test_PR115_generic_reducer_operation.py

# BSD 3-Clause License; see https://github.com/jpivarski/awkward-1.0/blob/master/LICENSE

from __future__ import absolute_import

import sys

import pytest
import numpy

import awkward1

primes = [x for x in range(2, 1000) if all(x % n != 0 for n in range(2, x))]

def test_reproduce_numpy():
    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:2*3*5], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20, 25, 30], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(axis=-1)) == [
         [  2 *   3 *   5 *   7 *  11,
           13 *  17 *  19 *  23 *  29,
           31 *  37 *  41 *  43 *  47],
         [ 53 *  59 *  61 *  67 *  71,
           73 *  79 *  83 *  89 *  97,
          101 * 103 * 107 * 109 * 113]]
    assert awkward1.tolist(depth2.prod(axis=2)) == [
         [  2 *   3 *   5 *   7 *  11,
           13 *  17 *  19 *  23 *  29,
           31 *  37 *  41 *  43 *  47],
         [ 53 *  59 *  61 *  67 *  71,
           73 *  79 *  83 *  89 *  97,
          101 * 103 * 107 * 109 * 113]]

    assert awkward1.tolist(depth2.prod(axis=-2)) == [
        [2*13*31, 3*17*37, 5*19*41, 7*23*43, 11*29*47],
        [53*73*101, 59*79*103, 61*83*107, 67*89*109, 71*97*113]]
    assert awkward1.tolist(depth2.prod(axis=1)) == [
        [2*13*31, 3*17*37, 5*19*41, 7*23*43, 11*29*47],
        [53*73*101, 59*79*103, 61*83*107, 67*89*109, 71*97*113]]

    assert awkward1.tolist(depth2.prod(axis=-3)) == [
        [2*53, 3*59, 5*61, 7*67, 11*71],
        [13*73, 17*79, 19*83, 23*89, 29*97],
        [31*101, 37*103, 41*107, 43*109, 47*113]]
    assert awkward1.tolist(depth2.prod(axis=0)) == [
        [2*53, 3*59, 5*61, 7*67, 11*71],
        [13*73, 17*79, 19*83, 23*89, 29*97],
        [31*101, 37*103, 41*107, 43*109, 47*113]]

    content2 = awkward1.layout.NumpyArray(numpy.array(primes[:12], dtype=numpy.int64))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 4, 8, 12], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)

    assert awkward1.tolist(depth1.prod(-1)) == [
        2*3*5*7,
        11*13*17*19,
        23*29*31*37]
    assert awkward1.tolist(depth1.prod(1)) == [
        2*3*5*7,
        11*13*17*19,
        23*29*31*37]

    assert awkward1.tolist(depth1.prod(-2)) == [
        2*11*23,
        3*13*29,
        5*17*31,
        7*19*37]
    assert awkward1.tolist(depth1.prod(0)) == [
        2*11*23,
        3*13*29,
        5*17*31,
        7*19*37]

def test_gaps():
    content1 = awkward1.layout.NumpyArray(numpy.array([123] + primes[:2*3*5], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 1, 6, 11, 16, 21, 26, 31], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([1, 4, 7], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 106,  177,  305,  469,  781],
        [ 949, 1343, 1577, 2047, 2813],
        [3131, 3811, 4387, 4687, 5311]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:2*3*5 - 1], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20, 25, 29], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109,    ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 106,  177,  305,  469,  781],
        [ 949, 1343, 1577, 2047, 2813],
        [3131, 3811, 4387, 4687,   47]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:2*3*5 - 2], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20, 25, 28], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107,         ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 106,  177,  305,  469,  781],
        [ 949, 1343, 1577, 2047, 2813],
        [3131, 3811, 4387,   43,   47]]

    content1 = awkward1.layout.NumpyArray(numpy.array([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 103, 107, 109], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20, 24, 28], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,    ],
         [101, 103, 107, 109     ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 106,  177,  305,  469, 781],
        [ 949, 1343, 1577, 2047,  29],
        [3131, 3811, 4387, 4687,  47]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[1:2*3*5], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 4, 9, 14, 19, 24, 29], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  3,   5,   7,  11     ],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 159,  295,  427,  737,   71],
        [ 949, 1343, 1577, 2047, 2813],
        [3131, 3811, 4387, 4687, 5311]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[2:2*3*5], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 8, 13, 18, 23, 28], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  5,   7,  11          ],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 265,  413,  671,   67,   71],
        [ 949, 1343, 1577, 2047, 2813],
        [3131, 3811, 4387, 4687, 5311]]

    content1 = awkward1.layout.NumpyArray(numpy.array([3, 5, 7, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 8, 13, 18, 23, 28], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  3,   5,   7,         ],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 159,  295,  427,   67,   71],
        [ 949, 1343, 1577, 2047, 2813],
        [3131, 3811, 4387, 4687, 5311]]

