arrayobj.py

"""
Implementation of operations on Array objects and objects supporting
the buffer protocol.
"""

from __future__ import print_function, absolute_import, division

import functools
import math
import operator

from llvmlite import ir
import llvmlite.llvmpy.core as lc
from llvmlite.llvmpy.core import Constant

import numpy as np

from numba import types, cgutils, typing, utils, extending, pndindex, errors
from numba.numpy_support import (as_dtype, carray, farray, is_contiguous,
                                 is_fortran)
from numba.numpy_support import version as numpy_version
from numba.numpy_support import type_can_asarray
from numba.numpy_support import is_nonelike
from numba.targets.imputils import (lower_builtin, lower_getattr,
                                    lower_getattr_generic,
                                    lower_setattr_generic,
                                    lower_cast, lower_constant,
                                    iternext_impl, impl_ret_borrowed,
                                    impl_ret_new_ref, impl_ret_untracked,
                                    RefType)
from numba.typing import signature
from numba.extending import register_jitable, overload, overload_method
from . import quicksort, mergesort, slicing


def set_range_metadata(builder, load, lower_bound, upper_bound):
    """
    Set the "range" metadata on a load instruction.
    Note the interval is in the form [lower_bound, upper_bound).
    """
    range_operands = [Constant.int(load.type, lower_bound),
                      Constant.int(load.type, upper_bound)]
    md = builder.module.add_metadata(range_operands)
    load.set_metadata("range", md)


def mark_positive(builder, load):
    """
    Mark the result of a load instruction as positive (or zero).
    """
    upper_bound = (1 << (load.type.width - 1)) - 1
    set_range_metadata(builder, load, 0, upper_bound)


def make_array(array_type):
    """
    Return the Structure representation of the given *array_type*
    (an instance of types.ArrayCompatible).

    Note this does not call __array_wrap__ in case a new array structure
    is being created (rather than populated).
    """
    real_array_type = array_type.as_array
    base = cgutils.create_struct_proxy(real_array_type)
    ndim = real_array_type.ndim

    class ArrayStruct(base):

        def _make_refs(self, ref):
            sig = signature(real_array_type, array_type)
            try:
                array_impl = self._context.get_function('__array__', sig)
            except NotImplementedError:
                return super(ArrayStruct, self)._make_refs(ref)

            # Return a wrapped structure and its unwrapped reference
            datamodel = self._context.data_model_manager[array_type]
            be_type = self._get_be_type(datamodel)
            if ref is None:
                outer_ref = cgutils.alloca_once(self._builder, be_type, zfill=True)
            else:
                outer_ref = ref
            # NOTE: __array__ is called with a pointer and expects a pointer
            # in return!
            ref = array_impl(self._builder, (outer_ref,))
            return outer_ref, ref

        @property
        def shape(self):
            """
            Override .shape to inform LLVM that its elements are all positive.
            """
            builder = self._builder
            if ndim == 0:
                return base.__getattr__(self, "shape")

            # Unfortunately, we can't use llvm.assume as its presence can
            # seriously pessimize performance,
            # *and* the range metadata currently isn't improving anything here,
            # see https://llvm.org/bugs/show_bug.cgi?id=23848 !
            ptr = self._get_ptr_by_name("shape")
            dims = []
            for i in range(ndim):
                dimptr = cgutils.gep_inbounds(builder, ptr, 0, i)
                load = builder.load(dimptr)
                dims.append(load)
                mark_positive(builder, load)

            return cgutils.pack_array(builder, dims)

    return ArrayStruct


def get_itemsize(context, array_type):
    """
    Return the item size for the given array or buffer type.
    """
    llty = context.get_data_type(array_type.dtype)
    return context.get_abi_sizeof(llty)


def load_item(context, builder, arrayty, ptr):
    """
    Load the item at the given array pointer.
    """
    align = None if arrayty.aligned else 1
    return context.unpack_value(builder, arrayty.dtype, ptr,
                                align=align)


def store_item(context, builder, arrayty, val, ptr):
    """
    Store the item at the given array pointer.
    """
    align = None if arrayty.aligned else 1
    return context.pack_value(builder, arrayty.dtype, val, ptr, align=align)


def fix_integer_index(context, builder, idxty, idx, size):
    """
    Fix the integer index' type and value for the given dimension size.
    """
    if idxty.signed:
        ind = context.cast(builder, idx, idxty, types.intp)
        ind = slicing.fix_index(builder, ind, size)
    else:
        ind = context.cast(builder, idx, idxty, types.uintp)
    return ind


def normalize_index(context, builder, idxty, idx):
    """
    Normalize the index type and value.  0-d arrays are converted to scalars.
    """
    if isinstance(idxty, types.Array) and idxty.ndim == 0:
        assert isinstance(idxty.dtype, types.Integer)
        idxary = make_array(idxty)(context, builder, idx)
        idxval = load_item(context, builder, idxty, idxary.data)
        return idxty.dtype, idxval
    else:
        return idxty, idx


def normalize_indices(context, builder, index_types, indices):
    """
    Same as normalize_index(), but operating on sequences of
    index types and values.
    """
    if len(indices):
        index_types, indices = zip(*[normalize_index(context, builder, idxty, idx)
                                     for idxty, idx in zip(index_types, indices)])
    return index_types, indices


def populate_array(array, data, shape, strides, itemsize, meminfo,
                   parent=None):
    """
    Helper function for populating array structures.
    This avoids forgetting to set fields.

    *shape* and *strides* can be Python tuples or LLVM arrays.
    """
    context = array._context
    builder = array._builder
    datamodel = array._datamodel
    required_fields = set(datamodel._fields)

    if meminfo is None:
        meminfo = Constant.null(context.get_value_type(
            datamodel.get_type('meminfo')))

    intp_t = context.get_value_type(types.intp)
    if isinstance(shape, (tuple, list)):
        shape = cgutils.pack_array(builder, shape, intp_t)
    if isinstance(strides, (tuple, list)):
        strides = cgutils.pack_array(builder, strides, intp_t)
    if isinstance(itemsize, utils.INT_TYPES):
        itemsize = intp_t(itemsize)

    attrs = dict(shape=shape,
                 strides=strides,
                 data=data,
                 itemsize=itemsize,
                 meminfo=meminfo,)

    # Set `parent` attribute
    if parent is None:
        attrs['parent'] = Constant.null(context.get_value_type(
            datamodel.get_type('parent')))
    else:
        attrs['parent'] = parent
    # Calc num of items from shape
    nitems = context.get_constant(types.intp, 1)
    unpacked_shape = cgutils.unpack_tuple(builder, shape, shape.type.count)
    # (note empty shape => 0d array therefore nitems = 1)
    for axlen in unpacked_shape:
        nitems = builder.mul(nitems, axlen, flags=['nsw'])
    attrs['nitems'] = nitems

    # Make sure that we have all the fields
    got_fields = set(attrs.keys())
    if got_fields != required_fields:
        raise ValueError("missing {0}".format(required_fields - got_fields))

    # Set field value
    for k, v in attrs.items():
        setattr(array, k, v)

    return array


def update_array_info(aryty, array):
    """
    Update some auxiliary information in *array* after some of its fields
    were changed.  `itemsize` and `nitems` are updated.
    """
    context = array._context
    builder = array._builder

    # Calc num of items from shape
    nitems = context.get_constant(types.intp, 1)
    unpacked_shape = cgutils.unpack_tuple(builder, array.shape, aryty.ndim)
    for axlen in unpacked_shape:
        nitems = builder.mul(nitems, axlen, flags=['nsw'])
    array.nitems = nitems

    array.itemsize = context.get_constant(types.intp,
                                          get_itemsize(context, aryty))


@lower_builtin('getiter', types.Buffer)
def getiter_array(context, builder, sig, args):
    [arrayty] = sig.args
    [array] = args

    iterobj = context.make_helper(builder, sig.return_type)

    zero = context.get_constant(types.intp, 0)
    indexptr = cgutils.alloca_once_value(builder, zero)

    iterobj.index = indexptr
    iterobj.array = array

    # Incref array
    if context.enable_nrt:
        context.nrt.incref(builder, arrayty, array)

    res = iterobj._getvalue()

    # Note: a decref on the iterator will dereference all internal MemInfo*
    out = impl_ret_new_ref(context, builder, sig.return_type, res)
    return out


def _getitem_array1d(context, builder, arrayty, array, idx, wraparound):
    """
    Look up and return an element from a 1D array.
    """
    ptr = cgutils.get_item_pointer(builder, arrayty, array, [idx],
                                   wraparound=wraparound)
    return load_item(context, builder, arrayty, ptr)


@lower_builtin('iternext', types.ArrayIterator)
@iternext_impl(RefType.BORROWED)
def iternext_array(context, builder, sig, args, result):
    [iterty] = sig.args
    [iter] = args
    arrayty = iterty.array_type

    if arrayty.ndim != 1:
        # TODO
        raise NotImplementedError("iterating over %dD array" % arrayty.ndim)

    iterobj = context.make_helper(builder, iterty, value=iter)
    ary = make_array(arrayty)(context, builder, value=iterobj.array)

    nitems, = cgutils.unpack_tuple(builder, ary.shape, count=1)

    index = builder.load(iterobj.index)
    is_valid = builder.icmp(lc.ICMP_SLT, index, nitems)
    result.set_valid(is_valid)

    with builder.if_then(is_valid):
        value = _getitem_array1d(context, builder, arrayty, ary, index,
                                 wraparound=False)
        result.yield_(value)
        nindex = cgutils.increment_index(builder, index)
        builder.store(nindex, iterobj.index)


#-------------------------------------------------------------------------------
# Basic indexing (with integers and slices only)

def basic_indexing(context, builder, aryty, ary, index_types, indices):
    """
    Perform basic indexing on the given array.
    A (data pointer, shapes, strides) tuple is returned describing
    the corresponding view.
    """
    zero = context.get_constant(types.intp, 0)

    shapes = cgutils.unpack_tuple(builder, ary.shape, aryty.ndim)
    strides = cgutils.unpack_tuple(builder, ary.strides, aryty.ndim)

    output_indices = []
    output_shapes = []
    output_strides = []

    ax = 0
    for indexval, idxty in zip(indices, index_types):
        if idxty is types.ellipsis:
            # Fill up missing dimensions at the middle
            n_missing = aryty.ndim - len(indices) + 1
            for i in range(n_missing):
                output_indices.append(zero)
                output_shapes.append(shapes[ax])
                output_strides.append(strides[ax])
                ax += 1
            continue
        # Regular index value
        if isinstance(idxty, types.SliceType):
            slice = context.make_helper(builder, idxty, value=indexval)
            slicing.guard_invalid_slice(context, builder, idxty, slice)
            slicing.fix_slice(builder, slice, shapes[ax])
            output_indices.append(slice.start)
            sh = slicing.get_slice_length(builder, slice)
            st = slicing.fix_stride(builder, slice, strides[ax])
            output_shapes.append(sh)
            output_strides.append(st)
        elif isinstance(idxty, types.Integer):
            ind = fix_integer_index(context, builder, idxty, indexval,
                                    shapes[ax])
            output_indices.append(ind)
        else:
            raise NotImplementedError("unexpected index type: %s" % (idxty,))
        ax += 1

    # Fill up missing dimensions at the end
    assert ax <= aryty.ndim
    while ax < aryty.ndim:
        output_shapes.append(shapes[ax])
        output_strides.append(strides[ax])
        ax += 1

    # No need to check wraparound, as negative indices were already
    # fixed in the loop above.
    dataptr = cgutils.get_item_pointer(builder, aryty, ary,
                                       output_indices,
                                       wraparound=False)
    return (dataptr, output_shapes, output_strides)


def make_view(context, builder, aryty, ary, return_type,
              data, shapes, strides):
    """
    Build a view over the given array with the given parameters.
    """
    retary = make_array(return_type)(context, builder)
    populate_array(retary,
                   data=data,
                   shape=shapes,
                   strides=strides,
                   itemsize=ary.itemsize,
                   meminfo=ary.meminfo,
                   parent=ary.parent)
    return retary


def _getitem_array_generic(context, builder, return_type, aryty, ary,
                           index_types, indices):
    """
    Return the result of indexing *ary* with the given *indices*,
    returning either a scalar or a view.
    """
    dataptr, view_shapes, view_strides = \
        basic_indexing(context, builder, aryty, ary, index_types, indices)

    if isinstance(return_type, types.Buffer):
        # Build array view
        retary = make_view(context, builder, aryty, ary, return_type,
                           dataptr, view_shapes, view_strides)
        return retary._getvalue()
    else:
        # Load scalar from 0-d result
        assert not view_shapes
        return load_item(context, builder, aryty, dataptr)


@lower_builtin(operator.getitem, types.Buffer, types.Integer)
@lower_builtin(operator.getitem, types.Buffer, types.SliceType)
def getitem_arraynd_intp(context, builder, sig, args):
    """
    Basic indexing with an integer or a slice.
    """
    aryty, idxty = sig.args
    ary, idx = args

    assert aryty.ndim >= 1
    ary = make_array(aryty)(context, builder, ary)

    res = _getitem_array_generic(context, builder, sig.return_type,
                                 aryty, ary, (idxty,), (idx,))
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin(operator.getitem, types.Buffer, types.BaseTuple)
def getitem_array_tuple(context, builder, sig, args):
    """
    Basic or advanced indexing with a tuple.
    """
    aryty, tupty = sig.args
    ary, tup = args
    ary = make_array(aryty)(context, builder, ary)

    index_types = tupty.types
    indices = cgutils.unpack_tuple(builder, tup, count=len(tupty))

    index_types, indices = normalize_indices(context, builder,
                                             index_types, indices)

    if any(isinstance(ty, types.Array) for ty in index_types):
        # Advanced indexing
        return fancy_getitem(context, builder, sig, args,
                             aryty, ary, index_types, indices)

    res = _getitem_array_generic(context, builder, sig.return_type,
                                 aryty, ary, index_types, indices)
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin(operator.setitem, types.Buffer, types.Any, types.Any)
def setitem_array(context, builder, sig, args):
    """
    array[a] = scalar_or_array
    array[a,..,b] = scalar_or_array
    """
    aryty, idxty, valty = sig.args
    ary, idx, val = args

    if isinstance(idxty, types.BaseTuple):
        index_types = idxty.types
        indices = cgutils.unpack_tuple(builder, idx, count=len(idxty))
    else:
        index_types = (idxty,)
        indices = (idx,)

    ary = make_array(aryty)(context, builder, ary)

    # First try basic indexing to see if a single array location is denoted.
    index_types, indices = normalize_indices(context, builder,
                                             index_types, indices)
    try:
        dataptr, shapes, strides = \
            basic_indexing(context, builder, aryty, ary, index_types, indices)
    except NotImplementedError:
        use_fancy_indexing = True
    else:
        use_fancy_indexing = bool(shapes)

    if use_fancy_indexing:
        # Index describes a non-trivial view => use generic slice assignment
        # (NOTE: this also handles scalar broadcasting)
        return fancy_setslice(context, builder, sig, args,
                              index_types, indices)

    # Store source value the given location
    val = context.cast(builder, val, valty, aryty.dtype)
    store_item(context, builder, aryty, val, dataptr)


@lower_builtin(len, types.Buffer)
def array_len(context, builder, sig, args):
    (aryty,) = sig.args
    (ary,) = args
    arystty = make_array(aryty)
    ary = arystty(context, builder, ary)
    shapeary = ary.shape
    res = builder.extract_value(shapeary, 0)
    return impl_ret_untracked(context, builder, sig.return_type, res)


@lower_builtin("array.item", types.Array)
def array_item(context, builder, sig, args):
    aryty, = sig.args
    ary, = args
    ary = make_array(aryty)(context, builder, ary)

    nitems = ary.nitems
    with builder.if_then(builder.icmp_signed('!=', nitems, nitems.type(1)),
                         likely=False):
        msg = "item(): can only convert an array of size 1 to a Python scalar"
        context.call_conv.return_user_exc(builder, ValueError, (msg,))

    return load_item(context, builder, aryty, ary.data)


@lower_builtin("array.itemset", types.Array, types.Any)
def array_itemset(context, builder, sig, args):
    aryty, valty = sig.args
    ary, val = args
    assert valty == aryty.dtype
    ary = make_array(aryty)(context, builder, ary)

    nitems = ary.nitems
    with builder.if_then(builder.icmp_signed('!=', nitems, nitems.type(1)),
                         likely=False):
        msg = "itemset(): can only write to an array of size 1"
        context.call_conv.return_user_exc(builder, ValueError, (msg,))

    store_item(context, builder, aryty, val, ary.data)
    return context.get_dummy_value()


#-------------------------------------------------------------------------------
# Advanced / fancy indexing


class Indexer(object):
    """
    Generic indexer interface, for generating indices over a fancy indexed
    array on a single dimension.
    """

    def prepare(self):
        """
        Prepare the indexer by initializing any required variables, basic
        blocks...
        """
        raise NotImplementedError

    def get_size(self):
        """
        Return this dimension's size as an integer.
        """
        raise NotImplementedError

    def get_shape(self):
        """
        Return this dimension's shape as a tuple.
        """
        raise NotImplementedError

    def get_index_bounds(self):
        """
        Return a half-open [lower, upper) range of indices this dimension
        is guaranteed not to step out of.
        """
        raise NotImplementedError

    def loop_head(self):
        """
        Start indexation loop.  Return a (index, count) tuple.
        *index* is an integer LLVM value representing the index over this
        dimension.
        *count* is either an integer LLVM value representing the current
        iteration count, or None if this dimension should be omitted from
        the indexation result.
        """
        raise NotImplementedError

    def loop_tail(self):
        """
        Finish indexation loop.
        """
        raise NotImplementedError


class EntireIndexer(Indexer):
    """
    Compute indices along an entire array dimension.
    """

    def __init__(self, context, builder, aryty, ary, dim):
        self.context = context
        self.builder = builder
        self.aryty = aryty
        self.ary = ary
        self.dim = dim
        self.ll_intp = self.context.get_value_type(types.intp)

    def prepare(self):
        builder = self.builder
        self.size = builder.extract_value(self.ary.shape, self.dim)
        self.index = cgutils.alloca_once(builder, self.ll_intp)
        self.bb_start = builder.append_basic_block()
        self.bb_end = builder.append_basic_block()

    def get_size(self):
        return self.size

    def get_shape(self):
        return (self.size,)

    def get_index_bounds(self):
        # [0, size)
        return (self.ll_intp(0), self.size)

    def loop_head(self):
        builder = self.builder
        # Initialize loop variable
        self.builder.store(Constant.int(self.ll_intp, 0), self.index)
        builder.branch(self.bb_start)
        builder.position_at_end(self.bb_start)
        cur_index = builder.load(self.index)
        with builder.if_then(builder.icmp_signed('>=', cur_index, self.size),
                             likely=False):
            builder.branch(self.bb_end)
        return cur_index, cur_index

    def loop_tail(self):
        builder = self.builder
        next_index = cgutils.increment_index(builder, builder.load(self.index))
        builder.store(next_index, self.index)
        builder.branch(self.bb_start)
        builder.position_at_end(self.bb_end)


class IntegerIndexer(Indexer):
    """
    Compute indices from a single integer.
    """

    def __init__(self, context, builder, idx):
        self.context = context
        self.builder = builder
        self.idx = idx
        self.ll_intp = self.context.get_value_type(types.intp)

    def prepare(self):
        pass

    def get_size(self):
        return Constant.int(self.ll_intp, 1)

    def get_shape(self):
        return ()

    def get_index_bounds(self):
        # [idx, idx+1)
        return (self.idx, self.builder.add(self.idx, self.get_size()))

    def loop_head(self):
        return self.idx, None

    def loop_tail(self):
        pass


class IntegerArrayIndexer(Indexer):
    """
    Compute indices from an array of integer indices.
    """

    def __init__(self, context, builder, idxty, idxary, size):
        self.context = context
        self.builder = builder
        self.idxty = idxty
        self.idxary = idxary
        self.size = size
        assert idxty.ndim == 1
        self.ll_intp = self.context.get_value_type(types.intp)

