assertEqual(m.nbytes, expected_len)
                self.assertEqual(m.itemsize, itemsize)
                self.assertEqual(m.format, fmt)
                self.assertEqual(m.readonly, expected_readonly)
                self.assertEqual(m.ndim, ndim)
                self.assertEqual(m.shape, tuple(shape))
                if not (sliced and suboffsets):
                    self.assertEqual(m.strides, tuple(strides))
                self.assertEqual(m.suboffsets, tuple(suboffsets))

                n = 1 if ndim == 0 else len(lst)
                self.assertEqual(len(m), n)

                rep = result.tolist() if fmt else result.tobytes()
                self.assertEqual(rep, lst)
                self.assertEqual(m, result)

            check_memoryview(m)
            with m.toreadonly() as mm:
                check_memoryview(mm, expected_readonly=True)
            m.tobytes()  # Releasing mm didn't release m

    def verify_getbuf(self, orig_ex, ex, req, sliced=False):
        def simple_fmt(ex):
            return ex.format == '' or ex.format == 'B'
        def match(req, flag):
            return ((req&flag) == flag)

        if (# writable request to read-only exporter
            (ex.readonly and match(req, PyBUF_WRITABLE)) or
            # cannot match explicit contiguity request
            (match(req, PyBUF_C_CONTIGUOUS) and not ex.c_contiguous) or
            (match(req, PyBUF_F_CONTIGUOUS) and not ex.f_contiguous) or
            (match(req, PyBUF_ANY_CONTIGUOUS) and not ex.contiguous) or
            # buffer needs suboffsets
            (not match(req, PyBUF_INDIRECT) and ex.suboffsets) or
            # buffer without strides must be C-contiguous
            (not match(req, PyBUF_STRIDES) and not ex.c_contiguous) or
            # PyBUF_SIMPLE|PyBUF_FORMAT and PyBUF_WRITABLE|PyBUF_FORMAT
            (not match(req, PyBUF_ND) and match(req, PyBUF_FORMAT))):

            self.assertRaises(BufferError, ndarray, ex, getbuf=req)
            return

        if isinstance(ex, ndarray) or is_memoryview_format(ex.format):
            lst = ex.tolist()
        else:
            nd = ndarray(ex, getbuf=PyBUF_FULL_RO)
            lst = nd.tolist()

        # The consumer may have requested default values or a NULL format.
        ro = False if match(req, PyBUF_WRITABLE) else ex.readonly
        fmt = ex.format
        itemsize = ex.itemsize
        ndim = ex.ndim
        if not match(req, PyBUF_FORMAT):
            # itemsize refers to the original itemsize before the cast.
            # The equality product(shape) * itemsize = len still holds.
            # The equality calcsize(format) = itemsize does _not_ hold.
            fmt = ''
            lst = orig_ex.tobytes() # Issue 12834
        if not match(req, PyBUF_ND):
            ndim = 1
        shape = orig_ex.shape if match(req, PyBUF_ND) else ()
        strides = orig_ex.strides if match(req, PyBUF_STRIDES) else ()

        nd = ndarray(ex, getbuf=req)
        self.verify(nd, obj=ex,
                    itemsize=itemsize, fmt=fmt, readonly=ro,
                    ndim=ndim, shape=shape, strides=strides,
                    lst=lst, sliced=sliced)

    def test_ndarray_getbuf(self):
        requests = (
            # distinct flags
            PyBUF_INDIRECT, PyBUF_STRIDES, PyBUF_ND, PyBUF_SIMPLE,
            PyBUF_C_CONTIGUOUS, PyBUF_F_CONTIGUOUS, PyBUF_ANY_CONTIGUOUS,
            # compound requests
            PyBUF_FULL, PyBUF_FULL_RO,
            PyBUF_RECORDS, PyBUF_RECORDS_RO,
            PyBUF_STRIDED, PyBUF_STRIDED_RO,
            PyBUF_CONTIG, PyBUF_CONTIG_RO,
        )
        # items and format
        items_fmt = (
            ([True if x % 2 else False for x in range(12)], '?'),
            ([1,2,3,4,5,6,7,8,9,10,11,12], 'b'),
            ([1,2,3,4,5,6,7,8,9,10,11,12], 'B'),
            ([(2**31-x) if x % 2 else (-2**31+x) for x in range(12)], 'l')
        )
        # shape, strides, offset
        structure = (
            ([], [], 0),
            ([1,3,1], [], 0),
            ([12], [], 0),
            ([12], [-1], 11),
            ([6], [2], 0),
            ([6], [-2], 11),
            ([3, 4], [], 0),
            ([3, 4], [-4, -1], 11),
            ([2, 2], [4, 1], 4),
            ([2, 2], [-4, -1], 8)
        )
        # ndarray creation flags
        ndflags = (
            0, ND_WRITABLE, ND_FORTRAN, ND_FORTRAN|ND_WRITABLE,
            ND_PIL, ND_PIL|ND_WRITABLE
        )
        # flags that can actually be used as flags
        real_flags = (0, PyBUF_WRITABLE, PyBUF_FORMAT,
                      PyBUF_WRITABLE|PyBUF_FORMAT)

        for items, fmt in items_fmt:
            itemsize = struct.calcsize(fmt)
            for shape, strides, offset in structure:
                strides = [v * itemsize for v in strides]
                offset *= itemsize
                for flags in ndflags:

                    if strides and (flags&ND_FORTRAN):
                        continue
                    if not shape and (flags&ND_PIL):
                        continue

                    _items = items if shape else items[0]
                    ex1 = ndarray(_items, format=fmt, flags=flags,
                                  shape=shape, strides=strides, offset=offset)
                    ex2 = ex1[::-2] if shape else None

                    m1 = memoryview(ex1)
                    if ex2:
                        m2 = memoryview(ex2)
                    if ex1.ndim == 0 or (ex1.ndim == 1 and shape and strides):
                        self.assertEqual(m1, ex1)
                    if ex2 and ex2.ndim == 1 and shape and strides:
                        self.assertEqual(m2, ex2)

                    for req in requests:
                        for bits in real_flags:
                            self.verify_getbuf(ex1, ex1, req|bits)
                            self.verify_getbuf(ex1, m1, req|bits)
                            if ex2:
                                self.verify_getbuf(ex2, ex2, req|bits,
                                                   sliced=True)
                                self.verify_getbuf(ex2, m2, req|bits,
                                                   sliced=True)

        items = [1,2,3,4,5,6,7,8,9,10,11,12]

        # ND_GETBUF_FAIL
        ex = ndarray(items, shape=[12], flags=ND_GETBUF_FAIL)
        self.assertRaises(BufferError, ndarray, ex)

        # Request complex structure from a simple exporter. In this
        # particular case the test object is not PEP-3118 compliant.
        base = ndarray([9], [1])
        ex = ndarray(base, getbuf=PyBUF_SIMPLE)
        self.assertRaises(BufferError, ndarray, ex, getbuf=PyBUF_WRITABLE)
        self.assertRaises(BufferError, ndarray, ex, getbuf=PyBUF_ND)
        self.assertRaises(BufferError, ndarray, ex, getbuf=PyBUF_STRIDES)
        self.assertRaises(BufferError, ndarray, ex, getbuf=PyBUF_C_CONTIGUOUS)
        self.assertRaises(BufferError, ndarray, ex, getbuf=PyBUF_F_CONTIGUOUS)
        self.assertRaises(BufferError, ndarray, ex, getbuf=PyBUF_ANY_CONTIGUOUS)
        nd = ndarray(ex, getbuf=PyBUF_SIMPLE)

        # Issue #22445: New precise contiguity definition.
        for shape in [1,12,1], [7,0,7]:
            for order in 0, ND_FORTRAN:
                ex = ndarray(items, shape=shape, flags=order|ND_WRITABLE)
                self.assertTrue(is_contiguous(ex, 'F'))
                self.assertTrue(is_contiguous(ex, 'C'))

                for flags in requests:
                    nd = ndarray(ex, getbuf=flags)
                    self.assertTrue(is_contiguous(nd, 'F'))
                    self.assertTrue(is_contiguous(nd, 'C'))

    def test_ndarray_exceptions(self):
        nd = ndarray([9], [1])
        ndm = ndarray([9], [1], flags=ND_VAREXPORT)

        # Initialization of a new ndarray or mutation of an existing array.
        for c in (ndarray, nd.push, ndm.push):
            # Invalid types.
            self.assertRaises(TypeError, c, {1,2,3})
            self.assertRaises(TypeError, c, [1,2,'3'])
            self.assertRaises(TypeError, c, [1,2,(3,4)])
            self.assertRaises(TypeError, c, [1,2,3], shape={3})
            self.assertRaises(TypeError, c, [1,2,3], shape=[3], strides={1})
            self.assertRaises(TypeError, c, [1,2,3], shape=[3], offset=[])
            self.assertRaises(TypeError, c, [1], shape=[1], format={})
            self.assertRaises(TypeError, c, [1], shape=[1], flags={})
            self.assertRaises(TypeError, c, [1], shape=[1], getbuf={})

            # ND_FORTRAN flag is only valid without strides.
            self.assertRaises(TypeError, c, [1], shape=[1], strides=[1],
                              flags=ND_FORTRAN)

            # ND_PIL flag is only valid with ndim > 0.
            self.assertRaises(TypeError, c, [1], shape=[], flags=ND_PIL)

            # Invalid items.
            self.assertRaises(ValueError, c, [], shape=[1])
            self.assertRaises(ValueError, c, ['XXX'], shape=[1], format="L")
            # Invalid combination of items and format.
            self.assertRaises(struct.error, c, [1000], shape=[1], format="B")
            self.assertRaises(ValueError, c, [1,(2,3)], shape=[2], format="B")
            self.assertRaises(ValueError, c, [1,2,3], shape=[3], format="QL")

            # Invalid ndim.
            n = ND_MAX_NDIM+1
            self.assertRaises(ValueError, c, [1]*n, shape=[1]*n)

            # Invalid shape.
            self.assertRaises(ValueError, c, [1], shape=[-1])
            self.assertRaises(ValueError, c, [1,2,3], shape=['3'])
            self.assertRaises(OverflowError, c, [1], shape=[2**128])
            # prod(shape) * itemsize != len(items)
            self.assertRaises(ValueError, c, [1,2,3,4,5], shape=[2,2], offset=3)

            # Invalid strides.
            self.assertRaises(ValueError, c, [1,2,3], shape=[3], strides=['1'])
            self.assertRaises(OverflowError, c, [1], shape=[1],
                              strides=[2**128])

            # Invalid combination of strides and shape.
            self.assertRaises(ValueError, c, [1,2], shape=[2,1], strides=[1])
            # Invalid combination of strides and format.
            self.assertRaises(ValueError, c, [1,2,3,4], shape=[2], strides=[3],
                              format="L")

            # Invalid offset.
            self.assertRaises(ValueError, c, [1,2,3], shape=[3], offset=4)
            self.assertRaises(ValueError, c, [1,2,3], shape=[1], offset=3,
                              format="L")

            # Invalid format.
            self.assertRaises(ValueError, c, [1,2,3], shape=[3], format="")
            self.assertRaises(struct.error, c, [(1,2,3)], shape=[1],
                              format="@#$")

            # Striding out of the memory bounds.
            items = [1,2,3,4,5,6,7,8,9,10]
            self.assertRaises(ValueError, c, items, shape=[2,3],
                              strides=[-3, -2], offset=5)

            # Constructing consumer: format argument invalid.
            self.assertRaises(TypeError, c, bytearray(), format="Q")

            # Constructing original base object: getbuf argument invalid.
            self.assertRaises(TypeError, c, [1], shape=[1], getbuf=PyBUF_FULL)

            # Shape argument is mandatory for original base objects.
            self.assertRaises(TypeError, c, [1])


        # PyBUF_WRITABLE request to read-only provider.
        self.assertRaises(BufferError, ndarray, b'123', getbuf=PyBUF_WRITABLE)

        # ND_VAREXPORT can only be specified during construction.
        nd = ndarray([9], [1], flags=ND_VAREXPORT)
        self.assertRaises(ValueError, nd.push, [1], [1], flags=ND_VAREXPORT)

        # Invalid operation for consumers: push/pop
        nd = ndarray(b'123')
        self.assertRaises(BufferError, nd.push, [1], [1])
        self.assertRaises(BufferError, nd.pop)

        # ND_VAREXPORT not set: push/pop fail with exported buffers
        nd = ndarray([9], [1])
        nd.push([1], [1])
        m = memoryview(nd)
        self.assertRaises(BufferError, nd.push, [1], [1])
        self.assertRaises(BufferError, nd.pop)
        m.release()
        nd.pop()

        # Single remaining buffer: pop fails
        self.assertRaises(BufferError, nd.pop)
        del nd

        # get_pointer()
        self.assertRaises(TypeError, get_pointer, {}, [1,2,3])
        self.assertRaises(TypeError, get_pointer, b'123', {})

        nd = ndarray(list(range(100)), shape=[1]*100)
        self.assertRaises(ValueError, get_pointer, nd, [5])

        nd = ndarray(list(range(12)), shape=[3,4])
        self.assertRaises(ValueError, get_pointer, nd, [2,3,4])
        self.assertRaises(ValueError, get_pointer, nd, [3,3])
        self.assertRaises(ValueError, get_pointer, nd, [-3,3])
        self.assertRaises(OverflowError, get_pointer, nd, [1<<64,3])

        # tolist() needs format
        ex = ndarray([1,2,3], shape=[3], format='L')
        nd = ndarray(ex, getbuf=PyBUF_SIMPLE)
        self.assertRaises(ValueError, nd.tolist)

        # memoryview_from_buffer()
        ex1 = ndarray([1,2,3], shape=[3], format='L')
        ex2 = ndarray(ex1)
        nd = ndarray(ex2)
        self.assertRaises(TypeError, nd.memoryview_from_buffer)

        nd = ndarray([(1,)*200], shape=[1], format='L'*200)
        self.assertRaises(TypeError, nd.memoryview_from_buffer)

        n = ND_MAX_NDIM
        nd = ndarray(list(range(n)), shape=[1]*n)
        self.assertRaises(ValueError, nd.memoryview_from_buffer)

