from __future__ import absolute_import, division, print_function

import warnings

from functools import partial, wraps
from itertools import product, repeat
from math import factorial, log, ceil
import operator

import numpy as np
from toolz import compose, partition_all, get, accumulate, pluck

from . import chunk
from .core import _concatenate2, Array, atop, lol_tuples, handle_out
from .ufunc import sqrt
from .wrap import zeros, ones
from .numpy_compat import ma_divide, divide as np_divide
from ..compatibility import getargspec, builtins
from ..base import tokenize
from ..context import _globals
from ..utils import ignoring, funcname, Dispatch
from .. import sharedict


# Generic functions to support chunks of different types
empty_lookup = Dispatch('empty')
empty_lookup.register((object, np.ndarray), np.empty)
empty_lookup.register(np.ma.masked_array, np.ma.empty)
divide_lookup = Dispatch('divide')
divide_lookup.register((object, np.ndarray), np_divide)
divide_lookup.register(np.ma.masked_array, ma_divide)


def divide(a, b, dtype=None):
    key = lambda x: getattr(x, '__array_priority__', float('-inf'))
    f = divide_lookup.dispatch(type(builtins.max(a, b, key=key)))
    return f(a, b, dtype=dtype)


def reduction(x, chunk, aggregate, axis=None, keepdims=None, dtype=None,
              split_every=None, combine=None, name=None, out=None):
    """ General version of reductions

    >>> reduction(my_array, np.sum, np.sum, axis=0, keepdims=False)  # doctest: +SKIP
    """
    if axis is None:
        axis = tuple(range(x.ndim))
    if isinstance(axis, int):
        axis = (axis,)
    axis = tuple(validate_axis(x.ndim, a) for a in axis)

    if dtype is None:
        raise ValueError("Must specify dtype")
    if 'dtype' in getargspec(chunk).args:
        chunk = partial(chunk, dtype=dtype)
    if 'dtype' in getargspec(aggregate).args:
        aggregate = partial(aggregate, dtype=dtype)

    # Map chunk across all blocks
    inds = tuple(range(x.ndim))
    # The dtype of `tmp` doesn't actually matter, and may be incorrect.
    tmp = atop(chunk, inds, x, inds, axis=axis, keepdims=True, dtype=x.dtype)
    tmp._chunks = tuple((1, ) * len(c) if i in axis else c for (i, c)
                        in enumerate(tmp.chunks))

    result = _tree_reduce(tmp, aggregate, axis, keepdims, dtype, split_every,
                          combine, name=name)
    return handle_out(out, result)


def _tree_reduce(x, aggregate, axis, keepdims, dtype, split_every=None,
                 combine=None, name=None):
    """Perform the tree reduction step of a reduction.

    Lower level, users should use ``reduction`` or ``arg_reduction`` directly.
    """
    # Normalize split_every
    split_every = split_every or _globals.get('split_every', 4)
    if isinstance(split_every, dict):
        split_every = dict((k, split_every.get(k, 2)) for k in axis)
    elif isinstance(split_every, int):
        n = builtins.max(int(split_every ** (1 / (len(axis) or 1))), 2)
        split_every = dict.fromkeys(axis, n)
    else:
        split_every = dict((k, v) for (k, v) in enumerate(x.numblocks) if k in axis)

    # Reduce across intermediates
    depth = 1
    for i, n in enumerate(x.numblocks):
        if i in split_every and split_every[i] != 1:
            depth = int(builtins.max(depth, ceil(log(n, split_every[i]))))
    func = compose(partial(combine or aggregate, axis=axis, keepdims=True),
                   partial(_concatenate2, axes=axis))
    for i in range(depth - 1):
        x = partial_reduce(func, x, split_every, True, dtype=dtype,
                           name=(name or funcname(combine or aggregate)) + '-partial')
    func = compose(partial(aggregate, axis=axis, keepdims=keepdims),
                   partial(_concatenate2, axes=axis))
    return partial_reduce(func, x, split_every, keepdims=keepdims, dtype=dtype,
                          name=(name or funcname(aggregate)) + '-aggregate')


def partial_reduce(func, x, split_every, keepdims=False, dtype=None, name=None):
    """Partial reduction across multiple axes.