    content1 = awkward1.layout.NumpyArray(numpy.array([3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 4, 8, 13, 18, 23, 28], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  3,   5,   7,  11     ],
         [ 13,  17,  19,  23     ],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 159,  295,  427,  737,   71],
        [ 949, 1343, 1577, 2047,   97],
        [3131, 3811, 4387, 4687, 5311]]

    content1 = awkward1.layout.NumpyArray(numpy.array([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 14, 19, 24, 28], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43     ]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109     ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 106,  177,  305,  469,  781],
        [ 949, 1343, 1577, 2047, 2813],
        [3131, 3811, 4387, 4687]]

    content1 = awkward1.layout.NumpyArray(numpy.array([2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 101, 103, 107, 109, 113], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 9, 14, 19, 23, 28], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23     ],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89     ],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 106,  177,  305,  469,  781],
        [ 949, 1343, 1577, 2047      ],
        [3131, 3811, 4387, 4687, 5311]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:9], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 4, 6, 6, 7, 9], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 2, 4, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[      2,   3, 5],
         [      7        ]],
        [[     11,  13   ],
         [               ]],
        [[     17        ],
         [     19,  23   ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [2*11*17, 3*13, 5],
        [7*19   , 23     ]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:9], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 4, 6, 7, 9], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 2, 3, 5], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[      2,   3, 5],
         [      7        ]],
        [[     11,  13   ]],
        [[     17        ],
         [     19,  23   ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [2*11*17, 3*13, 5],
        [7*19   , 23     ]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:10], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 5, 6, 8, 9, 10], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[ 2,  3, 5],
         [ 7, 11   ],
         [13       ]],
        [[17, 19   ],
         [23       ],
         [29       ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [ 34, 57, 5],
        [161, 11   ],
        [377       ]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:9], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6, 8, 9], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 4, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[ 2,  3, 5],
         [         ],
         [ 7, 11   ],
         [13       ]],
        [[17, 19   ],
         [23       ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [34, 57, 5],
        [23       ],
        [ 7, 11   ],
        [13       ]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:9], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6, 8, 9], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 4, 4, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[ 2,  3, 5],
         [         ],
         [ 7, 11   ],
         [13       ]],
        [],
        [[17, 19   ],
         [23       ]]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [34, 57, 5],
        [23       ],
        [ 7, 11   ],
        [13       ]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:2*3*5], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20, 25, 30], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(-1)) == [
        [  2 *   3 *   5 *   7 *  11,
          13 *  17 *  19 *  23 *  29,
          31 *  37 *  41 *  43 *  47],
        [ 53 *  59 *  61 *  67 *  71,
          73 *  79 *  83 *  89 *  97,
         101 * 103 * 107 * 109 * 113]]

    assert awkward1.tolist(depth2.prod(-2)) == [
        [2*13*31, 3*17*37, 5*19*41, 7*23*43, 11*29*47],
        [53*73*101, 59*79*103, 61*83*107, 67*89*109, 71*97*113]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:9], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6, 8, 9], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 4, 4, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[ 2,  3, 5],
         [         ],
         [ 7, 11   ],
         [13       ]],
        [],
        [[17, 19   ],
         [23       ]]]

    assert awkward1.tolist(depth2.prod(-1)) == [
        [2*3*5, 1, 7*11, 13],
        [],
        [17*19, 23]]

    assert awkward1.tolist(depth2.prod(-2)) == [
        [2*7*13, 3*11, 5],
        [],
        [17*23, 19]]

def test_complicated():
    offsets1 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5], dtype=numpy.int64))
    content1 = awkward1.layout.ListOffsetArray64(offsets1, awkward1.layout.NumpyArray(numpy.array(primes[:5], dtype=numpy.int64)))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6, 8, 9], dtype=numpy.int64))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 4, 4, 6], dtype=numpy.int64))
    content2 = awkward1.layout.ListOffsetArray64(offsets3, awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.NumpyArray(numpy.array(primes[:9], dtype=numpy.int64))))
    offsets4 = awkward1.layout.Index64(numpy.array([0, 1, 1, 3], dtype=numpy.int64))
    complicated = awkward1.layout.ListOffsetArray64(offsets4, awkward1.layout.RecordArray([content1, content2], ["x", "y"]))

    assert awkward1.tolist(complicated) == [[{"x": [2, 3, 5], "y": [[2, 3, 5], [], [7, 11], [13]]}], [], [{"x": [], "y": []}, {"x": [7, 11], "y": [[17, 19], [23]]}]]