    def prepare(self):
        builder = self.builder
        self.idx_size = cgutils.unpack_tuple(builder, self.idxary.shape)[0]
        self.idx_index = cgutils.alloca_once(builder, self.ll_intp)
        self.bb_start = builder.append_basic_block()
        self.bb_end = builder.append_basic_block()

    def get_size(self):
        return self.idx_size

    def get_shape(self):
        return (self.idx_size,)

    def get_index_bounds(self):
        # Pessimal heuristic, as we don't want to scan for the min and max
        return (self.ll_intp(0), self.size)

    def loop_head(self):
        builder = self.builder
        # Initialize loop variable
        self.builder.store(Constant.int(self.ll_intp, 0), self.idx_index)
        builder.branch(self.bb_start)
        builder.position_at_end(self.bb_start)
        cur_index = builder.load(self.idx_index)
        with builder.if_then(builder.icmp_signed('>=', cur_index, self.idx_size),
                             likely=False):
            builder.branch(self.bb_end)
        # Load the actual index from the array of indices
        index = _getitem_array1d(self.context, builder,
                                 self.idxty, self.idxary,
                                 cur_index, wraparound=False)
        index = fix_integer_index(self.context, builder,
                                  self.idxty.dtype, index, self.size)
        return index, cur_index

    def loop_tail(self):
        builder = self.builder
        next_index = cgutils.increment_index(builder,
                                             builder.load(self.idx_index))
        builder.store(next_index, self.idx_index)
        builder.branch(self.bb_start)
        builder.position_at_end(self.bb_end)


class BooleanArrayIndexer(Indexer):
    """
    Compute indices from an array of boolean predicates.
    """

    def __init__(self, context, builder, idxty, idxary):
        self.context = context
        self.builder = builder
        self.idxty = idxty
        self.idxary = idxary
        assert idxty.ndim == 1
        self.ll_intp = self.context.get_value_type(types.intp)
        self.zero = Constant.int(self.ll_intp, 0)

    def prepare(self):
        builder = self.builder
        self.size = cgutils.unpack_tuple(builder, self.idxary.shape)[0]
        self.idx_index = cgutils.alloca_once(builder, self.ll_intp)
        self.count = cgutils.alloca_once(builder, self.ll_intp)
        self.bb_start = builder.append_basic_block()
        self.bb_tail = builder.append_basic_block()
        self.bb_end = builder.append_basic_block()

    def get_size(self):
        builder = self.builder
        count = cgutils.alloca_once_value(builder, self.zero)
        # Sum all true values
        with cgutils.for_range(builder, self.size) as loop:
            c = builder.load(count)
            pred = _getitem_array1d(self.context, builder,
                                    self.idxty, self.idxary,
                                    loop.index, wraparound=False)
            c = builder.add(c, builder.zext(pred, c.type))
            builder.store(c, count)

        return builder.load(count)

    def get_shape(self):
        return (self.get_size(),)

    def get_index_bounds(self):
        # Pessimal heuristic, as we don't want to scan for the
        # first and last true items
        return (self.ll_intp(0), self.size)

    def loop_head(self):
        builder = self.builder
        # Initialize loop variable
        self.builder.store(self.zero, self.idx_index)
        self.builder.store(self.zero, self.count)
        builder.branch(self.bb_start)
        builder.position_at_end(self.bb_start)
        cur_index = builder.load(self.idx_index)
        cur_count = builder.load(self.count)
        with builder.if_then(builder.icmp_signed('>=', cur_index, self.size),
                             likely=False):
            builder.branch(self.bb_end)
        # Load the predicate and branch if false
        pred = _getitem_array1d(self.context, builder,
                                self.idxty, self.idxary,
                                cur_index, wraparound=False)
        with builder.if_then(builder.not_(pred)):
            builder.branch(self.bb_tail)
        # Increment the count for next iteration
        next_count = cgutils.increment_index(builder, cur_count)
        builder.store(next_count, self.count)
        return cur_index, cur_count

    def loop_tail(self):
        builder = self.builder
        builder.branch(self.bb_tail)
        builder.position_at_end(self.bb_tail)
        next_index = cgutils.increment_index(builder,
                                             builder.load(self.idx_index))
        builder.store(next_index, self.idx_index)
        builder.branch(self.bb_start)
        builder.position_at_end(self.bb_end)


class SliceIndexer(Indexer):
    """
    Compute indices along a slice.
    """

    def __init__(self, context, builder, aryty, ary, dim, idxty, slice):
        self.context = context
        self.builder = builder
        self.aryty = aryty
        self.ary = ary
        self.dim = dim
        self.idxty = idxty
        self.slice = slice
        self.ll_intp = self.context.get_value_type(types.intp)
        self.zero = Constant.int(self.ll_intp, 0)

    def prepare(self):
        builder = self.builder
        # Fix slice for the dimension's size
        self.dim_size = builder.extract_value(self.ary.shape, self.dim)
        slicing.guard_invalid_slice(self.context, builder, self.idxty,
                                    self.slice)
        slicing.fix_slice(builder, self.slice, self.dim_size)
        self.is_step_negative = cgutils.is_neg_int(builder, self.slice.step)
        # Create loop entities
        self.index = cgutils.alloca_once(builder, self.ll_intp)
        self.count = cgutils.alloca_once(builder, self.ll_intp)
        self.bb_start = builder.append_basic_block()
        self.bb_end = builder.append_basic_block()

    def get_size(self):
        return slicing.get_slice_length(self.builder, self.slice)

    def get_shape(self):
        return (self.get_size(),)

    def get_index_bounds(self):
        lower, upper = slicing.get_slice_bounds(self.builder, self.slice)
        return lower, upper

    def loop_head(self):
        builder = self.builder
        # Initialize loop variable
        self.builder.store(self.slice.start, self.index)
        self.builder.store(self.zero, self.count)
        builder.branch(self.bb_start)
        builder.position_at_end(self.bb_start)
        cur_index = builder.load(self.index)
        cur_count = builder.load(self.count)
        is_finished = builder.select(self.is_step_negative,
                                     builder.icmp_signed('<=', cur_index,
                                                         self.slice.stop),
                                     builder.icmp_signed('>=', cur_index,
                                                         self.slice.stop))
        with builder.if_then(is_finished, likely=False):
            builder.branch(self.bb_end)
        return cur_index, cur_count

    def loop_tail(self):
        builder = self.builder
        next_index = builder.add(builder.load(self.index), self.slice.step,
                                 flags=['nsw'])
        builder.store(next_index, self.index)
        next_count = cgutils.increment_index(builder, builder.load(self.count))
        builder.store(next_count, self.count)
        builder.branch(self.bb_start)
        builder.position_at_end(self.bb_end)


class FancyIndexer(object):
    """
    Perform fancy indexing on the given array.
    """

    def __init__(self, context, builder, aryty, ary, index_types, indices):
        self.context = context
        self.builder = builder
        self.aryty = aryty
        self.shapes = cgutils.unpack_tuple(builder, ary.shape, aryty.ndim)
        self.strides = cgutils.unpack_tuple(builder, ary.strides, aryty.ndim)
        self.ll_intp = self.context.get_value_type(types.intp)

        indexers = []

        ax = 0
        for indexval, idxty in zip(indices, index_types):
            if idxty is types.ellipsis:
                # Fill up missing dimensions at the middle
                n_missing = aryty.ndim - len(indices) + 1
                for i in range(n_missing):
                    indexer = EntireIndexer(context, builder, aryty, ary, ax)
                    indexers.append(indexer)
                    ax += 1
                continue

            # Regular index value
            if isinstance(idxty, types.SliceType):
                slice = context.make_helper(builder, idxty, indexval)
                indexer = SliceIndexer(context, builder, aryty, ary, ax,
                                       idxty, slice)
                indexers.append(indexer)
            elif isinstance(idxty, types.Integer):
                ind = fix_integer_index(context, builder, idxty, indexval,
                                        self.shapes[ax])
                indexer = IntegerIndexer(context, builder, ind)
                indexers.append(indexer)
            elif isinstance(idxty, types.Array):
                idxary = make_array(idxty)(context, builder, indexval)
                if isinstance(idxty.dtype, types.Integer):
                    indexer = IntegerArrayIndexer(context, builder,
                                                  idxty, idxary,
                                                  self.shapes[ax])
                elif isinstance(idxty.dtype, types.Boolean):
                    indexer = BooleanArrayIndexer(context, builder,
                                                  idxty, idxary)
                else:
                    assert 0
                indexers.append(indexer)
            else:
                raise AssertionError("unexpected index type: %s" % (idxty,))
            ax += 1

        # Fill up missing dimensions at the end
        assert ax <= aryty.ndim, (ax, aryty.ndim)
        while ax < aryty.ndim:
            indexer = EntireIndexer(context, builder, aryty, ary, ax)
            indexers.append(indexer)
            ax += 1

        assert len(indexers) == aryty.ndim, (len(indexers), aryty.ndim)
        self.indexers = indexers

    def prepare(self):
        for i in self.indexers:
            i.prepare()
        # Compute the resulting shape
        self.indexers_shape = sum([i.get_shape() for i in self.indexers], ())

    def get_shape(self):
        """
        Get the resulting data shape as Python tuple.
        """
        return self.indexers_shape

    def get_offset_bounds(self, strides, itemsize):
        """
        Get a half-open [lower, upper) range of byte offsets spanned by
        the indexer with the given strides and itemsize.  The indexer is
        guaranteed to not go past those bounds.
        """
        assert len(strides) == self.aryty.ndim
        builder = self.builder
        is_empty = cgutils.false_bit
        zero = self.ll_intp(0)
        one = self.ll_intp(1)
        lower = zero
        upper = zero
        for indexer, shape, stride in zip(self.indexers, self.indexers_shape,
                                          strides):
            is_empty = builder.or_(is_empty,
                                   builder.icmp_unsigned('==', shape, zero))
            # Compute [lower, upper) indices on this dimension
            lower_index, upper_index = indexer.get_index_bounds()
            lower_offset = builder.mul(stride, lower_index)
            upper_offset = builder.mul(stride, builder.sub(upper_index, one))
            # Adjust total interval
            is_downwards = builder.icmp_signed('<', stride, zero)
            lower = builder.add(lower,
                                builder.select(is_downwards, upper_offset, lower_offset))
            upper = builder.add(upper,
                                builder.select(is_downwards, lower_offset, upper_offset))
        # Make interval half-open
        upper = builder.add(upper, itemsize)
        # Adjust for empty shape
        lower = builder.select(is_empty, zero, lower)
        upper = builder.select(is_empty, zero, upper)
        return lower, upper

    def begin_loops(self):
        indices, counts = zip(*(i.loop_head() for i in self.indexers))
        return indices, counts

    def end_loops(self):
        for i in reversed(self.indexers):
            i.loop_tail()


def fancy_getitem(context, builder, sig, args,
                  aryty, ary, index_types, indices):

    shapes = cgutils.unpack_tuple(builder, ary.shape)
    strides = cgutils.unpack_tuple(builder, ary.strides)
    data = ary.data

    indexer = FancyIndexer(context, builder, aryty, ary,
                           index_types, indices)
    indexer.prepare()

    # Construct output array
    out_ty = sig.return_type
    out_shapes = indexer.get_shape()

    out = _empty_nd_impl(context, builder, out_ty, out_shapes)
    out_data = out.data
    out_idx = cgutils.alloca_once_value(builder,
                                        context.get_constant(types.intp, 0))

    # Loop on source and copy to destination
    indices, _ = indexer.begin_loops()

    # No need to check for wraparound, as the indexers all ensure
    # a positive index is returned.
    ptr = cgutils.get_item_pointer2(builder, data, shapes, strides,
                                    aryty.layout, indices, wraparound=False)
    val = load_item(context, builder, aryty, ptr)

    # Since the destination is C-contiguous, no need for multi-dimensional
    # indexing.
    cur = builder.load(out_idx)
    ptr = builder.gep(out_data, [cur])
    store_item(context, builder, out_ty, val, ptr)
    next_idx = cgutils.increment_index(builder, cur)
    builder.store(next_idx, out_idx)

    indexer.end_loops()

    return impl_ret_new_ref(context, builder, out_ty, out._getvalue())


@lower_builtin(operator.getitem, types.Buffer, types.Array)
def fancy_getitem_array(context, builder, sig, args):
    """
    Advanced or basic indexing with an array.
    """
    aryty, idxty = sig.args
    ary, idx = args
    ary = make_array(aryty)(context, builder, ary)
    if idxty.ndim == 0:
        # 0-d array index acts as a basic integer index
        idxty, idx = normalize_index(context, builder, idxty, idx)
        res = _getitem_array_generic(context, builder, sig.return_type,
                                     aryty, ary, (idxty,), (idx,))
        return impl_ret_borrowed(context, builder, sig.return_type, res)
    else:
        # Advanced indexing
        return fancy_getitem(context, builder, sig, args,
                             aryty, ary, (idxty,), (idx,))


def offset_bounds_from_strides(context, builder, arrty, arr, shapes, strides):
    """
    Compute a half-open range [lower, upper) of byte offsets from the
    array's data pointer, that bound the in-memory extent of the array.

    This mimicks offset_bounds_from_strides() from numpy/core/src/private/mem_overlap.c
    """
    itemsize = arr.itemsize
    zero = itemsize.type(0)
    one = zero.type(1)
    if arrty.layout in 'CF':
        # Array is contiguous: contents are laid out sequentially
        # starting from arr.data and upwards
        lower = zero
        upper = builder.mul(itemsize, arr.nitems)
    else:
        # Non-contiguous array: need to examine strides
        lower = zero
        upper = zero
        for i in range(arrty.ndim):
            # Compute the largest byte offset on this dimension
            #   max_axis_offset = strides[i] * (shapes[i] - 1)
            # (shapes[i] == 0 is catered for by the empty array case below)
            max_axis_offset = builder.mul(strides[i],
                                          builder.sub(shapes[i], one))
            is_upwards = builder.icmp_signed('>=', max_axis_offset, zero)
            # Expand either upwards or downwards depending on stride
            upper = builder.select(is_upwards,
                                   builder.add(upper, max_axis_offset), upper)
            lower = builder.select(is_upwards,
                                   lower, builder.add(lower, max_axis_offset))
        # Return a half-open range
        upper = builder.add(upper, itemsize)
        # Adjust for empty arrays
        is_empty = builder.icmp_signed('==', arr.nitems, zero)
        upper = builder.select(is_empty, zero, upper)
        lower = builder.select(is_empty, zero, lower)

    return lower, upper


def compute_memory_extents(context, builder, lower, upper, data):
    """
    Given [lower, upper) byte offsets and a base data pointer,
    compute the memory pointer bounds as pointer-sized integers.
    """
    data_ptr_as_int = builder.ptrtoint(data, lower.type)
    start = builder.add(data_ptr_as_int, lower)
    end = builder.add(data_ptr_as_int, upper)
    return start, end


def get_array_memory_extents(context, builder, arrty, arr, shapes, strides, data):
    """
    Compute a half-open range [start, end) of pointer-sized integers
    which fully contain the array data.
    """
    lower, upper = offset_bounds_from_strides(context, builder, arrty, arr,
                                              shapes, strides)
    return compute_memory_extents(context, builder, lower, upper, data)


def extents_may_overlap(context, builder, a_start, a_end, b_start, b_end):
    """
    Whether two memory extents [a_start, a_end) and [b_start, b_end)
    may overlap.
    """
    # Comparisons are unsigned, since we are really comparing pointers
    may_overlap = builder.and_(
        builder.icmp_unsigned('<', a_start, b_end),
        builder.icmp_unsigned('<', b_start, a_end),
    )
    return may_overlap


def maybe_copy_source(context, builder, use_copy,
                      srcty, src, src_shapes, src_strides, src_data):
    ptrty = src_data.type

    copy_layout = 'C'
    copy_data = cgutils.alloca_once_value(builder, src_data)
    copy_shapes = src_shapes
    copy_strides = None  # unneeded for contiguous arrays

    with builder.if_then(use_copy, likely=False):
        # Allocate temporary scratchpad
        # XXX: should we use a stack-allocated array for very small
        # data sizes?
        allocsize = builder.mul(src.itemsize, src.nitems)
        data = context.nrt.allocate(builder, allocsize)
        voidptrty = data.type
        data = builder.bitcast(data, ptrty)
        builder.store(data, copy_data)

        # Copy source data into scratchpad
        intp_t = context.get_value_type(types.intp)

        with cgutils.loop_nest(builder, src_shapes, intp_t) as indices:
            src_ptr = cgutils.get_item_pointer2(builder, src_data,
                                                src_shapes, src_strides,
                                                srcty.layout, indices)
            dest_ptr = cgutils.get_item_pointer2(builder, data,
                                                 copy_shapes, copy_strides,
                                                 copy_layout, indices)
            builder.store(builder.load(src_ptr), dest_ptr)

    def src_getitem(source_indices):
        assert len(source_indices) == srcty.ndim
        src_ptr = cgutils.alloca_once(builder, ptrty)
        with builder.if_else(use_copy, likely=False) as (if_copy, otherwise):
            with if_copy:
                builder.store(
                    cgutils.get_item_pointer2(builder, builder.load(copy_data),
                                              copy_shapes, copy_strides,
                                              copy_layout, source_indices,
                                              wraparound=False),
                    src_ptr)
            with otherwise:
                builder.store(
                    cgutils.get_item_pointer2(builder, src_data,
                                              src_shapes, src_strides,
                                              srcty.layout, source_indices,
                                              wraparound=False),
                    src_ptr)
        return load_item(context, builder, srcty, builder.load(src_ptr))

    def src_cleanup():
        # Deallocate memory
        with builder.if_then(use_copy, likely=False):
            data = builder.load(copy_data)
            data = builder.bitcast(data, voidptrty)
            context.nrt.free(builder, data)

    return src_getitem, src_cleanup


def _bc_adjust_dimension(context, builder, shapes, strides, target_shape):
    """
    Preprocess dimension for broadcasting.
    Returns (shapes, strides) such that the ndim match *target_shape*.
    When expanding to higher ndim, the returning shapes and strides are
    prepended with ones and zeros, respectively.
    When truncating to lower ndim, the shapes are checked (in runtime).
    All extra dimension must have size of 1.
    """
    zero = context.get_constant(types.uintp, 0)
    one = context.get_constant(types.uintp, 1)