    Parameters
    ----------
    func : function
    x : Array
    split_every : dict
        Maximum reduction block sizes in each dimension.

    Examples
    --------
    Reduce across axis 0 and 2, merging a maximum of 1 block in the 0th
    dimension, and 3 blocks in the 2nd dimension:

    >>> partial_reduce(np.min, x, {0: 1, 2: 3})    # doctest: +SKIP
    """
    name = (name or funcname(func)) + '-' + tokenize(func, x, split_every,
                                                     keepdims, dtype)
    parts = [list(partition_all(split_every.get(i, 1), range(n))) for (i, n)
             in enumerate(x.numblocks)]
    keys = product(*map(range, map(len, parts)))
    out_chunks = [tuple(1 for p in partition_all(split_every[i], c)) if i
                  in split_every else c for (i, c) in enumerate(x.chunks)]
    if not keepdims:
        out_axis = [i for i in range(x.ndim) if i not in split_every]
        getter = lambda k: get(out_axis, k)
        keys = map(getter, keys)
        out_chunks = list(getter(out_chunks))
    dsk = {}
    for k, p in zip(keys, product(*parts)):
        decided = dict((i, j[0]) for (i, j) in enumerate(p) if len(j) == 1)
        dummy = dict(i for i in enumerate(p) if i[0] not in decided)
        g = lol_tuples((x.name,), range(x.ndim), decided, dummy)
        dsk[(name,) + k] = (func, g)
    return Array(sharedict.merge(x.dask, (name, dsk)), name, out_chunks, dtype=dtype)


@wraps(chunk.sum)
def sum(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None):
    if dtype is not None:
        dt = dtype
    else:
        dt = np.empty((1,), dtype=a.dtype).sum().dtype
    return reduction(a, chunk.sum, chunk.sum, axis=axis, keepdims=keepdims,
                     dtype=dt, split_every=split_every, out=out)


@wraps(chunk.prod)
def prod(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None):
    if dtype is not None:
        dt = dtype
    else:
        dt = np.empty((1,), dtype=a.dtype).prod().dtype
    return reduction(a, chunk.prod, chunk.prod, axis=axis, keepdims=keepdims,
                     dtype=dt, split_every=split_every, out=out)


@wraps(chunk.min)
def min(a, axis=None, keepdims=False, split_every=None, out=None):
    return reduction(a, chunk.min, chunk.min, axis=axis, keepdims=keepdims,
                     dtype=a.dtype, split_every=split_every, out=out)


@wraps(chunk.max)
def max(a, axis=None, keepdims=False, split_every=None, out=None):
    return reduction(a, chunk.max, chunk.max, axis=axis, keepdims=keepdims,
                     dtype=a.dtype, split_every=split_every, out=out)


@wraps(chunk.any)
def any(a, axis=None, keepdims=False, split_every=None, out=None):
    return reduction(a, chunk.any, chunk.any, axis=axis, keepdims=keepdims,
                     dtype='bool', split_every=split_every, out=out)


@wraps(chunk.all)
def all(a, axis=None, keepdims=False, split_every=None, out=None):
    return reduction(a, chunk.all, chunk.all, axis=axis, keepdims=keepdims,
                     dtype='bool', split_every=split_every, out=out)


@wraps(chunk.nansum)
def nansum(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None):
    if dtype is not None:
        dt = dtype
    else:
        dt = chunk.nansum(np.empty((1,), dtype=a.dtype)).dtype
    return reduction(a, chunk.nansum, chunk.sum, axis=axis, keepdims=keepdims,
                     dtype=dt, split_every=split_every, out=out)


with ignoring(AttributeError):
    @wraps(chunk.nanprod)
    def nanprod(a, axis=None, dtype=None, keepdims=False, split_every=None,
                out=None):
        if dtype is not None:
            dt = dtype
        else:
            dt = chunk.nanprod(np.empty((1,), dtype=a.dtype)).dtype
        return reduction(a, chunk.nanprod, chunk.prod, axis=axis,
                         keepdims=keepdims, dtype=dt, split_every=split_every,
                         out=out)