    assert awkward1.tolist(complicated["x"]) == [
        [[2, 3, 5]],
        [],
        [[],
         [7, 11]]]
    assert awkward1.tolist(complicated["y"]) == [
        [[[ 2,  3, 5],
          [         ],
          [ 7, 11   ],
          [13       ]]],
        [             ],
        [[          ],
         [[17, 19   ],
          [23       ]]]]

    assert awkward1.tolist(complicated.prod(-1)) == [{"x": [30], "y": [[30, 1, 77, 13]]}, {"x": [], "y": []}, {"x": [1, 77], "y": [[], [323, 23]]}]
    assert awkward1.tolist(complicated["x"].prod(-1)) == [[30], [], [1, 77]]
    assert awkward1.tolist(complicated["y"].prod(-1)) == [[[30, 1, 77, 13]], [], [[], [323, 23]]]

    assert awkward1.tolist(complicated.prod(-2)) == [{"x": [2, 3, 5], "y": [[182, 33, 5]]}, {"x": [], "y": []}, {"x": [7, 11], "y": [[], [391, 19]]}]
    assert awkward1.tolist(complicated["x"].prod(-2)) == [[2, 3, 5], [], [7, 11]]
    assert awkward1.tolist(complicated["y"].prod(-2)) == [[[182, 33, 5]], [], [[], [391, 19]]]

    assert awkward1.tolist(complicated[0]) == [{"x": [2, 3, 5], "y": [[2, 3, 5], [], [7, 11], [13]]}]
    assert awkward1.tolist(complicated[0].prod(-1)) == {"x": [30], "y": [[30, 1, 77, 13]]}

def test_EmptyArray():
    offsets = awkward1.layout.Index64(numpy.array([0, 0, 0, 0], dtype=numpy.int64))
    array = awkward1.layout.ListOffsetArray64(offsets, awkward1.layout.EmptyArray())
    assert awkward1.tolist(array) == [[], [], []]

    assert awkward1.tolist(array.prod(-1)) == [1, 1, 1]

    offsets = awkward1.layout.Index64(numpy.array([0, 0, 0, 0], dtype=numpy.int64))
    array = awkward1.layout.ListOffsetArray64(offsets, awkward1.layout.NumpyArray(numpy.array([], dtype=numpy.int64)))
    assert awkward1.tolist(array) == [[], [], []]

    assert awkward1.tolist(array.prod(-1)) == [1, 1, 1]

def test_IndexedOptionArray():
    content = awkward1.layout.NumpyArray(numpy.array(primes[:2*3*5], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20, 25, 30], dtype=numpy.int64))
    listoffsetarray = awkward1.layout.ListOffsetArray64(offsets1, content)
    index = awkward1.layout.Index64(numpy.array([5, 4, 3, 2, 1, 0], dtype=numpy.int64))
    indexedarray = awkward1.layout.IndexedArray64(index, listoffsetarray)
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, indexedarray)
    assert awkward1.tolist(depth2) == [
        [[101, 103, 107, 109, 113],
         [ 73,  79,  83,  89,  97],
         [ 53,  59,  61,  67,  71]],
        [[ 31,  37,  41,  43,  47],
         [ 13,  17,  19,  23,  29],
         [  2,   3,   5,   7,  11]]]

    assert awkward1.tolist(depth2.prod(-1)) == [
        [101 * 103 * 107 * 109 * 113,
          73 *  79 *  83 *  89 *  97,
          53 *  59 *  61 *  67 *  71],
        [ 31 *  37 *  41 *  43 *  47,
          13 *  17 *  19 *  23 *  29,
           2 *   3 *   5 *   7 *  11]]

    assert awkward1.tolist(depth2.prod(-2)) == [
        [101*73*53, 103*79*59, 107*83*61, 109*89*67, 113*97*71],
        [  31*13*2,   37*17*3,   41*19*5,   43*23*7,  47*29*11]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [101*31, 103*37, 107*41, 109*43, 113*47],
        [ 73*13,  79*17,  83*19,  89*23,  97*29],
        [  53*2,   59*3,   61*5,   67*7,  71*11]]

    content = awkward1.layout.NumpyArray(numpy.array([2, 3, 5, 7, 11, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 101, 103, 107, 109, 113], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20], dtype=numpy.int64))
    listoffsetarray = awkward1.layout.ListOffsetArray64(offsets1, content)
    index = awkward1.layout.Index64(numpy.array([3, -1, 2, 1, -1, 0], dtype=numpy.int64))
    indexedoptionarray = awkward1.layout.IndexedOptionArray64(index, listoffsetarray)
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, indexedoptionarray)
    assert awkward1.tolist(depth2) == [
        [[101, 103, 107, 109, 113],
         None,
         [ 53,  59,  61,  67,  71]],
        [[ 31,  37,  41,  43,  47],
         None,
         [  2,   3,   5,   7,  11]]]