        # get_contiguous()
        nd = ndarray([1], shape=[1])
        self.assertRaises(TypeError, get_contiguous, 1, 2, 3, 4, 5)
        self.assertRaises(TypeError, get_contiguous, nd, "xyz", 'C')
        self.assertRaises(OverflowError, get_contiguous, nd, 2**64, 'C')
        self.assertRaises(TypeError, get_contiguous, nd, PyBUF_READ, 961)
        self.assertRaises(UnicodeEncodeError, get_contiguous, nd, PyBUF_READ,
                          '\u2007')
        self.assertRaises(ValueError, get_contiguous, nd, PyBUF_READ, 'Z')
        self.assertRaises(ValueError, get_contiguous, nd, 255, 'A')

        # cmp_contig()
        nd = ndarray([1], shape=[1])
        self.assertRaises(TypeError, cmp_contig, 1, 2, 3, 4, 5)
        self.assertRaises(TypeError, cmp_contig, {}, nd)
        self.assertRaises(TypeError, cmp_contig, nd, {})

        # is_contiguous()
        nd = ndarray([1], shape=[1])
        self.assertRaises(TypeError, is_contiguous, 1, 2, 3, 4, 5)
        self.assertRaises(TypeError, is_contiguous, {}, 'A')
        self.assertRaises(TypeError, is_contiguous, nd, 201)

    def test_ndarray_linked_list(self):
        for perm in permutations(range(5)):
            m = [0]*5
            nd = ndarray([1,2,3], shape=[3], flags=ND_VAREXPORT)
            m[0] = memoryview(nd)

            for i in range(1, 5):
                nd.push([1,2,3], shape=[3])
                m[i] = memoryview(nd)

            for i in range(5):
                m[perm[i]].release()

            self.assertRaises(BufferError, nd.pop)
            del nd

    def test_ndarray_format_scalar(self):
        # ndim = 0: scalar
        for fmt, scalar, _ in iter_format(0):
            itemsize = struct.calcsize(fmt)
            nd = ndarray(scalar, shape=(), format=fmt)
            self.verify(nd, obj=None,
                        itemsize=itemsize, fmt=fmt, readonly=True,
                        ndim=0, shape=(), strides=(),
                        lst=scalar)

    def test_ndarray_format_shape(self):
        # ndim = 1, shape = [n]
        nitems =  randrange(1, 10)
        for fmt, items, _ in iter_format(nitems):
            itemsize = struct.calcsize(fmt)
            for flags in (0, ND_PIL):
                nd = ndarray(items, shape=[nitems], format=fmt, flags=flags)
                self.verify(nd, obj=None,
                            itemsize=itemsize, fmt=fmt, readonly=True,
                            ndim=1, shape=(nitems,), strides=(itemsize,),
                            lst=items)

    def test_ndarray_format_strides(self):
        # ndim = 1, strides
        nitems = randrange(1, 30)
        for fmt, items, _ in iter_format(nitems):
            itemsize = struct.calcsize(fmt)
            for step in range(-5, 5):
                if step == 0:
                    continue

                shape = [len(items[::step])]
                strides = [step*itemsize]
                offset = itemsize*(nitems-1) if step < 0 else 0

                for flags in (0, ND_PIL):
                    nd = ndarray(items, shape=shape, strides=strides,
                                 format=fmt, offset=offset, flags=flags)
                    self.verify(nd, obj=None,
                                itemsize=itemsize, fmt=fmt, readonly=True,
                                ndim=1, shape=shape, strides=strides,
                                lst=items[::step])

    def test_ndarray_fortran(self):
        items = [1,2,3,4,5,6,7,8,9,10,11,12]
        ex = ndarray(items, shape=(3, 4), strides=(1, 3))
        nd = ndarray(ex, getbuf=PyBUF_F_CONTIGUOUS|PyBUF_FORMAT)
        self.assertEqual(nd.tolist(), farray(items, (3, 4)))

    def test_ndarray_multidim(self):
        for ndim in range(5):
            shape_t = [randrange(2, 10) for _ in range(ndim)]
            nitems = prod(shape_t)
            for shape in permutations(shape_t):

                fmt, items, _ = randitems(nitems)
                itemsize = struct.calcsize(fmt)

                for flags in (0, ND_PIL):
                    if ndim == 0 and flags == ND_PIL:
                        continue

                    # C array
                    nd = ndarray(items, shape=shape, format=fmt, flags=flags)

                    strides = strides_from_shape(ndim, shape, itemsize, 'C')
                    lst = carray(items, shape)
                    self.verify(nd, obj=None,
                                itemsize=itemsize, fmt=fmt, readonly=True,
                                ndim=ndim, shape=shape, strides=strides,
                                lst=lst)

                    if is_memoryview_format(fmt):
                        # memoryview: reconstruct strides
                        ex = ndarray(items, shape=shape, format=fmt)
                        nd = ndarray(ex, getbuf=PyBUF_CONTIG_RO|PyBUF_FORMAT)
                        self.assertTrue(nd.strides == ())
                        mv = nd.memoryview_from_buffer()
                        self.verify(mv, obj=None,
                                    itemsize=itemsize, fmt=fmt, readonly=True,
                                    ndim=ndim, shape=shape, strides=strides,
                                    lst=lst)

                    # Fortran array
                    nd = ndarray(items, shape=shape, format=fmt,
                                 flags=flags|ND_FORTRAN)

                    strides = strides_from_shape(ndim, shape, itemsize, 'F')
                    lst = farray(items, shape)
                    self.verify(nd, obj=None,
                                itemsize=itemsize, fmt=fmt, readonly=True,
                                ndim=ndim, shape=shape, strides=strides,
                                lst=lst)

    def test_ndarray_index_invalid(self):
        # not writable
        nd = ndarray([1], shape=[1])
        self.assertRaises(TypeError, nd.__setitem__, 1, 8)
        mv = memoryview(nd)
        self.assertEqual(mv, nd)
        self.assertRaises(TypeError, mv.__setitem__, 1, 8)

        # cannot be deleted
        nd = ndarray([1], shape=[1], flags=ND_WRITABLE)
        self.assertRaises(TypeError, nd.__delitem__, 1)
        mv = memoryview(nd)
        self.assertEqual(mv, nd)
        self.assertRaises(TypeError, mv.__delitem__, 1)

        # overflow
        nd = ndarray([1], shape=[1], flags=ND_WRITABLE)
        self.assertRaises(OverflowError, nd.__getitem__, 1<<64)
        self.assertRaises(OverflowError, nd.__setitem__, 1<<64, 8)
        mv = memoryview(nd)
        self.assertEqual(mv, nd)
        self.assertRaises(IndexError, mv.__getitem__, 1<<64)
        self.assertRaises(IndexError, mv.__setitem__, 1<<64, 8)

        # format
        items = [1,2,3,4,5,6,7,8]
        nd = ndarray(items, shape=[len(items)], format="B", flags=ND_WRITABLE)
        self.assertRaises(struct.error, nd.__setitem__, 2, 300)
        self.assertRaises(ValueError, nd.__setitem__, 1, (100, 200))
        mv = memoryview(nd)
        self.assertEqual(mv, nd)
        self.assertRaises(ValueError, mv.__setitem__, 2, 300)
        self.assertRaises(TypeError, mv.__setitem__, 1, (100, 200))

        items = [(1,2), (3,4), (5,6)]
        nd = ndarray(items, shape=[len(items)], format="LQ", flags=ND_WRITABLE)
        self.assertRaises(ValueError, nd.__setitem__, 2, 300)
        self.assertRaises(struct.error, nd.__setitem__, 1, (b'\x001', 200))

    def test_ndarray_index_scalar(self):
        # scalar
        nd = ndarray(1, shape=(), flags=ND_WRITABLE)
        mv = memoryview(nd)
        self.assertEqual(mv, nd)

        x = nd[()];  self.assertEqual(x, 1)
        x = nd[...]; self.assertEqual(x.tolist(), nd.tolist())

        x = mv[()];  self.assertEqual(x, 1)
        x = mv[...]; self.assertEqual(x.tolist(), nd.tolist())

        self.assertRaises(TypeError, nd.__getitem__, 0)
        self.assertRaises(TypeError, mv.__getitem__, 0)
        self.assertRaises(TypeError, nd.__setitem__, 0, 8)
        self.assertRaises(TypeError, mv.__setitem__, 0, 8)

        self.assertEqual(nd.tolist(), 1)
        self.assertEqual(mv.tolist(), 1)

        nd[()] = 9; self.assertEqual(nd.tolist(), 9)
        mv[()] = 9; self.assertEqual(mv.tolist(), 9)

        nd[...] = 5; self.assertEqual(nd.tolist(), 5)
        mv[...] = 5; self.assertEqual(mv.tolist(), 5)

    def test_ndarray_index_null_strides(self):
        ex = ndarray(list(range(2*4)), shape=[2, 4], flags=ND_WRITABLE)
        nd = ndarray(ex, getbuf=PyBUF_CONTIG)

        # Sub-views are only possible for full exporters.
        self.assertRaises(BufferError, nd.__getitem__, 1)
        # Same for slices.
        self.assertRaises(BufferError, nd.__getitem__, slice(3,5,1))

    def test_ndarray_index_getitem_single(self):
        # getitem
        for fmt, items, _ in iter_format(5):
            nd = ndarray(items, shape=[5], format=fmt)
            for i in range(-5, 5):
                self.assertEqual(nd[i], items[i])

            self.assertRaises(IndexError, nd.__getitem__, -6)
            self.assertRaises(IndexError, nd.__getitem__, 5)

            if is_memoryview_format(fmt):
                mv = memoryview(nd)
                self.assertEqual(mv, nd)
                for i in range(-5, 5):
                    self.assertEqual(mv[i], items[i])

                self.assertRaises(IndexError, mv.__getitem__, -6)
                self.assertRaises(IndexError, mv.__getitem__, 5)

        # getitem with null strides
        for fmt, items, _ in iter_format(5):
            ex = ndarray(items, shape=[5], flags=ND_WRITABLE, format=fmt)
            nd = ndarray(ex, getbuf=PyBUF_CONTIG|PyBUF_FORMAT)

            for i in range(-5, 5):
                self.assertEqual(nd[i], items[i])

            if is_memoryview_format(fmt):
                mv = nd.memoryview_from_buffer()
                self.assertIs(mv.__eq__(nd), NotImplemented)
                for i in range(-5, 5):
                    self.assertEqual(mv[i], items[i])

        # getitem with null format
        items = [1,2,3,4,5]
        ex = ndarray(items, shape=[5])
        nd = ndarray(ex, getbuf=PyBUF_CONTIG_RO)
        for i in range(-5, 5):
            self.assertEqual(nd[i], items[i])

        # getitem with null shape/strides/format
        items = [1,2,3,4,5]
        ex = ndarray(items, shape=[5])
        nd = ndarray(ex, getbuf=PyBUF_SIMPLE)

        for i in range(-5, 5):
            self.assertEqual(nd[i], items[i])

    def test_ndarray_index_setitem_single(self):
        # assign single value
        for fmt, items, single_item in iter_format(5):
            nd = ndarray(items, shape=[5], format=fmt, flags=ND_WRITABLE)
            for i in range(5):
                items[i] = single_item
                nd[i] = single_item
            self.assertEqual(nd.tolist(), items)

            self.assertRaises(IndexError, nd.__setitem__, -6, single_item)
            self.assertRaises(IndexError, nd.__setitem__, 5, single_item)

            if not is_memoryview_format(fmt):
                continue

            nd = ndarray(items, shape=[5], format=fmt, flags=ND_WRITABLE)
            mv = memoryview(nd)
            self.assertEqual(mv, nd)
            for i in range(5):
                items[i] = single_item
                mv[i] = single_item
            self.assertEqual(mv.tolist(), items)

            self.assertRaises(IndexError, mv.__setitem__, -6, single_item)
            self.assertRaises(IndexError, mv.__setitem__, 5, single_item)


        # assign single value: lobject = robject
        for fmt, items, single_item in iter_format(5):
            nd = ndarray(items, shape=[5], format=fmt, flags=ND_WRITABLE)
            for i in range(-5, 4):
                items[i] = items[i+1]
                nd[i] = nd[i+1]
            self.assertEqual(nd.tolist(), items)

            if not is_memoryview_format(fmt):
                continue

            nd = ndarray(items, shape=[5], format=fmt, flags=ND_WRITABLE)
            mv = memoryview(nd)
            self.assertEqual(mv, nd)
            for i in range(-5, 4):
                items[i] = items[i+1]
                mv[i] = mv[i+1]
            self.assertEqual(mv.tolist(), items)

    def test_ndarray_index_getitem_multidim(self):
        shape_t = (2, 3, 5)
        nitems = prod(shape_t)
        for shape in permutations(shape_t):

            fmt, items, _ = randitems(nitems)

            for flags in (0, ND_PIL):
                # C array
                nd = ndarray(items, shape=shape, format=fmt, flags=flags)
                lst = carray(items, shape)

                for i in range(-shape[0], shape[0]):
                    self.assertEqual(lst[i], nd[i].tolist())
                    for j in range(-shape[1], shape[1]):
                        self.assertEqual(lst[i][j], nd[i][j].tolist())
                        for k in range(-shape[2], shape[2]):
                            self.assertEqual(lst[i][j][k], nd[i][j][k])