    # Adjust for broadcasting to higher dimension
    if len(target_shape) > len(shapes):
        nd_diff = len(target_shape) - len(shapes)
        # Fill missing shapes with one, strides with zeros
        shapes = [one] * nd_diff + shapes
        strides = [zero] * nd_diff + strides
    # Adjust for broadcasting to lower dimension
    elif len(target_shape) < len(shapes):
        # Accepted if all extra dims has shape 1
        nd_diff = len(shapes) - len(target_shape)
        dim_is_one = [builder.icmp_unsigned('==', sh, one)
                      for sh in shapes[:nd_diff]]
        accepted = functools.reduce(builder.and_, dim_is_one,
                                    cgutils.true_bit)
        # Check error
        with builder.if_then(builder.not_(accepted), likely=False):
            msg = "cannot broadcast source array for assignment"
            context.call_conv.return_user_exc(builder, ValueError, (msg,))
        # Truncate extra shapes, strides
        shapes = shapes[nd_diff:]
        strides = strides[nd_diff:]

    return shapes, strides


def _bc_adjust_shape_strides(context, builder, shapes, strides, target_shape):
    """
    Broadcast shapes and strides to target_shape given that their ndim already
    matches.  For each location where the shape is 1 and does not match the
    dim for target, it is set to the value at the target and the stride is
    set to zero.
    """
    bc_shapes = []
    bc_strides = []
    zero = context.get_constant(types.uintp, 0)
    one = context.get_constant(types.uintp, 1)
    # Adjust all mismatching ones in shape
    mismatch = [builder.icmp_signed('!=', tar, old)
                for tar, old in zip(target_shape, shapes)]
    src_is_one = [builder.icmp_signed('==', old, one) for old in shapes]
    preds = [builder.and_(x, y) for x, y in zip(mismatch, src_is_one)]
    bc_shapes = [builder.select(p, tar, old)
                 for p, tar, old in zip(preds, target_shape, shapes)]
    bc_strides = [builder.select(p, zero, old)
                  for p, old in zip(preds, strides)]
    return bc_shapes, bc_strides


def _broadcast_to_shape(context, builder, arrtype, arr, target_shape):
    """
    Broadcast the given array to the target_shape.
    Returns (array_type, array)
    """
    # Compute broadcasted shape and strides
    shapes = cgutils.unpack_tuple(builder, arr.shape)
    strides = cgutils.unpack_tuple(builder, arr.strides)

    shapes, strides = _bc_adjust_dimension(context, builder, shapes, strides,
                                           target_shape)
    shapes, strides = _bc_adjust_shape_strides(context, builder, shapes,
                                               strides, target_shape)
    new_arrtype = arrtype.copy(ndim=len(target_shape), layout='A')
    # Create new view
    new_arr = make_array(new_arrtype)(context, builder)
    repl = dict(shape=cgutils.pack_array(builder, shapes),
                strides=cgutils.pack_array(builder, strides))
    cgutils.copy_struct(new_arr, arr, repl)
    return new_arrtype, new_arr


def fancy_setslice(context, builder, sig, args, index_types, indices):
    """
    Implement slice assignment for arrays.  This implementation works for
    basic as well as fancy indexing, since there's no functional difference
    between the two for indexed assignment.
    """
    aryty, _, srcty = sig.args
    ary, _, src = args

    ary = make_array(aryty)(context, builder, ary)
    dest_shapes = cgutils.unpack_tuple(builder, ary.shape)
    dest_strides = cgutils.unpack_tuple(builder, ary.strides)
    dest_data = ary.data

    indexer = FancyIndexer(context, builder, aryty, ary,
                           index_types, indices)
    indexer.prepare()

    if isinstance(srcty, types.Buffer):
        # Source is an array
        src_dtype = srcty.dtype
        index_shape = indexer.get_shape()
        src = make_array(srcty)(context, builder, src)
        # Broadcast source array to shape
        srcty, src = _broadcast_to_shape(context, builder, srcty, src, index_shape)
        src_shapes = cgutils.unpack_tuple(builder, src.shape)
        src_strides = cgutils.unpack_tuple(builder, src.strides)
        src_data = src.data

        # Check shapes are equal
        shape_error = cgutils.false_bit
        assert len(index_shape) == len(src_shapes)

        for u, v in zip(src_shapes, index_shape):
            shape_error = builder.or_(shape_error,
                                      builder.icmp_signed('!=', u, v))

        with builder.if_then(shape_error, likely=False):
            msg = "cannot assign slice from input of different size"
            context.call_conv.return_user_exc(builder, ValueError, (msg,))

        # Check for array overlap
        src_start, src_end = get_array_memory_extents(context, builder, srcty, src,
                                                      src_shapes, src_strides, src_data)

        dest_lower, dest_upper = indexer.get_offset_bounds(dest_strides, ary.itemsize)
        dest_start, dest_end = compute_memory_extents(context, builder,
                                                      dest_lower, dest_upper, dest_data)

        use_copy = extents_may_overlap(context, builder, src_start, src_end, dest_start, dest_end)

        src_getitem, src_cleanup = maybe_copy_source(context, builder, use_copy,
                                                     srcty, src, src_shapes,
                                                     src_strides, src_data)

    elif isinstance(srcty, types.Sequence):
        src_dtype = srcty.dtype

        # Check shape is equal to sequence length
        index_shape = indexer.get_shape()
        assert len(index_shape) == 1
        len_impl = context.get_function(len, signature(types.intp, srcty))
        seq_len = len_impl(builder, (src,))

        shape_error = builder.icmp_signed('!=', index_shape[0], seq_len)

        with builder.if_then(shape_error, likely=False):
            msg = "cannot assign slice from input of different size"
            context.call_conv.return_user_exc(builder, ValueError, (msg,))

        def src_getitem(source_indices):
            idx, = source_indices
            getitem_impl = context.get_function(
                operator.getitem,
                signature(src_dtype, srcty, types.intp),
            )
            return getitem_impl(builder, (src, idx))

        def src_cleanup():
            pass

    else:
        # Source is a scalar (broadcast or not, depending on destination
        # shape).
        src_dtype = srcty

        def src_getitem(source_indices):
            return src

        def src_cleanup():
            pass

    # Loop on destination and copy from source to destination
    dest_indices, counts = indexer.begin_loops()

    # Source is iterated in natural order
    source_indices = tuple(c for c in counts if c is not None)
    val = src_getitem(source_indices)

    # Cast to the destination dtype (cross-dtype slice assignement is allowed)
    val = context.cast(builder, val, src_dtype, aryty.dtype)

    # No need to check for wraparound, as the indexers all ensure
    # a positive index is returned.
    dest_ptr = cgutils.get_item_pointer2(builder, dest_data,
                                         dest_shapes, dest_strides,
                                         aryty.layout, dest_indices,
                                         wraparound=False)
    store_item(context, builder, aryty, val, dest_ptr)

    indexer.end_loops()

    src_cleanup()

    return context.get_dummy_value()


#-------------------------------------------------------------------------------
# Shape / layout altering

def vararg_to_tuple(context, builder, sig, args):
    aryty = sig.args[0]
    dimtys = sig.args[1:]
    # values
    ary = args[0]
    dims = args[1:]
    # coerce all types to intp
    dims = [context.cast(builder, val, ty, types.intp)
            for ty, val in zip(dimtys, dims)]
    # make a tuple
    shape = cgutils.pack_array(builder, dims, dims[0].type)

    shapety = types.UniTuple(dtype=types.intp, count=len(dims))
    new_sig = typing.signature(sig.return_type, aryty, shapety)
    new_args = ary, shape

    return new_sig, new_args


@lower_builtin('array.transpose', types.Array)
def array_transpose(context, builder, sig, args):
    return array_T(context, builder, sig.args[0], args[0])


def permute_arrays(axis, shape, strides):
    if len(axis) != len(set(axis)):
        raise ValueError("repeated axis in transpose")
    dim = len(shape)
    for x in axis:
        if x >= dim or abs(x) > dim:
            raise ValueError("axis is out of bounds for array of given dimension")

    shape[:] = shape[axis]
    strides[:] = strides[axis]


# Transposing an array involves permuting the shape and strides of the array
# based on the given axes.
@lower_builtin('array.transpose', types.Array, types.BaseTuple)
def array_transpose_tuple(context, builder, sig, args):
    aryty = sig.args[0]
    ary = make_array(aryty)(context, builder, args[0])

    axisty, axis = sig.args[1], args[1]
    num_axis, dtype = axisty.count, axisty.dtype

    ll_intp = context.get_value_type(types.intp)
    ll_ary_size = lc.Type.array(ll_intp, num_axis)

    # Allocate memory for axes, shapes, and strides arrays.
    arys = [axis, ary.shape, ary.strides]
    ll_arys = [cgutils.alloca_once(builder, ll_ary_size) for _ in arys]

    # Store axes, shapes, and strides arrays to the allocated memory.
    for src, dst in zip(arys, ll_arys):
        builder.store(src, dst)

    np_ary_ty = types.Array(dtype=dtype, ndim=1, layout='C')
    np_itemsize = context.get_constant(types.intp,
                                       context.get_abi_sizeof(ll_intp))

    # Form NumPy arrays for axes, shapes, and strides arrays.
    np_arys = [make_array(np_ary_ty)(context, builder) for _ in arys]

    # Roughly, `np_ary = np.array(ll_ary)` for each of axes, shapes, and strides.
    for np_ary, ll_ary in zip(np_arys, ll_arys):
        populate_array(np_ary,
                       data=builder.bitcast(ll_ary, ll_intp.as_pointer()),
                       shape=[context.get_constant(types.intp, num_axis)],
                       strides=[np_itemsize],
                       itemsize=np_itemsize,
                       meminfo=None)

    # Pass NumPy arrays formed above to permute_arrays function that permutes
    # shapes and strides based on axis contents.
    context.compile_internal(builder, permute_arrays,
                             typing.signature(types.void,
                                              np_ary_ty, np_ary_ty, np_ary_ty),
                             [a._getvalue() for a in np_arys])

    # Make a new array based on permuted shape and strides and return it.
    ret = make_array(sig.return_type)(context, builder)
    populate_array(ret,
                   data=ary.data,
                   shape=builder.load(ll_arys[1]),
                   strides=builder.load(ll_arys[2]),
                   itemsize=ary.itemsize,
                   meminfo=ary.meminfo,
                   parent=ary.parent)
    res = ret._getvalue()
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin('array.transpose', types.Array, types.VarArg(types.Any))
def array_transpose_vararg(context, builder, sig, args):
    new_sig, new_args = vararg_to_tuple(context, builder, sig, args)
    return array_transpose_tuple(context, builder, new_sig, new_args)


@overload(np.transpose)
def numpy_transpose(a, axes=None):
    if isinstance(a, types.BaseTuple):
        raise errors.UnsupportedError("np.transpose does not accept tuples")

    if axes is None:
        def np_transpose_impl(a, axes=None):
            return a.transpose()
    else:
        def np_transpose_impl(a, axes=None):
            return a.transpose(axes)

    return np_transpose_impl


@lower_getattr(types.Array, 'T')
def array_T(context, builder, typ, value):
    if typ.ndim <= 1:
        res = value
    else:
        ary = make_array(typ)(context, builder, value)
        ret = make_array(typ)(context, builder)
        shapes = cgutils.unpack_tuple(builder, ary.shape, typ.ndim)
        strides = cgutils.unpack_tuple(builder, ary.strides, typ.ndim)
        populate_array(ret,
                       data=ary.data,
                       shape=cgutils.pack_array(builder, shapes[::-1]),
                       strides=cgutils.pack_array(builder, strides[::-1]),
                       itemsize=ary.itemsize,
                       meminfo=ary.meminfo,
                       parent=ary.parent)
        res = ret._getvalue()
    return impl_ret_borrowed(context, builder, typ, res)


def _attempt_nocopy_reshape(context, builder, aryty, ary,
                            newnd, newshape, newstrides):
    """
    Call into Numba_attempt_nocopy_reshape() for the given array type
    and instance, and the specified new shape.

    Return value is non-zero if successful, and the array pointed to
    by *newstrides* will be filled up with the computed results.
    """
    ll_intp = context.get_value_type(types.intp)
    ll_intp_star = ll_intp.as_pointer()
    ll_intc = context.get_value_type(types.intc)
    fnty = lc.Type.function(ll_intc, [
        # nd, *dims, *strides
        ll_intp, ll_intp_star, ll_intp_star,
        # newnd, *newdims, *newstrides
        ll_intp, ll_intp_star, ll_intp_star,
        # itemsize, is_f_order
        ll_intp, ll_intc])
    fn = builder.module.get_or_insert_function(
        fnty, name="numba_attempt_nocopy_reshape")

    nd = ll_intp(aryty.ndim)
    shape = cgutils.gep_inbounds(builder, ary._get_ptr_by_name('shape'), 0, 0)
    strides = cgutils.gep_inbounds(builder, ary._get_ptr_by_name('strides'), 0, 0)
    newnd = ll_intp(newnd)
    newshape = cgutils.gep_inbounds(builder, newshape, 0, 0)
    newstrides = cgutils.gep_inbounds(builder, newstrides, 0, 0)
    is_f_order = ll_intc(0)
    res = builder.call(fn, [nd, shape, strides,
                            newnd, newshape, newstrides,
                            ary.itemsize, is_f_order])
    return res


def normalize_reshape_value(origsize, shape):
    num_neg_value = 0
    known_size = 1
    for ax, s in enumerate(shape):
        if s < 0:
            num_neg_value += 1
            neg_ax = ax
        else:
            known_size *= s

    if num_neg_value == 0:
        if origsize != known_size:
            raise ValueError("total size of new array must be unchanged")

    elif num_neg_value == 1:
        # Infer negative dimension
        if known_size == 0:
            inferred = 0
            ok = origsize == 0
        else:
            inferred = origsize // known_size
            ok = origsize % known_size == 0
        if not ok:
            raise ValueError("total size of new array must be unchanged")
        shape[neg_ax] = inferred

    else:
        raise ValueError("multiple negative shape values")


@lower_builtin('array.reshape', types.Array, types.BaseTuple)
def array_reshape(context, builder, sig, args):
    aryty = sig.args[0]
    retty = sig.return_type

    shapety = sig.args[1]
    shape = args[1]

    ll_intp = context.get_value_type(types.intp)
    ll_shape = lc.Type.array(ll_intp, shapety.count)

    ary = make_array(aryty)(context, builder, args[0])

    # We will change the target shape in this slot
    # (see normalize_reshape_value() below)
    newshape = cgutils.alloca_once(builder, ll_shape)
    builder.store(shape, newshape)

    # Create a shape array pointing to the value of newshape.
    # (roughly, `shape_ary = np.array(ary.shape)`)
    shape_ary_ty = types.Array(dtype=shapety.dtype, ndim=1, layout='C')
    shape_ary = make_array(shape_ary_ty)(context, builder)
    shape_itemsize = context.get_constant(types.intp,
                                          context.get_abi_sizeof(ll_intp))
    populate_array(shape_ary,
                   data=builder.bitcast(newshape, ll_intp.as_pointer()),
                   shape=[context.get_constant(types.intp, shapety.count)],
                   strides=[shape_itemsize],
                   itemsize=shape_itemsize,
                   meminfo=None)

    # Compute the original array size
    size = ary.nitems

    # Call our normalizer which will fix the shape array in case of negative
    # shape value
    context.compile_internal(builder, normalize_reshape_value,
                             typing.signature(types.void,
                                              types.uintp, shape_ary_ty),
                             [size, shape_ary._getvalue()])

    # Perform reshape (nocopy)
    newnd = shapety.count
    newstrides = cgutils.alloca_once(builder, ll_shape)

    ok = _attempt_nocopy_reshape(context, builder, aryty, ary, newnd,
                                 newshape, newstrides)
    fail = builder.icmp_unsigned('==', ok, ok.type(0))

    with builder.if_then(fail):
        msg = "incompatible shape for array"
        context.call_conv.return_user_exc(builder, NotImplementedError, (msg,))

    ret = make_array(retty)(context, builder)
    populate_array(ret,
                   data=ary.data,
                   shape=builder.load(newshape),
                   strides=builder.load(newstrides),
                   itemsize=ary.itemsize,
                   meminfo=ary.meminfo,
                   parent=ary.parent)
    res = ret._getvalue()
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin('array.reshape', types.Array, types.VarArg(types.Any))
def array_reshape_vararg(context, builder, sig, args):
    new_sig, new_args = vararg_to_tuple(context, builder, sig, args)
    return array_reshape(context, builder, new_sig, new_args)


@overload(np.reshape)
def np_reshape(a, shape):
    def np_reshape_impl(a, shape):
        return a.reshape(shape)
    return np_reshape_impl


@overload(np.append)
def np_append(arr, values, axis=None):

    if not type_can_asarray(arr):
        raise errors.TypingError('The first argument "arr" must be array-like')

    if not type_can_asarray(values):
        raise errors.TypingError('The second argument "values" must be array-like')

    if is_nonelike(axis):
        def impl(arr, values, axis=None):
            arr = np.ravel(np.asarray(arr))
            values = np.ravel(np.asarray(values))
            return np.concatenate((arr, values))
    else:

        if not isinstance(axis, types.Integer):
            raise errors.TypingError('The third argument "axis" must be an integer')

        def impl(arr, values, axis=None):
            return np.concatenate((arr, values), axis=axis)
    return impl


@lower_builtin('array.ravel', types.Array)
def array_ravel(context, builder, sig, args):
    # Only support no argument version (default order='C')
    def imp_nocopy(ary):
        """No copy version"""
        return ary.reshape(ary.size)

    def imp_copy(ary):
        """Copy version"""
        return ary.flatten()

    # If the input array is C layout already, use the nocopy version
    if sig.args[0].layout == 'C':
        imp = imp_nocopy
    # otherwise, use flatten under-the-hood
    else:
        imp = imp_copy

    res = context.compile_internal(builder, imp, sig, args)
    res = impl_ret_new_ref(context, builder, sig.return_type, res)
    return res


@lower_builtin(np.ravel, types.Array)
def np_ravel(context, builder, sig, args):
    def np_ravel_impl(a):
        return a.ravel()

    return context.compile_internal(builder, np_ravel_impl, sig, args)


@lower_builtin('array.flatten', types.Array)
def array_flatten(context, builder, sig, args):
    # Only support flattening to C layout currently.
    def imp(ary):
        return ary.copy().reshape(ary.size)

    res = context.compile_internal(builder, imp, sig, args)
    res = impl_ret_new_ref(context, builder, sig.return_type, res)
    return res


def _change_dtype(context, builder, oldty, newty, ary):
    """
    Attempt to fix up *ary* for switching from *oldty* to *newty*.

    See Numpy's array_descr_set()
    (np/core/src/multiarray/getset.c).
    Attempt to fix the array's shape and strides for a new dtype.
    False is returned on failure, True on success.
    """
    assert oldty.ndim == newty.ndim
    assert oldty.layout == newty.layout

    new_layout = ord(newty.layout)
    any_layout = ord('A')
    c_layout = ord('C')
    f_layout = ord('F')

    int8 = types.int8

    def imp(nd, dims, strides, old_itemsize, new_itemsize, layout):
        # Attempt to update the layout due to limitation of the numba
        # type system.
        if layout == any_layout:
            # Test rightmost stride to be contiguous
            if strides[-1] == old_itemsize:
                # Process this as if it is C contiguous
                layout = int8(c_layout)
            # Test leftmost stride to be F contiguous
            elif strides[0] == old_itemsize:
                # Process this as if it is F contiguous
                layout = int8(f_layout)

        if old_itemsize != new_itemsize and (layout == any_layout or nd == 0):
            return False

        if layout == c_layout:
            i = nd - 1
        else:
            i = 0

        if new_itemsize < old_itemsize:
            # If it is compatible, increase the size of the dimension
            # at the end (or at the front if F-contiguous)
            if (old_itemsize % new_itemsize) != 0:
                return False

            newdim = old_itemsize // new_itemsize
            dims[i] *= newdim
            strides[i] = new_itemsize

        elif new_itemsize > old_itemsize:
            # Determine if last (or first if F-contiguous) dimension
            # is compatible
            bytelength = dims[i] * old_itemsize
            if (bytelength % new_itemsize) != 0:
                return False

            dims[i] = bytelength // new_itemsize
            strides[i] = new_itemsize

        else:
            # Same item size: nothing to do (this also works for
            # non-contiguous arrays).
            pass

        return True

    old_itemsize = context.get_constant(types.intp,
                                        get_itemsize(context, oldty))
    new_itemsize = context.get_constant(types.intp,
                                        get_itemsize(context, newty))

    nd = context.get_constant(types.intp, newty.ndim)
    shape_data = cgutils.gep_inbounds(builder, ary._get_ptr_by_name('shape'),
                                      0, 0)
    strides_data = cgutils.gep_inbounds(builder,
                                        ary._get_ptr_by_name('strides'), 0, 0)

    shape_strides_array_type = types.Array(dtype=types.intp, ndim=1, layout='C')
    arycls = context.make_array(shape_strides_array_type)

    shape_constant = cgutils.pack_array(builder,
                                        [context.get_constant(types.intp,
                                                              newty.ndim)])

    sizeof_intp = context.get_abi_sizeof(context.get_data_type(types.intp))
    sizeof_intp = context.get_constant(types.intp, sizeof_intp)
    strides_constant = cgutils.pack_array(builder, [sizeof_intp])

    shape_ary = arycls(context, builder)

    populate_array(shape_ary,
                   data=shape_data,
                   shape=shape_constant,
                   strides=strides_constant,
                   itemsize=sizeof_intp,
                   meminfo=None)

    strides_ary = arycls(context, builder)
    populate_array(strides_ary,
                   data=strides_data,
                   shape=shape_constant,
                   strides=strides_constant,
                   itemsize=sizeof_intp,
                   meminfo=None)

    shape = shape_ary._getvalue()
    strides = strides_ary._getvalue()
    args = [nd, shape, strides, old_itemsize, new_itemsize,
            context.get_constant(types.int8, new_layout)]

    sig = signature(types.boolean,
                    types.intp,  # nd
                    shape_strides_array_type,  # dims
                    shape_strides_array_type,  # strides
                    types.intp,  # old_itemsize
                    types.intp,  # new_itemsize
                    types.int8,  # layout
                    )

    res = context.compile_internal(builder, imp, sig, args)
    update_array_info(newty, ary)
    res = impl_ret_borrowed(context, builder, sig.return_type, res)
    return res


