python/flatbuffers/builder.py

# Copyright 2014 Google Inc. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from . import number_types as N
from .number_types import (UOffsetTFlags, SOffsetTFlags, VOffsetTFlags)

from . import encode
from . import packer

from . import compat
from .compat import range_func
from .compat import memoryview_type
from .compat import import_numpy, NumpyRequiredForThisFeature

import warnings

np = import_numpy()
## @file
## @addtogroup flatbuffers_python_api
## @{

## @cond FLATBUFFERS_INTERNAL
class OffsetArithmeticError(RuntimeError):
    """
    Error caused by an Offset arithmetic error. Probably caused by bad
    writing of fields. This is considered an unreachable situation in
    normal circumstances.
    """
    pass


class IsNotNestedError(RuntimeError):
    """
    Error caused by using a Builder to write Object data when not inside
    an Object.
    """
    pass


class IsNestedError(RuntimeError):
    """
    Error caused by using a Builder to begin an Object when an Object is
    already being built.
    """
    pass


class StructIsNotInlineError(RuntimeError):
    """
    Error caused by using a Builder to write a Struct at a location that
    is not the current Offset.
    """
    pass


class BuilderSizeError(RuntimeError):
    """
    Error caused by causing a Builder to exceed the hardcoded limit of 2
    gigabytes.
    """
    pass

class BuilderNotFinishedError(RuntimeError):
    """
    Error caused by not calling `Finish` before calling `Output`.
    """
    pass

class EndVectorLengthMismatched(RuntimeError):
    """
    The number of elements passed to EndVector does not match the number 
    specified in StartVector.
    """
    pass


# VtableMetadataFields is the count of metadata fields in each vtable.
VtableMetadataFields = 2
## @endcond

class Builder(object):
    """ A Builder is used to construct one or more FlatBuffers.

    Typically, Builder objects will be used from code generated by the `flatc`
    compiler.

    A Builder constructs byte buffers in a last-first manner for simplicity and
    performance during reading.

    Internally, a Builder is a state machine for creating FlatBuffer objects.

    It holds the following internal state:
        - Bytes: an array of bytes.
        - current_vtable: a list of integers.
        - vtables: a hash of vtable entries.

    Attributes:
      Bytes: The internal `bytearray` for the Builder.
      finished: A boolean determining if the Builder has been finalized.
    """

    ## @cond FLATBUFFERS_INTENRAL
    __slots__ = ("Bytes", "current_vtable", "head", "minalign", "objectEnd",
                 "vtables", "nested", "forceDefaults", "finished", "vectorNumElems")

    """Maximum buffer size constant, in bytes.

    Builder will never allow it's buffer grow over this size.
    Currently equals 2Gb.
    """
    MAX_BUFFER_SIZE = 2**31
    ## @endcond

    def __init__(self, initialSize=1024):
        """Initializes a Builder of size `initial_size`.

        The internal buffer is grown as needed.
        """

        if not (0 <= initialSize <= Builder.MAX_BUFFER_SIZE):
            msg = "flatbuffers: Cannot create Builder larger than 2 gigabytes."
            raise BuilderSizeError(msg)

        self.Bytes = bytearray(initialSize)
        ## @cond FLATBUFFERS_INTERNAL
        self.current_vtable = None
        self.head = UOffsetTFlags.py_type(initialSize)
        self.minalign = 1
        self.objectEnd = None
        self.vtables = {}
        self.nested = False
        self.forceDefaults = False
        ## @endcond
        self.finished = False

    def Output(self):
        """Return the portion of the buffer that has been used for writing data.

        This is the typical way to access the FlatBuffer data inside the
        builder. If you try to access `Builder.Bytes` directly, you would need
        to manually index it with `Head()`, since the buffer is constructed
        backwards.

