bigarray: Add ArrayRef utility

ArrayRef is a tool to find out for a NumPy array its top-level root
parent and remember instructions how to recreate original array from
the root. For example if

	root = arange(1E7)
	z = root[1000:2000]
	a = z[10:20]

`ArrayRef(a)` will find out that the root array for `a` is `root` and
that `a` occupies 1010:1020 bytes in it. The vice versa operation is
also possible, for example given

	aref = ArrayRef(a)

it is possible to restore original `a` from `aref`:

	a_ = aref.deref()
	assert array_equal(a_, a)

the restoration works without copying by creating appropriate view of
root.

ArrayRef should work reliably for arrays of arbitrary dimensions,
strides etc - even fancy arrays created via stride tricks such as arrays
whose elements overlap each other should be supported.

This patch adds ArrayRef with support for regular ndarrays only.

The next patch will add ArrayRef support for BigArray and description
for ArrayRef rationale.

bigarray/__init__.py

 # -*- coding: utf-8 -*-
 # BigArray submodule for Wendelin
-# Copyright (C) 2014-2015  Nexedi SA and Contributors.
+# Copyright (C) 2014-2018  Nexedi SA and Contributors.
 #                          Kirill Smelkov <kirr@nexedi.com>
 #
 # This program is free software: you can Use, Study, Modify and Redistribute
@@ -38,7 +38,8 @@ of physical RAM.
 
 from __future__ import print_function
 from wendelin.lib.calc import mul
-from numpy import ndarray, dtype, sign, newaxis, asarray, argmax
+from numpy import ndarray, dtype, sign, newaxis, asarray, argmax, uint8
+from numpy.lib.stride_tricks import DummyArray
 import logging
 