@overload(np.shape)
def np_shape(a):
    if not type_can_asarray(a):
        raise errors.TypingError("The argument to np.shape must be array-like")

    def impl(a):
        return np.asarray(a).shape
    return impl

#-------------------------------------------------------------------------------


@overload(np.unique)
def np_unique(a):
    def np_unique_impl(a):
        b = np.sort(a.ravel())
        head = list(b[:1])
        tail = [x for i, x in enumerate(b[1:]) if b[i] != x]
        return np.array(head + tail)
    return np_unique_impl


@overload(np.repeat)
def np_repeat(a, repeats):
    # Implementation for repeats being a scalar is a module global function
    # (see below) because it might be called from the implementation below.

    def np_repeat_impl_repeats_array_like(a, repeats):
        # implementation if repeats is an array like
        repeats_array = np.asarray(repeats, dtype=np.int64)
        # if it is a singleton array, invoke the scalar implementation
        if repeats_array.shape[0] == 1:
            return np_repeat_impl_repeats_scaler(a, repeats_array[0])
        if np.any(repeats_array < 0):
            raise ValueError("negative dimensions are not allowed")
        asa = np.asarray(a)
        aravel = asa.ravel()
        n = aravel.shape[0]
        if aravel.shape != repeats_array.shape:
            raise ValueError(
                "operands could not be broadcast together")
        to_return = np.empty(np.sum(repeats_array), dtype=asa.dtype)
        pos = 0
        for i in range(n):
            to_return[pos : pos + repeats_array[i]] = aravel[i]
            pos += repeats_array[i]
        return to_return

    # type checking
    if isinstance(a, (types.Array,
                      types.List,
                      types.BaseTuple,
                      types.Number,
                      types.Boolean,
                      )
                  ):
        if isinstance(repeats, types.Integer):
            return np_repeat_impl_repeats_scaler
        elif isinstance(repeats, (types.Array, types.List)):
            if isinstance(repeats.dtype, types.Integer):
                return np_repeat_impl_repeats_array_like

        raise errors.TypingError(
            "The repeats argument must be an integer "
            "or an array-like of integer dtype")


@register_jitable
def np_repeat_impl_repeats_scaler(a, repeats):
    if repeats < 0:
        raise ValueError("negative dimensions are not allowed")
    asa = np.asarray(a)
    aravel = asa.ravel()
    n = aravel.shape[0]
    if repeats == 0:
        return np.empty(0, dtype=asa.dtype)
    elif repeats == 1:
        return np.copy(aravel)
    else:
        to_return = np.empty(n * repeats, dtype=asa.dtype)
        for i in range(n):
            to_return[i * repeats : (i + 1) * repeats] = aravel[i]
        return to_return


@extending.overload_method(types.Array, 'repeat')
def array_repeat(a, repeats):
    def array_repeat_impl(a, repeat):
        return np.repeat(a, repeat)

    return array_repeat_impl


@lower_builtin('array.view', types.Array, types.DTypeSpec)
def array_view(context, builder, sig, args):
    aryty = sig.args[0]
    retty = sig.return_type

    ary = make_array(aryty)(context, builder, args[0])
    ret = make_array(retty)(context, builder)
    # Copy all fields, casting the "data" pointer appropriately
    fields = set(ret._datamodel._fields)
    for k in sorted(fields):
        val = getattr(ary, k)
        if k == 'data':
            ptrty = ret.data.type
            ret.data = builder.bitcast(val, ptrty)
        else:
            setattr(ret, k, val)

    ok = _change_dtype(context, builder, aryty, retty, ret)
    fail = builder.icmp_unsigned('==', ok, lc.Constant.int(ok.type, 0))

    with builder.if_then(fail):
        msg = "new type not compatible with array"
        context.call_conv.return_user_exc(builder, ValueError, (msg,))

    res = ret._getvalue()
    return impl_ret_borrowed(context, builder, sig.return_type, res)


#-------------------------------------------------------------------------------
# Array attributes

@lower_getattr(types.Array, "dtype")
def array_dtype(context, builder, typ, value):
    res = context.get_dummy_value()
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.Array, "shape")
@lower_getattr(types.MemoryView, "shape")
def array_shape(context, builder, typ, value):
    arrayty = make_array(typ)
    array = arrayty(context, builder, value)
    res = array.shape
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.Array, "strides")
@lower_getattr(types.MemoryView, "strides")
def array_strides(context, builder, typ, value):
    arrayty = make_array(typ)
    array = arrayty(context, builder, value)
    res = array.strides
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.Array, "ndim")
@lower_getattr(types.MemoryView, "ndim")
def array_ndim(context, builder, typ, value):
    res = context.get_constant(types.intp, typ.ndim)
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.Array, "size")
def array_size(context, builder, typ, value):
    arrayty = make_array(typ)
    array = arrayty(context, builder, value)
    res = array.nitems
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.Array, "itemsize")
@lower_getattr(types.MemoryView, "itemsize")
def array_itemsize(context, builder, typ, value):
    arrayty = make_array(typ)
    array = arrayty(context, builder, value)
    res = array.itemsize
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.MemoryView, "nbytes")
def array_nbytes(context, builder, typ, value):
    """
    nbytes = size * itemsize
    """
    arrayty = make_array(typ)
    array = arrayty(context, builder, value)
    res = builder.mul(array.nitems, array.itemsize)
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.MemoryView, "contiguous")
def array_contiguous(context, builder, typ, value):
    res = context.get_constant(types.boolean, typ.is_contig)
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.MemoryView, "c_contiguous")
def array_c_contiguous(context, builder, typ, value):
    res = context.get_constant(types.boolean, typ.is_c_contig)
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.MemoryView, "f_contiguous")
def array_f_contiguous(context, builder, typ, value):
    res = context.get_constant(types.boolean, typ.is_f_contig)
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.MemoryView, "readonly")
def array_readonly(context, builder, typ, value):
    res = context.get_constant(types.boolean, not typ.mutable)
    return impl_ret_untracked(context, builder, typ, res)


# array.ctypes

@lower_getattr(types.Array, "ctypes")
def array_ctypes(context, builder, typ, value):
    arrayty = make_array(typ)
    array = arrayty(context, builder, value)
    # Create new ArrayCType structure
    act = types.ArrayCTypes(typ)
    ctinfo = context.make_helper(builder, act)
    ctinfo.data = array.data
    ctinfo.meminfo = array.meminfo
    res = ctinfo._getvalue()
    return impl_ret_borrowed(context, builder, act, res)


@lower_getattr(types.ArrayCTypes, "data")
def array_ctypes_data(context, builder, typ, value):
    ctinfo = context.make_helper(builder, typ, value=value)
    res = ctinfo.data
    # Convert it to an integer
    res = builder.ptrtoint(res, context.get_value_type(types.intp))
    return impl_ret_untracked(context, builder, typ, res)


@lower_cast(types.ArrayCTypes, types.CPointer)
@lower_cast(types.ArrayCTypes, types.voidptr)
def array_ctypes_to_pointer(context, builder, fromty, toty, val):
    ctinfo = context.make_helper(builder, fromty, value=val)
    res = ctinfo.data
    res = builder.bitcast(res, context.get_value_type(toty))
    return impl_ret_untracked(context, builder, toty, res)


def _call_contiguous_check(checker, context, builder, aryty, ary):
    """Helper to invoke the contiguous checker function on an array

    Args
    ----
    checker :
        ``numba.numpy_supports.is_contiguous``, or
        ``numba.numpy_supports.is_fortran``.
    context : target context
    builder : llvm ir builder
    aryty : numba type
    ary : llvm value
    """
    ary = make_array(aryty)(context, builder, value=ary)
    tup_intp = types.UniTuple(types.intp, aryty.ndim)
    itemsize = context.get_abi_sizeof(context.get_value_type(aryty.dtype))
    check_sig = signature(types.bool_, tup_intp, tup_intp, types.intp)
    check_args = [ary.shape, ary.strides,
                  context.get_constant(types.intp, itemsize)]
    is_contig = context.compile_internal(builder, checker, check_sig,
                                         check_args)
    return is_contig


# array.flags

@lower_getattr(types.Array, "flags")
def array_flags(context, builder, typ, value):
    flagsobj = context.make_helper(builder, types.ArrayFlags(typ))
    flagsobj.parent = value
    res = flagsobj._getvalue()
    return impl_ret_new_ref(context, builder, typ, res)


@lower_getattr(types.ArrayFlags, "contiguous")
@lower_getattr(types.ArrayFlags, "c_contiguous")
def array_flags_c_contiguous(context, builder, typ, value):
    if typ.array_type.layout != 'C':
        # any layout can stil be contiguous
        flagsobj = context.make_helper(builder, typ, value=value)
        res = _call_contiguous_check(is_contiguous, context, builder,
                                     typ.array_type, flagsobj.parent)
    else:
        val = typ.array_type.layout == 'C'
        res = context.get_constant(types.boolean, val)
    return impl_ret_untracked(context, builder, typ, res)


@lower_getattr(types.ArrayFlags, "f_contiguous")
def array_flags_f_contiguous(context, builder, typ, value):
    if typ.array_type.layout != 'F':
        # any layout can stil be contiguous
        flagsobj = context.make_helper(builder, typ, value=value)
        res = _call_contiguous_check(is_fortran, context, builder,
                                     typ.array_type, flagsobj.parent)
    else:
        layout = typ.array_type.layout
        val = layout == 'F' if typ.array_type.ndim > 1 else layout in 'CF'
        res = context.get_constant(types.boolean, val)
    return impl_ret_untracked(context, builder, typ, res)


#-------------------------------------------------------------------------------
# .real / .imag

@lower_getattr(types.Array, "real")
def array_real_part(context, builder, typ, value):
    if typ.dtype in types.complex_domain:
        return array_complex_attr(context, builder, typ, value, attr='real')
    elif typ.dtype in types.number_domain:
        # as an identity function
        return impl_ret_borrowed(context, builder, typ, value)
    else:
        raise NotImplementedError('unsupported .real for {}'.format(type.dtype))


@lower_getattr(types.Array, "imag")
def array_imag_part(context, builder, typ, value):
    if typ.dtype in types.complex_domain:
        return array_complex_attr(context, builder, typ, value, attr='imag')
    elif typ.dtype in types.number_domain:
        # return a readonly zero array
        sig = signature(typ.copy(readonly=True), typ)
        return numpy_zeros_like_nd(context, builder, sig, [value])
    else:
        raise NotImplementedError('unsupported .imag for {}'.format(type.dtype))


@overload_method(types.Array, 'conj')
@overload_method(types.Array, 'conjugate')
def array_conj(arr):
    def impl(arr):
        return np.conj(arr)
    return impl


def array_complex_attr(context, builder, typ, value, attr):
    """
    Given a complex array, it's memory layout is:

        R C R C R C
        ^   ^   ^

    (`R` indicates a float for the real part;
     `C` indicates a float for the imaginery part;
     the `^` indicates the start of each element)

    To get the real part, we can simply change the dtype and itemsize to that
    of the underlying float type.  The new layout is:

        R x R x R x
        ^   ^   ^

    (`x` indicates unused)

    A load operation will use the dtype to determine the number of bytes to
    load.

    To get the imaginary part, we shift the pointer by 1 float offset and
    change the dtype and itemsize.  The new layout is:

        x C x C x C
          ^   ^   ^
    """
    if attr not in ['real', 'imag'] or typ.dtype not in types.complex_domain:
        raise NotImplementedError("cannot get attribute `{}`".format(attr))

    arrayty = make_array(typ)
    array = arrayty(context, builder, value)

    # sizeof underlying float type
    flty = typ.dtype.underlying_float
    sizeof_flty = context.get_abi_sizeof(context.get_data_type(flty))
    itemsize = array.itemsize.type(sizeof_flty)

    # cast data pointer to float type
    llfltptrty = context.get_value_type(flty).as_pointer()
    dataptr = builder.bitcast(array.data, llfltptrty)

    # add offset
    if attr == 'imag':
        dataptr = builder.gep(dataptr, [ir.IntType(32)(1)])

    # make result
    resultty = typ.copy(dtype=flty, layout='A')
    result = make_array(resultty)(context, builder)
    repl = dict(data=dataptr, itemsize=itemsize)
    cgutils.copy_struct(result, array, repl)
    return impl_ret_borrowed(context, builder, resultty, result._getvalue())


#-------------------------------------------------------------------------------
# DType attribute

def dtype_type(context, builder, dtypety, dtypeval):
    # Just return a dummy opaque value
    return context.get_dummy_value()


lower_getattr(types.DType, 'type')(dtype_type)
lower_getattr(types.DType, 'kind')(dtype_type)


#-------------------------------------------------------------------------------
# Structured / record lookup

@lower_getattr_generic(types.Array)
def array_record_getattr(context, builder, typ, value, attr):
    """
    Generic getattr() implementation for record arrays: fetch the given
    record member, i.e. a subarray.
    """
    arrayty = make_array(typ)
    array = arrayty(context, builder, value)

    rectype = typ.dtype
    if not isinstance(rectype, types.Record):
        raise NotImplementedError("attribute %r of %s not defined" % (attr, typ))
    dtype = rectype.typeof(attr)
    offset = rectype.offset(attr)

    resty = typ.copy(dtype=dtype, layout='A')

    raryty = make_array(resty)

    rary = raryty(context, builder)

    constoffset = context.get_constant(types.intp, offset)

    newdataptr = cgutils.pointer_add(
        builder, array.data, constoffset,  return_type=rary.data.type,
    )
    datasize = context.get_abi_sizeof(context.get_data_type(dtype))
    populate_array(rary,
                   data=newdataptr,
                   shape=array.shape,
                   strides=array.strides,
                   itemsize=context.get_constant(types.intp, datasize),
                   meminfo=array.meminfo,
                   parent=array.parent)
    res = rary._getvalue()
    return impl_ret_borrowed(context, builder, resty, res)


@lower_builtin('static_getitem', types.Array, types.StringLiteral)
def array_record_getitem(context, builder, sig, args):
    index = args[1]
    if not isinstance(index, str):
        # This will fallback to normal getitem
        raise NotImplementedError
    return array_record_getattr(context, builder, sig.args[0], args[0], index)


@lower_getattr_generic(types.Record)
def record_getattr(context, builder, typ, value, attr):
    """
    Generic getattr() implementation for records: fetch the given
    record member, i.e. a scalar.
    """
    context.sentry_record_alignment(typ, attr)
    offset = typ.offset(attr)
    elemty = typ.typeof(attr)

    if isinstance(elemty, types.NestedArray):
        # Only a nested array's *data* is stored in a structured array,
        # so we create an array structure to point to that data.
        aryty = make_array(elemty)
        ary = aryty(context, builder)
        dtype = elemty.dtype
        newshape = [context.get_constant(types.intp, s) for s in
                    elemty.shape]
        newstrides = [context.get_constant(types.intp, s) for s in
                      elemty.strides]
        newdata = cgutils.get_record_member(builder, value, offset,
                                            context.get_data_type(dtype))
        populate_array(
            ary,
            data=newdata,
            shape=cgutils.pack_array(builder, newshape),
            strides=cgutils.pack_array(builder, newstrides),
            itemsize=context.get_constant(types.intp, elemty.size),
            meminfo=None,
            parent=None,
        )
        res = ary._getvalue()
        return impl_ret_borrowed(context, builder, typ, res)
    else:
        dptr = cgutils.get_record_member(builder, value, offset,
                                         context.get_data_type(elemty))
        align = None if typ.aligned else 1
        res = context.unpack_value(builder, elemty, dptr, align)
        return impl_ret_borrowed(context, builder, typ, res)


@lower_setattr_generic(types.Record)
def record_setattr(context, builder, sig, args, attr):
    """
    Generic setattr() implementation for records: set the given
    record member, i.e. a scalar.
    """
    typ, valty = sig.args
    target, val = args

    context.sentry_record_alignment(typ, attr)
    offset = typ.offset(attr)
    elemty = typ.typeof(attr)

    dptr = cgutils.get_record_member(builder, target, offset,
                                     context.get_data_type(elemty))
    val = context.cast(builder, val, valty, elemty)
    align = None if typ.aligned else 1
    context.pack_value(builder, elemty, val, dptr, align=align)


@lower_builtin('static_getitem', types.Record, types.StringLiteral)
def record_getitem(context, builder, sig, args):
    """
    Record.__getitem__ redirects to getattr()
    """
    impl = context.get_getattr(sig.args[0], args[1])
    return impl(context, builder, sig.args[0], args[0], args[1])


@lower_builtin('static_setitem', types.Record, types.StringLiteral, types.Any)
def record_setitem(context, builder, sig, args):
    """
    Record.__setitem__ redirects to setattr()
    """
    recty, _, valty = sig.args
    rec, idx, val = args
    getattr_sig = signature(sig.return_type, recty, valty)
    impl = context.get_setattr(idx, getattr_sig)
    assert impl is not None
    return impl(builder, (rec, val))


#-------------------------------------------------------------------------------
# Constant arrays and records


@lower_constant(types.Array)
def constant_array(context, builder, ty, pyval):
    """
    Create a constant array (mechanism is target-dependent).
    """
    return context.make_constant_array(builder, ty, pyval)


@lower_constant(types.Record)
def constant_record(context, builder, ty, pyval):
    """
    Create a record constant as a stack-allocated array of bytes.
    """
    lty = ir.ArrayType(ir.IntType(8), pyval.nbytes)
    val = lty(bytearray(pyval.tostring()))
    return cgutils.alloca_once_value(builder, val)


@lower_constant(types.Bytes)
def constant_bytes(context, builder, ty, pyval):
    """
    Create a constant array from bytes (mechanism is target-dependent).
    """
    buf = np.array(bytearray(pyval), dtype=np.uint8)
    return context.make_constant_array(builder, ty, buf)

#-------------------------------------------------------------------------------
# Comparisons


@lower_builtin(operator.is_, types.Array, types.Array)
def array_is(context, builder, sig, args):
    aty, bty = sig.args
    if aty != bty:
        return cgutils.false_bit

    def array_is_impl(a, b):
        return (a.shape == b.shape and
                a.strides == b.strides and
                a.ctypes.data == b.ctypes.data)

    return context.compile_internal(builder, array_is_impl, sig, args)


#-------------------------------------------------------------------------------
# builtin `np.flat` implementation

def make_array_flat_cls(flatiterty):
    """
    Return the Structure representation of the given *flatiterty* (an
    instance of types.NumpyFlatType).
    """
    return _make_flattening_iter_cls(flatiterty, 'flat')


def make_array_ndenumerate_cls(nditerty):
    """
    Return the Structure representation of the given *nditerty* (an
    instance of types.NumpyNdEnumerateType).
    """
    return _make_flattening_iter_cls(nditerty, 'ndenumerate')


def _increment_indices(context, builder, ndim, shape, indices, end_flag=None,
                       loop_continue=None, loop_break=None):
    zero = context.get_constant(types.intp, 0)

    bbend = builder.append_basic_block('end_increment')

    if end_flag is not None:
        builder.store(cgutils.false_byte, end_flag)

    for dim in reversed(range(ndim)):
        idxptr = cgutils.gep_inbounds(builder, indices, dim)
        idx = cgutils.increment_index(builder, builder.load(idxptr))

        count = shape[dim]
        in_bounds = builder.icmp_signed('<', idx, count)
        with cgutils.if_likely(builder, in_bounds):
            # New index is still in bounds
            builder.store(idx, idxptr)
            if loop_continue is not None:
                loop_continue(dim)
            builder.branch(bbend)
        # Index out of bounds => reset it and proceed it to outer index
        builder.store(zero, idxptr)
        if loop_break is not None:
            loop_break(dim)

    if end_flag is not None:
        builder.store(cgutils.true_byte, end_flag)
    builder.branch(bbend)

    builder.position_at_end(bbend)


def _increment_indices_array(context, builder, arrty, arr, indices, end_flag=None):
    shape = cgutils.unpack_tuple(builder, arr.shape, arrty.ndim)
    _increment_indices(context, builder, arrty.ndim, shape, indices, end_flag)


def make_nditer_cls(nditerty):
    """
    Return the Structure representation of the given *nditerty* (an
    instance of types.NumpyNdIterType).
    """
    ndim = nditerty.ndim
    layout = nditerty.layout
    narrays = len(nditerty.arrays)
    nshapes = ndim if nditerty.need_shaped_indexing else 1

    class BaseSubIter(object):
        """
        Base class for sub-iterators of a nditer() instance.
        """

        def __init__(self, nditer, member_name, start_dim, end_dim):
            self.nditer = nditer
            self.member_name = member_name
            self.start_dim = start_dim
            self.end_dim = end_dim
            self.ndim = end_dim - start_dim

        def set_member_ptr(self, ptr):
            setattr(self.nditer, self.member_name, ptr)