    assert awkward1.tolist(depth2.prod(-1)) == [
        [101 * 103 * 107 * 109 * 113,
          53 *  59 *  61 *  67 *  71],
        [ 31 *  37 *  41 *  43 *  47,
           2 *   3 *   5 *   7 *  11]]

    assert awkward1.tolist(depth2.prod(-2)) == [
        [101*53, 103*59, 107*61, 109*67, 113*71],
        [  31*2,   37*3,   41*5,   43*7,  47*11]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [101*31, 103*37, 107*41, 109*43, 113*47],
        [],
        [  53*2,   59*3,   61*5,   67*7,  71*11]]

    content = awkward1.layout.NumpyArray(numpy.array([2, 3, 5, 7, 11, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 101, 103, 107, 109, 113], dtype=numpy.int64))
    index = awkward1.layout.Index64(numpy.array([15, 16, 17, 18, 19, -1, -1, -1, -1, -1, 10, 11, 12, 13, 14, 5, 6, 7, 8, 9, -1, -1, -1, -1, -1, 0, 1, 2, 3, 4], dtype=numpy.int64))
    indexedoptionarray = awkward1.layout.IndexedOptionArray64(index, content)
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20, 25, 30], dtype=numpy.int64))
    listoffsetarray = awkward1.layout.ListOffsetArray64(offsets1, indexedoptionarray)
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, listoffsetarray)
    assert awkward1.tolist(depth2) == [
        [[ 101,  103,  107,  109,  113],
         [None, None, None, None, None],
         [  53,   59,   61,   67,   71]],
        [[  31,   37,   41,   43,   47],
         [None, None, None, None, None],
         [   2,    3,    5,    7,   11]]]

    assert awkward1.tolist(depth2.prod(-1)) == [
        [101 * 103 * 107 * 109 * 113,
           1 *   1 *   1 *   1 *   1,
          53 *  59 *  61 *  67 *  71],
        [ 31 *  37 *  41 *  43 *  47,
           1 *   1 *   1 *   1 *   1,
           2 *   3 *   5 *   7 *  11]]

    assert awkward1.tolist(depth2.prod(-2)) == [
        [101*53, 103*59, 107*61, 109*67, 113*71],
        [  31*2,   37*3,   41*5,   43*7,  47*11]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [101*31, 103*37, 107*41, 109*43, 113*47],
        [     1,      1,      1,      1,      1],
        [  53*2,   59*3,   61*5,   67*7,  71*11]]

    content = awkward1.layout.NumpyArray(numpy.array([2, 3, 5, 7, 11, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 101, 103, 107, 109, 113], dtype=numpy.int64))
    index = awkward1.layout.Index64(numpy.array([15, 16, 17, 18, 19, -1, 10, 11, 12, 13, 14, 5, 6, 7, 8, 9, -1, 0, 1, 2, 3, 4], dtype=numpy.int64))
    indexedoptionarray = awkward1.layout.IndexedOptionArray64(index, content)
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 6, 11, 16, 17, 22], dtype=numpy.int64))
    listoffsetarray = awkward1.layout.ListOffsetArray64(offsets1, indexedoptionarray)
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, listoffsetarray)
    assert awkward1.tolist(depth2) == [
        [[ 101,  103,  107,  109,  113],
         [None],
         [  53,   59,   61,   67,   71]],
        [[  31,   37,   41,   43,   47],
         [None],
         [   2,    3,    5,    7,   11]]]

    assert awkward1.tolist(depth2.prod(-1)) == [
        [101 * 103 * 107 * 109 * 113,
           1,
          53 *  59 *  61 *  67 *  71],
        [ 31 *  37 *  41 *  43 *  47,
           1,
           2 *   3 *   5 *   7 *  11]]

    assert awkward1.tolist(depth2.prod(-2)) == [
        [101*53, 103*59, 107*61, 109*67, 113*71],
        [  31*2,   37*3,   41*5,   43*7,  47*11]]

    assert awkward1.tolist(depth2.prod(-3)) == [
        [101*31, 103*37, 107*41, 109*43, 113*47],
        [     1],
        [  53*2,   59*3,   61*5,   67*7,  71*11]]

def test_UnionArray():
    content1 = awkward1.Array([
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]]]).layout
    content2 = awkward1.Array([
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]).layout