        It raises BuilderNotFinishedError if the buffer has not been finished
        with `Finish`.
        """

        if not self.finished:
            raise BuilderNotFinishedError()

        return self.Bytes[self.Head():]

    ## @cond FLATBUFFERS_INTERNAL
    def StartObject(self, numfields):
        """StartObject initializes bookkeeping for writing a new object."""

        self.assertNotNested()

        # use 32-bit offsets so that arithmetic doesn't overflow.
        self.current_vtable = [0 for _ in range_func(numfields)]
        self.objectEnd = self.Offset()
        self.nested = True

    def WriteVtable(self):
        """
        WriteVtable serializes the vtable for the current object, if needed.

        Before writing out the vtable, this checks pre-existing vtables for
        equality to this one. If an equal vtable is found, point the object to
        the existing vtable and return.

        Because vtable values are sensitive to alignment of object data, not
        all logically-equal vtables will be deduplicated.

        A vtable has the following format:
          <VOffsetT: size of the vtable in bytes, including this value>
          <VOffsetT: size of the object in bytes, including the vtable offset>
          <VOffsetT: offset for a field> * N, where N is the number of fields
                     in the schema for this type. Includes deprecated fields.
        Thus, a vtable is made of 2 + N elements, each VOffsetT bytes wide.

        An object has the following format:
          <SOffsetT: offset to this object's vtable (may be negative)>
          <byte: data>+
        """

        # Prepend a zero scalar to the object. Later in this function we'll
        # write an offset here that points to the object's vtable:
        self.PrependSOffsetTRelative(0)

        objectOffset = self.Offset()

        vtKey = []
        trim = True
        for elem in reversed(self.current_vtable):
            if elem == 0:
                if trim:
                    continue
            else:
                elem = objectOffset - elem
                trim = False

            vtKey.append(elem)

        vtKey = tuple(vtKey)
        vt2Offset = self.vtables.get(vtKey)
        if vt2Offset is None:
            # Did not find a vtable, so write this one to the buffer.

            # Write out the current vtable in reverse , because
            # serialization occurs in last-first order:
            i = len(self.current_vtable) - 1
            trailing = 0
            trim = True
            while i >= 0:
                off = 0
                elem = self.current_vtable[i]
                i -= 1

                if elem == 0:
                    if trim:
                        trailing += 1
                        continue
                else:
                    # Forward reference to field;
                    # use 32bit number to ensure no overflow:
                    off = objectOffset - elem
                    trim = False

                self.PrependVOffsetT(off)

            # The two metadata fields are written last.

            # First, store the object bytesize:
            objectSize = UOffsetTFlags.py_type(objectOffset - self.objectEnd)
            self.PrependVOffsetT(VOffsetTFlags.py_type(objectSize))

            # Second, store the vtable bytesize:
            vBytes = len(self.current_vtable) - trailing + VtableMetadataFields
            vBytes *= N.VOffsetTFlags.bytewidth
            self.PrependVOffsetT(VOffsetTFlags.py_type(vBytes))

            # Next, write the offset to the new vtable in the
            # already-allocated SOffsetT at the beginning of this object:
            objectStart = SOffsetTFlags.py_type(len(self.Bytes) - objectOffset)
            encode.Write(packer.soffset, self.Bytes, objectStart,
                         SOffsetTFlags.py_type(self.Offset() - objectOffset))

            # Finally, store this vtable in memory for future
            # deduplication:
            self.vtables[vtKey] = self.Offset()
        else:
            # Found a duplicate vtable.
            objectStart = SOffsetTFlags.py_type(len(self.Bytes) - objectOffset)
            self.head = UOffsetTFlags.py_type(objectStart)

            # Write the offset to the found vtable in the
            # already-allocated SOffsetT at the beginning of this object:
            encode.Write(packer.soffset, self.Bytes, self.Head(),
                         SOffsetTFlags.py_type(vt2Offset - objectOffset))

        self.current_vtable = None
        return objectOffset

    def EndObject(self):
        """EndObject writes data necessary to finish object construction."""
        self.assertNested()
        self.nested = False
        return self.WriteVtable()

    def growByteBuffer(self):
        """Doubles the size of the byteslice, and copies the old data towards
           the end of the new buffer (since we build the buffer backwards)."""
        if len(self.Bytes) == Builder.MAX_BUFFER_SIZE:
            msg = "flatbuffers: cannot grow buffer beyond 2 gigabytes"
            raise BuilderSizeError(msg)

        newSize = min(len(self.Bytes) * 2, Builder.MAX_BUFFER_SIZE)
        if newSize == 0:
            newSize = 1
        bytes2 = bytearray(newSize)
        bytes2[newSize-len(self.Bytes):] = self.Bytes
        self.Bytes = bytes2
    ## @endcond

    def Head(self):
        """Get the start of useful data in the underlying byte buffer.