                # Fortran array
                nd = ndarray(items, shape=shape, format=fmt,
                             flags=flags|ND_FORTRAN)
                lst = farray(items, shape)

                for i in range(-shape[0], shape[0]):
                    self.assertEqual(lst[i], nd[i].tolist())
                    for j in range(-shape[1], shape[1]):
                        self.assertEqual(lst[i][j], nd[i][j].tolist())
                        for k in range(shape[2], shape[2]):
                            self.assertEqual(lst[i][j][k], nd[i][j][k])

    def test_ndarray_sequence(self):
        nd = ndarray(1, shape=())
        self.assertRaises(TypeError, eval, "1 in nd", locals())
        mv = memoryview(nd)
        self.assertEqual(mv, nd)
        self.assertRaises(TypeError, eval, "1 in mv", locals())

        for fmt, items, _ in iter_format(5):
            nd = ndarray(items, shape=[5], format=fmt)
            for i, v in enumerate(nd):
                self.assertEqual(v, items[i])
                self.assertTrue(v in nd)

            if is_memoryview_format(fmt):
                mv = memoryview(nd)
                for i, v in enumerate(mv):
                    self.assertEqual(v, items[i])
                    self.assertTrue(v in mv)

    def test_ndarray_slice_invalid(self):
        items = [1,2,3,4,5,6,7,8]

        # rvalue is not an exporter
        xl = ndarray(items, shape=[8], flags=ND_WRITABLE)
        ml = memoryview(xl)
        self.assertRaises(TypeError, xl.__setitem__, slice(0,8,1), items)
        self.assertRaises(TypeError, ml.__setitem__, slice(0,8,1), items)

        # rvalue is not a full exporter
        xl = ndarray(items, shape=[8], flags=ND_WRITABLE)
        ex = ndarray(items, shape=[8], flags=ND_WRITABLE)
        xr = ndarray(ex, getbuf=PyBUF_ND)
        self.assertRaises(BufferError, xl.__setitem__, slice(0,8,1), xr)

        # zero step
        nd = ndarray(items, shape=[8], format="L", flags=ND_WRITABLE)
        mv = memoryview(nd)
        self.assertRaises(ValueError, nd.__getitem__, slice(0,1,0))
        self.assertRaises(ValueError, mv.__getitem__, slice(0,1,0))

        nd = ndarray(items, shape=[2,4], format="L", flags=ND_WRITABLE)
        mv = memoryview(nd)

        self.assertRaises(ValueError, nd.__getitem__,
                          (slice(0,1,1), slice(0,1,0)))
        self.assertRaises(ValueError, nd.__getitem__,
                          (slice(0,1,0), slice(0,1,1)))
        self.assertRaises(TypeError, nd.__getitem__, "@%$")
        self.assertRaises(TypeError, nd.__getitem__, ("@%$", slice(0,1,1)))
        self.assertRaises(TypeError, nd.__getitem__, (slice(0,1,1), {}))

        # memoryview: not implemented
        self.assertRaises(NotImplementedError, mv.__getitem__,
                          (slice(0,1,1), slice(0,1,0)))
        self.assertRaises(TypeError, mv.__getitem__, "@%$")

        # differing format
        xl = ndarray(items, shape=[8], format="B", flags=ND_WRITABLE)
        xr = ndarray(items, shape=[8], format="b")
        ml = memoryview(xl)
        mr = memoryview(xr)
        self.assertRaises(ValueError, xl.__setitem__, slice(0,1,1), xr[7:8])
        self.assertEqual(xl.tolist(), items)
        self.assertRaises(ValueError, ml.__setitem__, slice(0,1,1), mr[7:8])
        self.assertEqual(ml.tolist(), items)

        # differing itemsize
        xl = ndarray(items, shape=[8], format="B", flags=ND_WRITABLE)
        yr = ndarray(items, shape=[8], format="L")
        ml = memoryview(xl)
        mr = memoryview(xr)
        self.assertRaises(ValueError, xl.__setitem__, slice(0,1,1), xr[7:8])
        self.assertEqual(xl.tolist(), items)
        self.assertRaises(ValueError, ml.__setitem__, slice(0,1,1), mr[7:8])
        self.assertEqual(ml.tolist(), items)

        # differing ndim
        xl = ndarray(items, shape=[2, 4], format="b", flags=ND_WRITABLE)
        xr = ndarray(items, shape=[8], format="b")
        ml = memoryview(xl)
        mr = memoryview(xr)
        self.assertRaises(ValueError, xl.__setitem__, slice(0,1,1), xr[7:8])
        self.assertEqual(xl.tolist(), [[1,2,3,4], [5,6,7,8]])
        self.assertRaises(NotImplementedError, ml.__setitem__, slice(0,1,1),
                          mr[7:8])

        # differing shape
        xl = ndarray(items, shape=[8], format="b", flags=ND_WRITABLE)
        xr = ndarray(items, shape=[8], format="b")
        ml = memoryview(xl)
        mr = memoryview(xr)
        self.assertRaises(ValueError, xl.__setitem__, slice(0,2,1), xr[7:8])
        self.assertEqual(xl.tolist(), items)
        self.assertRaises(ValueError, ml.__setitem__, slice(0,2,1), mr[7:8])
        self.assertEqual(ml.tolist(), items)

        # _testbuffer.c module functions
        self.assertRaises(TypeError, slice_indices, slice(0,1,2), {})
        self.assertRaises(TypeError, slice_indices, "###########", 1)
        self.assertRaises(ValueError, slice_indices, slice(0,1,0), 4)

        x = ndarray(items, shape=[8], format="b", flags=ND_PIL)
        self.assertRaises(TypeError, x.add_suboffsets)

        ex = ndarray(items, shape=[8], format="B")
        x = ndarray(ex, getbuf=PyBUF_SIMPLE)
        self.assertRaises(TypeError, x.add_suboffsets)

    def test_ndarray_slice_zero_shape(self):
        items = [1,2,3,4,5,6,7,8,9,10,11,12]

        x = ndarray(items, shape=[12], format="L", flags=ND_WRITABLE)
        y = ndarray(items, shape=[12], format="L")
        x[4:4] = y[9:9]
        self.assertEqual(x.tolist(), items)

        ml = memoryview(x)
        mr = memoryview(y)
        self.assertEqual(ml, x)
        self.assertEqual(ml, y)
        ml[4:4] = mr[9:9]
        self.assertEqual(ml.tolist(), items)

        x = ndarray(items, shape=[3, 4], format="L", flags=ND_WRITABLE)
        y = ndarray(items, shape=[4, 3], format="L")
        x[1:2, 2:2] = y[1:2, 3:3]
        self.assertEqual(x.tolist(), carray(items, [3, 4]))

    def test_ndarray_slice_multidim(self):
        shape_t = (2, 3, 5)
        ndim = len(shape_t)
        nitems = prod(shape_t)
        for shape in permutations(shape_t):

            fmt, items, _ = randitems(nitems)
            itemsize = struct.calcsize(fmt)

            for flags in (0, ND_PIL):
                nd = ndarray(items, shape=shape, format=fmt, flags=flags)
                lst = carray(items, shape)

                for slices in rslices_ndim(ndim, shape):

                    listerr = None
                    try:
                        sliced = multislice(lst, slices)
                    except Exception as e:
                        listerr = e.__class__

                    nderr = None
                    try:
                        ndsliced = nd[slices]
                    except Exception as e:
                        nderr = e.__class__

                    if nderr or listerr:
                        self.assertIs(nderr, listerr)
                    else:
                        self.assertEqual(ndsliced.tolist(), sliced)

    def test_ndarray_slice_redundant_suboffsets(self):
        shape_t = (2, 3, 5, 2)
        ndim = len(shape_t)
        nitems = prod(shape_t)
        for shape in permutations(shape_t):

            fmt, items, _ = randitems(nitems)
            itemsize = struct.calcsize(fmt)

            nd = ndarray(items, shape=shape, format=fmt)
            nd.add_suboffsets()
            ex = ndarray(items, shape=shape, format=fmt)
            ex.add_suboffsets()
            mv = memoryview(ex)
            lst = carray(items, shape)

            for slices in rslices_ndim(ndim, shape):

                listerr = None
                try:
                    sliced = multislice(lst, slices)
                except Exception as e:
                    listerr = e.__class__

                nderr = None
                try:
                    ndsliced = nd[slices]
                except Exception as e:
                    nderr = e.__class__

                if nderr or listerr:
                    self.assertIs(nderr, listerr)
                else:
                    self.assertEqual(ndsliced.tolist(), sliced)

    def test_ndarray_slice_assign_single(self):
        for fmt, items, _ in iter_format(5):
            for lslice in genslices(5):
                for rslice in genslices(5):
                    for flags in (0, ND_PIL):

                        f = flags|ND_WRITABLE
                        nd = ndarray(items, shape=[5], format=fmt, flags=f)
                        ex = ndarray(items, shape=[5], format=fmt, flags=f)
                        mv = memoryview(ex)

                        lsterr = None
                        diff_structure = None
                        lst = items[:]
                        try:
                            lval = lst[lslice]
                            rval = lst[rslice]
                            lst[lslice] = lst[rslice]
                            diff_structure = len(lval) != len(rval)
                        except Exception as e:
                            lsterr = e.__class__

                        nderr = None
                        try:
                            nd[lslice] = nd[rslice]
                        except Exception as e:
                            nderr = e.__class__

                        if diff_structure: # ndarray cannot change shape
                            self.assertIs(nderr, ValueError)
                        else:
                            self.assertEqual(nd.tolist(), lst)
                            self.assertIs(nderr, lsterr)

                        if not is_memoryview_format(fmt):
                            continue

                        mverr = None
                        try:
                            mv[lslice] = mv[rslice]
                        except Exception as e:
                            mverr = e.__class__

                        if diff_structure: # memoryview cannot change shape
                            self.assertIs(mverr, ValueError)
                        else:
                            self.assertEqual(mv.tolist(), lst)
                            self.assertEqual(mv, nd)
                            self.assertIs(mverr, lsterr)
                            self.verify(mv, obj=ex,
                              itemsize=nd.itemsize, fmt=fmt, readonly=False,
                              ndim=nd.ndim, shape=nd.shape, strides=nd.strides,
                              lst=nd.tolist())

    def test_ndarray_slice_assign_multidim(self):
        shape_t = (2, 3, 5)
        ndim = len(shape_t)
        nitems = prod(shape_t)
        for shape in permutations(shape_t):

            fmt, items, _ = randitems(nitems)

            for flags in (0, ND_PIL):
                for _ in range(ITERATIONS):
                    lslices, rslices = randslice_from_shape(ndim, shape)

                    nd = ndarray(items, shape=shape, format=fmt,
                                 flags=flags|ND_WRITABLE)
                    lst = carray(items, shape)

                    listerr = None
                    try:
                        result = multislice_assign(lst, lst, lslices, rslices)
                    except Exception as e:
                        listerr = e.__class__

                    nderr = None
                    try:
                        nd[lslices] = nd[rslices]
                    except Exception as e:
                        nderr = e.__class__

                    if nderr or listerr:
                        self.assertIs(nderr, listerr)
                    else:
                        self.assertEqual(nd.tolist(), result)

    def test_ndarray_random(self):
        # construction of valid arrays
        for _ in range(ITERATIONS):
            for fmt in fmtdict['@']:
                itemsize = struct.calcsize(fmt)

                t = rand_structure(itemsize, True, maxdim=MAXDIM,
                                   maxshape=MAXSHAPE)
                self.assertTrue(verify_structure(*t))
                items = randitems_from_structure(fmt, t)

                x = ndarray_from_structure(items, fmt, t)
                xlist = x.tolist()

                mv = memoryview(x)
                if is_memoryview_format(fmt):
                    mvlist = mv.tolist()
                    self.assertEqual(mvlist, xlist)

                if t[2] > 0:
                    # ndim > 0: test against suboffsets representation.
                    y = ndarray_from_structure(items, fmt, t, flags=ND_PIL)
                    ylist = y.tolist()
                    self.assertEqual(xlist, ylist)

                    mv = memoryview(y)
                    if is_memoryview_format(fmt):
                        self.assertEqual(mv, y)
                        mvlist = mv.tolist()
                        self.assertEqual(mvlist, ylist)

                if numpy_array:
                    shape = t[3]
                    if 0 in shape:
                        continue # http://projects.scipy.org/numpy/ticket/1910
                    z = numpy_array_from_structure(items, fmt, t)
                    self.verify(x, obj=None,
                                itemsize=z.itemsize, fmt=fmt, readonly=False,
                                ndim=z.ndim, shape=z.shape, strides=z.strides,
                                lst=z.tolist())

    def test_ndarray_random_invalid(self):
        # exceptions during construction of invalid arrays
        for _ in range(ITERATIONS):
            for fmt in fmtdict['@']:
                itemsize = struct.calcsize(fmt)

                t = rand_structure(itemsize, False, maxdim=MAXDIM,
                                   maxshape=MAXSHAPE)
                self.assertFalse(verify_structure(*t))
                items = randitems_from_structure(fmt, t)

                nderr = False
                try:
                    x = ndarray_from_structure(items, fmt, t)
                except Exception as e:
                    nderr = e.__class__
                self.assertTrue(nderr)

                if numpy_array:
                    numpy_err = False
                    try:
                        y = numpy_array_from_structure(items, fmt, t)
                    except Exception as e:
                        numpy_err = e.__class__

                    if 0: # http://projects.scipy.org/numpy/ticket/1910
                        self.assertTrue(numpy_err)

    def test_ndarray_random_slice_assign(self):
        # valid slice assignments
        for _ in range(ITERATIONS):
            for fmt in fmtdict['@']:
                itemsize = struct.calcsize(fmt)

                lshape, rshape, lslices, rslices = \
                    rand_aligned_slices(maxdim=MAXDIM, maxshape=MAXSHAPE)
                tl = rand_structure(itemsize, True, shape=lshape)
                tr = rand_structure(itemsize, True, shape=rshape)
                self.assertTrue(verify_structure(*tl))
                self.assertTrue(verify_structure(*tr))
                litems = randitems_from_structure(fmt, tl)
                ritems = randitems_from_structure(fmt, tr)

                xl = ndarray_from_structure(litems, fmt, tl)
                xr = ndarray_from_structure(ritems, fmt, tr)
                xl[lslices] = xr[rslices]
                xllist = xl.tolist()
                xrlist = xr.tolist()

                ml = memoryview(xl)
                mr = memoryview(xr)
                self.assertEqual(ml.tolist(), xllist)
                self.assertEqual(mr.tolist(), xrlist)