        @utils.cached_property
        def member_ptr(self):
            return getattr(self.nditer, self.member_name)

        def init_specific(self, context, builder):
            pass

        def loop_continue(self, context, builder, logical_dim):
            pass

        def loop_break(self, context, builder, logical_dim):
            pass

    class FlatSubIter(BaseSubIter):
        """
        Sub-iterator walking a contiguous array in physical order, with
        support for broadcasting (the index is reset on the outer dimension).
        """

        def init_specific(self, context, builder):
            zero = context.get_constant(types.intp, 0)
            self.set_member_ptr(cgutils.alloca_once_value(builder, zero))

        def compute_pointer(self, context, builder, indices, arrty, arr):
            index = builder.load(self.member_ptr)
            return builder.gep(arr.data, [index])

        def loop_continue(self, context, builder, logical_dim):
            if logical_dim == self.ndim - 1:
                # Only increment index inside innermost logical dimension
                index = builder.load(self.member_ptr)
                index = cgutils.increment_index(builder, index)
                builder.store(index, self.member_ptr)

        def loop_break(self, context, builder, logical_dim):
            if logical_dim == 0:
                # At the exit of outermost logical dimension, reset index
                zero = context.get_constant(types.intp, 0)
                builder.store(zero, self.member_ptr)
            elif logical_dim == self.ndim - 1:
                # Inside innermost logical dimension, increment index
                index = builder.load(self.member_ptr)
                index = cgutils.increment_index(builder, index)
                builder.store(index, self.member_ptr)

    class TrivialFlatSubIter(BaseSubIter):
        """
        Sub-iterator walking a contiguous array in physical order,
        *without* support for broadcasting.
        """

        def init_specific(self, context, builder):
            assert not nditerty.need_shaped_indexing

        def compute_pointer(self, context, builder, indices, arrty, arr):
            assert len(indices) <= 1, len(indices)
            return builder.gep(arr.data, indices)

    class IndexedSubIter(BaseSubIter):
        """
        Sub-iterator walking an array in logical order.
        """

        def compute_pointer(self, context, builder, indices, arrty, arr):
            assert len(indices) == self.ndim
            return cgutils.get_item_pointer(builder, arrty, arr,
                                            indices, wraparound=False)

    class ZeroDimSubIter(BaseSubIter):
        """
        Sub-iterator "walking" a 0-d array.
        """

        def compute_pointer(self, context, builder, indices, arrty, arr):
            return arr.data

    class ScalarSubIter(BaseSubIter):
        """
        Sub-iterator "walking" a scalar value.
        """

        def compute_pointer(self, context, builder, indices, arrty, arr):
            return arr

    class NdIter(cgutils.create_struct_proxy(nditerty)):
        """
        .nditer() implementation.

        Note: 'F' layout means the shape is iterated in reverse logical order,
        so indices and shapes arrays have to be reversed as well.
        """

        @utils.cached_property
        def subiters(self):
            l = []
            factories = {'flat': FlatSubIter if nditerty.need_shaped_indexing
                         else TrivialFlatSubIter,
                         'indexed': IndexedSubIter,
                         '0d': ZeroDimSubIter,
                         'scalar': ScalarSubIter,
                         }
            for i, sub in enumerate(nditerty.indexers):
                kind, start_dim, end_dim, _ = sub
                member_name = 'index%d' % i
                factory = factories[kind]
                l.append(factory(self, member_name, start_dim, end_dim))
            return l

        def init_specific(self, context, builder, arrtys, arrays):
            """
            Initialize the nditer() instance for the specific array inputs.
            """
            zero = context.get_constant(types.intp, 0)

            # Store inputs
            self.arrays = context.make_tuple(builder, types.Tuple(arrtys),
                                             arrays)
            # Create slots for scalars
            for i, ty in enumerate(arrtys):
                if not isinstance(ty, types.Array):
                    member_name = 'scalar%d' % i
                    # XXX as_data()?
                    slot = cgutils.alloca_once_value(builder, arrays[i])
                    setattr(self, member_name, slot)

            arrays = self._arrays_or_scalars(context, builder, arrtys, arrays)

            # Extract iterator shape (the shape of the most-dimensional input)
            main_shape_ty = types.UniTuple(types.intp, ndim)
            main_shape = None
            main_nitems = None
            for i, arrty in enumerate(arrtys):
                if isinstance(arrty, types.Array) and arrty.ndim == ndim:
                    main_shape = arrays[i].shape
                    main_nitems = arrays[i].nitems
                    break
            else:
                # Only scalar inputs => synthesize a dummy shape
                assert ndim == 0
                main_shape = context.make_tuple(builder, main_shape_ty, ())
                main_nitems = context.get_constant(types.intp, 1)

            # Validate shapes of array inputs
            def check_shape(shape, main_shape):
                n = len(shape)
                for i in range(n):
                    if shape[i] != main_shape[len(main_shape) - n + i]:
                        raise ValueError("nditer(): operands could not be broadcast together")

            for arrty, arr in zip(arrtys, arrays):
                if isinstance(arrty, types.Array) and arrty.ndim > 0:
                    context.compile_internal(builder, check_shape,
                                             signature(types.none,
                                                       types.UniTuple(types.intp, arrty.ndim),
                                                       main_shape_ty),
                                             (arr.shape, main_shape))

            # Compute shape and size
            shapes = cgutils.unpack_tuple(builder, main_shape)
            if layout == 'F':
                shapes = shapes[::-1]

            # If shape is empty, mark iterator exhausted
            shape_is_empty = builder.icmp_signed('==', main_nitems, zero)
            exhausted = builder.select(shape_is_empty, cgutils.true_byte,
                                       cgutils.false_byte)

            if not nditerty.need_shaped_indexing:
                # Flatten shape to make iteration faster on small innermost
                # dimensions (e.g. a (100000, 3) shape)
                shapes = (main_nitems,)
            assert len(shapes) == nshapes

            indices = cgutils.alloca_once(builder, zero.type, size=nshapes)
            for dim in range(nshapes):
                idxptr = cgutils.gep_inbounds(builder, indices, dim)
                builder.store(zero, idxptr)

            self.indices = indices
            self.shape = cgutils.pack_array(builder, shapes, zero.type)
            self.exhausted = cgutils.alloca_once_value(builder, exhausted)

            # Initialize subiterators
            for subiter in self.subiters:
                subiter.init_specific(context, builder)

        def iternext_specific(self, context, builder, result):
            """
            Compute next iteration of the nditer() instance.
            """
            bbend = builder.append_basic_block('end')

            # Branch early if exhausted
            exhausted = cgutils.as_bool_bit(builder, builder.load(self.exhausted))
            with cgutils.if_unlikely(builder, exhausted):
                result.set_valid(False)
                builder.branch(bbend)

            arrtys = nditerty.arrays
            arrays = cgutils.unpack_tuple(builder, self.arrays)
            arrays = self._arrays_or_scalars(context, builder, arrtys, arrays)
            indices = self.indices

            # Compute iterated results
            result.set_valid(True)
            views = self._make_views(context, builder, indices, arrtys, arrays)
            views = [v._getvalue() for v in views]
            if len(views) == 1:
                result.yield_(views[0])
            else:
                result.yield_(context.make_tuple(builder, nditerty.yield_type,
                                                 views))

            shape = cgutils.unpack_tuple(builder, self.shape)
            _increment_indices(context, builder, len(shape), shape,
                               indices, self.exhausted,
                               functools.partial(self._loop_continue, context, builder),
                               functools.partial(self._loop_break, context, builder),
                               )

            builder.branch(bbend)
            builder.position_at_end(bbend)

        def _loop_continue(self, context, builder, dim):
            for sub in self.subiters:
                if sub.start_dim <= dim < sub.end_dim:
                    sub.loop_continue(context, builder, dim - sub.start_dim)

        def _loop_break(self, context, builder, dim):
            for sub in self.subiters:
                if sub.start_dim <= dim < sub.end_dim:
                    sub.loop_break(context, builder, dim - sub.start_dim)

        def _make_views(self, context, builder, indices, arrtys, arrays):
            """
            Compute the views to be yielded.
            """
            views = [None] * narrays
            indexers = nditerty.indexers
            subiters = self.subiters
            rettys = nditerty.yield_type
            if isinstance(rettys, types.BaseTuple):
                rettys = list(rettys)
            else:
                rettys = [rettys]
            indices = [builder.load(cgutils.gep_inbounds(builder, indices, i))
                       for i in range(nshapes)]

            for sub, subiter in zip(indexers, subiters):
                _, _, _, array_indices = sub
                sub_indices = indices[subiter.start_dim:subiter.end_dim]
                if layout == 'F':
                    sub_indices = sub_indices[::-1]
                for i in array_indices:
                    assert views[i] is None
                    views[i] = self._make_view(context, builder, sub_indices,
                                               rettys[i],
                                               arrtys[i], arrays[i], subiter)
            assert all(v for v in views)
            return views

        def _make_view(self, context, builder, indices, retty, arrty, arr, subiter):
            """
            Compute a 0d view for a given input array.
            """
            assert isinstance(retty, types.Array) and retty.ndim == 0

            ptr = subiter.compute_pointer(context, builder, indices, arrty, arr)
            view = context.make_array(retty)(context, builder)

            itemsize = get_itemsize(context, retty)
            shape = context.make_tuple(builder, types.UniTuple(types.intp, 0), ())
            strides = context.make_tuple(builder, types.UniTuple(types.intp, 0), ())
            # HACK: meminfo=None avoids expensive refcounting operations
            # on ephemeral views
            populate_array(view, ptr, shape, strides, itemsize, meminfo=None)
            return view

        def _arrays_or_scalars(self, context, builder, arrtys, arrays):
            # Return a list of either array structures or pointers to
            # scalar slots
            l = []
            for i, (arrty, arr) in enumerate(zip(arrtys, arrays)):
                if isinstance(arrty, types.Array):
                    l.append(context.make_array(arrty)(context, builder, value=arr))
                else:
                    l.append(getattr(self, "scalar%d" % i))
            return l

    return NdIter


def make_ndindex_cls(nditerty):
    """
    Return the Structure representation of the given *nditerty* (an
    instance of types.NumpyNdIndexType).
    """
    ndim = nditerty.ndim

    class NdIndexIter(cgutils.create_struct_proxy(nditerty)):
        """
        .ndindex() implementation.
        """

        def init_specific(self, context, builder, shapes):
            zero = context.get_constant(types.intp, 0)
            indices = cgutils.alloca_once(builder, zero.type,
                                          size=context.get_constant(types.intp,
                                                                    ndim))
            exhausted = cgutils.alloca_once_value(builder, cgutils.false_byte)

            for dim in range(ndim):
                idxptr = cgutils.gep_inbounds(builder, indices, dim)
                builder.store(zero, idxptr)
                # 0-sized dimensions really indicate an empty array,
                # but we have to catch that condition early to avoid
                # a bug inside the iteration logic.
                dim_size = shapes[dim]
                dim_is_empty = builder.icmp(lc.ICMP_EQ, dim_size, zero)
                with cgutils.if_unlikely(builder, dim_is_empty):
                    builder.store(cgutils.true_byte, exhausted)

            self.indices = indices
            self.exhausted = exhausted
            self.shape = cgutils.pack_array(builder, shapes, zero.type)

        def iternext_specific(self, context, builder, result):
            zero = context.get_constant(types.intp, 0)

            bbend = builder.append_basic_block('end')

            exhausted = cgutils.as_bool_bit(builder, builder.load(self.exhausted))
            with cgutils.if_unlikely(builder, exhausted):
                result.set_valid(False)
                builder.branch(bbend)

            indices = [builder.load(cgutils.gep_inbounds(builder, self.indices, dim))
                       for dim in range(ndim)]
            for load in indices:
                mark_positive(builder, load)

            result.yield_(cgutils.pack_array(builder, indices, zero.type))
            result.set_valid(True)

            shape = cgutils.unpack_tuple(builder, self.shape, ndim)
            _increment_indices(context, builder, ndim, shape,
                               self.indices, self.exhausted)

            builder.branch(bbend)
            builder.position_at_end(bbend)

    return NdIndexIter


def _make_flattening_iter_cls(flatiterty, kind):
    assert kind in ('flat', 'ndenumerate')

    array_type = flatiterty.array_type

    if array_type.layout == 'C':
        class CContiguousFlatIter(cgutils.create_struct_proxy(flatiterty)):
            """
            .flat() / .ndenumerate() implementation for C-contiguous arrays.
            """

            def init_specific(self, context, builder, arrty, arr):
                zero = context.get_constant(types.intp, 0)
                self.index = cgutils.alloca_once_value(builder, zero)
                # We can't trust strides[-1] to always contain the right
                # step value, see
                # http://docs.scipy.org/doc/numpy-dev/release.html#npy-relaxed-strides-checking
                self.stride = arr.itemsize

                if kind == 'ndenumerate':
                    # Zero-initialize the indices array.
                    indices = cgutils.alloca_once(
                        builder, zero.type,
                        size=context.get_constant(types.intp, arrty.ndim))

                    for dim in range(arrty.ndim):
                        idxptr = cgutils.gep_inbounds(builder, indices, dim)
                        builder.store(zero, idxptr)

                    self.indices = indices

            # NOTE: Using gep() instead of explicit pointer addition helps
            # LLVM vectorize the loop (since the stride is known and
            # constant).  This is not possible in the non-contiguous case,
            # where the strides are unknown at compile-time.

            def iternext_specific(self, context, builder, arrty, arr, result):
                ndim = arrty.ndim
                nitems = arr.nitems

                index = builder.load(self.index)
                is_valid = builder.icmp(lc.ICMP_SLT, index, nitems)
                result.set_valid(is_valid)

                with cgutils.if_likely(builder, is_valid):
                    ptr = builder.gep(arr.data, [index])
                    value = load_item(context, builder, arrty, ptr)
                    if kind == 'flat':
                        result.yield_(value)
                    else:
                        # ndenumerate(): fetch and increment indices
                        indices = self.indices
                        idxvals = [builder.load(cgutils.gep_inbounds(builder, indices, dim))
                                   for dim in range(ndim)]
                        idxtuple = cgutils.pack_array(builder, idxvals)
                        result.yield_(
                            cgutils.make_anonymous_struct(builder, [idxtuple, value]))
                        _increment_indices_array(context, builder, arrty, arr, indices)

                    index = cgutils.increment_index(builder, index)
                    builder.store(index, self.index)

            def getitem(self, context, builder, arrty, arr, index):
                ptr = builder.gep(arr.data, [index])
                return load_item(context, builder, arrty, ptr)

            def setitem(self, context, builder, arrty, arr, index, value):
                ptr = builder.gep(arr.data, [index])
                store_item(context, builder, arrty, value, ptr)

        return CContiguousFlatIter

    else:
        class FlatIter(cgutils.create_struct_proxy(flatiterty)):
            """
            Generic .flat() / .ndenumerate() implementation for
            non-contiguous arrays.
            It keeps track of pointers along each dimension in order to
            minimize computations.
            """

            def init_specific(self, context, builder, arrty, arr):
                zero = context.get_constant(types.intp, 0)
                data = arr.data
                ndim = arrty.ndim
                shapes = cgutils.unpack_tuple(builder, arr.shape, ndim)

                indices = cgutils.alloca_once(builder, zero.type,
                                              size=context.get_constant(types.intp,
                                                                        arrty.ndim))
                pointers = cgutils.alloca_once(builder, data.type,
                                               size=context.get_constant(types.intp,
                                                                         arrty.ndim))
                exhausted = cgutils.alloca_once_value(builder, cgutils.false_byte)

                # Initialize indices and pointers with their start values.
                for dim in range(ndim):
                    idxptr = cgutils.gep_inbounds(builder, indices, dim)
                    ptrptr = cgutils.gep_inbounds(builder, pointers, dim)
                    builder.store(data, ptrptr)
                    builder.store(zero, idxptr)
                    # 0-sized dimensions really indicate an empty array,
                    # but we have to catch that condition early to avoid
                    # a bug inside the iteration logic (see issue #846).
                    dim_size = shapes[dim]
                    dim_is_empty = builder.icmp(lc.ICMP_EQ, dim_size, zero)
                    with cgutils.if_unlikely(builder, dim_is_empty):
                        builder.store(cgutils.true_byte, exhausted)

                self.indices = indices
                self.pointers = pointers
                self.exhausted = exhausted

            def iternext_specific(self, context, builder, arrty, arr, result):
                ndim = arrty.ndim
                shapes = cgutils.unpack_tuple(builder, arr.shape, ndim)
                strides = cgutils.unpack_tuple(builder, arr.strides, ndim)
                indices = self.indices
                pointers = self.pointers

                zero = context.get_constant(types.intp, 0)

                bbend = builder.append_basic_block('end')

                # Catch already computed iterator exhaustion
                is_exhausted = cgutils.as_bool_bit(
                    builder, builder.load(self.exhausted))
                with cgutils.if_unlikely(builder, is_exhausted):
                    result.set_valid(False)
                    builder.branch(bbend)
                result.set_valid(True)

                # Current pointer inside last dimension
                last_ptr = cgutils.gep_inbounds(builder, pointers, ndim - 1)
                ptr = builder.load(last_ptr)
                value = load_item(context, builder, arrty, ptr)
                if kind == 'flat':
                    result.yield_(value)
                else:
                    # ndenumerate() => yield (indices, value)
                    idxvals = [builder.load(cgutils.gep_inbounds(builder, indices, dim))
                               for dim in range(ndim)]
                    idxtuple = cgutils.pack_array(builder, idxvals)
                    result.yield_(
                        cgutils.make_anonymous_struct(builder, [idxtuple, value]))

                # Update indices and pointers by walking from inner
                # dimension to outer.
                for dim in reversed(range(ndim)):
                    idxptr = cgutils.gep_inbounds(builder, indices, dim)
                    idx = cgutils.increment_index(builder,
                                                  builder.load(idxptr))

                    count = shapes[dim]
                    stride = strides[dim]
                    in_bounds = builder.icmp(lc.ICMP_SLT, idx, count)
                    with cgutils.if_likely(builder, in_bounds):
                        # Index is valid => pointer can simply be incremented.
                        builder.store(idx, idxptr)
                        ptrptr = cgutils.gep_inbounds(builder, pointers, dim)
                        ptr = builder.load(ptrptr)
                        ptr = cgutils.pointer_add(builder, ptr, stride)
                        builder.store(ptr, ptrptr)
                        # Reset pointers in inner dimensions
                        for inner_dim in range(dim + 1, ndim):
                            ptrptr = cgutils.gep_inbounds(builder, pointers, inner_dim)
                            builder.store(ptr, ptrptr)
                        builder.branch(bbend)
                    # Reset index and continue with next dimension
                    builder.store(zero, idxptr)

                # End of array
                builder.store(cgutils.true_byte, self.exhausted)
                builder.branch(bbend)

                builder.position_at_end(bbend)

            def _ptr_for_index(self, context, builder, arrty, arr, index):
                ndim = arrty.ndim
                shapes = cgutils.unpack_tuple(builder, arr.shape, count=ndim)
                strides = cgutils.unpack_tuple(builder, arr.strides, count=ndim)