 
@@ -473,3 +474,247 @@ class BigArray(object):
             logging.warn('... address space can not be mapped at once and have to be')
             logging.warn('... processed in chunks.')
             raise
+
+
+# ----------------------------------------
+
+# InvalidArrayRef is the exception raised when ArrayRef was tried to be
+# dereferenced but found invalid.
+class InvalidArrayRef(Exception):
+    pass
+
+# _flatbytev returns []byte view of array a with index ↑ along with memory
+def _flatbytev(a):
+    b = a[:].view(uint8)
+    # XXX vvv strictly speaking this might raise internally if numpy sees
+    # it cannot reshape without copy.
+    b.shape = -1  # flatten without copy
+    assert len(b.strides) == 1
+    if b.strides[0] < 0:
+        b = b[::-1]
+    assert b.strides[0] == +1
+    return b
+
+# ArrayRef is a reference to NumPy array.
+#
+# The reference is represented by root array object and instructions how to
+# create original array as some view of the root.
+#
+# Use ArrayRef(array) to create reference to an ndarray.
+#
+# Use .deref() to convert ArrayRef to pointed array object.
+class ArrayRef(object):
+    # .root         top-level array object
+    #
+    #   below broot is []byte view of .root array with index ↑ along with memory
+    #
+    # .lo, .hi      raw array data is broot[lo:hi]
+    # .z0           array[0,0,...,0] is pointing ->z0 in broot[lo:hi]
+    #
+    # .shape        shape and strides of the array with data taken from
+    # .stridev      broot[lo:hi] with .z0 as zero offset.
+    #
+    # .dtype        dtype of the array
+    # .atype        type of the array  (e.g. np.ndarray, np.recarray, etc...)
+
+
+    # deref returns ndarray represented by this reference.
+    #
+    # if the reference was found invalid - e.g. it had nonsensical data or
+    # shape/stride out of range - InvalidArrayRef is raised.
+    def deref(self):
+        # broot is []byte view of root array with index ↑ along with memory
+        broot = _flatbytev(self.root)
+
+        # check lo:hi is in within correct range.
+        if not (0 <= self.lo <= self.hi <= len(broot)):
+            raise InvalidArrayRef("lo:hi ([%d, %d]) out of correct [0, %d] range" %
+                    (self.lo, self.hi, len(broot)))
+
+        # bchild is raw []byte underling data for recreated array
+        bchild  = broot[self.lo:self.hi]
+        if not (0 <= self.z0 < len(bchild)):
+            raise InvalidArrayRef("z0 (%d) out of correct [0, %d) range" %
+                    (self.z0, len(bchild)))
+
+        # check .shape and .stridev are within correct range, before
+        # applying unsafe stride tricks.
+        if len(self.shape) != len(self.stridev):
+            raise InvalidArrayRef("shape/stridev len mismatch  (#shape: %d;  #stridev: %d)" %
+                    (len(self.shape), len(self.stridev)))
+
+        # [boffmin:boffmax) is recreated array's byte range rooted at its zero point
+        boffmin = 0
+        boffmax = 0
+        for n, s in zip(self.shape, self.stridev):
+            if n < 0 or int(n) != n:
+                raise InvalidArrayRef("shape (%s) has invalid element: %s" % (self.shape, n))
+            if int(s) != s:
+                raise InvalidArrayRef("stridev %s has invalid element: %s" % (self.stridev, s))
+            if n == 0:
+                continue    # [0] dimension - does not affect anything
+
+            if s > 0:
+                boffmax += s*(n-1)
+            else:
+                boffmin += s*(n-1)
+
+        # when element is read - memory is accessed ↑ for itemsize bytes.
+        # we need to adjust only boffmax because for boffmin it grows ↑ too.
+        boffmax += self.dtype.itemsize
+
+        # [xlo,xhi) is the bchild's range accessed with .shape and .stridev
+        xlo = self.z0 + boffmin
+        xhi = self.z0 + boffmax
+
+        if not (0 <= xlo <= xhi <= len(bchild)):
+            raise InvalidArrayRef(
+                    "shape/stride invalid: cover [%d, %d) while raw data range is [%d, %d)" %
+                    (self.lo + xlo, self.lo + xhi, self.lo, self.hi))
+
+
+        # bchild_z0 points to the same underlying data buffer as bchild, but
+        # zero offset corresponds to zero offset of original array.
+        #
+        # len(bchild_z0) == 1, so that we can be sure bchild_z0 -> bchild
+        # memory pinning always works, not only for positive offsets(*).
+        #
+        # (*) we cannot make len(bchild_z0) == 0 since then, when creating
+        #     empty slice, numpy won't adjust the array pointer at all.
+        #
+        #     it could be also possible to adjust 'data' in __array_interface__
+        #     for += z0, but going explicitly via slicing is more safe.
+        bchild_z0 = bchild[self.z0: self.z0 + 1]
+
+        # restore original array shape/strides/dtype via unsafe trick.