                if tl[2] > 0 and tr[2] > 0:
                    # ndim > 0: test against suboffsets representation.
                    yl = ndarray_from_structure(litems, fmt, tl, flags=ND_PIL)
                    yr = ndarray_from_structure(ritems, fmt, tr, flags=ND_PIL)
                    yl[lslices] = yr[rslices]
                    yllist = yl.tolist()
                    yrlist = yr.tolist()
                    self.assertEqual(xllist, yllist)
                    self.assertEqual(xrlist, yrlist)

                    ml = memoryview(yl)
                    mr = memoryview(yr)
                    self.assertEqual(ml.tolist(), yllist)
                    self.assertEqual(mr.tolist(), yrlist)

                if numpy_array:
                    if 0 in lshape or 0 in rshape:
                        continue # http://projects.scipy.org/numpy/ticket/1910

                    zl = numpy_array_from_structure(litems, fmt, tl)
                    zr = numpy_array_from_structure(ritems, fmt, tr)
                    zl[lslices] = zr[rslices]

                    if not is_overlapping(tl) and not is_overlapping(tr):
                        # Slice assignment of overlapping structures
                        # is undefined in NumPy.
                        self.verify(xl, obj=None,
                                    itemsize=zl.itemsize, fmt=fmt, readonly=False,
                                    ndim=zl.ndim, shape=zl.shape,
                                    strides=zl.strides, lst=zl.tolist())

                    self.verify(xr, obj=None,
                                itemsize=zr.itemsize, fmt=fmt, readonly=False,
                                ndim=zr.ndim, shape=zr.shape,
                                strides=zr.strides, lst=zr.tolist())

    def test_ndarray_re_export(self):
        items = [1,2,3,4,5,6,7,8,9,10,11,12]

        nd = ndarray(items, shape=[3,4], flags=ND_PIL)
        ex = ndarray(nd)

        self.assertTrue(ex.flags & ND_PIL)
        self.assertIs(ex.obj, nd)
        self.assertEqual(ex.suboffsets, (0, -1))
        self.assertFalse(ex.c_contiguous)
        self.assertFalse(ex.f_contiguous)
        self.assertFalse(ex.contiguous)

    def test_ndarray_zero_shape(self):
        # zeros in shape
        for flags in (0, ND_PIL):
            nd = ndarray([1,2,3], shape=[0], flags=flags)
            mv = memoryview(nd)
            self.assertEqual(mv, nd)
            self.assertEqual(nd.tolist(), [])
            self.assertEqual(mv.tolist(), [])

            nd = ndarray([1,2,3], shape=[0,3,3], flags=flags)
            self.assertEqual(nd.tolist(), [])

            nd = ndarray([1,2,3], shape=[3,0,3], flags=flags)
            self.assertEqual(nd.tolist(), [[], [], []])

            nd = ndarray([1,2,3], shape=[3,3,0], flags=flags)
            self.assertEqual(nd.tolist(),
                             [[[], [], []], [[], [], []], [[], [], []]])

    def test_ndarray_zero_strides(self):
        # zero strides
        for flags in (0, ND_PIL):
            nd = ndarray([1], shape=[5], strides=[0], flags=flags)
            mv = memoryview(nd)
            self.assertEqual(mv, nd)
            self.assertEqual(nd.tolist(), [1, 1, 1, 1, 1])
            self.assertEqual(mv.tolist(), [1, 1, 1, 1, 1])

    def test_ndarray_offset(self):
        nd = ndarray(list(range(20)), shape=[3], offset=7)
        self.assertEqual(nd.offset, 7)
        self.assertEqual(nd.tolist(), [7,8,9])

    def test_ndarray_memoryview_from_buffer(self):
        for flags in (0, ND_PIL):
            nd = ndarray(list(range(3)), shape=[3], flags=flags)
            m = nd.memoryview_from_buffer()
            self.assertEqual(m, nd)

    def test_ndarray_get_pointer(self):
        for flags in (0, ND_PIL):
            nd = ndarray(list(range(3)), shape=[3], flags=flags)
            for i in range(3):
                self.assertEqual(nd[i], get_pointer(nd, [i]))

    def test_ndarray_tolist_null_strides(self):
        ex = ndarray(list(range(20)), shape=[2,2,5])

        nd = ndarray(ex, getbuf=PyBUF_ND|PyBUF_FORMAT)
        self.assertEqual(nd.tolist(), ex.tolist())

        m = memoryview(ex)
        self.assertEqual(m.tolist(), ex.tolist())

    def test_ndarray_cmp_contig(self):

        self.assertFalse(cmp_contig(b"123", b"456"))

        x = ndarray(list(range(12)), shape=[3,4])
        y = ndarray(list(range(12)), shape=[4,3])
        self.assertFalse(cmp_contig(x, y))

        x = ndarray([1], shape=[1], format="B")
        self.assertTrue(cmp_contig(x, b'\x01'))
        self.assertTrue(cmp_contig(b'\x01', x))

    def test_ndarray_hash(self):

        a = array.array('L', [1,2,3])
        nd = ndarray(a)
        self.assertRaises(ValueError, hash, nd)

        # one-dimensional
        b = bytes(list(range(12)))

        nd = ndarray(list(range(12)), shape=[12])
        self.assertEqual(hash(nd), hash(b))

        # C-contiguous
        nd = ndarray(list(range(12)), shape=[3,4])
        self.assertEqual(hash(nd), hash(b))

        nd = ndarray(list(range(12)), shape=[3,2,2])
        self.assertEqual(hash(nd), hash(b))

        # Fortran contiguous
        b = bytes(transpose(list(range(12)), shape=[4,3]))
        nd = ndarray(list(range(12)), shape=[3,4], flags=ND_FORTRAN)
        self.assertEqual(hash(nd), hash(b))

        b = bytes(transpose(list(range(12)), shape=[2,3,2]))
        nd = ndarray(list(range(12)), shape=[2,3,2], flags=ND_FORTRAN)
        self.assertEqual(hash(nd), hash(b))

        # suboffsets
        b = bytes(list(range(12)))
        nd = ndarray(list(range(12)), shape=[2,2,3], flags=ND_PIL)
        self.assertEqual(hash(nd), hash(b))

        # non-byte formats
        nd = ndarray(list(range(12)), shape=[2,2,3], format='L')
        self.assertEqual(hash(nd), hash(nd.tobytes()))

    def test_py_buffer_to_contiguous(self):

        # The requests are used in _testbuffer.c:py_buffer_to_contiguous
        # to generate buffers without full information for testing.
        requests = (
            # distinct flags
            PyBUF_INDIRECT, PyBUF_STRIDES, PyBUF_ND, PyBUF_SIMPLE,
            # compound requests
            PyBUF_FULL, PyBUF_FULL_RO,
            PyBUF_RECORDS, PyBUF_RECORDS_RO,
            PyBUF_STRIDED, PyBUF_STRIDED_RO,
            PyBUF_CONTIG, PyBUF_CONTIG_RO,
        )

        # no buffer interface
        self.assertRaises(TypeError, py_buffer_to_contiguous, {}, 'F',
                          PyBUF_FULL_RO)

        # scalar, read-only request
        nd = ndarray(9, shape=(), format="L", flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            for request in requests:
                b = py_buffer_to_contiguous(nd, order, request)
                self.assertEqual(b, nd.tobytes())

        # zeros in shape
        nd = ndarray([1], shape=[0], format="L", flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            for request in requests:
                b = py_buffer_to_contiguous(nd, order, request)
                self.assertEqual(b, b'')

        nd = ndarray(list(range(8)), shape=[2, 0, 7], format="L",
                     flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            for request in requests:
                b = py_buffer_to_contiguous(nd, order, request)
                self.assertEqual(b, b'')

        ### One-dimensional arrays are trivial, since Fortran and C order
        ### are the same.

        # one-dimensional
        for f in [0, ND_FORTRAN]:
            nd = ndarray([1], shape=[1], format="h", flags=f|ND_WRITABLE)
            ndbytes = nd.tobytes()
            for order in ['C', 'F', 'A']:
                for request in requests:
                    b = py_buffer_to_contiguous(nd, order, request)
                    self.assertEqual(b, ndbytes)

            nd = ndarray([1, 2, 3], shape=[3], format="b", flags=f|ND_WRITABLE)
            ndbytes = nd.tobytes()
            for order in ['C', 'F', 'A']:
                for request in requests:
                    b = py_buffer_to_contiguous(nd, order, request)
                    self.assertEqual(b, ndbytes)

        # one-dimensional, non-contiguous input
        nd = ndarray([1, 2, 3], shape=[2], strides=[2], flags=ND_WRITABLE)
        ndbytes = nd.tobytes()
        for order in ['C', 'F', 'A']:
            for request in [PyBUF_STRIDES, PyBUF_FULL]:
                b = py_buffer_to_contiguous(nd, order, request)
                self.assertEqual(b, ndbytes)

        nd = nd[::-1]
        ndbytes = nd.tobytes()
        for order in ['C', 'F', 'A']:
            for request in requests:
                try:
                    b = py_buffer_to_contiguous(nd, order, request)
                except BufferError:
                    continue
                self.assertEqual(b, ndbytes)

        ###
        ### Multi-dimensional arrays:
        ###
        ### The goal here is to preserve the logical representation of the
        ### input array but change the physical representation if necessary.
        ###
        ### _testbuffer example:
        ### ====================
        ###
        ###    C input array:
        ###    --------------
        ###       >>> nd = ndarray(list(range(12)), shape=[3, 4])
        ###       >>> nd.tolist()
        ###       [[0, 1, 2, 3],
        ###        [4, 5, 6, 7],
        ###        [8, 9, 10, 11]]
        ###
        ###    Fortran output:
        ###    ---------------
        ###       >>> py_buffer_to_contiguous(nd, 'F', PyBUF_FULL_RO)
        ###       >>> b'\x00\x04\x08\x01\x05\t\x02\x06\n\x03\x07\x0b'
        ###
        ###    The return value corresponds to this input list for
        ###    _testbuffer's ndarray:
        ###       >>> nd = ndarray([0,4,8,1,5,9,2,6,10,3,7,11], shape=[3,4],
        ###                        flags=ND_FORTRAN)
        ###       >>> nd.tolist()
        ###       [[0, 1, 2, 3],
        ###        [4, 5, 6, 7],
        ###        [8, 9, 10, 11]]
        ###
        ###    The logical array is the same, but the values in memory are now
        ###    in Fortran order.
        ###
        ### NumPy example:
        ### ==============
        ###    _testbuffer's ndarray takes lists to initialize the memory.
        ###    Here's the same sequence in NumPy:
        ###
        ###    C input:
        ###    --------
        ###       >>> nd = ndarray(buffer=bytearray(list(range(12))),
        ###                        shape=[3, 4], dtype='B')
        ###       >>> nd
        ###       array([[ 0,  1,  2,  3],
        ###              [ 4,  5,  6,  7],
        ###              [ 8,  9, 10, 11]], dtype=uint8)
        ###
        ###    Fortran output:
        ###    ---------------
        ###       >>> fortran_buf = nd.tostring(order='F')
        ###       >>> fortran_buf
        ###       b'\x00\x04\x08\x01\x05\t\x02\x06\n\x03\x07\x0b'
        ###
        ###       >>> nd = ndarray(buffer=fortran_buf, shape=[3, 4],
        ###                        dtype='B', order='F')
        ###
        ###       >>> nd
        ###       array([[ 0,  1,  2,  3],
        ###              [ 4,  5,  6,  7],
        ###              [ 8,  9, 10, 11]], dtype=uint8)
        ###

        # multi-dimensional, contiguous input
        lst = list(range(12))
        for f in [0, ND_FORTRAN]:
            nd = ndarray(lst, shape=[3, 4], flags=f|ND_WRITABLE)
            if numpy_array:
                na = numpy_array(buffer=bytearray(lst),
                                 shape=[3, 4], dtype='B',
                                 order='C' if f == 0 else 'F')

            # 'C' request
            if f == ND_FORTRAN: # 'F' to 'C'
                x = ndarray(transpose(lst, [4, 3]), shape=[3, 4],
                            flags=ND_WRITABLE)
                expected = x.tobytes()
            else:
                expected = nd.tobytes()
            for request in requests:
                try:
                    b = py_buffer_to_contiguous(nd, 'C', request)
                except BufferError:
                    continue

                self.assertEqual(b, expected)

                # Check that output can be used as the basis for constructing
                # a C array that is logically identical to the input array.
                y = ndarray([v for v in b], shape=[3, 4], flags=ND_WRITABLE)
                self.assertEqual(memoryview(y), memoryview(nd))

                if numpy_array:
                    self.assertEqual(b, na.tostring(order='C'))

            # 'F' request
            if f == 0: # 'C' to 'F'
                x = ndarray(transpose(lst, [3, 4]), shape=[4, 3],
                            flags=ND_WRITABLE)
            else:
                x = ndarray(lst, shape=[3, 4], flags=ND_WRITABLE)
            expected = x.tobytes()
            for request in [PyBUF_FULL, PyBUF_FULL_RO, PyBUF_INDIRECT,
                            PyBUF_STRIDES, PyBUF_ND]:
                try:
                    b = py_buffer_to_contiguous(nd, 'F', request)
                except BufferError:
                    continue
                self.assertEqual(b, expected)

                # Check that output can be used as the basis for constructing
                # a Fortran array that is logically identical to the input array.
                y = ndarray([v for v in b], shape=[3, 4], flags=ND_FORTRAN|ND_WRITABLE)
                self.assertEqual(memoryview(y), memoryview(nd))

                if numpy_array:
                    self.assertEqual(b, na.tostring(order='F'))

            # 'A' request
            if f == ND_FORTRAN:
                x = ndarray(lst, shape=[3, 4], flags=ND_WRITABLE)
                expected = x.tobytes()
            else:
                expected = nd.tobytes()
            for request in [PyBUF_FULL, PyBUF_FULL_RO, PyBUF_INDIRECT,
                            PyBUF_STRIDES, PyBUF_ND]:
                try:
                    b = py_buffer_to_contiguous(nd, 'A', request)
                except BufferError:
                    continue

                self.assertEqual(b, expected)