                # First convert the flattened index into a regular n-dim index
                indices = []
                for dim in reversed(range(ndim)):
                    indices.append(builder.urem(index, shapes[dim]))
                    index = builder.udiv(index, shapes[dim])
                indices.reverse()

                ptr = cgutils.get_item_pointer2(builder, arr.data, shapes,
                                                strides, arrty.layout, indices)
                return ptr

            def getitem(self, context, builder, arrty, arr, index):
                ptr = self._ptr_for_index(context, builder, arrty, arr, index)
                return load_item(context, builder, arrty, ptr)

            def setitem(self, context, builder, arrty, arr, index, value):
                ptr = self._ptr_for_index(context, builder, arrty, arr, index)
                store_item(context, builder, arrty, value, ptr)

        return FlatIter


@lower_getattr(types.Array, "flat")
def make_array_flatiter(context, builder, arrty, arr):
    flatitercls = make_array_flat_cls(types.NumpyFlatType(arrty))
    flatiter = flatitercls(context, builder)

    flatiter.array = arr

    arrcls = context.make_array(arrty)
    arr = arrcls(context, builder, ref=flatiter._get_ptr_by_name('array'))

    flatiter.init_specific(context, builder, arrty, arr)

    res = flatiter._getvalue()
    return impl_ret_borrowed(context, builder, types.NumpyFlatType(arrty), res)


@lower_builtin('iternext', types.NumpyFlatType)
@iternext_impl(RefType.BORROWED)
def iternext_numpy_flatiter(context, builder, sig, args, result):
    [flatiterty] = sig.args
    [flatiter] = args

    flatitercls = make_array_flat_cls(flatiterty)
    flatiter = flatitercls(context, builder, value=flatiter)

    arrty = flatiterty.array_type
    arrcls = context.make_array(arrty)
    arr = arrcls(context, builder, value=flatiter.array)

    flatiter.iternext_specific(context, builder, arrty, arr, result)


@lower_builtin(operator.getitem, types.NumpyFlatType, types.Integer)
def iternext_numpy_getitem(context, builder, sig, args):
    flatiterty = sig.args[0]
    flatiter, index = args

    flatitercls = make_array_flat_cls(flatiterty)
    flatiter = flatitercls(context, builder, value=flatiter)

    arrty = flatiterty.array_type
    arrcls = context.make_array(arrty)
    arr = arrcls(context, builder, value=flatiter.array)

    res = flatiter.getitem(context, builder, arrty, arr, index)
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin(operator.setitem, types.NumpyFlatType, types.Integer,
               types.Any)
def iternext_numpy_getitem_any(context, builder, sig, args):
    flatiterty = sig.args[0]
    flatiter, index, value = args

    flatitercls = make_array_flat_cls(flatiterty)
    flatiter = flatitercls(context, builder, value=flatiter)

    arrty = flatiterty.array_type
    arrcls = context.make_array(arrty)
    arr = arrcls(context, builder, value=flatiter.array)

    flatiter.setitem(context, builder, arrty, arr, index, value)
    return context.get_dummy_value()


@lower_builtin(len, types.NumpyFlatType)
def iternext_numpy_getitem_flat(context, builder, sig, args):
    flatiterty = sig.args[0]
    flatitercls = make_array_flat_cls(flatiterty)
    flatiter = flatitercls(context, builder, value=args[0])

    arrcls = context.make_array(flatiterty.array_type)
    arr = arrcls(context, builder, value=flatiter.array)
    return arr.nitems


@lower_builtin(np.ndenumerate, types.Array)
def make_array_ndenumerate(context, builder, sig, args):
    arrty, = sig.args
    arr, = args
    nditercls = make_array_ndenumerate_cls(types.NumpyNdEnumerateType(arrty))
    nditer = nditercls(context, builder)

    nditer.array = arr

    arrcls = context.make_array(arrty)
    arr = arrcls(context, builder, ref=nditer._get_ptr_by_name('array'))

    nditer.init_specific(context, builder, arrty, arr)

    res = nditer._getvalue()
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin('iternext', types.NumpyNdEnumerateType)
@iternext_impl(RefType.BORROWED)
def iternext_numpy_nditer(context, builder, sig, args, result):
    [nditerty] = sig.args
    [nditer] = args

    nditercls = make_array_ndenumerate_cls(nditerty)
    nditer = nditercls(context, builder, value=nditer)

    arrty = nditerty.array_type
    arrcls = context.make_array(arrty)
    arr = arrcls(context, builder, value=nditer.array)

    nditer.iternext_specific(context, builder, arrty, arr, result)


@lower_builtin(pndindex, types.VarArg(types.Integer))
@lower_builtin(np.ndindex, types.VarArg(types.Integer))
def make_array_ndindex(context, builder, sig, args):
    """ndindex(*shape)"""
    shape = [context.cast(builder, arg, argty, types.intp)
             for argty, arg in zip(sig.args, args)]

    nditercls = make_ndindex_cls(types.NumpyNdIndexType(len(shape)))
    nditer = nditercls(context, builder)
    nditer.init_specific(context, builder, shape)

    res = nditer._getvalue()
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin(pndindex, types.BaseTuple)
@lower_builtin(np.ndindex, types.BaseTuple)
def make_array_ndindex_tuple(context, builder, sig, args):
    """ndindex(shape)"""
    ndim = sig.return_type.ndim
    if ndim > 0:
        idxty = sig.args[0].dtype
        tup = args[0]

        shape = cgutils.unpack_tuple(builder, tup, ndim)
        shape = [context.cast(builder, idx, idxty, types.intp)
                 for idx in shape]
    else:
        shape = []

    nditercls = make_ndindex_cls(types.NumpyNdIndexType(len(shape)))
    nditer = nditercls(context, builder)
    nditer.init_specific(context, builder, shape)

    res = nditer._getvalue()
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin('iternext', types.NumpyNdIndexType)
@iternext_impl(RefType.BORROWED)
def iternext_numpy_ndindex(context, builder, sig, args, result):
    [nditerty] = sig.args
    [nditer] = args

    nditercls = make_ndindex_cls(nditerty)
    nditer = nditercls(context, builder, value=nditer)

    nditer.iternext_specific(context, builder, result)


@lower_builtin(np.nditer, types.Any)
def make_array_nditer(context, builder, sig, args):
    """
    nditer(...)
    """
    nditerty = sig.return_type
    arrtys = nditerty.arrays

    if isinstance(sig.args[0], types.BaseTuple):
        arrays = cgutils.unpack_tuple(builder, args[0])
    else:
        arrays = [args[0]]

    nditer = make_nditer_cls(nditerty)(context, builder)
    nditer.init_specific(context, builder, arrtys, arrays)

    res = nditer._getvalue()
    return impl_ret_borrowed(context, builder, nditerty, res)


@lower_builtin('iternext', types.NumpyNdIterType)
@iternext_impl(RefType.BORROWED)
def iternext_numpy_nditer2(context, builder, sig, args, result):
    [nditerty] = sig.args
    [nditer] = args

    nditer = make_nditer_cls(nditerty)(context, builder, value=nditer)
    nditer.iternext_specific(context, builder, result)


# -----------------------------------------------------------------------------
# Numpy array constructors

def _empty_nd_impl(context, builder, arrtype, shapes):
    """Utility function used for allocating a new array during LLVM code
    generation (lowering).  Given a target context, builder, array
    type, and a tuple or list of lowered dimension sizes, returns a
    LLVM value pointing at a Numba runtime allocated array.
    """
    arycls = make_array(arrtype)
    ary = arycls(context, builder)

    datatype = context.get_data_type(arrtype.dtype)
    itemsize = context.get_constant(types.intp, get_itemsize(context, arrtype))

    # compute array length
    arrlen = context.get_constant(types.intp, 1)
    for s in shapes:
        arrlen = builder.mul(arrlen, s)

    if arrtype.ndim == 0:
        strides = ()
    elif arrtype.layout == 'C':
        strides = [itemsize]
        for dimension_size in reversed(shapes[1:]):
            strides.append(builder.mul(strides[-1], dimension_size))
        strides = tuple(reversed(strides))
    elif arrtype.layout == 'F':
        strides = [itemsize]
        for dimension_size in shapes[:-1]:
            strides.append(builder.mul(strides[-1], dimension_size))
        strides = tuple(strides)
    else:
        raise NotImplementedError(
            "Don't know how to allocate array with layout '{0}'.".format(
                arrtype.layout))

    allocsize = builder.mul(itemsize, arrlen)
    align = context.get_preferred_array_alignment(arrtype.dtype)
    meminfo = context.nrt.meminfo_alloc_aligned(builder, size=allocsize,
                                                align=align)

    data = context.nrt.meminfo_data(builder, meminfo)

    intp_t = context.get_value_type(types.intp)
    shape_array = cgutils.pack_array(builder, shapes, ty=intp_t)
    strides_array = cgutils.pack_array(builder, strides, ty=intp_t)

    populate_array(ary,
                   data=builder.bitcast(data, datatype.as_pointer()),
                   shape=shape_array,
                   strides=strides_array,
                   itemsize=itemsize,
                   meminfo=meminfo)

    return ary


def _zero_fill_array(context, builder, ary):
    """
    Zero-fill an array.  The array must be contiguous.
    """
    cgutils.memset(builder, ary.data, builder.mul(ary.itemsize, ary.nitems), 0)


def _parse_shape(context, builder, ty, val):
    """
    Parse the shape argument to an array constructor.
    """
    if isinstance(ty, types.Integer):
        ndim = 1
        shapes = [context.cast(builder, val, ty, types.intp)]
    else:
        assert isinstance(ty, types.BaseTuple)
        ndim = ty.count
        shapes = cgutils.unpack_tuple(builder, val, count=ndim)

    zero = context.get_constant_generic(builder, types.intp, 0)
    for dim in range(ndim):
        is_neg = builder.icmp_signed('<', shapes[dim], zero)
        with cgutils.if_unlikely(builder, is_neg):
            context.call_conv.return_user_exc(builder, ValueError,
                                              ("negative dimensions not allowed",))

    return shapes


def _parse_empty_args(context, builder, sig, args):
    """
    Parse the arguments of a np.empty(), np.zeros() or np.ones() call.
    """
    arrshapetype = sig.args[0]
    arrshape = args[0]
    arrtype = sig.return_type
    return arrtype, _parse_shape(context, builder, arrshapetype, arrshape)


def _parse_empty_like_args(context, builder, sig, args):
    """
    Parse the arguments of a np.empty_like(), np.zeros_like() or
    np.ones_like() call.
    """
    arytype = sig.args[0]
    if isinstance(arytype, types.Array):
        ary = make_array(arytype)(context, builder, value=args[0])
        shapes = cgutils.unpack_tuple(builder, ary.shape, count=arytype.ndim)
        return sig.return_type, shapes
    else:
        return sig.return_type, ()


@lower_builtin(np.empty, types.Any)
@lower_builtin(np.empty, types.Any, types.Any)
def numpy_empty_nd(context, builder, sig, args):
    arrtype, shapes = _parse_empty_args(context, builder, sig, args)
    ary = _empty_nd_impl(context, builder, arrtype, shapes)
    return impl_ret_new_ref(context, builder, sig.return_type, ary._getvalue())


@lower_builtin(np.empty_like, types.Any)
@lower_builtin(np.empty_like, types.Any, types.DTypeSpec)
def numpy_empty_like_nd(context, builder, sig, args):
    arrtype, shapes = _parse_empty_like_args(context, builder, sig, args)
    ary = _empty_nd_impl(context, builder, arrtype, shapes)
    return impl_ret_new_ref(context, builder, sig.return_type, ary._getvalue())


@lower_builtin(np.zeros, types.Any)
@lower_builtin(np.zeros, types.Any, types.Any)
def numpy_zeros_nd(context, builder, sig, args):
    arrtype, shapes = _parse_empty_args(context, builder, sig, args)
    ary = _empty_nd_impl(context, builder, arrtype, shapes)
    _zero_fill_array(context, builder, ary)
    return impl_ret_new_ref(context, builder, sig.return_type, ary._getvalue())


@lower_builtin(np.zeros_like, types.Any)
@lower_builtin(np.zeros_like, types.Any, types.DTypeSpec)
def numpy_zeros_like_nd(context, builder, sig, args):
    arrtype, shapes = _parse_empty_like_args(context, builder, sig, args)
    ary = _empty_nd_impl(context, builder, arrtype, shapes)
    _zero_fill_array(context, builder, ary)
    return impl_ret_new_ref(context, builder, sig.return_type, ary._getvalue())


if numpy_version >= (1, 8):
    @lower_builtin(np.full, types.Any, types.Any)
    def numpy_full_nd(context, builder, sig, args):
        if numpy_version < (1, 12):
            # np < 1.12 returns float64 full regardless of value type
            def full(shape, value):
                arr = np.empty(shape)
                val = np.float64(value.real)
                for idx in np.ndindex(arr.shape):
                    arr[idx] = val
                return arr
        else:
            def full(shape, value):
                arr = np.empty(shape, type(value))
                for idx in np.ndindex(arr.shape):
                    arr[idx] = value
                return arr

        res = context.compile_internal(builder, full, sig, args)
        return impl_ret_new_ref(context, builder, sig.return_type, res)

    @lower_builtin(np.full, types.Any, types.Any, types.DTypeSpec)
    def numpy_full_dtype_nd(context, builder, sig, args):

        def full(shape, value, dtype):
            arr = np.empty(shape, dtype)
            for idx in np.ndindex(arr.shape):
                arr[idx] = value
            return arr

        res = context.compile_internal(builder, full, sig, args)
        return impl_ret_new_ref(context, builder, sig.return_type, res)

    @lower_builtin(np.full_like, types.Any, types.Any)
    def numpy_full_like_nd(context, builder, sig, args):

        def full_like(arr, value):
            arr = np.empty_like(arr)
            for idx in np.ndindex(arr.shape):
                arr[idx] = value
            return arr

        res = context.compile_internal(builder, full_like, sig, args)
        return impl_ret_new_ref(context, builder, sig.return_type, res)

    @lower_builtin(np.full_like, types.Any, types.Any, types.DTypeSpec)
    def numpy_full_like_nd_type_spec(context, builder, sig, args):

        def full_like(arr, value, dtype):
            arr = np.empty_like(arr, dtype)
            for idx in np.ndindex(arr.shape):
                arr[idx] = value
            return arr

        res = context.compile_internal(builder, full_like, sig, args)
        return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.ones, types.Any)
def numpy_ones_nd(context, builder, sig, args):

    def ones(shape):
        arr = np.empty(shape)
        for idx in np.ndindex(arr.shape):
            arr[idx] = 1
        return arr

    valty = sig.return_type.dtype
    res = context.compile_internal(builder, ones, sig, args,
                                   locals={'c': valty})
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.ones, types.Any, types.DTypeSpec)
def numpy_ones_dtype_nd(context, builder, sig, args):

    def ones(shape, dtype):
        arr = np.empty(shape, dtype)
        for idx in np.ndindex(arr.shape):
            arr[idx] = 1
        return arr

    res = context.compile_internal(builder, ones, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.ones_like, types.Any)
def numpy_ones_like_nd(context, builder, sig, args):

    def ones_like(arr):
        arr = np.empty_like(arr)
        for idx in np.ndindex(arr.shape):
            arr[idx] = 1
        return arr

    res = context.compile_internal(builder, ones_like, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.ones_like, types.Any, types.DTypeSpec)
def numpy_ones_like_dtype_nd(context, builder, sig, args):

    def ones_like(arr, dtype):
        arr = np.empty_like(arr, dtype)
        for idx in np.ndindex(arr.shape):
            arr[idx] = 1
        return arr

    res = context.compile_internal(builder, ones_like, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.identity, types.Integer)
def numpy_identity(context, builder, sig, args):

    def identity(n):
        arr = np.zeros((n, n))
        for i in range(n):
            arr[i, i] = 1
        return arr

    res = context.compile_internal(builder, identity, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.identity, types.Integer, types.DTypeSpec)
def numpy_identity_type_spec(context, builder, sig, args):

    def identity(n, dtype):
        arr = np.zeros((n, n), dtype)
        for i in range(n):
            arr[i, i] = 1
        return arr

    res = context.compile_internal(builder, identity, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


def _eye_none_handler(N, M):
    pass


@extending.overload(_eye_none_handler)
def _eye_none_handler_impl(N, M):
    if isinstance(M, types.NoneType):
        def impl(N, M):
            return N
    else:
        def impl(N, M):
            return M
    return impl


@extending.overload(np.eye)
def numpy_eye(N, M=None, k=0, dtype=float):

    if dtype is None or isinstance(dtype, types.NoneType):
        dt = np.dtype(float)
    elif isinstance(dtype, (types.DTypeSpec, types.Number)):
        # dtype or instance of dtype
        dt = as_dtype(getattr(dtype, 'dtype', dtype))
    else:
        dt = np.dtype(dtype)

    def impl(N, M=None, k=0, dtype=float):
        _M = _eye_none_handler(N, M)
        arr = np.zeros((N, _M), dt)
        if k >= 0:
            d = min(N, _M - k)
            for i in range(d):
                arr[i, i + k] = 1
        else:
            d = min(N + k, _M)
            for i in range(d):
                arr[i - k, i] = 1
        return arr
    return impl


@lower_builtin(np.diag, types.Array)
def numpy_diag(context, builder, sig, args):
    def diag_impl(val):
        return np.diag(val, k=0)
    return context.compile_internal(builder, diag_impl, sig, args)


@lower_builtin(np.diag, types.Array, types.Integer)
def numpy_diag_kwarg(context, builder, sig, args):
    arg = sig.args[0]
    if arg.ndim == 1:
        # vector context
        def diag_impl(arr, k=0):
            s = arr.shape
            n = s[0] + abs(k)
            ret = np.zeros((n, n), arr.dtype)
            if k >= 0:
                for i in range(n - k):
                    ret[i, k + i] = arr[i]
            else:
                for i in range(n + k):
                    ret[i - k, i] = arr[i]
            return ret
    elif arg.ndim == 2:
        # matrix context
        def diag_impl(arr, k=0):
            #Will return arr.diagonal(v, k) when axis args are supported
            rows, cols = arr.shape
            if k < 0:
                rows = rows + k
            if k > 0:
                cols = cols - k
            n = max(min(rows, cols), 0)
            ret = np.empty(n, arr.dtype)
            if k >= 0:
                for i in range(n):
                    ret[i] = arr[i, k + i]
            else:
                for i in range(n):
                    ret[i] = arr[i - k, i]
            return ret
    else:
        #invalid input
        raise ValueError("Input must be 1- or 2-d.")

    res = context.compile_internal(builder, diag_impl, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.take, types.Array, types.Integer)
@lower_builtin('array.take', types.Array, types.Integer)
def numpy_take_1(context, builder, sig, args):

    def take_impl(a, indices):
        if indices > (a.size - 1) or indices < -a.size:
            raise IndexError("Index out of bounds")
        return a.ravel()[np.int(indices)]

    res = context.compile_internal(builder, take_impl, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin('array.take', types.Array, types.Array)
@lower_builtin(np.take, types.Array, types.Array)
def numpy_take_2(context, builder, sig, args):