    tags = awkward1.layout.Index8(numpy.array([0, 1], dtype=numpy.int8))
    index = awkward1.layout.Index64(numpy.array([0, 0], dtype=numpy.int64))
    depth2 = awkward1.layout.UnionArray8_64(tags, index, [content1, content2])
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(axis=-1)) == [
         [  2 *   3 *   5 *   7 *  11,
           13 *  17 *  19 *  23 *  29,
           31 *  37 *  41 *  43 *  47],
         [ 53 *  59 *  61 *  67 *  71,
           73 *  79 *  83 *  89 *  97,
          101 * 103 * 107 * 109 * 113]]
    assert awkward1.tolist(depth2.prod(axis=2)) == [
         [  2 *   3 *   5 *   7 *  11,
           13 *  17 *  19 *  23 *  29,
           31 *  37 *  41 *  43 *  47],
         [ 53 *  59 *  61 *  67 *  71,
           73 *  79 *  83 *  89 *  97,
          101 * 103 * 107 * 109 * 113]]

    assert awkward1.tolist(depth2.prod(axis=-2)) == [
        [2*13*31, 3*17*37, 5*19*41, 7*23*43, 11*29*47],
        [53*73*101, 59*79*103, 61*83*107, 67*89*109, 71*97*113]]
    assert awkward1.tolist(depth2.prod(axis=1)) == [
        [2*13*31, 3*17*37, 5*19*41, 7*23*43, 11*29*47],
        [53*73*101, 59*79*103, 61*83*107, 67*89*109, 71*97*113]]

    assert awkward1.tolist(depth2.prod(axis=-3)) == [
        [2*53, 3*59, 5*61, 7*67, 11*71],
        [13*73, 17*79, 19*83, 23*89, 29*97],
        [31*101, 37*103, 41*107, 43*109, 47*113]]
    assert awkward1.tolist(depth2.prod(axis=0)) == [
        [2*53, 3*59, 5*61, 7*67, 11*71],
        [13*73, 17*79, 19*83, 23*89, 29*97],
        [31*101, 37*103, 41*107, 43*109, 47*113]]

    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:2*3*5], dtype=numpy.int64))
    offsets1a = awkward1.layout.Index64(numpy.array([0, 5, 10, 15], dtype=numpy.int64))
    offsets1b = awkward1.layout.Index64(numpy.array([15, 20, 25, 30], dtype=numpy.int64))
    tags = awkward1.layout.Index8(numpy.array([0, 0, 0, 1, 1, 1], dtype=numpy.int8))
    index = awkward1.layout.Index64(numpy.array([0, 1, 2, 0, 1, 2], dtype=numpy.int64))
    unionarray = awkward1.layout.UnionArray8_64(tags, index, [awkward1.layout.ListOffsetArray64(offsets1a, content1), awkward1.layout.ListOffsetArray64(offsets1b, content1)])
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, unionarray)
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(axis=-1)) == [
         [  2 *   3 *   5 *   7 *  11,
           13 *  17 *  19 *  23 *  29,
           31 *  37 *  41 *  43 *  47],
         [ 53 *  59 *  61 *  67 *  71,
           73 *  79 *  83 *  89 *  97,
          101 * 103 * 107 * 109 * 113]]
    assert awkward1.tolist(depth2.prod(axis=2)) == [
         [  2 *   3 *   5 *   7 *  11,
           13 *  17 *  19 *  23 *  29,
           31 *  37 *  41 *  43 *  47],
         [ 53 *  59 *  61 *  67 *  71,
           73 *  79 *  83 *  89 *  97,
          101 * 103 * 107 * 109 * 113]]

    assert awkward1.tolist(depth2.prod(axis=-2)) == [
        [2*13*31, 3*17*37, 5*19*41, 7*23*43, 11*29*47],
        [53*73*101, 59*79*103, 61*83*107, 67*89*109, 71*97*113]]
    assert awkward1.tolist(depth2.prod(axis=1)) == [
        [2*13*31, 3*17*37, 5*19*41, 7*23*43, 11*29*47],
        [53*73*101, 59*79*103, 61*83*107, 67*89*109, 71*97*113]]

    assert awkward1.tolist(depth2.prod(axis=-3)) == [
        [2*53, 3*59, 5*61, 7*67, 11*71],
        [13*73, 17*79, 19*83, 23*89, 29*97],
        [31*101, 37*103, 41*107, 43*109, 47*113]]
    assert awkward1.tolist(depth2.prod(axis=0)) == [
        [2*53, 3*59, 5*61, 7*67, 11*71],
        [13*73, 17*79, 19*83, 23*89, 29*97],
        [31*101, 37*103, 41*107, 43*109, 47*113]]

def test_sum():
    content2 = awkward1.layout.NumpyArray(numpy.array([1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048], dtype=numpy.int64))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 4, 8, 12], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)