                # Check that output can be used as the basis for constructing
                # an array with order=f that is logically identical to the input
                # array.
                y = ndarray([v for v in b], shape=[3, 4], flags=f|ND_WRITABLE)
                self.assertEqual(memoryview(y), memoryview(nd))

                if numpy_array:
                    self.assertEqual(b, na.tostring(order='A'))

        # multi-dimensional, non-contiguous input
        nd = ndarray(list(range(12)), shape=[3, 4], flags=ND_WRITABLE|ND_PIL)

        # 'C'
        b = py_buffer_to_contiguous(nd, 'C', PyBUF_FULL_RO)
        self.assertEqual(b, nd.tobytes())
        y = ndarray([v for v in b], shape=[3, 4], flags=ND_WRITABLE)
        self.assertEqual(memoryview(y), memoryview(nd))

        # 'F'
        b = py_buffer_to_contiguous(nd, 'F', PyBUF_FULL_RO)
        x = ndarray(transpose(lst, [3, 4]), shape=[4, 3], flags=ND_WRITABLE)
        self.assertEqual(b, x.tobytes())
        y = ndarray([v for v in b], shape=[3, 4], flags=ND_FORTRAN|ND_WRITABLE)
        self.assertEqual(memoryview(y), memoryview(nd))

        # 'A'
        b = py_buffer_to_contiguous(nd, 'A', PyBUF_FULL_RO)
        self.assertEqual(b, nd.tobytes())
        y = ndarray([v for v in b], shape=[3, 4], flags=ND_WRITABLE)
        self.assertEqual(memoryview(y), memoryview(nd))

    def test_memoryview_construction(self):

        items_shape = [(9, []), ([1,2,3], [3]), (list(range(2*3*5)), [2,3,5])]

        # NumPy style, C-contiguous:
        for items, shape in items_shape:

            # From PEP-3118 compliant exporter:
            ex = ndarray(items, shape=shape)
            m = memoryview(ex)
            self.assertTrue(m.c_contiguous)
            self.assertTrue(m.contiguous)

            ndim = len(shape)
            strides = strides_from_shape(ndim, shape, 1, 'C')
            lst = carray(items, shape)

            self.verify(m, obj=ex,
                        itemsize=1, fmt='B', readonly=True,
                        ndim=ndim, shape=shape, strides=strides,
                        lst=lst)

            # From memoryview:
            m2 = memoryview(m)
            self.verify(m2, obj=ex,
                        itemsize=1, fmt='B', readonly=True,
                        ndim=ndim, shape=shape, strides=strides,
                        lst=lst)

            # PyMemoryView_FromBuffer(): no strides
            nd = ndarray(ex, getbuf=PyBUF_CONTIG_RO|PyBUF_FORMAT)
            self.assertEqual(nd.strides, ())
            m = nd.memoryview_from_buffer()
            self.verify(m, obj=None,
                        itemsize=1, fmt='B', readonly=True,
                        ndim=ndim, shape=shape, strides=strides,
                        lst=lst)

            # PyMemoryView_FromBuffer(): no format, shape, strides
            nd = ndarray(ex, getbuf=PyBUF_SIMPLE)
            self.assertEqual(nd.format, '')
            self.assertEqual(nd.shape, ())
            self.assertEqual(nd.strides, ())
            m = nd.memoryview_from_buffer()

            lst = [items] if ndim == 0 else items
            self.verify(m, obj=None,
                        itemsize=1, fmt='B', readonly=True,
                        ndim=1, shape=[ex.nbytes], strides=(1,),
                        lst=lst)

        # NumPy style, Fortran contiguous:
        for items, shape in items_shape:

            # From PEP-3118 compliant exporter:
            ex = ndarray(items, shape=shape, flags=ND_FORTRAN)
            m = memoryview(ex)
            self.assertTrue(m.f_contiguous)
            self.assertTrue(m.contiguous)

            ndim = len(shape)
            strides = strides_from_shape(ndim, shape, 1, 'F')
            lst = farray(items, shape)

            self.verify(m, obj=ex,
                        itemsize=1, fmt='B', readonly=True,
                        ndim=ndim, shape=shape, strides=strides,
                        lst=lst)

            # From memoryview:
            m2 = memoryview(m)
            self.verify(m2, obj=ex,
                        itemsize=1, fmt='B', readonly=True,
                        ndim=ndim, shape=shape, strides=strides,
                        lst=lst)

        # PIL style:
        for items, shape in items_shape[1:]:

            # From PEP-3118 compliant exporter:
            ex = ndarray(items, shape=shape, flags=ND_PIL)
            m = memoryview(ex)

            ndim = len(shape)
            lst = carray(items, shape)

            self.verify(m, obj=ex,
                        itemsize=1, fmt='B', readonly=True,
                        ndim=ndim, shape=shape, strides=ex.strides,
                        lst=lst)

            # From memoryview:
            m2 = memoryview(m)
            self.verify(m2, obj=ex,
                        itemsize=1, fmt='B', readonly=True,
                        ndim=ndim, shape=shape, strides=ex.strides,
                        lst=lst)

        # Invalid number of arguments:
        self.assertRaises(TypeError, memoryview, b'9', 'x')
        # Not a buffer provider:
        self.assertRaises(TypeError, memoryview, {})
        # Non-compliant buffer provider:
        ex = ndarray([1,2,3], shape=[3])
        nd = ndarray(ex, getbuf=PyBUF_SIMPLE)
        self.assertRaises(BufferError, memoryview, nd)
        nd = ndarray(ex, getbuf=PyBUF_CONTIG_RO|PyBUF_FORMAT)
        self.assertRaises(BufferError, memoryview, nd)

        # ndim > 64
        nd = ndarray([1]*128, shape=[1]*128, format='L')
        self.assertRaises(ValueError, memoryview, nd)
        self.assertRaises(ValueError, nd.memoryview_from_buffer)
        self.assertRaises(ValueError, get_contiguous, nd, PyBUF_READ, 'C')
        self.assertRaises(ValueError, get_contiguous, nd, PyBUF_READ, 'F')
        self.assertRaises(ValueError, get_contiguous, nd[::-1], PyBUF_READ, 'C')

    def test_memoryview_cast_zero_shape(self):
        # Casts are undefined if buffer is multidimensional and shape
        # contains zeros. These arrays are regarded as C-contiguous by
        # Numpy and PyBuffer_GetContiguous(), so they are not caught by
        # the test for C-contiguity in memory_cast().
        items = [1,2,3]
        for shape in ([0,3,3], [3,0,3], [0,3,3]):
            ex = ndarray(items, shape=shape)
            self.assertTrue(ex.c_contiguous)
            msrc = memoryview(ex)
            self.assertRaises(TypeError, msrc.cast, 'c')
        # Monodimensional empty view can be cast (issue #19014).
        for fmt, _, _ in iter_format(1, 'memoryview'):
            msrc = memoryview(b'')
            m = msrc.cast(fmt)
            self.assertEqual(m.tobytes(), b'')
            self.assertEqual(m.tolist(), [])

    check_sizeof = support.check_sizeof

    def test_memoryview_sizeof(self):
        check = self.check_sizeof
        vsize = support.calcvobjsize
        base_struct = 'Pnin 2P2n2i5P P'
        per_dim = '3n'

        items = list(range(8))
        check(memoryview(b''), vsize(base_struct + 1 * per_dim))
        a = ndarray(items, shape=[2, 4], format="b")
        check(memoryview(a), vsize(base_struct + 2 * per_dim))
        a = ndarray(items, shape=[2, 2, 2], format="b")
        check(memoryview(a), vsize(base_struct + 3 * per_dim))

    def test_memoryview_struct_module(self):

        class INT(object):
            def __init__(self, val):
                self.val = val
            def __int__(self):
                return self.val

        class IDX(object):
            def __init__(self, val):
                self.val = val
            def __index__(self):
                return self.val

        def f(): return 7

        values = [INT(9), IDX(9),
                  2.2+3j, Decimal("-21.1"), 12.2, Fraction(5, 2),
                  [1,2,3], {4,5,6}, {7:8}, (), (9,),
                  True, False, None, NotImplemented,
                  b'a', b'abc', bytearray(b'a'), bytearray(b'abc'),
                  'a', 'abc', r'a', r'abc',
                  f, lambda x: x]

        for fmt, items, item in iter_format(10, 'memoryview'):
            ex = ndarray(items, shape=[10], format=fmt, flags=ND_WRITABLE)
            nd = ndarray(items, shape=[10], format=fmt, flags=ND_WRITABLE)
            m = memoryview(ex)

            struct.pack_into(fmt, nd, 0, item)
            m[0] = item
            self.assertEqual(m[0], nd[0])

            itemsize = struct.calcsize(fmt)
            if 'P' in fmt:
                continue

            for v in values:
                struct_err = None
                try:
                    struct.pack_into(fmt, nd, itemsize, v)
                except struct.error:
                    struct_err = struct.error

                mv_err = None
                try:
                    m[1] = v
                except (TypeError, ValueError) as e:
                    mv_err = e.__class__

                if struct_err or mv_err:
                    self.assertIsNot(struct_err, None)
                    self.assertIsNot(mv_err, None)
                else:
                    self.assertEqual(m[1], nd[1])

    def test_memoryview_cast_zero_strides(self):
        # Casts are undefined if strides contains zeros. These arrays are
        # (sometimes!) regarded as C-contiguous by Numpy, but not by
        # PyBuffer_GetContiguous().
        ex = ndarray([1,2,3], shape=[3], strides=[0])
        self.assertFalse(ex.c_contiguous)
        msrc = memoryview(ex)
        self.assertRaises(TypeError, msrc.cast, 'c')

    def test_memoryview_cast_invalid(self):
        # invalid format
        for sfmt in NON_BYTE_FORMAT:
            sformat = '@' + sfmt if randrange(2) else sfmt
            ssize = struct.calcsize(sformat)
            for dfmt in NON_BYTE_FORMAT:
                dformat = '@' + dfmt if randrange(2) else dfmt
                dsize = struct.calcsize(dformat)
                ex = ndarray(list(range(32)), shape=[32//ssize], format=sformat)
                msrc = memoryview(ex)
                self.assertRaises(TypeError, msrc.cast, dfmt, [32//dsize])

        for sfmt, sitems, _ in iter_format(1):
            ex = ndarray(sitems, shape=[1], format=sfmt)
            msrc = memoryview(ex)
            for dfmt, _, _ in iter_format(1):
                if not is_memoryview_format(dfmt):
                    self.assertRaises(ValueError, msrc.cast, dfmt,
                                      [32//dsize])
                else:
                    if not is_byte_format(sfmt) and not is_byte_format(dfmt):
                        self.assertRaises(TypeError, msrc.cast, dfmt,
                                          [32//dsize])

        # invalid shape
        size_h = struct.calcsize('h')
        size_d = struct.calcsize('d')
        ex = ndarray(list(range(2*2*size_d)), shape=[2,2,size_d], format='h')
        msrc = memoryview(ex)
        self.assertRaises(TypeError, msrc.cast, shape=[2,2,size_h], format='d')

        ex = ndarray(list(range(120)), shape=[1,2,3,4,5])
        m = memoryview(ex)

        # incorrect number of args
        self.assertRaises(TypeError, m.cast)
        self.assertRaises(TypeError, m.cast, 1, 2, 3)

        # incorrect dest format type
        self.assertRaises(TypeError, m.cast, {})

        # incorrect dest format
        self.assertRaises(ValueError, m.cast, "X")
        self.assertRaises(ValueError, m.cast, "@X")
        self.assertRaises(ValueError, m.cast, "@XY")

        # dest format not implemented
        self.assertRaises(ValueError, m.cast, "=B")
        self.assertRaises(ValueError, m.cast, "!L")
        self.assertRaises(ValueError, m.cast, "<P")
        self.assertRaises(ValueError, m.cast, ">l")
        self.assertRaises(ValueError, m.cast, "BI")
        self.assertRaises(ValueError, m.cast, "xBI")

        # src format not implemented
        ex = ndarray([(1,2), (3,4)], shape=[2], format="II")
        m = memoryview(ex)
        self.assertRaises(NotImplementedError, m.__getitem__, 0)
        self.assertRaises(NotImplementedError, m.__setitem__, 0, 8)
        self.assertRaises(NotImplementedError, m.tolist)

        # incorrect shape type
        ex = ndarray(list(range(120)), shape=[1,2,3,4,5])
        m = memoryview(ex)
        self.assertRaises(TypeError, m.cast, "B", shape={})

        # incorrect shape elements
        ex = ndarray(list(range(120)), shape=[2*3*4*5])
        m = memoryview(ex)
        self.assertRaises(OverflowError, m.cast, "B", shape=[2**64])
        self.assertRaises(ValueError, m.cast, "B", shape=[-1])
        self.assertRaises(ValueError, m.cast, "B", shape=[2,3,4,5,6,7,-1])
        self.assertRaises(ValueError, m.cast, "B", shape=[2,3,4,5,6,7,0])
        self.assertRaises(TypeError, m.cast, "B", shape=[2,3,4,5,6,7,'x'])

        # N-D -> N-D cast
        ex = ndarray(list([9 for _ in range(3*5*7*11)]), shape=[3,5,7,11])
        m = memoryview(ex)
        self.assertRaises(TypeError, m.cast, "I", shape=[2,3,4,5])

        # cast with ndim > 64
        nd = ndarray(list(range(128)), shape=[128], format='I')
        m = memoryview(nd)
        self.assertRaises(ValueError, m.cast, 'I', [1]*128)

        # view->len not a multiple of itemsize
        ex = ndarray(list([9 for _ in range(3*5*7*11)]), shape=[3*5*7*11])
        m = memoryview(ex)
        self.assertRaises(TypeError, m.cast, "I", shape=[2,3,4,5])

        # product(shape) * itemsize != buffer size
        ex = ndarray(list([9 for _ in range(3*5*7*11)]), shape=[3*5*7*11])
        m = memoryview(ex)
        self.assertRaises(TypeError, m.cast, "B", shape=[2,3,4,5])