        Note: unlike other functions, this value is interpreted as from the
        left.
        """
        ## @cond FLATBUFFERS_INTERNAL
        return self.head
        ## @endcond

    ## @cond FLATBUFFERS_INTERNAL
    def Offset(self):
        """Offset relative to the end of the buffer."""
        return UOffsetTFlags.py_type(len(self.Bytes) - self.Head())

    def Pad(self, n):
        """Pad places zeros at the current offset."""
        for i in range_func(n):
            self.Place(0, N.Uint8Flags)

    def Prep(self, size, additionalBytes):
        """
        Prep prepares to write an element of `size` after `additional_bytes`
        have been written, e.g. if you write a string, you need to align
        such the int length field is aligned to SizeInt32, and the string
        data follows it directly.
        If all you need to do is align, `additionalBytes` will be 0.
        """

        # Track the biggest thing we've ever aligned to.
        if size > self.minalign:
            self.minalign = size

        # Find the amount of alignment needed such that `size` is properly
        # aligned after `additionalBytes`:
        alignSize = (~(len(self.Bytes) - self.Head() + additionalBytes)) + 1
        alignSize &= (size - 1)

        # Reallocate the buffer if needed:
        while self.Head() < alignSize+size+additionalBytes:
            oldBufSize = len(self.Bytes)
            self.growByteBuffer()
            updated_head = self.head + len(self.Bytes) - oldBufSize
            self.head = UOffsetTFlags.py_type(updated_head)
        self.Pad(alignSize)

    def PrependSOffsetTRelative(self, off):
        """
        PrependSOffsetTRelative prepends an SOffsetT, relative to where it
        will be written.
        """

        # Ensure alignment is already done:
        self.Prep(N.SOffsetTFlags.bytewidth, 0)
        if not (off <= self.Offset()):
            msg = "flatbuffers: Offset arithmetic error."
            raise OffsetArithmeticError(msg)
        off2 = self.Offset() - off + N.SOffsetTFlags.bytewidth
        self.PlaceSOffsetT(off2)
    ## @endcond

    def PrependUOffsetTRelative(self, off):
        """Prepends an unsigned offset into vector data, relative to where it
        will be written.
        """

        # Ensure alignment is already done:
        self.Prep(N.UOffsetTFlags.bytewidth, 0)
        if not (off <= self.Offset()):
            msg = "flatbuffers: Offset arithmetic error."
            raise OffsetArithmeticError(msg)
        off2 = self.Offset() - off + N.UOffsetTFlags.bytewidth
        self.PlaceUOffsetT(off2)

    ## @cond FLATBUFFERS_INTERNAL
    def StartVector(self, elemSize, numElems, alignment):
        """
        StartVector initializes bookkeeping for writing a new vector.

        A vector has the following format:
          - <UOffsetT: number of elements in this vector>
          - <T: data>+, where T is the type of elements of this vector.
        """

        self.assertNotNested()
        self.nested = True
        self.vectorNumElems = numElems
        self.Prep(N.Uint32Flags.bytewidth, elemSize*numElems)
        self.Prep(alignment, elemSize*numElems)  # In case alignment > int.
        return self.Offset()
    ## @endcond

    def EndVector(self, numElems = None):
        """EndVector writes data necessary to finish vector construction."""

        self.assertNested()
        ## @cond FLATBUFFERS_INTERNAL
        self.nested = False
        ## @endcond
               
        if numElems:
            warnings.warn("numElems is deprecated.", 
                          DeprecationWarning, stacklevel=2)
            if numElems != self.vectorNumElems:
                raise EndVectorLengthMismatched();