    F_order = sig.args[1].layout == 'F'

    def take_impl(a, indices):
        ret = np.empty(indices.size, dtype=a.dtype)
        if F_order:
            walker = indices.copy() # get C order
        else:
            walker = indices
        it = np.nditer(walker)
        i = 0
        flat = a.ravel()
        for x in it:
            if x > (a.size - 1) or x < -a.size:
                raise IndexError("Index out of bounds")
            ret[i] = flat[x]
            i = i + 1
        return ret.reshape(indices.shape)

    res = context.compile_internal(builder, take_impl, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin('array.take', types.Array, types.List)
@lower_builtin(np.take, types.Array, types.List)
@lower_builtin('array.take', types.Array, types.BaseTuple)
@lower_builtin(np.take, types.Array, types.BaseTuple)
def numpy_take_3(context, builder, sig, args):

    def take_impl(a, indices):
        convert = np.array(indices)
        ret = np.empty(convert.size, dtype=a.dtype)
        it = np.nditer(convert)
        i = 0
        flat = a.ravel()
        for x in it:
            if x > (a.size - 1) or x < -a.size:
                raise IndexError("Index out of bounds")
            ret[i] = flat[x]
            i = i + 1
        return ret.reshape(convert.shape)

    res = context.compile_internal(builder, take_impl, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.arange, types.Number)
def numpy_arange_1(context, builder, sig, args):
    dtype = as_dtype(sig.return_type.dtype)

    def arange(stop):
        return np.arange(0, stop, 1, dtype)

    res = context.compile_internal(builder, arange, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.arange, types.Number, types.Number)
def numpy_arange_2(context, builder, sig, args):
    dtype = as_dtype(sig.return_type.dtype)

    def arange(start, stop):
        return np.arange(start, stop, 1, dtype)

    res = context.compile_internal(builder, arange, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.arange, types.Number, types.Number,
               types.Number)
def numpy_arange_3(context, builder, sig, args):
    dtype = as_dtype(sig.return_type.dtype)

    def arange(start, stop, step):
        return np.arange(start, stop, step, dtype)

    res = context.compile_internal(builder, arange, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.arange, types.Number, types.Number,
               types.Number, types.DTypeSpec)
def numpy_arange_4(context, builder, sig, args):

    if any(isinstance(a, types.Complex) for a in sig.args):
        def arange(start, stop, step, dtype):
            nitems_c = (stop - start) / step
            nitems_r = math.ceil(nitems_c.real)
            nitems_i = math.ceil(nitems_c.imag)
            nitems = max(min(nitems_i, nitems_r), 0)
            arr = np.empty(nitems, dtype)
            val = start
            for i in range(nitems):
                arr[i] = val
                val += step
            return arr
    else:
        def arange(start, stop, step, dtype):
            nitems_r = math.ceil((stop - start) / step)
            nitems = max(nitems_r, 0)
            arr = np.empty(nitems, dtype)
            val = start
            for i in range(nitems):
                arr[i] = val
                val += step
            return arr

    res = context.compile_internal(builder, arange, sig, args,
                                   locals={'nitems': types.intp})
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.linspace, types.Number, types.Number)
def numpy_linspace_2(context, builder, sig, args):

    def linspace(start, stop):
        return np.linspace(start, stop, 50)

    res = context.compile_internal(builder, linspace, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


@lower_builtin(np.linspace, types.Number, types.Number,
               types.Integer)
def numpy_linspace_3(context, builder, sig, args):
    dtype = as_dtype(sig.return_type.dtype)

    def linspace(start, stop, num):
        arr = np.empty(num, dtype)
        div = num - 1
        delta = stop - start
        arr[0] = start
        for i in range(1, num):
            arr[i] = start + delta * (i / div)
        return arr

    res = context.compile_internal(builder, linspace, sig, args)
    return impl_ret_new_ref(context, builder, sig.return_type, res)


def _array_copy(context, builder, sig, args):
    """
    Array copy.
    """
    arytype = sig.args[0]
    ary = make_array(arytype)(context, builder, value=args[0])
    shapes = cgutils.unpack_tuple(builder, ary.shape)

    rettype = sig.return_type
    ret = _empty_nd_impl(context, builder, rettype, shapes)

    src_data = ary.data
    dest_data = ret.data

    assert rettype.layout in "CF"
    if arytype.layout == rettype.layout:
        # Fast path: memcpy
        cgutils.raw_memcpy(builder, dest_data, src_data, ary.nitems,
                           ary.itemsize, align=1)

    else:
        src_strides = cgutils.unpack_tuple(builder, ary.strides)
        dest_strides = cgutils.unpack_tuple(builder, ret.strides)
        intp_t = context.get_value_type(types.intp)

        with cgutils.loop_nest(builder, shapes, intp_t) as indices:
            src_ptr = cgutils.get_item_pointer2(builder, src_data,
                                                shapes, src_strides,
                                                arytype.layout, indices)
            dest_ptr = cgutils.get_item_pointer2(builder, dest_data,
                                                 shapes, dest_strides,
                                                 rettype.layout, indices)
            builder.store(builder.load(src_ptr), dest_ptr)

    return impl_ret_new_ref(context, builder, sig.return_type, ret._getvalue())


@lower_builtin("array.copy", types.Array)
def array_copy(context, builder, sig, args):
    return _array_copy(context, builder, sig, args)


@lower_builtin(np.copy, types.Array)
def numpy_copy(context, builder, sig, args):
    return _array_copy(context, builder, sig, args)


def _as_layout_array(context, builder, sig, args, output_layout):
    """
    Common logic for layout conversion function;
    e.g. ascontiguousarray and asfortranarray
    """
    retty = sig.return_type
    aryty = sig.args[0]
    assert retty.layout == output_layout, 'return-type has incorrect layout'

    if aryty.ndim == 0:
        # 0-dim input => asfortranarray() returns a 1-dim array
        assert retty.ndim == 1
        ary = make_array(aryty)(context, builder, value=args[0])
        ret = make_array(retty)(context, builder)

        shape = context.get_constant_generic(
            builder, types.UniTuple(types.intp, 1), (1,),
        )
        strides = context.make_tuple(builder,
                                     types.UniTuple(types.intp, 1),
                                     (ary.itemsize,))
        populate_array(ret, ary.data, shape, strides, ary.itemsize,
                       ary.meminfo, ary.parent)
        return impl_ret_borrowed(context, builder, retty, ret._getvalue())

    elif (retty.layout == aryty.layout
            or (aryty.ndim == 1 and aryty.layout in 'CF')):
        # 1-dim contiguous input => return the same array
        return impl_ret_borrowed(context, builder, retty, args[0])

    else:
        if aryty.layout == 'A':
            # There's still chance the array is in contiguous layout,
            # just that we don't know at compile time.
            # We can do a runtime check.

            # Prepare and call is_contiguous or is_fortran
            assert output_layout in 'CF'
            check_func = is_contiguous if output_layout == 'C' else is_fortran
            is_contig = _call_contiguous_check(check_func, context, builder, aryty, args[0])
            with builder.if_else(is_contig) as (then, orelse):
                # If the array is already contiguous, just return it
                with then:
                    out_then = impl_ret_borrowed(context, builder, retty,
                                                 args[0])
                    then_blk = builder.block
                # Otherwise, copy to a new contiguous region
                with orelse:
                    out_orelse = _array_copy(context, builder, sig, args)
                    orelse_blk = builder.block
            # Phi node for the return value
            ret_phi = builder.phi(out_then.type)
            ret_phi.add_incoming(out_then, then_blk)
            ret_phi.add_incoming(out_orelse, orelse_blk)
            return ret_phi

        else:
            # Return a copy with the right layout
            return _array_copy(context, builder, sig, args)


@lower_builtin(np.asfortranarray, types.Array)
def array_asfortranarray(context, builder, sig, args):
    return _as_layout_array(context, builder, sig, args, output_layout='F')


@lower_builtin(np.ascontiguousarray, types.Array)
def array_ascontiguousarray(context, builder, sig, args):
    return _as_layout_array(context, builder, sig, args, output_layout='C')


@lower_builtin("array.astype", types.Array, types.DTypeSpec)
def array_astype(context, builder, sig, args):
    arytype = sig.args[0]
    ary = make_array(arytype)(context, builder, value=args[0])
    shapes = cgutils.unpack_tuple(builder, ary.shape)

    rettype = sig.return_type
    ret = _empty_nd_impl(context, builder, rettype, shapes)

    src_data = ary.data
    dest_data = ret.data

    src_strides = cgutils.unpack_tuple(builder, ary.strides)
    dest_strides = cgutils.unpack_tuple(builder, ret.strides)
    intp_t = context.get_value_type(types.intp)

    with cgutils.loop_nest(builder, shapes, intp_t) as indices:
        src_ptr = cgutils.get_item_pointer2(builder, src_data,
                                            shapes, src_strides,
                                            arytype.layout, indices)
        dest_ptr = cgutils.get_item_pointer2(builder, dest_data,
                                             shapes, dest_strides,
                                             rettype.layout, indices)
        item = load_item(context, builder, arytype, src_ptr)
        item = context.cast(builder, item, arytype.dtype, rettype.dtype)
        store_item(context, builder, rettype, item, dest_ptr)

    return impl_ret_new_ref(context, builder, sig.return_type, ret._getvalue())


@lower_builtin(np.frombuffer, types.Buffer)
@lower_builtin(np.frombuffer, types.Buffer, types.DTypeSpec)
def np_frombuffer(context, builder, sig, args):
    bufty = sig.args[0]
    aryty = sig.return_type

    buf = make_array(bufty)(context, builder, value=args[0])
    out_ary_ty = make_array(aryty)
    out_ary = out_ary_ty(context, builder)
    out_datamodel = out_ary._datamodel

    itemsize = get_itemsize(context, aryty)
    ll_itemsize = lc.Constant.int(buf.itemsize.type, itemsize)
    nbytes = builder.mul(buf.nitems, buf.itemsize)

    # Check that the buffer size is compatible
    rem = builder.srem(nbytes, ll_itemsize)
    is_incompatible = cgutils.is_not_null(builder, rem)
    with builder.if_then(is_incompatible, likely=False):
        msg = "buffer size must be a multiple of element size"
        context.call_conv.return_user_exc(builder, ValueError, (msg,))

    shape = cgutils.pack_array(builder, [builder.sdiv(nbytes, ll_itemsize)])
    strides = cgutils.pack_array(builder, [ll_itemsize])
    data = builder.bitcast(buf.data,
                           context.get_value_type(out_datamodel.get_type('data')))

    populate_array(out_ary,
                   data=data,
                   shape=shape,
                   strides=strides,
                   itemsize=ll_itemsize,
                   meminfo=buf.meminfo,
                   parent=buf.parent,)

    res = out_ary._getvalue()
    return impl_ret_borrowed(context, builder, sig.return_type, res)


@lower_builtin(carray, types.Any, types.Any)
@lower_builtin(carray, types.Any, types.Any, types.DTypeSpec)
@lower_builtin(farray, types.Any, types.Any)
@lower_builtin(farray, types.Any, types.Any, types.DTypeSpec)
def np_cfarray(context, builder, sig, args):
    """
    numba.numpy_support.carray(...) and
    numba.numpy_support.farray(...).
    """
    ptrty, shapety = sig.args[:2]
    ptr, shape = args[:2]

    aryty = sig.return_type
    assert aryty.layout in 'CF'

    out_ary = make_array(aryty)(context, builder)

    itemsize = get_itemsize(context, aryty)
    ll_itemsize = cgutils.intp_t(itemsize)

    if isinstance(shapety, types.BaseTuple):
        shapes = cgutils.unpack_tuple(builder, shape)
    else:
        shapety = (shapety,)
        shapes = (shape,)
    shapes = [context.cast(builder, value, fromty, types.intp)
              for fromty, value in zip(shapety, shapes)]

    off = ll_itemsize
    strides = []
    if aryty.layout == 'F':
        for s in shapes:
            strides.append(off)
            off = builder.mul(off, s)
    else:
        for s in reversed(shapes):
            strides.append(off)
            off = builder.mul(off, s)
        strides.reverse()

    data = builder.bitcast(ptr,
                           context.get_data_type(aryty.dtype).as_pointer())

    populate_array(out_ary,
                   data=data,
                   shape=shapes,
                   strides=strides,
                   itemsize=ll_itemsize,
                   # Array is not memory-managed
                   meminfo=None,
                   )

    res = out_ary._getvalue()
    return impl_ret_new_ref(context, builder, sig.return_type, res)


def _get_seq_size(context, builder, seqty, seq):
    if isinstance(seqty, types.BaseTuple):
        return context.get_constant(types.intp, len(seqty))
    elif isinstance(seqty, types.Sequence):
        len_impl = context.get_function(len, signature(types.intp, seqty,))
        return len_impl(builder, (seq,))
    else:
        assert 0


def _get_borrowing_getitem(context, seqty):
    """
    Return a getitem() implementation that doesn't incref its result.
    """
    retty = seqty.dtype
    getitem_impl = context.get_function(operator.getitem,
                                        signature(retty, seqty, types.intp))

    def wrap(builder, args):
        ret = getitem_impl(builder, args)
        if context.enable_nrt:
            context.nrt.decref(builder, retty, ret)
        return ret

    return wrap


def compute_sequence_shape(context, builder, ndim, seqty, seq):
    """
    Compute the likely shape of a nested sequence (possibly 0d).
    """
    intp_t = context.get_value_type(types.intp)
    zero = Constant.int(intp_t, 0)

    def get_first_item(seqty, seq):
        if isinstance(seqty, types.BaseTuple):
            if len(seqty) == 0:
                return None, None
            else:
                return seqty[0], builder.extract_value(seq, 0)
        else:
            getitem_impl = _get_borrowing_getitem(context, seqty)
            return seqty.dtype, getitem_impl(builder, (seq, zero))

    # Compute shape by traversing the first element of each nested
    # sequence
    shapes = []
    innerty, inner = seqty, seq

    for i in range(ndim):
        if i > 0:
            innerty, inner = get_first_item(innerty, inner)
        shapes.append(_get_seq_size(context, builder, innerty, inner))

    return tuple(shapes)


def check_sequence_shape(context, builder, seqty, seq, shapes):
    """
    Check the nested sequence matches the given *shapes*.
    """

    def _fail():
        context.call_conv.return_user_exc(builder, ValueError,
                                          ("incompatible sequence shape",))

    def check_seq_size(seqty, seq, shapes):
        if len(shapes) == 0:
            return

        size = _get_seq_size(context, builder, seqty, seq)
        expected = shapes[0]
        mismatch = builder.icmp_signed('!=', size, expected)
        with builder.if_then(mismatch, likely=False):
            _fail()

        if len(shapes) == 1:
            return

        if isinstance(seqty, types.Sequence):
            getitem_impl = _get_borrowing_getitem(context, seqty)
            with cgutils.for_range(builder, size) as loop:
                innerty = seqty.dtype
                inner = getitem_impl(builder, (seq, loop.index))
                check_seq_size(innerty, inner, shapes[1:])

        elif isinstance(seqty, types.BaseTuple):
            for i in range(len(seqty)):
                innerty = seqty[i]
                inner = builder.extract_value(seq, i)
                check_seq_size(innerty, inner, shapes[1:])

        else:
            assert 0, seqty

    check_seq_size(seqty, seq, shapes)


def assign_sequence_to_array(context, builder, data, shapes, strides,
                             arrty, seqty, seq):
    """
    Assign a nested sequence contents to an array.  The shape must match
    the sequence's structure.
    """

    def assign_item(indices, valty, val):
        ptr = cgutils.get_item_pointer2(builder, data, shapes, strides,
                                        arrty.layout, indices, wraparound=False)
        val = context.cast(builder, val, valty, arrty.dtype)
        store_item(context, builder, arrty, val, ptr)

    def assign(seqty, seq, shapes, indices):
        if len(shapes) == 0:
            assert not isinstance(seqty, (types.Sequence, types.BaseTuple))
            assign_item(indices, seqty, seq)
            return

        size = shapes[0]

        if isinstance(seqty, types.Sequence):
            getitem_impl = _get_borrowing_getitem(context, seqty)
            with cgutils.for_range(builder, size) as loop:
                innerty = seqty.dtype
                inner = getitem_impl(builder, (seq, loop.index))
                assign(innerty, inner, shapes[1:], indices + (loop.index,))

        elif isinstance(seqty, types.BaseTuple):
            for i in range(len(seqty)):
                innerty = seqty[i]
                inner = builder.extract_value(seq, i)
                index = context.get_constant(types.intp, i)
                assign(innerty, inner, shapes[1:], indices + (index,))

        else:
            assert 0, seqty

    assign(seqty, seq, shapes, ())


@lower_builtin(np.array, types.Any)
@lower_builtin(np.array, types.Any, types.DTypeSpec)
def np_array(context, builder, sig, args):
    arrty = sig.return_type
    ndim = arrty.ndim
    seqty = sig.args[0]
    seq = args[0]

    shapes = compute_sequence_shape(context, builder, ndim, seqty, seq)
    assert len(shapes) == ndim

    check_sequence_shape(context, builder, seqty, seq, shapes)
    arr = _empty_nd_impl(context, builder, arrty, shapes)
    assign_sequence_to_array(context, builder, arr.data, shapes, arr.strides,
                             arrty, seqty, seq)

    return impl_ret_new_ref(context, builder, sig.return_type, arr._getvalue())


def _normalize_axis(context, builder, func_name, ndim, axis):
    zero = axis.type(0)
    ll_ndim = axis.type(ndim)

    # Normalize negative axis
    is_neg_axis = builder.icmp_signed('<', axis, zero)
    axis = builder.select(is_neg_axis, builder.add(axis, ll_ndim), axis)

    # Check axis for bounds
    axis_out_of_bounds = builder.or_(
        builder.icmp_signed('<', axis, zero),
        builder.icmp_signed('>=', axis, ll_ndim))
    with builder.if_then(axis_out_of_bounds, likely=False):
        msg = "%s(): axis out of bounds" % func_name
        context.call_conv.return_user_exc(builder, IndexError, (msg,))

    return axis


def _insert_axis_in_shape(context, builder, orig_shape, ndim, axis):
    """
    Compute shape with the new axis inserted
    e.g. given original shape (2, 3, 4) and axis=2,
    the returned new shape is (2, 3, 1, 4).
    """
    assert len(orig_shape) == ndim - 1

    ll_shty = ir.ArrayType(cgutils.intp_t, ndim)
    shapes = cgutils.alloca_once(builder, ll_shty)

    one = cgutils.intp_t(1)

    # 1. copy original sizes at appropriate places
    for dim in range(ndim - 1):
        ll_dim = cgutils.intp_t(dim)
        after_axis = builder.icmp_signed('>=', ll_dim, axis)
        sh = orig_shape[dim]
        idx = builder.select(after_axis,
                             builder.add(ll_dim, one),
                             ll_dim)
        builder.store(sh, cgutils.gep_inbounds(builder, shapes, 0, idx))

    # 2. insert new size (1) at axis dimension
    builder.store(one, cgutils.gep_inbounds(builder, shapes, 0, axis))

    return cgutils.unpack_tuple(builder, builder.load(shapes))


def _insert_axis_in_strides(context, builder, orig_strides, ndim, axis):
    """
    Same as _insert_axis_in_shape(), but with a strides array.
    """
    assert len(orig_strides) == ndim - 1

    ll_shty = ir.ArrayType(cgutils.intp_t, ndim)
    strides = cgutils.alloca_once(builder, ll_shty)

    one = cgutils.intp_t(1)
    zero = cgutils.intp_t(0)

    # 1. copy original strides at appropriate places
    for dim in range(ndim - 1):
        ll_dim = cgutils.intp_t(dim)
        after_axis = builder.icmp_signed('>=', ll_dim, axis)
        idx = builder.select(after_axis,
                             builder.add(ll_dim, one),
                             ll_dim)
        builder.store(orig_strides[dim],
                      cgutils.gep_inbounds(builder, strides, 0, idx))

    # 2. insert new stride at axis dimension
    # (the value is indifferent for a 1-sized dimension, we use 0)
    builder.store(zero, cgutils.gep_inbounds(builder, strides, 0, axis))

    return cgutils.unpack_tuple(builder, builder.load(strides))


def expand_dims(context, builder, sig, args, axis):
    """
    np.expand_dims() with the given axis.
    """
    retty = sig.return_type
    ndim = retty.ndim
    arrty = sig.args[0]

    arr = make_array(arrty)(context, builder, value=args[0])
    ret = make_array(retty)(context, builder)

    shapes = cgutils.unpack_tuple(builder, arr.shape)
    strides = cgutils.unpack_tuple(builder, arr.strides)

    new_shapes = _insert_axis_in_shape(context, builder, shapes, ndim, axis)
    new_strides = _insert_axis_in_strides(context, builder, strides, ndim, axis)

    populate_array(ret,
                   data=arr.data,
                   shape=new_shapes,
                   strides=new_strides,
                   itemsize=arr.itemsize,
                   meminfo=arr.meminfo,
                   parent=arr.parent)

    return ret._getvalue()