+        #
+        # it should be safe to cover memory corresponding to both negative and
+        # positive offsets to bchild_z0, because bchild_z0 holds reference to
+        # bchild and bchild covers whole raw data range.
+        #
+        # it is also safe because we checked .shape and .stridev not to escape
+        # from bchild data buffer.
+        #
+        # the code below is very close to
+        #
+        #   a = stride_tricks.as_strided(bchild_z0, shape=self.shape, strides=self.stridev)
+        #
+        # but we don't use as_strided() because we also have to change dtype
+        # with shape and strides in one go - else changing dtype after either
+        # via a.dtype = ..., or via a.view(dtype=...) can raise errors like
+        #
+        #   "When changing to a larger dtype, its size must be a
+        #    divisor of the total size in bytes of the last axis
+        #    of the array."
+        aiface = dict(bchild_z0.__array_interface__)
+        aiface['shape']   = tuple(self.shape)
+        aiface['strides'] = tuple(self.stridev)
+        # type: for now we only care that itemsize is the same
+        aiface['typestr'] = '|V%d' % self.dtype.itemsize
+        aiface['descr']   = [('', aiface['typestr'])]
+
+        a = asarray(DummyArray(aiface, base=bchild_z0))
+
+        # restore full dtype - it should not raise here, since itemsize is the same
+        a.dtype = self.dtype
+
+        # restore full array type
+        a = a.view(type=self.atype)
+
+        # we are done
+        return a
+
+
+    # ArrayRef(a) creates reference to ndarray a.
+    def __init__(aref, a):
+        # find root
+        root = a            # top-level ndarray
+        while 1:
+            base = root.base
+
+            # top-level ndarray
+            if base is None:
+                break
+
+            # it was an ndarray (sub)view.
+            if isinstance(base, ndarray):
+                root = base
+                continue
+
+            # it might be also ndarray proxy - e.g. np.lib.stride_tricks.DummyArray
+            # with holding valid .base but not being ndarray.
+            basebase = getattr(base, 'base', None)
+            if isinstance(basebase, ndarray):
+                root = basebase
+                continue
+
+            # base is neither ndarray (sub)class nor ndarray proxy.
+            #
+            # it is top-level ndarray with base taken from an object
+            # with buffer interface, e.g. as here:
+            #
+            #   In [1]: s = '123'
+            #   In [2]: x = ndarray(shape=(1,), buffer=s, dtype='|S3')
+            #   In [3]: x
+            #   Out[3]: array(['123'], dtype='|S3')
+            #   In [4]: x.base
+            #   Out[4]: '123'
+            #
+            # and so it should be treated as top-level ndarray.
+            break
+
+
+        # broot is []byte view of root with idx ↑ along memory
+        broot = _flatbytev(root)
+
+        # [boffmin:boffmax) is a's byte range rooted at its zero point
+        boffmin = 0
+        boffmax = 0
+        assert len(a.shape) == len(a.strides)
+        for n, s in zip(a.shape, a.strides):
+            assert n >= 0
+            if n == 0:
+                continue    # [0] dimension - does not affect anything
+            assert n >= 1
+
+            if s > 0:
+                boffmax += s*(n-1)
+            else:
+                boffmin += s*(n-1)
+
+        # when element is read - memory is accessed ↑ for itemsize bytes.
+        # we need to adjust only boffmax because for boffmin it grows ↑ too.
+        boffmax += a.itemsize
+
+
+        # compute bytes δz in between broot's and a's zero points.
+        # δz should  be >= 0, since broot ↑ along memory.
+        adata = a.__array_interface__.get('data')
+        rdata = broot.__array_interface__.get('data')
+        assert adata is not None, "TODO __array_interface__.data = None"
+        assert rdata is not None, "TODO __array_interface__.data = None"
+        assert isinstance(adata, tuple), "TODO __array_interface__.data is %r" % (adata,)
+        assert isinstance(rdata, tuple), "TODO __array_interface__.data is %r" % (rdata,)
+        # {a,r}data is (data, readonly)
+        zdelta = adata[0] - rdata[0]
+        assert zdelta >= 0
+
+        # broot[lo:hi] is raw []byte underlying data for a, with z0 pointing
+        # to a's zero point.
+        lo = zdelta + boffmin
+        hi = zdelta + boffmax
+        assert 0 <= lo <= hi <= len(broot)
+        z0 = zdelta - lo
+
+        # reference is ready for ndarray root
+        aref.root    = root
+        aref.lo      = lo
+        aref.hi      = hi
+        aref.z0      = z0
+        aref.shape   = a.shape
+        aref.stridev = a.strides
+        aref.dtype   = a.dtype
+        aref.atype   = type(a)
+
+        # we are done
+        return