        # we already made space for this, so write without PrependUint32
        self.PlaceUOffsetT(self.vectorNumElems)
        self.vectorNumElems = None
        return self.Offset()

    def CreateString(self, s, encoding='utf-8', errors='strict'):
        """CreateString writes a null-terminated byte string as a vector."""

        self.assertNotNested()
        ## @cond FLATBUFFERS_INTERNAL
        self.nested = True
        ## @endcond

        if isinstance(s, compat.string_types):
            x = s.encode(encoding, errors)
        elif isinstance(s, compat.binary_types):
            x = s
        else:
            raise TypeError("non-string passed to CreateString")

        self.Prep(N.UOffsetTFlags.bytewidth, (len(x)+1)*N.Uint8Flags.bytewidth)
        self.Place(0, N.Uint8Flags)

        l = UOffsetTFlags.py_type(len(s))
        ## @cond FLATBUFFERS_INTERNAL
        self.head = UOffsetTFlags.py_type(self.Head() - l)
        ## @endcond
        self.Bytes[self.Head():self.Head()+l] = x

        self.vectorNumElems = len(x)
        return self.EndVector()

    def CreateByteVector(self, x):
        """CreateString writes a byte vector."""

        self.assertNotNested()
        ## @cond FLATBUFFERS_INTERNAL
        self.nested = True
        ## @endcond

        if not isinstance(x, compat.binary_types):
            raise TypeError("non-byte vector passed to CreateByteVector")

        self.Prep(N.UOffsetTFlags.bytewidth, len(x)*N.Uint8Flags.bytewidth)

        l = UOffsetTFlags.py_type(len(x))
        ## @cond FLATBUFFERS_INTERNAL
        self.head = UOffsetTFlags.py_type(self.Head() - l)
        ## @endcond
        self.Bytes[self.Head():self.Head()+l] = x

        self.vectorNumElems = len(x)
        return self.EndVector()

    def CreateNumpyVector(self, x):
        """CreateNumpyVector writes a numpy array into the buffer."""

        if np is None:
            # Numpy is required for this feature
            raise NumpyRequiredForThisFeature("Numpy was not found.")

        if not isinstance(x, np.ndarray):
            raise TypeError("non-numpy-ndarray passed to CreateNumpyVector")

        if x.dtype.kind not in ['b', 'i', 'u', 'f']:
            raise TypeError("numpy-ndarray holds elements of unsupported datatype")

        if x.ndim > 1:
            raise TypeError("multidimensional-ndarray passed to CreateNumpyVector")

        self.StartVector(x.itemsize, x.size, x.dtype.alignment)

        # Ensure little endian byte ordering
        if x.dtype.str[0] == "<":
            x_lend = x
        else:
            x_lend = x.byteswap(inplace=False)

        # Calculate total length
        l = UOffsetTFlags.py_type(x_lend.itemsize * x_lend.size)
        ## @cond FLATBUFFERS_INTERNAL
        self.head = UOffsetTFlags.py_type(self.Head() - l)
        ## @endcond

        # tobytes ensures c_contiguous ordering
        self.Bytes[self.Head():self.Head()+l] = x_lend.tobytes(order='C')

        self.vectorNumElems = x.size
        return self.EndVector()

    ## @cond FLATBUFFERS_INTERNAL
    def assertNested(self):
        """
        Check that we are in the process of building an object.
        """

        if not self.nested:
            raise IsNotNestedError()

    def assertNotNested(self):
        """
        Check that no other objects are being built while making this
        object. If not, raise an exception.
        """

        if self.nested:
            raise IsNestedError()

    def assertStructIsInline(self, obj):
        """
        Structs are always stored inline, so need to be created right
        where they are used. You'll get this error if you created it
        elsewhere.
        """

        N.enforce_number(obj, N.UOffsetTFlags)
        if obj != self.Offset():
            msg = ("flatbuffers: Tried to write a Struct at an Offset that "
                   "is different from the current Offset of the Builder.")
            raise StructIsNotInlineError(msg)

    def Slot(self, slotnum):
        """
        Slot sets the vtable key `voffset` to the current location in the
        buffer.