        # product(shape) * itemsize overflow
        nd = ndarray(list(range(128)), shape=[128], format='I')
        m1 = memoryview(nd)
        nd = ndarray(list(range(128)), shape=[128], format='B')
        m2 = memoryview(nd)
        if sys.maxsize == 2**63-1:
            self.assertRaises(TypeError, m1.cast, 'B',
                              [7, 7, 73, 127, 337, 92737, 649657])
            self.assertRaises(ValueError, m1.cast, 'B',
                              [2**20, 2**20, 2**10, 2**10, 2**3])
            self.assertRaises(ValueError, m2.cast, 'I',
                              [2**20, 2**20, 2**10, 2**10, 2**1])
        else:
            self.assertRaises(TypeError, m1.cast, 'B',
                              [1, 2147483647])
            self.assertRaises(ValueError, m1.cast, 'B',
                              [2**10, 2**10, 2**5, 2**5, 2**1])
            self.assertRaises(ValueError, m2.cast, 'I',
                              [2**10, 2**10, 2**5, 2**3, 2**1])

    def test_memoryview_cast(self):
        bytespec = (
          ('B', lambda ex: list(ex.tobytes())),
          ('b', lambda ex: [x-256 if x > 127 else x for x in list(ex.tobytes())]),
          ('c', lambda ex: [bytes(chr(x), 'latin-1') for x in list(ex.tobytes())]),
        )

        def iter_roundtrip(ex, m, items, fmt):
            srcsize = struct.calcsize(fmt)
            for bytefmt, to_bytelist in bytespec:

                m2 = m.cast(bytefmt)
                lst = to_bytelist(ex)
                self.verify(m2, obj=ex,
                            itemsize=1, fmt=bytefmt, readonly=False,
                            ndim=1, shape=[31*srcsize], strides=(1,),
                            lst=lst, cast=True)

                m3 = m2.cast(fmt)
                self.assertEqual(m3, ex)
                lst = ex.tolist()
                self.verify(m3, obj=ex,
                            itemsize=srcsize, fmt=fmt, readonly=False,
                            ndim=1, shape=[31], strides=(srcsize,),
                            lst=lst, cast=True)

        # cast from ndim = 0 to ndim = 1
        srcsize = struct.calcsize('I')
        ex = ndarray(9, shape=[], format='I')
        destitems, destshape = cast_items(ex, 'B', 1)
        m = memoryview(ex)
        m2 = m.cast('B')
        self.verify(m2, obj=ex,
                    itemsize=1, fmt='B', readonly=True,
                    ndim=1, shape=destshape, strides=(1,),
                    lst=destitems, cast=True)

        # cast from ndim = 1 to ndim = 0
        destsize = struct.calcsize('I')
        ex = ndarray([9]*destsize, shape=[destsize], format='B')
        destitems, destshape = cast_items(ex, 'I', destsize, shape=[])
        m = memoryview(ex)
        m2 = m.cast('I', shape=[])
        self.verify(m2, obj=ex,
                    itemsize=destsize, fmt='I', readonly=True,
                    ndim=0, shape=(), strides=(),
                    lst=destitems, cast=True)

        # array.array: roundtrip to/from bytes
        for fmt, items, _ in iter_format(31, 'array'):
            ex = array.array(fmt, items)
            m = memoryview(ex)
            iter_roundtrip(ex, m, items, fmt)

        # ndarray: roundtrip to/from bytes
        for fmt, items, _ in iter_format(31, 'memoryview'):
            ex = ndarray(items, shape=[31], format=fmt, flags=ND_WRITABLE)
            m = memoryview(ex)
            iter_roundtrip(ex, m, items, fmt)

    def test_memoryview_cast_1D_ND(self):
        # Cast between C-contiguous buffers. At least one buffer must
        # be 1D, at least one format must be 'c', 'b' or 'B'.
        for _tshape in gencastshapes():
            for char in fmtdict['@']:
                tfmt = ('', '@')[randrange(2)] + char
                tsize = struct.calcsize(tfmt)
                n = prod(_tshape) * tsize
                obj = 'memoryview' if is_byte_format(tfmt) else 'bytefmt'
                for fmt, items, _ in iter_format(n, obj):
                    size = struct.calcsize(fmt)
                    shape = [n] if n > 0 else []
                    tshape = _tshape + [size]

                    ex = ndarray(items, shape=shape, format=fmt)
                    m = memoryview(ex)

                    titems, tshape = cast_items(ex, tfmt, tsize, shape=tshape)

                    if titems is None:
                        self.assertRaises(TypeError, m.cast, tfmt, tshape)
                        continue
                    if titems == 'nan':
                        continue # NaNs in lists are a recipe for trouble.

                    # 1D -> ND
                    nd = ndarray(titems, shape=tshape, format=tfmt)

                    m2 = m.cast(tfmt, shape=tshape)
                    ndim = len(tshape)
                    strides = nd.strides
                    lst = nd.tolist()
                    self.verify(m2, obj=ex,
                                itemsize=tsize, fmt=tfmt, readonly=True,
                                ndim=ndim, shape=tshape, strides=strides,
                                lst=lst, cast=True)

                    # ND -> 1D
                    m3 = m2.cast(fmt)
                    m4 = m2.cast(fmt, shape=shape)
                    ndim = len(shape)
                    strides = ex.strides
                    lst = ex.tolist()

                    self.verify(m3, obj=ex,
                                itemsize=size, fmt=fmt, readonly=True,
                                ndim=ndim, shape=shape, strides=strides,
                                lst=lst, cast=True)

                    self.verify(m4, obj=ex,
                                itemsize=size, fmt=fmt, readonly=True,
                                ndim=ndim, shape=shape, strides=strides,
                                lst=lst, cast=True)

        if ctypes:
            # format: "T{>l:x:>d:y:}"
            class BEPoint(ctypes.BigEndianStructure):
                _fields_ = [("x", ctypes.c_long), ("y", ctypes.c_double)]
            point = BEPoint(100, 200.1)
            m1 = memoryview(point)
            m2 = m1.cast('B')
            self.assertEqual(m2.obj, point)
            self.assertEqual(m2.itemsize, 1)
            self.assertIs(m2.readonly, False)
            self.assertEqual(m2.ndim, 1)
            self.assertEqual(m2.shape, (m2.nbytes,))
            self.assertEqual(m2.strides, (1,))
            self.assertEqual(m2.suboffsets, ())

            x = ctypes.c_double(1.2)
            m1 = memoryview(x)
            m2 = m1.cast('c')
            self.assertEqual(m2.obj, x)
            self.assertEqual(m2.itemsize, 1)
            self.assertIs(m2.readonly, False)
            self.assertEqual(m2.ndim, 1)
            self.assertEqual(m2.shape, (m2.nbytes,))
            self.assertEqual(m2.strides, (1,))
            self.assertEqual(m2.suboffsets, ())

    def test_memoryview_tolist(self):

        # Most tolist() tests are in self.verify() etc.

        a = array.array('h', list(range(-6, 6)))
        m = memoryview(a)
        self.assertEqual(m, a)
        self.assertEqual(m.tolist(), a.tolist())

        a = a[2::3]
        m = m[2::3]
        self.assertEqual(m, a)
        self.assertEqual(m.tolist(), a.tolist())

        ex = ndarray(list(range(2*3*5*7*11)), shape=[11,2,7,3,5], format='L')
        m = memoryview(ex)
        self.assertEqual(m.tolist(), ex.tolist())

        ex = ndarray([(2, 5), (7, 11)], shape=[2], format='lh')
        m = memoryview(ex)
        self.assertRaises(NotImplementedError, m.tolist)

        ex = ndarray([b'12345'], shape=[1], format="s")
        m = memoryview(ex)
        self.assertRaises(NotImplementedError, m.tolist)

        ex = ndarray([b"a",b"b",b"c",b"d",b"e",b"f"], shape=[2,3], format='s')
        m = memoryview(ex)
        self.assertRaises(NotImplementedError, m.tolist)

    def test_memoryview_repr(self):
        m = memoryview(bytearray(9))
        r = m.__repr__()
        self.assertTrue(r.startswith("<memory"))

        m.release()
        r = m.__repr__()
        self.assertTrue(r.startswith("<released"))

    def test_memoryview_sequence(self):

        for fmt in ('d', 'f'):
            inf = float(3e400)
            ex = array.array(fmt, [1.0, inf, 3.0])
            m = memoryview(ex)
            self.assertIn(1.0, m)
            self.assertIn(5e700, m)
            self.assertIn(3.0, m)

        ex = ndarray(9.0, [], format='f')
        m = memoryview(ex)
        self.assertRaises(TypeError, eval, "9.0 in m", locals())

    @contextlib.contextmanager
    def assert_out_of_bounds_error(self, dim):
        with self.assertRaises(IndexError) as cm:
            yield
        self.assertEqual(str(cm.exception),
                         "index out of bounds on dimension %d" % (dim,))

    def test_memoryview_index(self):

        # ndim = 0
        ex = ndarray(12.5, shape=[], format='d')
        m = memoryview(ex)
        self.assertEqual(m[()], 12.5)
        self.assertEqual(m[...], m)
        self.assertEqual(m[...], ex)
        self.assertRaises(TypeError, m.__getitem__, 0)

        ex = ndarray((1,2,3), shape=[], format='iii')
        m = memoryview(ex)
        self.assertRaises(NotImplementedError, m.__getitem__, ())

        # range
        ex = ndarray(list(range(7)), shape=[7], flags=ND_WRITABLE)
        m = memoryview(ex)

        self.assertRaises(IndexError, m.__getitem__, 2**64)
        self.assertRaises(TypeError, m.__getitem__, 2.0)
        self.assertRaises(TypeError, m.__getitem__, 0.0)

        # out of bounds
        self.assertRaises(IndexError, m.__getitem__, -8)
        self.assertRaises(IndexError, m.__getitem__, 8)

        # multi-dimensional
        ex = ndarray(list(range(12)), shape=[3,4], flags=ND_WRITABLE)
        m = memoryview(ex)

        self.assertEqual(m[0, 0], 0)
        self.assertEqual(m[2, 0], 8)
        self.assertEqual(m[2, 3], 11)
        self.assertEqual(m[-1, -1], 11)
        self.assertEqual(m[-3, -4], 0)

        # out of bounds
        for index in (3, -4):
            with self.assert_out_of_bounds_error(dim=1):
                m[index, 0]
        for index in (4, -5):
            with self.assert_out_of_bounds_error(dim=2):
                m[0, index]
        self.assertRaises(IndexError, m.__getitem__, (2**64, 0))
        self.assertRaises(IndexError, m.__getitem__, (0, 2**64))

        self.assertRaises(TypeError, m.__getitem__, (0, 0, 0))
        self.assertRaises(TypeError, m.__getitem__, (0.0, 0.0))

        # Not implemented: multidimensional sub-views
        self.assertRaises(NotImplementedError, m.__getitem__, ())
        self.assertRaises(NotImplementedError, m.__getitem__, 0)

    def test_memoryview_assign(self):

        # ndim = 0
        ex = ndarray(12.5, shape=[], format='f', flags=ND_WRITABLE)
        m = memoryview(ex)
        m[()] = 22.5
        self.assertEqual(m[()], 22.5)
        m[...] = 23.5
        self.assertEqual(m[()], 23.5)
        self.assertRaises(TypeError, m.__setitem__, 0, 24.7)

        # read-only
        ex = ndarray(list(range(7)), shape=[7])
        m = memoryview(ex)
        self.assertRaises(TypeError, m.__setitem__, 2, 10)

        # range
        ex = ndarray(list(range(7)), shape=[7], flags=ND_WRITABLE)
        m = memoryview(ex)

        self.assertRaises(IndexError, m.__setitem__, 2**64, 9)
        self.assertRaises(TypeError, m.__setitem__, 2.0, 10)
        self.assertRaises(TypeError, m.__setitem__, 0.0, 11)

        # out of bounds
        self.assertRaises(IndexError, m.__setitem__, -8, 20)
        self.assertRaises(IndexError, m.__setitem__, 8, 25)

        # pack_single() success:
        for fmt in fmtdict['@']:
            if fmt == 'c' or fmt == '?':
                continue
            ex = ndarray([1,2,3], shape=[3], format=fmt, flags=ND_WRITABLE)
            m = memoryview(ex)
            i = randrange(-3, 3)
            m[i] = 8
            self.assertEqual(m[i], 8)
            self.assertEqual(m[i], ex[i])

        ex = ndarray([b'1', b'2', b'3'], shape=[3], format='c',
                     flags=ND_WRITABLE)
        m = memoryview(ex)
        m[2] = b'9'
        self.assertEqual(m[2], b'9')

        ex = ndarray([True, False, True], shape=[3], format='?',
                     flags=ND_WRITABLE)
        m = memoryview(ex)
        m[1] = True
        self.assertIs(m[1], True)

        # pack_single() exceptions:
        nd = ndarray([b'x'], shape=[1], format='c', flags=ND_WRITABLE)
        m = memoryview(nd)
        self.assertRaises(TypeError, m.__setitem__, 0, 100)

        ex = ndarray(list(range(120)), shape=[1,2,3,4,5], flags=ND_WRITABLE)
        m1 = memoryview(ex)

        for fmt, _range in fmtdict['@'].items():
            if (fmt == '?'): # PyObject_IsTrue() accepts anything
                continue
            if fmt == 'c': # special case tested above
                continue
            m2 = m1.cast(fmt)
            lo, hi = _range
            if fmt == 'd' or fmt == 'f':
                lo, hi = -2**1024, 2**1024
            if fmt != 'P': # PyLong_AsVoidPtr() accepts negative numbers
                self.assertRaises(ValueError, m2.__setitem__, 0, lo-1)
                self.assertRaises(TypeError, m2.__setitem__, 0, "xyz")
            self.assertRaises(ValueError, m2.__setitem__, 0, hi)