bigarray/tests/test_basic.py

+# -*- coding: utf-8 -*-
 # Wendeling.core.bigarray | Basic tests
-# Copyright (C) 2014-2015  Nexedi SA and Contributors.
+# Copyright (C) 2014-2018  Nexedi SA and Contributors.
 #                          Kirill Smelkov <kirr@nexedi.com>
 #
 # This program is free software: you can Use, Study, Modify and Redistribute
@@ -18,12 +19,13 @@
 # See COPYING file for full licensing terms.
 # See https://www.nexedi.com/licensing for rationale and options.
 
-from wendelin.bigarray import BigArray
+from wendelin.bigarray import BigArray, ArrayRef, _flatbytev
 from wendelin.bigfile import BigFile
 from wendelin.lib.mem import memcpy
 from wendelin.lib.calc import mul
-from numpy import ndarray, dtype, int64, int32, uint32, uint8, all, zeros, arange, \
-        array_equal, asarray
+from numpy import ndarray, dtype, int64, int32, uint32, int16, uint8, all, zeros, arange, \
+        array_equal, asarray, newaxis, swapaxes
+from numpy.lib.stride_tricks import as_strided
 import numpy
 
 from pytest import raises
@@ -588,3 +590,227 @@ def test_bigarray_to_ndarray():
     for i in range(48,65):
         C = BigArray(((1<<i)-1,), uint8, Zh)
         raises(MemoryError, 'asarray(C)')
+
+
+
+
+def test_arrayref():
+    # test data - all items are unique - so we can check array by content
+    data = zeros(PS, dtype=uint8)
+    data32 = data.view(uint32)
+    data32[:] = arange(len(data32), dtype=uint32)
+    data[:256] = arange(256, dtype=uint8)   # first starting bytes are all unique
+
+    # regular ndarray without parent at all
+    ref = ArrayRef(data)
+    assert ref.root is data
+    assert ref.lo == 0
+    assert ref.hi == len(data)
+    assert ref.z0 == 0
+    assert ref.shape == data.shape
+    assert ref.stridev == data.strides
+    assert ref.dtype == data.dtype
+    assert array_equal(ref.deref(), data)
+
+    # regular ndarrays with parent
+    ref = ArrayRef(data32)
+    assert ref.root is data
+    assert ref.lo == 0
+    assert ref.hi == len(data)
+    assert ref.z0 == 0
+    assert ref.shape == data32.shape
+    assert ref.stridev == data32.strides
+    assert ref.dtype == data32.dtype
+    assert array_equal(ref.deref(), data32)
+
+    a = data[100:140]
+    ref = ArrayRef(a)
+    assert ref.root is data
+    assert ref.lo == 100
+    assert ref.hi == 140
+    assert ref.z0 == 0
+    assert ref.shape == (40,)
+    assert ref.stridev == (1,)
+    assert ref.dtype == data.dtype
+    assert array_equal(ref.deref(), a)
+
+    a = data[140:100:-1]
+    ref = ArrayRef(a)
+    assert ref.root is data
+    assert ref.lo == 101
+    assert ref.hi == 141
+    assert ref.z0 == 39
+    assert ref.shape == (40,)
+    assert ref.stridev == (-1,)
+    assert ref.dtype == data.dtype
+    assert array_equal(ref.deref(), a)
+
+    a = data[100:140:-1]   # empty
+    ref = ArrayRef(a)
+    assert ref.root is data
+    assert ref.lo == 0
+    assert ref.hi == 1
+    assert ref.z0 == 0
+    assert ref.shape == (0,)
+    assert ref.stridev == (1,)
+    assert ref.dtype == data.dtype
+    assert array_equal(ref.deref(), a)
+
+    # rdata is the same as data[::-1] but without base - i.e. it is toplevel
+    m = memoryview(data[::-1])
+    rdata = asarray(m)
+    assert array_equal(rdata[::-1], data)
+    assert rdata.strides == (-1,)
+    m_ = rdata.base
+    assert isinstance(m_, memoryview)
+    #assert m_ is m  XXX strangely it is another object, not exactly m
+    # XXX however rdata.strides<0 and no rdata.base.base is enough for us here.
+    raises(AttributeError, 'm_.base')
+
+    a = rdata[100:140]
+    ref = ArrayRef(a)
+    assert ref.root is rdata
+    assert ref.lo == PS - 140
+    assert ref.hi == PS - 100
+    assert ref.z0 == 39
+    assert ref.shape == (40,)
+    assert ref.stridev == (-1,)
+    assert ref.dtype == data.dtype
+    assert array_equal(ref.deref(), a)
+
+
+    for root in (data, rdata):
+        # refok verifies whether ArrayRef(x) works ok
+        def refok(x):
+            ref = ArrayRef(x)
+            assert ref.root is root
+            x_ = ref.deref()
+            assert array_equal(x_, x)