    @wraps(chunk.nancumsum)
    def nancumsum(x, axis, dtype=None, out=None):
        return cumreduction(chunk.nancumsum, operator.add, 0, x, axis, dtype,
                            out=out)

    @wraps(chunk.nancumprod)
    def nancumprod(x, axis, dtype=None, out=None):
        return cumreduction(chunk.nancumprod, operator.mul, 1, x, axis, dtype,
                            out=out)


@wraps(chunk.nanmin)
def nanmin(a, axis=None, keepdims=False, split_every=None, out=None):
    return reduction(a, chunk.nanmin, chunk.nanmin, axis=axis,
                     keepdims=keepdims, dtype=a.dtype, split_every=split_every,
                     out=out)


@wraps(chunk.nanmax)
def nanmax(a, axis=None, keepdims=False, split_every=None, out=None):
    return reduction(a, chunk.nanmax, chunk.nanmax, axis=axis,
                     keepdims=keepdims, dtype=a.dtype, split_every=split_every,
                     out=out)


def numel(x, **kwargs):
    """ A reduction to count the number of elements """
    return chunk.sum(np.ones_like(x), **kwargs)


def nannumel(x, **kwargs):
    """ A reduction to count the number of elements """
    return chunk.sum(~np.isnan(x), **kwargs)


def mean_chunk(x, sum=chunk.sum, numel=numel, dtype='f8', **kwargs):
    n = numel(x, dtype=dtype, **kwargs)
    total = sum(x, dtype=dtype, **kwargs)
    empty = empty_lookup.dispatch(type(n))
    result = empty(n.shape, dtype=[('total', total.dtype), ('n', n.dtype)])
    result['n'] = n
    result['total'] = total
    return result


def mean_combine(pair, sum=chunk.sum, numel=numel, dtype='f8', **kwargs):
    n = sum(pair['n'], **kwargs)
    total = sum(pair['total'], **kwargs)
    empty = empty_lookup.dispatch(type(n))
    result = empty(n.shape, dtype=pair.dtype)
    result['n'] = n
    result['total'] = total
    return result


def mean_agg(pair, dtype='f8', **kwargs):
    return divide(pair['total'].sum(dtype=dtype, **kwargs),
                  pair['n'].sum(dtype=dtype, **kwargs), dtype=dtype)


@wraps(chunk.mean)
def mean(a, axis=None, dtype=None, keepdims=False, split_every=None, out=None):
    if dtype is not None:
        dt = dtype
    else:
        dt = np.mean(np.empty(shape=(1,), dtype=a.dtype)).dtype
    return reduction(a, mean_chunk, mean_agg, axis=axis, keepdims=keepdims,
                     dtype=dt, split_every=split_every, combine=mean_combine,
                     out=out)


def nanmean(a, axis=None, dtype=None, keepdims=False, split_every=None,
            out=None):
    if dtype is not None:
        dt = dtype
    else:
        dt = np.mean(np.empty(shape=(1,), dtype=a.dtype)).dtype
    return reduction(a, partial(mean_chunk, sum=chunk.nansum, numel=nannumel),
                     mean_agg, axis=axis, keepdims=keepdims, dtype=dt,
                     split_every=split_every, out=out,
                     combine=partial(mean_combine, sum=chunk.nansum, numel=nannumel))


with ignoring(AttributeError):
    nanmean = wraps(chunk.nanmean)(nanmean)