    assert awkward1.tolist(depth1.sum(-1)) == [
        1 + 2 + 4 + 8,
        16 + 32 + 64 + 128,
        256 + 512 + 1024 + 2048]
    assert awkward1.tolist(depth1.sum(1)) == [
        1 + 2 + 4 + 8,
        16 + 32 + 64 + 128,
        256 + 512 + 1024 + 2048]

    assert awkward1.tolist(depth1.sum(-2)) == [
        1 + 16 + 256,
        2 + 32 + 512,
        4 + 64 + 1024,
        8 + 128 + 2048]
    assert awkward1.tolist(depth1.sum(0)) == [
        1 + 16 + 256,
        2 + 32 + 512,
        4 + 64 + 1024,
        8 + 128 + 2048]

def test_sumprod_types():
    def prod(xs):
        out = 1
        for x in xs:
            out *= x
        return out

    array = numpy.array([[True, False, False], [True, False, False]])
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

    array = numpy.array([[0, 1, 2], [3, 4, 5]], dtype=numpy.int8)
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

    array = numpy.array([[0, 1, 2], [3, 4, 5]], dtype=numpy.uint8)
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

    array = numpy.array([[0, 1, 2], [3, 4, 5]], dtype=numpy.int16)
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

    array = numpy.array([[0, 1, 2], [3, 4, 5]], dtype=numpy.uint16)
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

    array = numpy.array([[0, 1, 2], [3, 4, 5]], dtype=numpy.int32)
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

    array = numpy.array([[0, 1, 2], [3, 4, 5]], dtype=numpy.uint32)
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

    array = numpy.array([[0, 1, 2], [3, 4, 5]], dtype=numpy.int64)
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

    array = numpy.array([[0, 1, 2], [3, 4, 5]], dtype=numpy.uint64)
    content2 = awkward1.layout.NumpyArray(array.reshape(-1))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert numpy.sum(array, axis=-1).dtype == numpy.asarray(depth1.sum(axis=-1)).dtype
    assert numpy.prod(array, axis=-1).dtype == numpy.asarray(depth1.prod(axis=-1)).dtype
    assert sum(awkward1.tolist(numpy.sum(array, axis=-1))) == sum(awkward1.tolist(depth1.sum(axis=-1)))
    assert prod(awkward1.tolist(numpy.prod(array, axis=-1))) == prod(awkward1.tolist(depth1.prod(axis=-1)))

def test_any():
    content2 = awkward1.layout.NumpyArray(numpy.array([1.1, 2.2, 3.3, 0.0, 2.2, 0.0, 0.0, 0.0, 0.0, 0.0]))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 6, 10], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert awkward1.tolist(depth1) == [
        [1.1, 2.2, 3.3],
        [0.0, 2.2, 0.0],
        [0.0, 0.0, 0.0, 0.0]]

    assert awkward1.tolist(depth1.any(-1)) == [
        True,
        True,
        False]
    assert awkward1.tolist(depth1.any(1)) == [
        True,
        True,
        False]

    assert awkward1.tolist(depth1.any(-2)) == [
        True,
        True,
        True,
        False]
    assert awkward1.tolist(depth1.any(0)) == [
        True,
        True,
        True,
        False]

def test_all():
    content2 = awkward1.layout.NumpyArray(numpy.array([1.1, 2.2, 3.3, 0.0, 2.2, 0.0, 0.0, 2.2, 0.0, 4.4]))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 6, 10], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert awkward1.tolist(depth1) == [
        [1.1, 2.2, 3.3],
        [0.0, 2.2, 0.0],
        [0.0, 2.2, 0.0, 4.4]]

    assert awkward1.tolist(depth1.all(-1)) == [
        True,
        False,
        False]
    assert awkward1.tolist(depth1.all(1)) == [
        True,
        False,
        False]

    assert awkward1.tolist(depth1.all(-2)) == [
        False,
        True,
        False,
        True]
    assert awkward1.tolist(depth1.all(0)) == [
        False,
        True,
        False,
        True]

def test_count():
    content2 = awkward1.layout.NumpyArray(numpy.array([1.1, 2.2, 3.3, 0.0, 2.2, 0.0, 0.0, 2.2, 0.0, 4.4]))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 6, 10], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert awkward1.tolist(depth1) == [
        [1.1, 2.2, 3.3],
        [0.0, 2.2, 0.0],
        [0.0, 2.2, 0.0, 4.4]]

    assert awkward1.tolist(depth1.count(-1)) == [
        3,
        3,
        4]
    assert awkward1.tolist(depth1.count(1)) == [
        3,
        3,
        4]

    assert awkward1.tolist(depth1.count(-2)) == [
        3,
        3,
        3,
        1]
    assert awkward1.tolist(depth1.count(0)) == [
        3,
        3,
        3,
        1]