        # invalid item
        m2 = m1.cast('c')
        self.assertRaises(ValueError, m2.__setitem__, 0, b'\xff\xff')

        # format not implemented
        ex = ndarray(list(range(1)), shape=[1], format="xL", flags=ND_WRITABLE)
        m = memoryview(ex)
        self.assertRaises(NotImplementedError, m.__setitem__, 0, 1)

        ex = ndarray([b'12345'], shape=[1], format="s", flags=ND_WRITABLE)
        m = memoryview(ex)
        self.assertRaises(NotImplementedError, m.__setitem__, 0, 1)

        # multi-dimensional
        ex = ndarray(list(range(12)), shape=[3,4], flags=ND_WRITABLE)
        m = memoryview(ex)
        m[0,1] = 42
        self.assertEqual(ex[0][1], 42)
        m[-1,-1] = 43
        self.assertEqual(ex[2][3], 43)
        # errors
        for index in (3, -4):
            with self.assert_out_of_bounds_error(dim=1):
                m[index, 0] = 0
        for index in (4, -5):
            with self.assert_out_of_bounds_error(dim=2):
                m[0, index] = 0
        self.assertRaises(IndexError, m.__setitem__, (2**64, 0), 0)
        self.assertRaises(IndexError, m.__setitem__, (0, 2**64), 0)

        self.assertRaises(TypeError, m.__setitem__, (0, 0, 0), 0)
        self.assertRaises(TypeError, m.__setitem__, (0.0, 0.0), 0)

        # Not implemented: multidimensional sub-views
        self.assertRaises(NotImplementedError, m.__setitem__, 0, [2, 3])

    def test_memoryview_slice(self):

        ex = ndarray(list(range(12)), shape=[12], flags=ND_WRITABLE)
        m = memoryview(ex)

        # zero step
        self.assertRaises(ValueError, m.__getitem__, slice(0,2,0))
        self.assertRaises(ValueError, m.__setitem__, slice(0,2,0),
                          bytearray([1,2]))

        # 0-dim slicing (identity function)
        self.assertRaises(NotImplementedError, m.__getitem__, ())

        # multidimensional slices
        ex = ndarray(list(range(12)), shape=[12], flags=ND_WRITABLE)
        m = memoryview(ex)

        self.assertRaises(NotImplementedError, m.__getitem__,
                          (slice(0,2,1), slice(0,2,1)))
        self.assertRaises(NotImplementedError, m.__setitem__,
                          (slice(0,2,1), slice(0,2,1)), bytearray([1,2]))

        # invalid slice tuple
        self.assertRaises(TypeError, m.__getitem__, (slice(0,2,1), {}))
        self.assertRaises(TypeError, m.__setitem__, (slice(0,2,1), {}),
                          bytearray([1,2]))

        # rvalue is not an exporter
        self.assertRaises(TypeError, m.__setitem__, slice(0,1,1), [1])

        # non-contiguous slice assignment
        for flags in (0, ND_PIL):
            ex1 = ndarray(list(range(12)), shape=[12], strides=[-1], offset=11,
                          flags=ND_WRITABLE|flags)
            ex2 = ndarray(list(range(24)), shape=[12], strides=[2], flags=flags)
            m1 = memoryview(ex1)
            m2 = memoryview(ex2)

            ex1[2:5] = ex1[2:5]
            m1[2:5] = m2[2:5]

            self.assertEqual(m1, ex1)
            self.assertEqual(m2, ex2)

            ex1[1:3][::-1] = ex2[0:2][::1]
            m1[1:3][::-1] = m2[0:2][::1]

            self.assertEqual(m1, ex1)
            self.assertEqual(m2, ex2)

            ex1[4:1:-2][::-1] = ex1[1:4:2][::1]
            m1[4:1:-2][::-1] = m1[1:4:2][::1]

            self.assertEqual(m1, ex1)
            self.assertEqual(m2, ex2)

    def test_memoryview_array(self):

        def cmptest(testcase, a, b, m, singleitem):
            for i, _ in enumerate(a):
                ai = a[i]
                mi = m[i]
                testcase.assertEqual(ai, mi)
                a[i] = singleitem
                if singleitem != ai:
                    testcase.assertNotEqual(a, m)
                    testcase.assertNotEqual(a, b)
                else:
                    testcase.assertEqual(a, m)
                    testcase.assertEqual(a, b)
                m[i] = singleitem
                testcase.assertEqual(a, m)
                testcase.assertEqual(b, m)
                a[i] = ai
                m[i] = mi

        for n in range(1, 5):
            for fmt, items, singleitem in iter_format(n, 'array'):
                for lslice in genslices(n):
                    for rslice in genslices(n):

                        a = array.array(fmt, items)
                        b = array.array(fmt, items)
                        m = memoryview(b)

                        self.assertEqual(m, a)
                        self.assertEqual(m.tolist(), a.tolist())
                        self.assertEqual(m.tobytes(), a.tobytes())
                        self.assertEqual(len(m), len(a))

                        cmptest(self, a, b, m, singleitem)

                        array_err = None
                        have_resize = None
                        try:
                            al = a[lslice]
                            ar = a[rslice]
                            a[lslice] = a[rslice]
                            have_resize = len(al) != len(ar)
                        except Exception as e:
                            array_err = e.__class__

                        m_err = None
                        try:
                            m[lslice] = m[rslice]
                        except Exception as e:
                            m_err = e.__class__

                        if have_resize: # memoryview cannot change shape
                            self.assertIs(m_err, ValueError)
                        elif m_err or array_err:
                            self.assertIs(m_err, array_err)
                        else:
                            self.assertEqual(m, a)
                            self.assertEqual(m.tolist(), a.tolist())
                            self.assertEqual(m.tobytes(), a.tobytes())
                            cmptest(self, a, b, m, singleitem)

    def test_memoryview_compare_special_cases(self):

        a = array.array('L', [1, 2, 3])
        b = array.array('L', [1, 2, 7])

        # Ordering comparisons raise:
        v = memoryview(a)
        w = memoryview(b)
        for attr in ('__lt__', '__le__', '__gt__', '__ge__'):
            self.assertIs(getattr(v, attr)(w), NotImplemented)
            self.assertIs(getattr(a, attr)(v), NotImplemented)

        # Released views compare equal to themselves:
        v = memoryview(a)
        v.release()
        self.assertEqual(v, v)
        self.assertNotEqual(v, a)
        self.assertNotEqual(a, v)

        v = memoryview(a)
        w = memoryview(a)
        w.release()
        self.assertNotEqual(v, w)
        self.assertNotEqual(w, v)

        # Operand does not implement the buffer protocol:
        v = memoryview(a)
        self.assertNotEqual(v, [1, 2, 3])

        # 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)

        # Depends on issue #15625: the struct module does not understand 'u'.
        a = array.array('u', 'xyz')
        v = memoryview(a)
        self.assertNotEqual(a, v)
        self.assertNotEqual(v, a)

        # 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)

    def test_memoryview_compare_ndim_zero(self):

        nd1 = ndarray(1729, shape=[], format='@L')
        nd2 = ndarray(1729, shape=[], format='L', 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)

        self.assertFalse(v.__ne__(w))
        self.assertFalse(w.__ne__(v))

        w[()] = 1728
        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.assertFalse(v.__eq__(w))
        self.assertFalse(w.__eq__(v))

        nd = ndarray(list(range(12)), shape=[12], flags=ND_WRITABLE|ND_PIL)
        ex = ndarray(list(range(12)), shape=[12], flags=ND_WRITABLE|ND_PIL)
        m = memoryview(ex)

        self.assertEqual(m, nd)
        m[9] = 100
        self.assertNotEqual(m, nd)

        # 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)
        w = memoryview(nd2)

        self.assertEqual(v, nd1)
        self.assertEqual(w, nd2)
        self.assertNotEqual(v, nd2)
        self.assertNotEqual(w, nd1)
        self.assertNotEqual(v, w)

        # 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)
        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, 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)
        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, 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)
        w = memoryview(nd2)

        self.assertEqual(v, nd1)
        self.assertEqual(w, nd2)
        self.assertEqual(v, nd2)
        self.assertEqual(w, nd1)
        self.assertEqual(v, w)

        # 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)
        w = memoryview(nd2)

        self.assertEqual(v, nd1)
        self.assertEqual(w, nd2)
        self.assertEqual(v, nd2)
        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)
            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)

        # 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)
        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 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)
        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, 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)

        self.assertEqual(v, nd1)
        self.assertEqual(w, nd2)
        self.assertNotEqual(v, nd2)
        self.assertNotEqual(w, nd1)
        self.assertNotEqual(v, w)

        # 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',
                      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 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',
                      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, struct module
        nd1 = ndarray(list(range(-15, 15)), shape=[2, 3, 5], format='0ll',
                      flags=ND_FORTRAN)
        nd2 = ndarray(list(range(-15, 15)), shape=[3, 2, 5], format='l',
                      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 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')
        nd2 = ndarray(lst2, shape=[3, 2, 5], format='l', flags=ND_FORTRAN)
        v = memoryview(nd1)
        w = memoryview(nd2)

        self.assertEqual(v, nd1)
        self.assertEqual(w, nd2)
        self.assertEqual(v, w)

        # 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')
        nd2 = ex2[1:3:1, ::-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)

        # 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]
        nd2 = ndarray(list(range(30)), shape=[3, 2, 5], format='b')
        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)

        # 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=[3, 2, 5], format='b')
        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)

        # 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)
        w = memoryview(nd2)

        self.assertEqual(v, nd1)
        self.assertEqual(w, nd2)
        self.assertNotEqual(v, nd2)
        self.assertNotEqual(w, nd1)
        self.assertNotEqual(v, w)

        # 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)
        w = memoryview(nd2)

        self.assertEqual(v, nd1)
        self.assertEqual(w, nd2)
        self.assertEqual(v, nd2)
        self.assertEqual(w, nd1)
        self.assertEqual(v, w)
        self.assertEqual(v.tolist(), w.tolist())

        # 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)
        nd2 = ex2[1:3:1, ::-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, 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]
        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 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]
        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)

        # initialize mixed C/Fortran + suboffsets
        lst1 = list(range(-15, 15))
        lst2 = transpose(lst1, [3, 2, 5])
        nd1 = ndarray(lst1, shape=[3, 2, 5], format='@l', flags=ND_PIL)
        nd2 = ndarray(lst2, shape=[3, 2, 5], format='l', flags=ND_FORTRAN|ND_PIL)
        v = memoryview(nd1)
        w = memoryview(nd2)

        self.assertEqual(v, nd1)
        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])

        m = memoryview(a)
        m.release()

        # PyMemoryView_FromObject()
        self.assertRaises(ValueError, memoryview, m)
        # memoryview.cast()
        self.assertRaises(ValueError, m.cast, 'c')
        # getbuffer()
        self.assertRaises(ValueError, ndarray, m)
        # memoryview.tolist()
        self.assertRaises(ValueError, m.tolist)
        # memoryview.tobytes()
        self.assertRaises(ValueError, m.tobytes)
        # sequence
        self.assertRaises(ValueError, eval, "1.0 in m", locals())
        # subscript
        self.assertRaises(ValueError, m.__getitem__, 0)
        # assignment
        self.assertRaises(ValueError, m.__setitem__, 0, 1)

        for attr in ('obj', 'nbytes', 'readonly', 'itemsize', 'format', 'ndim',
                     'shape', 'strides', 'suboffsets', 'c_contiguous',
                     'f_contiguous', 'contiguous'):
            self.assertRaises(ValueError, m.__getattribute__, attr)

        # richcompare
        b = array.array('d', [1.1, 2.2, 3.3])
        m1 = memoryview(a)
        m2 = memoryview(b)

        self.assertEqual(m1, m2)
        m1.release()
        self.assertNotEqual(m1, m2)
        self.assertNotEqual(m1, a)
        self.assertEqual(m1, m1)

    def test_memoryview_tobytes(self):
        # Many implicit tests are already in self.verify().

        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().

        # no buffer interface
        self.assertRaises(TypeError, get_contiguous, {}, PyBUF_READ, 'F')

        # writable request to read-only object
        self.assertRaises(BufferError, get_contiguous, b'x', PyBUF_WRITE, 'C')

        # writable request to non-contiguous object
        nd = ndarray([1, 2, 3], shape=[2], strides=[2])
        self.assertRaises(BufferError, get_contiguous, nd, PyBUF_WRITE, 'A')

        # scalar, read-only request from read-only exporter
        nd = ndarray(9, shape=(), format="L")
        for order in ['C', 'F', 'A']:
            m = get_contiguous(nd, PyBUF_READ, order)
            self.assertEqual(m, nd)
            self.assertEqual(m[()], 9)

        # scalar, read-only request from writable exporter
        nd = ndarray(9, shape=(), format="L", flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            m = get_contiguous(nd, PyBUF_READ, order)
            self.assertEqual(m, nd)
            self.assertEqual(m[()], 9)

        # scalar, writable request
        for order in ['C', 'F', 'A']:
            nd[()] = 9
            m = get_contiguous(nd, PyBUF_WRITE, order)
            self.assertEqual(m, nd)
            self.assertEqual(m[()], 9)

            m[()] = 10
            self.assertEqual(m[()], 10)
            self.assertEqual(nd[()], 10)

        # zeros in shape
        nd = ndarray([1], shape=[0], format="L", flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            m = get_contiguous(nd, PyBUF_READ, order)
            self.assertRaises(IndexError, m.__getitem__, 0)
            self.assertEqual(m, nd)
            self.assertEqual(m.tolist(), [])

        nd = ndarray(list(range(8)), shape=[2, 0, 7], format="L",
                     flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            m = get_contiguous(nd, PyBUF_READ, order)
            self.assertEqual(ndarray(m).tolist(), [[], []])

        # one-dimensional
        nd = ndarray([1], shape=[1], format="h", flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            m = get_contiguous(nd, PyBUF_WRITE, order)
            self.assertEqual(m, nd)
            self.assertEqual(m.tolist(), nd.tolist())

        nd = ndarray([1, 2, 3], shape=[3], format="b", flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            m = get_contiguous(nd, PyBUF_WRITE, order)
            self.assertEqual(m, nd)
            self.assertEqual(m.tolist(), nd.tolist())