def moment_chunk(A, order=2, sum=chunk.sum, numel=numel, dtype='f8', **kwargs):
    total = sum(A, dtype=dtype, **kwargs)
    n = numel(A, **kwargs).astype(np.int64)
    u = total / n
    empty = empty_lookup.dispatch(type(n))
    M = empty(n.shape + (order - 1,), dtype=dtype)
    for i in range(2, order + 1):
        M[..., i - 2] = sum((A - u)**i, dtype=dtype, **kwargs)
    result = empty(n.shape, dtype=[('total', total.dtype),
                                   ('n', n.dtype),
                                   ('M', M.dtype, (order - 1,))])
    result['total'] = total
    result['n'] = n
    result['M'] = M
    return result


def _moment_helper(Ms, ns, inner_term, order, sum, kwargs):
    M = Ms[..., order - 2].sum(**kwargs) + sum(ns * inner_term ** order, **kwargs)
    for k in range(1, order - 1):
        coeff = factorial(order) / (factorial(k) * factorial(order - k))
        M += coeff * sum(Ms[..., order - k - 2] * inner_term**k, **kwargs)
    return M


def moment_combine(data, order=2, ddof=0, dtype='f8', sum=np.sum, **kwargs):
    kwargs['dtype'] = dtype
    kwargs['keepdims'] = True

    totals = data['total']
    ns = data['n']
    Ms = data['M']
    total = totals.sum(**kwargs)
    n = sum(ns, **kwargs)
    mu = divide(total, n, dtype=dtype)
    inner_term = divide(totals, ns, dtype=dtype) - mu
    empty = empty_lookup.dispatch(type(n))
    M = empty(n.shape + (order - 1,), dtype=dtype)

    for o in range(2, order + 1):
        M[..., o - 2] = _moment_helper(Ms, ns, inner_term, o, sum, kwargs)

    result = empty(n.shape, dtype=[('total', total.dtype),
                                   ('n', n.dtype),
                                   ('M', Ms.dtype, (order - 1,))])
    result['total'] = total
    result['n'] = n
    result['M'] = M
    return result


def moment_agg(data, order=2, ddof=0, dtype='f8', sum=np.sum, **kwargs):
    totals = data['total']
    ns = data['n']
    Ms = data['M']

    kwargs['dtype'] = dtype
    # To properly handle ndarrays, the original dimensions need to be kept for
    # part of the calculation.
    keepdim_kw = kwargs.copy()
    keepdim_kw['keepdims'] = True

    n = sum(ns, **keepdim_kw)
    mu = divide(totals.sum(**keepdim_kw), n, dtype=dtype)
    inner_term = divide(totals, ns, dtype=dtype) - mu

    M = _moment_helper(Ms, ns, inner_term, order, sum, kwargs)
    return divide(M, sum(n, **kwargs) - ddof, dtype=dtype)


def moment(a, order, axis=None, dtype=None, keepdims=False, ddof=0,
           split_every=None, out=None):
    if not isinstance(order, int) or order < 0:
        raise ValueError("Order must be an integer >= 0")

    if order < 2:
        reduced = a.sum(axis=axis)   # get reduced shape and chunks
        if order == 0:
            # When order equals 0, the result is 1, by definition.
            return ones(reduced.shape, chunks=reduced.chunks, dtype='f8')
        # By definition the first order about the mean is 0.
        return zeros(reduced.shape, chunks=reduced.chunks, dtype='f8')

    if dtype is not None:
        dt = dtype
    else:
        dt = np.var(np.ones(shape=(1,), dtype=a.dtype)).dtype
    return reduction(a, partial(moment_chunk, order=order),
                     partial(moment_agg, order=order, ddof=ddof),
                     axis=axis, keepdims=keepdims,
                     dtype=dt, split_every=split_every, out=out,
                     combine=partial(moment_combine, order=order))