def test_count_nonzero():
    content2 = awkward1.layout.NumpyArray(numpy.array([1.1, 2.2, 3.3, 0.0, 2.2, 0.0, 0.0, 2.2, 0.0, 4.4]))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 6, 10], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert awkward1.tolist(depth1) == [
        [1.1, 2.2, 3.3],
        [0.0, 2.2, 0.0],
        [0.0, 2.2, 0.0, 4.4]]

    assert awkward1.tolist(depth1.count_nonzero(-1)) == [
        3,
        1,
        2]
    assert awkward1.tolist(depth1.count_nonzero(1)) == [
        3,
        1,
        2]

    assert awkward1.tolist(depth1.count_nonzero(-2)) == [
        1,
        3,
        1,
        1]
    assert awkward1.tolist(depth1.count_nonzero(0)) == [
        1,
        3,
        1,
        1]

def test_count_min():
    content2 = awkward1.layout.NumpyArray(numpy.array([1.1, 2.2, 3.3, 0.0, 2.2, 0.0, 0.0, 2.2, 0.0, 4.4]))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 6, 10], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert awkward1.tolist(depth1) == [
        [1.1, 2.2, 3.3],
        [0.0, 2.2, 0.0],
        [0.0, 2.2, 0.0, 4.4]]

    assert awkward1.tolist(depth1.min(-1)) == [
        1.1,
        0.0,
        0.0]
    assert awkward1.tolist(depth1.min(1)) == [
        1.1,
        0.0,
        0.0]

    assert awkward1.tolist(depth1.min(-2)) == [
        0.0,
        2.2,
        0.0,
        4.4]
    assert awkward1.tolist(depth1.min(0)) == [
        0.0,
        2.2,
        0.0,
        4.4]

    content2 = awkward1.layout.NumpyArray(numpy.array([True, True, True, False, True, False, False, True, False, True]))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 6, 10], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert awkward1.tolist(depth1) == [
        [ True,  True,  True],
        [False,  True, False],
        [False,  True, False, True]]

    assert awkward1.tolist(depth1.min(-1)) == [
        True,
        False,
        False]
    assert awkward1.tolist(depth1.min(1)) == [
        True,
        False,
        False]

    assert awkward1.tolist(depth1.min(-2)) == [
        False,
        True,
        False,
        True]
    assert awkward1.tolist(depth1.min(0)) == [
        False,
        True,
        False,
        True]

def test_count_max():
    content2 = awkward1.layout.NumpyArray(numpy.array([1.1, 2.2, 3.3, 0.0, 2.2, 0.0, 0.0, 2.2, 0.0, 4.4]))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 6, 10], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert awkward1.tolist(depth1) == [
        [1.1, 2.2, 3.3],
        [0.0, 2.2, 0.0],
        [0.0, 2.2, 0.0, 4.4]]

    assert awkward1.tolist(depth1.max(-1)) == [
        3.3,
        2.2,
        4.4]
    assert awkward1.tolist(depth1.max(1)) == [
        3.3,
        2.2,
        4.4]

    assert awkward1.tolist(depth1.max(-2)) == [
        1.1,
        2.2,
        3.3,
        4.4]
    assert awkward1.tolist(depth1.max(0)) == [
        1.1,
        2.2,
        3.3,
        4.4]

    content2 = awkward1.layout.NumpyArray(numpy.array([False, True, True, False, True, False, False, False, False, False]))
    offsets3 = awkward1.layout.Index64(numpy.array([0, 3, 6, 10], dtype=numpy.int64))
    depth1 = awkward1.layout.ListOffsetArray64(offsets3, content2)
    assert awkward1.tolist(depth1) == [
        [False,  True,  True],
        [False,  True, False],
        [False, False, False, False]]

    assert awkward1.tolist(depth1.max(-1)) == [
        True,
        True,
        False]
    assert awkward1.tolist(depth1.max(1)) == [
        True,
        True,
        False]

    assert awkward1.tolist(depth1.max(-2)) == [
        False,
        True,
        True,
        False]
    assert awkward1.tolist(depth1.max(0)) == [
        False,
        True,
        True,
        False]

def test_mask():
    content = awkward1.layout.NumpyArray(numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9]))
    offsets = awkward1.layout.Index64(numpy.array([0, 3, 3, 5, 6, 6, 6, 9], dtype=numpy.int64))
    array = awkward1.layout.ListOffsetArray64(offsets, content)

    assert awkward1.tolist(array.min(axis=-1, mask=False)) == [1.1, numpy.inf, 4.4, 6.6, numpy.inf, numpy.inf, 7.7]
    assert awkward1.tolist(array.min(axis=-1, mask=True)) == [1.1, None, 4.4, 6.6, None, None, 7.7]