        """
        self.assertNested()
        self.current_vtable[slotnum] = self.Offset()
    ## @endcond

    def __Finish(self, rootTable, sizePrefix, file_identifier=None):
        """Finish finalizes a buffer, pointing to the given `rootTable`."""
        N.enforce_number(rootTable, N.UOffsetTFlags)

        prepSize = N.UOffsetTFlags.bytewidth
        if file_identifier is not None:
            prepSize += N.Int32Flags.bytewidth
        if sizePrefix:
            prepSize += N.Int32Flags.bytewidth
        self.Prep(self.minalign, prepSize)

        if file_identifier is not None:
            self.Prep(N.UOffsetTFlags.bytewidth, encode.FILE_IDENTIFIER_LENGTH)

            # Convert bytes object file_identifier to an array of 4 8-bit integers,
            # and use big-endian to enforce size compliance.
            # https://docs.python.org/2/library/struct.html#format-characters
            file_identifier = N.struct.unpack(">BBBB", file_identifier)
            for i in range(encode.FILE_IDENTIFIER_LENGTH-1, -1, -1):
                # Place the bytes of the file_identifer in reverse order:
                self.Place(file_identifier[i], N.Uint8Flags)

        self.PrependUOffsetTRelative(rootTable)
        if sizePrefix:
            size = len(self.Bytes) - self.Head()
            N.enforce_number(size, N.Int32Flags)
            self.PrependInt32(size)
        self.finished = True
        return self.Head()

    def Finish(self, rootTable, file_identifier=None):
        """Finish finalizes a buffer, pointing to the given `rootTable`."""
        return self.__Finish(rootTable, False, file_identifier=file_identifier)

    def FinishSizePrefixed(self, rootTable, file_identifier=None):
        """
        Finish finalizes a buffer, pointing to the given `rootTable`,
        with the size prefixed.
        """
        return self.__Finish(rootTable, True, file_identifier=file_identifier)

    ## @cond FLATBUFFERS_INTERNAL
    def Prepend(self, flags, off):
        self.Prep(flags.bytewidth, 0)
        self.Place(off, flags)

    def PrependSlot(self, flags, o, x, d):
        if x is not None:
            N.enforce_number(x, flags)
        if d is not None:
            N.enforce_number(d, flags)
        if x != d or (self.forceDefaults and d is not None):
            self.Prepend(flags, x)
            self.Slot(o)

    def PrependBoolSlot(self, *args): self.PrependSlot(N.BoolFlags, *args)

    def PrependByteSlot(self, *args): self.PrependSlot(N.Uint8Flags, *args)

    def PrependUint8Slot(self, *args): self.PrependSlot(N.Uint8Flags, *args)

    def PrependUint16Slot(self, *args): self.PrependSlot(N.Uint16Flags, *args)

    def PrependUint32Slot(self, *args): self.PrependSlot(N.Uint32Flags, *args)

    def PrependUint64Slot(self, *args): self.PrependSlot(N.Uint64Flags, *args)

    def PrependInt8Slot(self, *args): self.PrependSlot(N.Int8Flags, *args)

    def PrependInt16Slot(self, *args): self.PrependSlot(N.Int16Flags, *args)

    def PrependInt32Slot(self, *args): self.PrependSlot(N.Int32Flags, *args)

    def PrependInt64Slot(self, *args): self.PrependSlot(N.Int64Flags, *args)

    def PrependFloat32Slot(self, *args): self.PrependSlot(N.Float32Flags,
                                                          *args)

    def PrependFloat64Slot(self, *args): self.PrependSlot(N.Float64Flags,
                                                          *args)

    def PrependUOffsetTRelativeSlot(self, o, x, d):
        """
        PrependUOffsetTRelativeSlot prepends an UOffsetT onto the object at
        vtable slot `o`. If value `x` equals default `d`, then the slot will
        be set to zero and no other data will be written.
        """

        if x != d or self.forceDefaults:
            self.PrependUOffsetTRelative(x)
            self.Slot(o)

    def PrependStructSlot(self, v, x, d):
        """
        PrependStructSlot prepends a struct onto the object at vtable slot `o`.
        Structs are stored inline, so nothing additional is being added.
        In generated code, `d` is always 0.
        """