+            assert x_.dtype == x.dtype
+            assert type(x_) == type(x)
+
+            # check that deref won't access range outside lo:hi - by copying
+            # root, setting bytes in adjusted root outside lo:hi to either 0x00
+            # or 0xff and tweaking ref.root = root_.
+            root_ = numpy.copy(_flatbytev(root[:]))
+            root_[:ref.lo] = 0
+            root_[ref.hi:] = 0
+            ref.root = root_
+            assert array_equal(ref.deref(), x)
+            root_[:ref.lo] = 0xff
+            root_[ref.hi:] = 0xff
+            assert array_equal(ref.deref(), x)
+
+
+        if root is rdata:
+            a = root[::-1]              # rdata
+        else:
+            a = root[:]                 # data
+        assert array_equal(a, data)
+
+        # subslices that is possible to get by just indexing
+        refok( a[:]         )
+        refok( a[1:2]       )
+        refok( a[1:10]      )
+        refok( a[1:10:2]    )
+        refok( a[1:10:3]    )
+        refok( a[1:10:-1]   )   # empty (.size = 0)
+        refok( a[10:1:-1]   )
+        refok( a[10:1:-2]   )
+        refok( a[10:1:-3]   )
+
+        # long chain root -> a -> a[...] -> a[...] -> leaf
+        l = a[2:118]
+        l = l.view(uint32)[3:20]
+        l = l[1:9]
+        refok(l)
+
+        # not aligned - it is not possible to get to resulting slice just by indexing A
+        refok( a.view(uint8)[2:-2].view(uint32)         )
+        refok( a.view(uint8)[2:-2].view(uint32)[::-1]   )
+
+        refok( a.view(int64)        )   # change of type ↑ in size
+        refok( a.view(int64)[::-1]  )
+        refok( a.view(int16)        )   # change of type ↓ in size
+        refok( a.view(int16)[::-1]  )
+
+        # change of type to size not multiple of original
+        refok( a[1:1+5*10].view('V5')       )   # 4 -> 5
+        refok( a[1:1+5*10].view('V5')[::-1] )
+        refok( a[1:1+3*10].view('V3')       )   # 4 -> 3
+        refok( a[1:1+3*10].view('V3')[::-1] )
+
+        # intermediate parent with <0 stride
+        r = a[1:1+3*10].view('V3')[::-1]
+        refok( r[-2:2:-1]   )
+
+        # 2d array
+        x = a.view(uint32).reshape((8, -1))
+        y = swapaxes(x, 0,1)
+        assert x.shape   == (8, PS//(4*8))
+        assert x.strides == (PS//8, 4)
+        assert y.shape   == (PS//(4*8), 8)
+        assert y.strides == (4, PS//8)
+
+        refok( x )
+        refok( y )
+
+        # array with both >0 and <0 strides
+        x_ = x[:,::-1]
+        y_ = y[:,::-1]
+        assert x_.shape   == x.shape
+        assert x_.strides == (PS//8, -4)
+        assert y_.shape   == y.shape
+        assert y_.strides == (4, -PS//8)
+
+        refok( x_ )
+        refok( y_ )
+
+        # array with [1] dimension
+        z1 = x[:, newaxis, :]
+        assert z1.shape   == (8, 1, PS//(4*8))
+        assert z1.strides == (PS//8, 0, 4)
+
+        refok(z1)
+
+        # array with [0] dimension
+        z0 = z1[:, 0:0, :]
+        assert z0.shape   == (8, 0, PS//(4*8))
+        assert z0.strides == (PS//8, 0, 4)
+
+        refok(z0)
+
+        # tricky array overlapping itself
+        t = a.view(uint32)
+        assert t.shape    == (PS//4,)
+        assert t.strides  == (4,)
+        assert t.itemsize == 4
+        t = as_strided(t, strides=(1,))
+        assert t.shape    == (PS//4,)
+        assert t.strides  == (1,)
+        assert t.itemsize == 4
+
+        refok(t)
+
+        # structured dtype
+        s = a.view(dtype=[('width', '<i2'), ('length', '<i2')])
+        assert s.shape    == (PS//4,)
+        assert s.strides  == (4,)
+        assert s.itemsize == 4
+        refok(s)
+
+        s_ = s['length']
+        assert s_.shape    == (PS//4,)
+        assert s_.strides  == (4,)
+        assert s_.itemsize == 2
+        refok(s_)
+
+
+        # ndarray subclass, e.g. np.recarray
+        r = s.view(type=numpy.recarray)
+        assert isinstance(r, numpy.recarray)
+        assert r.shape    == (PS//4,)
+        assert r.strides  == (4,)
+        assert r.itemsize == 4
+        assert array_equal(r.length, s['length'])
+        refok(r)