@wraps(chunk.var)
def var(a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None,
        out=None):
    if dtype is not None:
        dt = dtype
    else:
        dt = np.var(np.ones(shape=(1,), dtype=a.dtype)).dtype
    return reduction(a, moment_chunk, partial(moment_agg, ddof=ddof), axis=axis,
                     keepdims=keepdims, dtype=dt, split_every=split_every,
                     combine=moment_combine, name='var', out=out)


def nanvar(a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None,
           out=None):
    if dtype is not None:
        dt = dtype
    else:
        dt = np.var(np.ones(shape=(1,), dtype=a.dtype)).dtype
    return reduction(a, partial(moment_chunk, sum=chunk.nansum, numel=nannumel),
                     partial(moment_agg, sum=np.nansum, ddof=ddof), axis=axis,
                     keepdims=keepdims, dtype=dt, split_every=split_every,
                     combine=partial(moment_combine, sum=np.nansum), out=out)


with ignoring(AttributeError):
    nanvar = wraps(chunk.nanvar)(nanvar)


@wraps(chunk.std)
def std(a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None,
        out=None):
    result = sqrt(a.var(axis=axis, dtype=dtype, keepdims=keepdims, ddof=ddof,
                        split_every=split_every, out=out))
    if dtype and dtype != result.dtype:
        result = result.astype(dtype)
    return result


def nanstd(a, axis=None, dtype=None, keepdims=False, ddof=0, split_every=None,
           out=None):
    result = sqrt(nanvar(a, axis=axis, dtype=dtype, keepdims=keepdims,
                         ddof=ddof, split_every=split_every, out=out))
    if dtype and dtype != result.dtype:
        result = result.astype(dtype)
    return result


with ignoring(AttributeError):
    nanstd = wraps(chunk.nanstd)(nanstd)


def vnorm(a, ord=None, axis=None, dtype=None, keepdims=False, split_every=None,
          out=None):
    """ Vector norm

    See np.linalg.norm
    """

    warnings.warn(
        "DeprecationWarning: Please use `dask.array.linalg.norm` instead.",
        UserWarning
    )

    if ord is None or ord == 'fro':
        ord = 2
    if ord == np.inf:
        return max(abs(a), axis=axis, keepdims=keepdims,
                   split_every=split_every, out=out)
    elif ord == -np.inf:
        return min(abs(a), axis=axis, keepdims=keepdims,
                   split_every=split_every, out=out)
    elif ord == 1:
        return sum(abs(a), axis=axis, dtype=dtype, keepdims=keepdims,
                   split_every=split_every, out=out)
    else:
        return sum(abs(a) ** ord, axis=axis, dtype=dtype, keepdims=keepdims,
                   split_every=split_every, out=out) ** (1. / ord)


def _arg_combine(data, axis, argfunc, keepdims=False):
    """Merge intermediate results from ``arg_*`` functions"""
    axis = None if len(axis) == data.ndim or data.ndim == 1 else axis[0]
    vals = data['vals']
    arg = data['arg']
    if axis is None:
        local_args = argfunc(vals, axis=axis, keepdims=keepdims)
        vals = vals.ravel()[local_args]
        arg = arg.ravel()[local_args]
    else:
        local_args = argfunc(vals, axis=axis)
        inds = np.ogrid[tuple(map(slice, local_args.shape))]
        inds.insert(axis, local_args)
        vals = vals[inds]
        arg = arg[inds]
        if keepdims:
            vals = np.expand_dims(vals, axis)
            arg = np.expand_dims(arg, axis)
    return arg, vals


def arg_chunk(func, argfunc, x, axis, offset_info):
    arg_axis = None if len(axis) == x.ndim or x.ndim == 1 else axis[0]
    vals = func(x, axis=arg_axis, keepdims=True)
    arg = argfunc(x, axis=arg_axis, keepdims=True)
    if arg_axis is None:
        offset, total_shape = offset_info
        ind = np.unravel_index(arg.ravel()[0], x.shape)
        total_ind = tuple(o + i for (o, i) in zip(offset, ind))
        arg[:] = np.ravel_multi_index(total_ind, total_shape)
    else:
        arg += offset_info

    if isinstance(vals, np.ma.masked_array):
        if 'min' in argfunc.__name__:
            fill_value = np.ma.minimum_fill_value(vals)
        else:
            fill_value = np.ma.maximum_fill_value(vals)
        vals = np.ma.filled(vals, fill_value)