        # one-dimensional, non-contiguous
        nd = ndarray([1, 2, 3], shape=[2], strides=[2], flags=ND_WRITABLE)
        for order in ['C', 'F', 'A']:
            m = get_contiguous(nd, PyBUF_READ, order)
            self.assertEqual(m, nd)
            self.assertEqual(m.tolist(), nd.tolist())
            self.assertRaises(TypeError, m.__setitem__, 1, 20)
            self.assertEqual(m[1], 3)
            self.assertEqual(nd[1], 3)

        nd = nd[::-1]
        for order in ['C', 'F', 'A']:
            m = get_contiguous(nd, PyBUF_READ, order)
            self.assertEqual(m, nd)
            self.assertEqual(m.tolist(), nd.tolist())
            self.assertRaises(TypeError, m.__setitem__, 1, 20)
            self.assertEqual(m[1], 1)
            self.assertEqual(nd[1], 1)

        # multi-dimensional, contiguous input
        nd = ndarray(list(range(12)), shape=[3, 4], flags=ND_WRITABLE)
        for order in ['C', 'A']:
            m = get_contiguous(nd, PyBUF_WRITE, order)
            self.assertEqual(ndarray(m).tolist(), nd.tolist())

        self.assertRaises(BufferError, get_contiguous, nd, PyBUF_WRITE, 'F')
        m = get_contiguous(nd, PyBUF_READ, order)
        self.assertEqual(ndarray(m).tolist(), nd.tolist())

        nd = ndarray(list(range(12)), shape=[3, 4],
                     flags=ND_WRITABLE|ND_FORTRAN)
        for order in ['F', 'A']:
            m = get_contiguous(nd, PyBUF_WRITE, order)
            self.assertEqual(ndarray(m).tolist(), nd.tolist())

        self.assertRaises(BufferError, get_contiguous, nd, PyBUF_WRITE, 'C')
        m = get_contiguous(nd, PyBUF_READ, order)
        self.assertEqual(ndarray(m).tolist(), nd.tolist())

        # multi-dimensional, non-contiguous input
        nd = ndarray(list(range(12)), shape=[3, 4], flags=ND_WRITABLE|ND_PIL)
        for order in ['C', 'F', 'A']:
            self.assertRaises(BufferError, get_contiguous, nd, PyBUF_WRITE,
                              order)
            m = get_contiguous(nd, PyBUF_READ, order)
            self.assertEqual(ndarray(m).tolist(), nd.tolist())

        # flags
        nd = ndarray([1,2,3,4,5], shape=[3], strides=[2])
        m = get_contiguous(nd, PyBUF_READ, 'C')
        self.assertTrue(m.c_contiguous)

    def test_memoryview_serializing(self):

        # C-contiguous
        size = struct.calcsize('i')
        a = array.array('i', [1,2,3,4,5])
        m = memoryview(a)
        buf = io.BytesIO(m)
        b = bytearray(5*size)
        buf.readinto(b)
        self.assertEqual(m.tobytes(), b)

        # C-contiguous, multi-dimensional
        size = struct.calcsize('L')
        nd = ndarray(list(range(12)), shape=[2,3,2], format="L")
        m = memoryview(nd)
        buf = io.BytesIO(m)
        b = bytearray(2*3*2*size)
        buf.readinto(b)
        self.assertEqual(m.tobytes(), b)

        # Fortran contiguous, multi-dimensional
        #size = struct.calcsize('L')
        #nd = ndarray(list(range(12)), shape=[2,3,2], format="L",
        #             flags=ND_FORTRAN)
        #m = memoryview(nd)
        #buf = io.BytesIO(m)
        #b = bytearray(2*3*2*size)
        #buf.readinto(b)
        #self.assertEqual(m.tobytes(), b)

    def test_memoryview_hash(self):

        # bytes exporter
        b = bytes(list(range(12)))
        m = memoryview(b)
        self.assertEqual(hash(b), hash(m))

        # C-contiguous
        mc = m.cast('c', shape=[3,4])
        self.assertEqual(hash(mc), hash(b))

        # non-contiguous
        mx = m[::-2]
        b = bytes(list(range(12))[::-2])
        self.assertEqual(hash(mx), hash(b))

        # Fortran contiguous
        nd = ndarray(list(range(30)), shape=[3,2,5], flags=ND_FORTRAN)
        m = memoryview(nd)
        self.assertEqual(hash(m), hash(nd))

        # multi-dimensional slice
        nd = ndarray(list(range(30)), shape=[3,2,5])
        x = nd[::2, ::, ::-1]
        m = memoryview(x)
        self.assertEqual(hash(m), hash(x))

        # multi-dimensional slice with suboffsets
        nd = ndarray(list(range(30)), shape=[2,5,3], flags=ND_PIL)
        x = nd[::2, ::, ::-1]
        m = memoryview(x)
        self.assertEqual(hash(m), hash(x))

        # equality-hash invariant
        x = ndarray(list(range(12)), shape=[12], format='B')
        a = memoryview(x)

        y = ndarray(list(range(12)), shape=[12], format='b')
        b = memoryview(y)

        self.assertEqual(a, b)
        self.assertEqual(hash(a), hash(b))

        # non-byte formats
        nd = ndarray(list(range(12)), shape=[2,2,3], format='L')
        m = memoryview(nd)
        self.assertRaises(ValueError, m.__hash__)

        nd = ndarray(list(range(-6, 6)), shape=[2,2,3], format='h')
        m = memoryview(nd)
        self.assertRaises(ValueError, m.__hash__)

        nd = ndarray(list(range(12)), shape=[2,2,3], format='= L')
        m = memoryview(nd)
        self.assertRaises(ValueError, m.__hash__)

        nd = ndarray(list(range(-6, 6)), shape=[2,2,3], format='< h')
        m = memoryview(nd)
        self.assertRaises(ValueError, m.__hash__)

    def test_memoryview_release(self):

        # Create re-exporter from getbuffer(memoryview), then release the view.
        a = bytearray([1,2,3])
        m = memoryview(a)
        nd = ndarray(m) # re-exporter
        self.assertRaises(BufferError, m.release)
        del nd
        m.release()

        a = bytearray([1,2,3])
        m = memoryview(a)
        nd1 = ndarray(m, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        nd2 = ndarray(nd1, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        self.assertIs(nd2.obj, m)
        self.assertRaises(BufferError, m.release)
        del nd1, nd2
        m.release()

        # chained views
        a = bytearray([1,2,3])
        m1 = memoryview(a)
        m2 = memoryview(m1)
        nd = ndarray(m2) # re-exporter
        m1.release()
        self.assertRaises(BufferError, m2.release)
        del nd
        m2.release()

        a = bytearray([1,2,3])
        m1 = memoryview(a)
        m2 = memoryview(m1)
        nd1 = ndarray(m2, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        nd2 = ndarray(nd1, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        self.assertIs(nd2.obj, m2)
        m1.release()
        self.assertRaises(BufferError, m2.release)
        del nd1, nd2
        m2.release()

        # Allow changing layout while buffers are exported.
        nd = ndarray([1,2,3], shape=[3], flags=ND_VAREXPORT)
        m1 = memoryview(nd)

        nd.push([4,5,6,7,8], shape=[5]) # mutate nd
        m2 = memoryview(nd)

        x = memoryview(m1)
        self.assertEqual(x.tolist(), m1.tolist())

        y = memoryview(m2)
        self.assertEqual(y.tolist(), m2.tolist())
        self.assertEqual(y.tolist(), nd.tolist())
        m2.release()
        y.release()

        nd.pop() # pop the current view
        self.assertEqual(x.tolist(), nd.tolist())

        del nd
        m1.release()
        x.release()

        # If multiple memoryviews share the same managed buffer, implicit
        # release() in the context manager's __exit__() method should still
        # work.
        def catch22(b):
            with memoryview(b) as m2:
                pass

        x = bytearray(b'123')
        with memoryview(x) as m1:
            catch22(m1)
            self.assertEqual(m1[0], ord(b'1'))

        x = ndarray(list(range(12)), shape=[2,2,3], format='l')
        y = ndarray(x, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        z = ndarray(y, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        self.assertIs(z.obj, x)
        with memoryview(z) as m:
            catch22(m)
            self.assertEqual(m[0:1].tolist(), [[[0, 1, 2], [3, 4, 5]]])

        # Test garbage collection.
        for flags in (0, ND_REDIRECT):
            x = bytearray(b'123')
            with memoryview(x) as m1:
                del x
                y = ndarray(m1, getbuf=PyBUF_FULL_RO, flags=flags)
                with memoryview(y) as m2:
                    del y
                    z = ndarray(m2, getbuf=PyBUF_FULL_RO, flags=flags)
                    with memoryview(z) as m3:
                        del z
                        catch22(m3)
                        catch22(m2)
                        catch22(m1)
                        self.assertEqual(m1[0], ord(b'1'))
                        self.assertEqual(m2[1], ord(b'2'))
                        self.assertEqual(m3[2], ord(b'3'))
                        del m3
                    del m2
                del m1

            x = bytearray(b'123')
            with memoryview(x) as m1:
                del x
                y = ndarray(m1, getbuf=PyBUF_FULL_RO, flags=flags)
                with memoryview(y) as m2:
                    del y
                    z = ndarray(m2, getbuf=PyBUF_FULL_RO, flags=flags)
                    with memoryview(z) as m3:
                        del z
                        catch22(m1)
                        catch22(m2)
                        catch22(m3)
                        self.assertEqual(m1[0], ord(b'1'))
                        self.assertEqual(m2[1], ord(b'2'))
                        self.assertEqual(m3[2], ord(b'3'))
                        del m1, m2, m3

        # memoryview.release() fails if the view has exported buffers.
        x = bytearray(b'123')
        with self.assertRaises(BufferError):
            with memoryview(x) as m:
                ex = ndarray(m)
                m[0] == ord(b'1')

    def test_memoryview_redirect(self):

        nd = ndarray([1.0 * x for x in range(12)], shape=[12], format='d')
        a = array.array('d', [1.0 * x for x in range(12)])

        for x in (nd, a):
            y = ndarray(x, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
            z = ndarray(y, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
            m = memoryview(z)

            self.assertIs(y.obj, x)
            self.assertIs(z.obj, x)
            self.assertIs(m.obj, x)

            self.assertEqual(m, x)
            self.assertEqual(m, y)
            self.assertEqual(m, z)

            self.assertEqual(m[1:3], x[1:3])
            self.assertEqual(m[1:3], y[1:3])
            self.assertEqual(m[1:3], z[1:3])
            del y, z
            self.assertEqual(m[1:3], x[1:3])

    def test_memoryview_from_static_exporter(self):

        fmt = 'B'
        lst = [0,1,2,3,4,5,6,7,8,9,10,11]

        # exceptions
        self.assertRaises(TypeError, staticarray, 1, 2, 3)

        # view.obj==x
        x = staticarray()
        y = memoryview(x)
        self.verify(y, obj=x,
                    itemsize=1, fmt=fmt, readonly=True,
                    ndim=1, shape=[12], strides=[1],
                    lst=lst)
        for i in range(12):
            self.assertEqual(y[i], i)
        del x
        del y

        x = staticarray()
        y = memoryview(x)
        del y
        del x

        x = staticarray()
        y = ndarray(x, getbuf=PyBUF_FULL_RO)
        z = ndarray(y, getbuf=PyBUF_FULL_RO)
        m = memoryview(z)
        self.assertIs(y.obj, x)
        self.assertIs(m.obj, z)
        self.verify(m, obj=z,
                    itemsize=1, fmt=fmt, readonly=True,
                    ndim=1, shape=[12], strides=[1],
                    lst=lst)
        del x, y, z, m

        x = staticarray()
        y = ndarray(x, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        z = ndarray(y, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        m = memoryview(z)
        self.assertIs(y.obj, x)
        self.assertIs(z.obj, x)
        self.assertIs(m.obj, x)
        self.verify(m, obj=x,
                    itemsize=1, fmt=fmt, readonly=True,
                    ndim=1, shape=[12], strides=[1],
                    lst=lst)
        del x, y, z, m

        # view.obj==NULL
        x = staticarray(legacy_mode=True)
        y = memoryview(x)
        self.verify(y, obj=None,
                    itemsize=1, fmt=fmt, readonly=True,
                    ndim=1, shape=[12], strides=[1],
                    lst=lst)
        for i in range(12):
            self.assertEqual(y[i], i)
        del x
        del y

        x = staticarray(legacy_mode=True)
        y = memoryview(x)
        del y
        del x

        x = staticarray(legacy_mode=True)
        y = ndarray(x, getbuf=PyBUF_FULL_RO)
        z = ndarray(y, getbuf=PyBUF_FULL_RO)
        m = memoryview(z)
        self.assertIs(y.obj, None)
        self.assertIs(m.obj, z)
        self.verify(m, obj=z,
                    itemsize=1, fmt=fmt, readonly=True,
                    ndim=1, shape=[12], strides=[1],
                    lst=lst)
        del x, y, z, m

        x = staticarray(legacy_mode=True)
        y = ndarray(x, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        z = ndarray(y, getbuf=PyBUF_FULL_RO, flags=ND_REDIRECT)
        m = memoryview(z)
        # Clearly setting view.obj==NULL is inferior, since it
        # messes up the redirection chain:
        self.assertIs(y.obj, None)
        self.assertIs(z.obj, y)
        self.assertIs(m.obj, y)
        self.verify(m, obj=y,
                    itemsize=1, fmt=fmt, readonly=True,
                    ndim=1, shape=[12], strides=[1],
                    lst=lst)
        del x, y, z, m

    def test_memoryview_getbuffer_undefined(self):

        # getbufferproc does not adhere to the new documentation
        nd = ndarray([1,2,3], [3], flags=ND_GETBUF_FAIL|ND_GETBUF_UNDEFINED)
        self.assertRaises(BufferError, memoryview, nd)

    def test_issue_7385(self):
        x = ndarray([1,2,3], shape=[3], flags=ND_GETBUF_FAIL)
        self.assertRaises(BufferError, memoryview, x)


if __name__ == "__main__":
    unittest.main()