        N.enforce_number(d, N.UOffsetTFlags)
        if x != d:
            self.assertStructIsInline(x)
            self.Slot(v)

    ## @endcond

    def PrependBool(self, x):
        """Prepend a `bool` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.BoolFlags, x)

    def PrependByte(self, x):
        """Prepend a `byte` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Uint8Flags, x)

    def PrependUint8(self, x):
        """Prepend an `uint8` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Uint8Flags, x)

    def PrependUint16(self, x):
        """Prepend an `uint16` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Uint16Flags, x)

    def PrependUint32(self, x):
        """Prepend an `uint32` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Uint32Flags, x)

    def PrependUint64(self, x):
        """Prepend an `uint64` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Uint64Flags, x)

    def PrependInt8(self, x):
        """Prepend an `int8` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Int8Flags, x)

    def PrependInt16(self, x):
        """Prepend an `int16` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Int16Flags, x)

    def PrependInt32(self, x):
        """Prepend an `int32` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Int32Flags, x)

    def PrependInt64(self, x):
        """Prepend an `int64` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Int64Flags, x)

    def PrependFloat32(self, x):
        """Prepend a `float32` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Float32Flags, x)

    def PrependFloat64(self, x):
        """Prepend a `float64` to the Builder buffer.

        Note: aligns and checks for space.
        """
        self.Prepend(N.Float64Flags, x)

    def ForceDefaults(self, forceDefaults):
        """
        In order to save space, fields that are set to their default value
        don't get serialized into the buffer. Forcing defaults provides a
        way to manually disable this optimization. When set to `True`, will
        always serialize default values.
        """
        self.forceDefaults = forceDefaults

##############################################################

    ## @cond FLATBUFFERS_INTERNAL
    def PrependVOffsetT(self, x): self.Prepend(N.VOffsetTFlags, x)

    def Place(self, x, flags):
        """
        Place prepends a value specified by `flags` to the Builder,
        without checking for available space.
        """

        N.enforce_number(x, flags)
        self.head = self.head - flags.bytewidth
        encode.Write(flags.packer_type, self.Bytes, self.Head(), x)

    def PlaceVOffsetT(self, x):
        """PlaceVOffsetT prepends a VOffsetT to the Builder, without checking
        for space.
        """
        N.enforce_number(x, N.VOffsetTFlags)
        self.head = self.head - N.VOffsetTFlags.bytewidth
        encode.Write(packer.voffset, self.Bytes, self.Head(), x)

    def PlaceSOffsetT(self, x):
        """PlaceSOffsetT prepends a SOffsetT to the Builder, without checking
        for space.
        """
        N.enforce_number(x, N.SOffsetTFlags)
        self.head = self.head - N.SOffsetTFlags.bytewidth
        encode.Write(packer.soffset, self.Bytes, self.Head(), x)

    def PlaceUOffsetT(self, x):
        """PlaceUOffsetT prepends a UOffsetT to the Builder, without checking
        for space.
        """
        N.enforce_number(x, N.UOffsetTFlags)
        self.head = self.head - N.UOffsetTFlags.bytewidth
        encode.Write(packer.uoffset, self.Bytes, self.Head(), x)
    ## @endcond

## @cond FLATBUFFERS_INTERNAL
def vtableEqual(a, objectStart, b):
    """vtableEqual compares an unwritten vtable to a written vtable."""

    N.enforce_number(objectStart, N.UOffsetTFlags)

    if len(a) * N.VOffsetTFlags.bytewidth != len(b):
        return False

    for i, elem in enumerate(a):
        x = encode.Get(packer.voffset, b, i * N.VOffsetTFlags.bytewidth)

        # Skip vtable entries that indicate a default value.
        if x == 0 and elem == 0:
            pass
        else:
            y = objectStart - elem
            if x != y:
                return False
    return True
## @endcond
## @}