    result = np.empty(shape=vals.shape, dtype=[('vals', vals.dtype),
                                               ('arg', arg.dtype)])
    result['vals'] = vals
    result['arg'] = arg
    return result


def arg_combine(func, argfunc, data, axis=None, **kwargs):
    arg, vals = _arg_combine(data, axis, argfunc, keepdims=True)
    result = np.empty(shape=vals.shape, dtype=[('vals', vals.dtype),
                                               ('arg', arg.dtype)])
    result['vals'] = vals
    result['arg'] = arg
    return result


def arg_agg(func, argfunc, data, axis=None, **kwargs):
    return _arg_combine(data, axis, argfunc, keepdims=False)[0]


def nanarg_agg(func, argfunc, data, axis=None, **kwargs):
    arg, vals = _arg_combine(data, axis, argfunc, keepdims=False)
    if np.any(np.isnan(vals)):
        raise ValueError("All NaN slice encountered")
    return arg


def arg_reduction(x, chunk, combine, agg, axis=None, split_every=None, out=None):
    """Generic function for argreduction.

    Parameters
    ----------
    x : Array
    chunk : callable
        Partialed ``arg_chunk``.
    combine : callable
        Partialed ``arg_combine``.
    agg : callable
        Partialed ``arg_agg``.
    axis : int, optional
    split_every : int or dict, optional
    """
    if axis is None:
        axis = tuple(range(x.ndim))
        ravel = True
    elif isinstance(axis, int):
        if axis < 0:
            axis += x.ndim
        if axis < 0 or axis >= x.ndim:
            raise ValueError("axis entry is out of bounds")
        axis = (axis,)
        ravel = x.ndim == 1
    else:
        raise TypeError("axis must be either `None` or int, "
                        "got '{0}'".format(axis))

    # Map chunk across all blocks
    name = 'arg-reduce-chunk-{0}'.format(tokenize(chunk, axis))
    old = x.name
    keys = list(product(*map(range, x.numblocks)))
    offsets = list(product(*(accumulate(operator.add, bd[:-1], 0)
                             for bd in x.chunks)))
    if ravel:
        offset_info = zip(offsets, repeat(x.shape))
    else:
        offset_info = pluck(axis[0], offsets)

    chunks = tuple((1, ) * len(c) if i in axis else c for (i, c)
                   in enumerate(x.chunks))
    dsk = dict(((name,) + k, (chunk, (old,) + k, axis, off)) for (k, off)
               in zip(keys, offset_info))
    # The dtype of `tmp` doesn't actually matter, just need to provide something
    tmp = Array(sharedict.merge(x.dask, (name, dsk)), name, chunks, dtype=x.dtype)
    dtype = np.argmin([1]).dtype
    result = _tree_reduce(tmp, agg, axis, False, dtype, split_every, combine)
    return handle_out(out, result)


def make_arg_reduction(func, argfunc, is_nan_func=False):
    """Create a argreduction callable.

    Parameters
    ----------
    func : callable
        The reduction (e.g. ``min``)
    argfunc : callable
        The argreduction (e.g. ``argmin``)
    """
    chunk = partial(arg_chunk, func, argfunc)
    combine = partial(arg_combine, func, argfunc)
    if is_nan_func:
        agg = partial(nanarg_agg, func, argfunc)
    else:
        agg = partial(arg_agg, func, argfunc)