@lower_builtin(np.expand_dims, types.Array, types.Integer)
def np_expand_dims(context, builder, sig, args):
    axis = context.cast(builder, args[1], sig.args[1], types.intp)
    axis = _normalize_axis(context, builder, "np.expand_dims",
                           sig.return_type.ndim, axis)

    ret = expand_dims(context, builder, sig, args, axis)
    return impl_ret_borrowed(context, builder, sig.return_type, ret)


def _atleast_nd(context, builder, sig, args, transform):
    arrtys = sig.args
    arrs = args

    if isinstance(sig.return_type, types.BaseTuple):
        rettys = list(sig.return_type)
    else:
        rettys = [sig.return_type]
    assert len(rettys) == len(arrtys)

    rets = [transform(context, builder, arr, arrty, retty)
            for arr, arrty, retty in zip(arrs, arrtys, rettys)]

    if isinstance(sig.return_type, types.BaseTuple):
        ret = context.make_tuple(builder, sig.return_type, rets)
    else:
        ret = rets[0]
    return impl_ret_borrowed(context, builder, sig.return_type, ret)


def _atleast_nd_transform(min_ndim, axes):
    """
    Return a callback successively inserting 1-sized dimensions at the
    following axes.
    """
    assert min_ndim == len(axes)

    def transform(context, builder, arr, arrty, retty):
        for i in range(min_ndim):
            ndim = i + 1
            if arrty.ndim < ndim:
                axis = cgutils.intp_t(axes[i])
                newarrty = arrty.copy(ndim=arrty.ndim + 1)
                arr = expand_dims(context, builder,
                                  typing.signature(newarrty, arrty), (arr,),
                                  axis)
                arrty = newarrty

        return arr

    return transform


@lower_builtin(np.atleast_1d, types.VarArg(types.Array))
def np_atleast_1d(context, builder, sig, args):
    transform = _atleast_nd_transform(1, [0])

    return _atleast_nd(context, builder, sig, args, transform)


@lower_builtin(np.atleast_2d, types.VarArg(types.Array))
def np_atleast_2d(context, builder, sig, args):
    transform = _atleast_nd_transform(2, [0, 0])

    return _atleast_nd(context, builder, sig, args, transform)


@lower_builtin(np.atleast_3d, types.VarArg(types.Array))
def np_atleast_3d(context, builder, sig, args):
    transform = _atleast_nd_transform(3, [0, 0, 2])

    return _atleast_nd(context, builder, sig, args, transform)


def _do_concatenate(context, builder, axis,
                    arrtys, arrs, arr_shapes, arr_strides,
                    retty, ret_shapes):
    """
    Concatenate arrays along the given axis.
    """
    assert len(arrtys) == len(arrs) == len(arr_shapes) == len(arr_strides)

    zero = cgutils.intp_t(0)

    # Allocate return array
    ret = _empty_nd_impl(context, builder, retty, ret_shapes)
    ret_strides = cgutils.unpack_tuple(builder, ret.strides)

    # Compute the offset by which to bump the destination pointer
    # after copying each input array.
    # Morally, we need to copy each input array at different start indices
    # into the destination array; bumping the destination pointer
    # is simply easier than offsetting all destination indices.
    copy_offsets = []

    for arr_sh in arr_shapes:
        # offset = ret_strides[axis] * input_shape[axis]
        offset = zero
        for dim, (size, stride) in enumerate(zip(arr_sh, ret_strides)):
            is_axis = builder.icmp_signed('==', axis.type(dim), axis)
            addend = builder.mul(size, stride)
            offset = builder.select(is_axis,
                                    builder.add(offset, addend),
                                    offset)
        copy_offsets.append(offset)

    # Copy input arrays into the return array
    ret_data = ret.data

    for arrty, arr, arr_sh, arr_st, offset in zip(arrtys, arrs, arr_shapes,
                                                  arr_strides, copy_offsets):
        arr_data = arr.data

        # Do the copy loop
        # Note the loop nesting is optimized for the destination layout
        loop_nest = cgutils.loop_nest(builder, arr_sh, cgutils.intp_t,
                                      order=retty.layout)

        with loop_nest as indices:
            src_ptr = cgutils.get_item_pointer2(builder, arr_data,
                                                arr_sh, arr_st,
                                                arrty.layout, indices)
            val = load_item(context, builder, arrty, src_ptr)
            val = context.cast(builder, val, arrty.dtype, retty.dtype)
            dest_ptr = cgutils.get_item_pointer2(builder, ret_data,
                                                 ret_shapes, ret_strides,
                                                 retty.layout, indices)
            store_item(context, builder, retty, val, dest_ptr)

        # Bump destination pointer
        ret_data = cgutils.pointer_add(builder, ret_data, offset)

    return ret


def _np_concatenate(context, builder, arrtys, arrs, retty, axis):
    ndim = retty.ndim

    arrs = [make_array(aty)(context, builder, value=a)
            for aty, a in zip(arrtys, arrs)]

    axis = _normalize_axis(context, builder, "np.concatenate", ndim, axis)

    # Get input shapes
    arr_shapes = [cgutils.unpack_tuple(builder, arr.shape) for arr in arrs]
    arr_strides = [cgutils.unpack_tuple(builder, arr.strides) for arr in arrs]

    # Compute return shape:
    # - the dimension for the concatenation axis is summed over all inputs
    # - other dimensions must match exactly for each input
    ret_shapes = [cgutils.alloca_once_value(builder, sh)
                  for sh in arr_shapes[0]]

    for dim in range(ndim):
        is_axis = builder.icmp_signed('==', axis.type(dim), axis)
        ret_shape_ptr = ret_shapes[dim]
        ret_sh = builder.load(ret_shape_ptr)
        other_shapes = [sh[dim] for sh in arr_shapes[1:]]

        with builder.if_else(is_axis) as (on_axis, on_other_dim):
            with on_axis:
                sh = functools.reduce(
                    builder.add,
                    other_shapes + [ret_sh])
                builder.store(sh, ret_shape_ptr)

            with on_other_dim:
                is_ok = cgutils.true_bit
                for sh in other_shapes:
                    is_ok = builder.and_(is_ok,
                                         builder.icmp_signed('==', sh, ret_sh))
                with builder.if_then(builder.not_(is_ok), likely=False):
                    context.call_conv.return_user_exc(
                        builder, ValueError,
                        ("np.concatenate(): input sizes over dimension %d do not match" % dim,))

    ret_shapes = [builder.load(sh) for sh in ret_shapes]

    ret = _do_concatenate(context, builder, axis,
                          arrtys, arrs, arr_shapes, arr_strides,
                          retty, ret_shapes)
    return impl_ret_new_ref(context, builder, retty, ret._getvalue())


def _np_stack(context, builder, arrtys, arrs, retty, axis):
    ndim = retty.ndim

    zero = cgutils.intp_t(0)
    one = cgutils.intp_t(1)
    ll_narrays = cgutils.intp_t(len(arrs))

    arrs = [make_array(aty)(context, builder, value=a)
            for aty, a in zip(arrtys, arrs)]

    axis = _normalize_axis(context, builder, "np.stack", ndim, axis)

    # Check input arrays have the same shape
    orig_shape = cgutils.unpack_tuple(builder, arrs[0].shape)

    for arr in arrs[1:]:
        is_ok = cgutils.true_bit
        for sh, orig_sh in zip(cgutils.unpack_tuple(builder, arr.shape),
                               orig_shape):
            is_ok = builder.and_(is_ok, builder.icmp_signed('==', sh, orig_sh))
            with builder.if_then(builder.not_(is_ok), likely=False):
                context.call_conv.return_user_exc(
                    builder, ValueError,
                    ("np.stack(): all input arrays must have the same shape",))

    orig_strides = [cgutils.unpack_tuple(builder, arr.strides) for arr in arrs]

    # Compute input shapes and return shape with the new axis inserted
    # e.g. given 5 input arrays of shape (2, 3, 4) and axis=1,
    # corrected input shape is (2, 1, 3, 4) and return shape is (2, 5, 3, 4).
    ll_shty = ir.ArrayType(cgutils.intp_t, ndim)

    input_shapes = cgutils.alloca_once(builder, ll_shty)
    ret_shapes = cgutils.alloca_once(builder, ll_shty)

    # 1. copy original sizes at appropriate places
    for dim in range(ndim - 1):
        ll_dim = cgutils.intp_t(dim)
        after_axis = builder.icmp_signed('>=', ll_dim, axis)
        sh = orig_shape[dim]
        idx = builder.select(after_axis,
                             builder.add(ll_dim, one),
                             ll_dim)
        builder.store(sh, cgutils.gep_inbounds(builder, input_shapes, 0, idx))
        builder.store(sh, cgutils.gep_inbounds(builder, ret_shapes, 0, idx))

    # 2. insert new size at axis dimension
    builder.store(one, cgutils.gep_inbounds(builder, input_shapes, 0, axis))
    builder.store(ll_narrays, cgutils.gep_inbounds(builder, ret_shapes, 0, axis))

    input_shapes = [cgutils.unpack_tuple(builder, builder.load(input_shapes))] * len(arrs)
    ret_shapes = cgutils.unpack_tuple(builder, builder.load(ret_shapes))

    # Compute input strides for each array with the new axis inserted
    input_strides = [cgutils.alloca_once(builder, ll_shty)
                     for i in range(len(arrs))]

    # 1. copy original strides at appropriate places
    for dim in range(ndim - 1):
        ll_dim = cgutils.intp_t(dim)
        after_axis = builder.icmp_signed('>=', ll_dim, axis)
        idx = builder.select(after_axis,
                             builder.add(ll_dim, one),
                             ll_dim)
        for i in range(len(arrs)):
            builder.store(orig_strides[i][dim],
                          cgutils.gep_inbounds(builder, input_strides[i], 0, idx))

    # 2. insert new stride at axis dimension
    # (the value is indifferent for a 1-sized dimension, we put 0)
    for i in range(len(arrs)):
        builder.store(zero, cgutils.gep_inbounds(builder, input_strides[i], 0, axis))

    input_strides = [cgutils.unpack_tuple(builder, builder.load(st))
                     for st in input_strides]

    # Create concatenated array
    ret = _do_concatenate(context, builder, axis,
                          arrtys, arrs, input_shapes, input_strides,
                          retty, ret_shapes)
    return impl_ret_new_ref(context, builder, retty, ret._getvalue())


@lower_builtin(np.concatenate, types.BaseTuple)
def np_concatenate(context, builder, sig, args):
    axis = context.get_constant(types.intp, 0)
    return _np_concatenate(context, builder,
                           list(sig.args[0]),
                           cgutils.unpack_tuple(builder, args[0]),
                           sig.return_type,
                           axis)


@lower_builtin(np.concatenate, types.BaseTuple, types.Integer)
def np_concatenate_axis(context, builder, sig, args):
    axis = context.cast(builder, args[1], sig.args[1], types.intp)
    return _np_concatenate(context, builder,
                           list(sig.args[0]),
                           cgutils.unpack_tuple(builder, args[0]),
                           sig.return_type,
                           axis)


@lower_builtin(np.column_stack, types.BaseTuple)
def np_column_stack(context, builder, sig, args):
    orig_arrtys = list(sig.args[0])
    orig_arrs = cgutils.unpack_tuple(builder, args[0])

    arrtys = []
    arrs = []

    axis = context.get_constant(types.intp, 1)

    for arrty, arr in zip(orig_arrtys, orig_arrs):
        if arrty.ndim == 2:
            arrtys.append(arrty)
            arrs.append(arr)
        else:
            # Convert 1d array to 2d column array: np.expand_dims(a, 1)
            assert arrty.ndim == 1
            newty = arrty.copy(ndim=2)
            expand_sig = typing.signature(newty, arrty)
            newarr = expand_dims(context, builder, expand_sig, (arr,), axis)

            arrtys.append(newty)
            arrs.append(newarr)

    return _np_concatenate(context, builder, arrtys, arrs,
                           sig.return_type, axis)


def _np_stack_common(context, builder, sig, args, axis):
    """
    np.stack() with the given axis value.
    """
    return _np_stack(context, builder,
                     list(sig.args[0]),
                     cgutils.unpack_tuple(builder, args[0]),
                     sig.return_type,
                     axis)


if numpy_version >= (1, 10):
    @lower_builtin(np.stack, types.BaseTuple)
    def np_stack(context, builder, sig, args):
        axis = context.get_constant(types.intp, 0)
        return _np_stack_common(context, builder, sig, args, axis)

    @lower_builtin(np.stack, types.BaseTuple, types.Integer)
    def np_stack_axis(context, builder, sig, args):
        axis = context.cast(builder, args[1], sig.args[1], types.intp)
        return _np_stack_common(context, builder, sig, args, axis)


@lower_builtin(np.hstack, types.BaseTuple)
def np_hstack(context, builder, sig, args):
    tupty = sig.args[0]
    ndim = tupty[0].ndim

    if ndim == 0:
        # hstack() on 0-d arrays returns a 1-d array
        axis = context.get_constant(types.intp, 0)
        return _np_stack_common(context, builder, sig, args, axis)

    else:
        # As a special case, dimension 0 of 1-dimensional arrays is "horizontal"
        axis = 0 if ndim == 1 else 1

        def np_hstack_impl(arrays):
            return np.concatenate(arrays, axis=axis)

        return context.compile_internal(builder, np_hstack_impl, sig, args)


@lower_builtin(np.vstack, types.BaseTuple)
def np_vstack(context, builder, sig, args):
    tupty = sig.args[0]
    ndim = tupty[0].ndim

    if ndim == 0:
        def np_vstack_impl(arrays):
            return np.expand_dims(np.hstack(arrays), 1)

    elif ndim == 1:
        # np.stack(arrays, axis=0)
        axis = context.get_constant(types.intp, 0)
        return _np_stack_common(context, builder, sig, args, axis)

    else:
        def np_vstack_impl(arrays):
            return np.concatenate(arrays, axis=0)

    return context.compile_internal(builder, np_vstack_impl, sig, args)


@lower_builtin(np.dstack, types.BaseTuple)
def np_dstack(context, builder, sig, args):
    tupty = sig.args[0]
    retty = sig.return_type
    ndim = tupty[0].ndim

    if ndim == 0:
        def np_vstack_impl(arrays):
            return np.hstack(arrays).reshape(1, 1, -1)

        return context.compile_internal(builder, np_vstack_impl, sig, args)

    elif ndim == 1:
        # np.expand_dims(np.stack(arrays, axis=1), axis=0)
        axis = context.get_constant(types.intp, 1)
        stack_retty = retty.copy(ndim=retty.ndim - 1)
        stack_sig = typing.signature(stack_retty, *sig.args)
        stack_ret = _np_stack_common(context, builder, stack_sig, args, axis)

        axis = context.get_constant(types.intp, 0)
        expand_sig = typing.signature(retty, stack_retty)
        return expand_dims(context, builder, expand_sig, (stack_ret,), axis)

    elif ndim == 2:
        # np.stack(arrays, axis=2)
        axis = context.get_constant(types.intp, 2)
        return _np_stack_common(context, builder, sig, args, axis)

    else:
        def np_vstack_impl(arrays):
            return np.concatenate(arrays, axis=2)

        return context.compile_internal(builder, np_vstack_impl, sig, args)


@extending.overload_method(types.Array, 'fill')
def arr_fill(arr, val):

    def fill_impl(arr, val):
        arr[:] = val
        return None

    return fill_impl


@extending.overload_method(types.Array, 'dot')
def array_dot(arr, other):
    def dot_impl(arr, other):
        return np.dot(arr, other)

    return dot_impl


# -----------------------------------------------------------------------------
# Sorting

_sorts = {}


def lt_floats(a, b):
    return math.isnan(b) or a < b


def get_sort_func(kind, is_float, is_argsort=False):
    """
    Get a sort implementation of the given kind.
    """
    key = kind, is_float, is_argsort
    try:
        return _sorts[key]
    except KeyError:
        if kind == 'quicksort':
            sort = quicksort.make_jit_quicksort(
                lt=lt_floats if is_float else None,
                is_argsort=is_argsort)
            func = sort.run_quicksort
        elif kind == 'mergesort':
            sort = mergesort.make_jit_mergesort(
                lt=lt_floats if is_float else None,
                is_argsort=is_argsort)
            func = sort.run_mergesort
        _sorts[key] = func
        return func


@lower_builtin("array.sort", types.Array)
def array_sort(context, builder, sig, args):
    arytype = sig.args[0]
    sort_func = get_sort_func(kind='quicksort',
                              is_float=isinstance(arytype.dtype, types.Float))

    def array_sort_impl(arr):
        # Note we clobber the return value
        sort_func(arr)

    return context.compile_internal(builder, array_sort_impl, sig, args)


@lower_builtin(np.sort, types.Array)
def np_sort(context, builder, sig, args):

    def np_sort_impl(a):
        res = a.copy()
        res.sort()
        return res

    return context.compile_internal(builder, np_sort_impl, sig, args)


@lower_builtin("array.argsort", types.Array, types.StringLiteral)
@lower_builtin(np.argsort, types.Array, types.StringLiteral)
def array_argsort(context, builder, sig, args):
    arytype, kind = sig.args
    sort_func = get_sort_func(kind=kind.literal_value,
                              is_float=isinstance(arytype.dtype, types.Float),
                              is_argsort=True)

    def array_argsort_impl(arr):
        return sort_func(arr)

    innersig = sig.replace(args=sig.args[:1])
    innerargs = args[:1]
    return context.compile_internal(builder, array_argsort_impl,
                                    innersig, innerargs)


# -----------------------------------------------------------------------------
# Implicit cast

@lower_cast(types.Array, types.Array)
def array_to_array(context, builder, fromty, toty, val):
    # Type inference should have prevented illegal array casting.
    assert fromty.mutable != toty.mutable or toty.layout == 'A'
    return val


# -----------------------------------------------------------------------------
# Stride tricks

def reshape_unchecked(a, shape, strides):
    """
    An intrinsic returning a derived array with the given shape and strides.
    """
    raise NotImplementedError


@extending.type_callable(reshape_unchecked)
def type_reshape_unchecked(context):
    def check_shape(shape):
        return (isinstance(shape, types.BaseTuple) and
                all(isinstance(v, types.Integer) for v in shape))

    def typer(a, shape, strides):
        if not isinstance(a, types.Array):
            return
        if not check_shape(shape) or not check_shape(strides):
            return
        if len(shape) != len(strides):
            return
        return a.copy(ndim=len(shape), layout='A')

    return typer


@lower_builtin(reshape_unchecked, types.Array, types.BaseTuple, types.BaseTuple)
def impl_shape_unchecked(context, builder, sig, args):
    aryty = sig.args[0]
    retty = sig.return_type

    ary = make_array(aryty)(context, builder, args[0])
    out = make_array(retty)(context, builder)
    shape = cgutils.unpack_tuple(builder, args[1])
    strides = cgutils.unpack_tuple(builder, args[2])

    populate_array(out,
                   data=ary.data,
                   shape=shape,
                   strides=strides,
                   itemsize=ary.itemsize,
                   meminfo=ary.meminfo,
                   )

    res = out._getvalue()
    return impl_ret_borrowed(context, builder, retty, res)


@extending.overload(np.lib.stride_tricks.as_strided)
def as_strided(x, shape=None, strides=None):
    if shape in (None, types.none):
        @register_jitable
        def get_shape(x, shape):
            return x.shape
    else:
        @register_jitable
        def get_shape(x, shape):
            return shape

    if strides in (None, types.none):
        # When *strides* is not passed, as_strided() does a non-size-checking
        # reshape(), possibly changing the original strides.  This is too
        # cumbersome to support right now, and a Web search shows all example
        # use cases of as_strided() pass explicit *strides*.
        raise NotImplementedError("as_strided() strides argument is mandatory")
    else:
        @register_jitable
        def get_strides(x, strides):
            return strides

    def as_strided_impl(x, shape=None, strides=None):
        x = reshape_unchecked(x, get_shape(x, shape), get_strides(x, strides))
        return x

    return as_strided_impl