    @wraps(argfunc)
    def _(x, axis=None, split_every=None, out=None):
        return arg_reduction(x, chunk, combine, agg, axis,
                             split_every=split_every, out=out)

    return _


def _nanargmin(x, axis, **kwargs):
    try:
        return chunk.nanargmin(x, axis, **kwargs)
    except ValueError:
        return chunk.nanargmin(np.where(np.isnan(x), np.inf, x), axis, **kwargs)


def _nanargmax(x, axis, **kwargs):
    try:
        return chunk.nanargmax(x, axis, **kwargs)
    except ValueError:
        return chunk.nanargmax(np.where(np.isnan(x), -np.inf, x), axis, **kwargs)


argmin = make_arg_reduction(chunk.min, chunk.argmin)
argmax = make_arg_reduction(chunk.max, chunk.argmax)
nanargmin = make_arg_reduction(chunk.nanmin, _nanargmin, True)
nanargmax = make_arg_reduction(chunk.nanmax, _nanargmax, True)


def cumreduction(func, binop, ident, x, axis=None, dtype=None, out=None):
    """ Generic function for cumulative reduction

    Parameters
    ----------
    func: callable
        Cumulative function like np.cumsum or np.cumprod
    binop: callable
        Associated binary operator like ``np.cumsum->add`` or ``np.cumprod->mul``
    ident: Number
        Associated identity like ``np.cumsum->0`` or ``np.cumprod->1``
    x: dask Array
    axis: int
    dtype: dtype

    Returns
    -------
    dask array

    See also
    --------
    cumsum
    cumprod
    """
    if axis is None:
        x = x.flatten()
        axis = 0
    if dtype is None:
        dtype = func(np.empty((0,), dtype=x.dtype)).dtype
    assert isinstance(axis, int)
    axis = validate_axis(x.ndim, axis)

    m = x.map_blocks(func, axis=axis, dtype=dtype)

    name = '%s-axis=%d-%s' % (func.__name__, axis, tokenize(x, dtype))
    n = x.numblocks[axis]
    full = slice(None, None, None)
    slc = (full,) * axis + (slice(-1, None),) + (full,) * (x.ndim - axis - 1)

    indices = list(product(*[range(nb) if i != axis else [0]
                             for i, nb in enumerate(x.numblocks)]))
    dsk = dict()
    for ind in indices:
        shape = tuple(x.chunks[i][ii] if i != axis else 1
                      for i, ii in enumerate(ind))
        dsk[(name, 'extra') + ind] = (np.full, shape, ident, m.dtype)
        dsk[(name,) + ind] = (m.name,) + ind

    for i in range(1, n):
        last_indices = indices
        indices = list(product(*[range(nb) if ii != axis else [i]
                                 for ii, nb in enumerate(x.numblocks)]))
        for old, ind in zip(last_indices, indices):
            this_slice = (name, 'extra') + ind
            dsk[this_slice] = (binop, (name, 'extra') + old,
                                      (operator.getitem, (m.name,) + old, slc))
            dsk[(name,) + ind] = (binop, this_slice, (m.name,) + ind)

    result = Array(sharedict.merge(m.dask, (name, dsk)), name, x.chunks, m.dtype)
    return handle_out(out, result)


def _cumsum_merge(a, b):
    if isinstance(a, np.ma.masked_array) or isinstance(b, np.ma.masked_array):
        values = np.ma.getdata(a) + np.ma.getdata(b)
        return np.ma.masked_array(values, mask=np.ma.getmaskarray(b))
    return a + b


def _cumprod_merge(a, b):
    if isinstance(a, np.ma.masked_array) or isinstance(b, np.ma.masked_array):
        values = np.ma.getdata(a) * np.ma.getdata(b)
        return np.ma.masked_array(values, mask=np.ma.getmaskarray(b))
    return a * b


@wraps(np.cumsum)
def cumsum(x, axis=None, dtype=None, out=None):
    return cumreduction(np.cumsum, _cumsum_merge, 0, x, axis, dtype, out=out)


@wraps(np.cumprod)
def cumprod(x, axis=None, dtype=None, out=None):
    return cumreduction(np.cumprod, _cumprod_merge, 1, x, axis, dtype, out=out)


def validate_axis(ndim, axis):
    """ Validate single axis dimension against number of dimensions """
    if axis > ndim - 1 or axis < -ndim:
        raise ValueError("Axis must be between -%d and %d, got %d" %
                         (ndim, ndim - 1, axis))
    if axis < 0:
        return axis + ndim
    else:
        return axis