def test_keepdims():
    nparray = numpy.array(primes[:2*3*5], dtype=numpy.int64).reshape(2, 3, 5)
    content1 = awkward1.layout.NumpyArray(numpy.array(primes[:2*3*5], dtype=numpy.int64))
    offsets1 = awkward1.layout.Index64(numpy.array([0, 5, 10, 15, 20, 25, 30], dtype=numpy.int64))
    offsets2 = awkward1.layout.Index64(numpy.array([0, 3, 6], dtype=numpy.int64))
    depth2 = awkward1.layout.ListOffsetArray64(offsets2, awkward1.layout.ListOffsetArray64(offsets1, content1))
    assert awkward1.tolist(depth2) == [
        [[  2,   3,   5,   7,  11],
         [ 13,  17,  19,  23,  29],
         [ 31,  37,  41,  43,  47]],
        [[ 53,  59,  61,  67,  71],
         [ 73,  79,  83,  89,  97],
         [101, 103, 107, 109, 113]]]

    assert awkward1.tolist(depth2.prod(axis=-1, keepdims=False)) == awkward1.tolist(nparray.prod(axis=-1, keepdims=False))
    assert awkward1.tolist(depth2.prod(axis=-2, keepdims=False)) == awkward1.tolist(nparray.prod(axis=-2, keepdims=False))
    assert awkward1.tolist(depth2.prod(axis=-3, keepdims=False)) == awkward1.tolist(nparray.prod(axis=-3, keepdims=False))

    assert awkward1.tolist(depth2.prod(axis=-1, keepdims=True)) == awkward1.tolist(nparray.prod(axis=-1, keepdims=True))
    assert awkward1.tolist(depth2.prod(axis=-2, keepdims=True)) == awkward1.tolist(nparray.prod(axis=-2, keepdims=True))
    assert awkward1.tolist(depth2.prod(axis=-3, keepdims=True)) == awkward1.tolist(nparray.prod(axis=-3, keepdims=True))

def test_highlevel():
    array = awkward1.Array([
        [[ 2,  3, 5],
         [         ],
         [ 7, 11   ],
         [13       ]],
        [],
        [[17, 19   ],
         [23       ]]])

    assert awkward1.count(array) == 9
    assert awkward1.tolist(awkward1.count(array, axis=-1)) == [
        [3, 0, 2, 1],
        [],
        [2, 1]]
    assert awkward1.tolist(awkward1.count(array, axis=2)) == [
        [3, 0, 2, 1],
        [],
        [2, 1]]
    assert awkward1.tolist(awkward1.count(array, axis=-1, keepdims=True)) == [
        [[3], [0], [2], [1]],
        [],
        [[2], [1]]]
    assert awkward1.tolist(awkward1.count(array, axis=-2)) == [
        [3, 2, 1],
        [],
        [2, 1]]
    assert awkward1.tolist(awkward1.count(array, axis=1)) == [
        [3, 2, 1],
        [],
        [2, 1]]
    assert awkward1.tolist(awkward1.count(array, axis=-2, keepdims=True)) == [
        [[3, 2, 1]],
        [[]],
        [[2, 1]]]

    assert awkward1.count_nonzero(array) == 9
    assert awkward1.tolist(awkward1.count_nonzero(array, axis=-1)) == [
        [3, 0, 2, 1],
        [],
        [2, 1]]
    assert awkward1.tolist(awkward1.count_nonzero(array, axis=-2)) == [
        [3, 2, 1],
        [],
        [2, 1]]

    assert awkward1.sum(array) == 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23
    assert awkward1.tolist(awkward1.sum(array, axis=-1)) == [
        [2 + 3 + 5, 0, 7 + 11, 13],
        [],
        [17 + 19, 23]]
    assert awkward1.tolist(awkward1.sum(array, axis=-2)) == [
        [2 + 7 + 13, 3 + 11, 5],
        [],
        [17 + 23, 19]]

    assert awkward1.prod(array) == 2*3*5*7*11*13*17*19*23
    assert awkward1.tolist(awkward1.prod(array, axis=-1)) == [
        [2*3*5, 1, 7*11, 13],
        [],
        [17*19, 23]]
    assert awkward1.tolist(awkward1.prod(array, axis=-2)) == [
        [2*7*13, 3*11, 5],
        [],
        [17*23, 19]]

    assert awkward1.min(array) == 2
    assert awkward1.tolist(awkward1.min(array, axis=-1)) == [
        [2, None, 7, 13],
        [],
        [17, 23]]
    assert awkward1.tolist(awkward1.min(array, axis=-2)) == [
        [2, 3, 5],
        [],
        [17, 19]]

    assert awkward1.max(array) == 23
    assert awkward1.tolist(awkward1.max(array, axis=-1)) == [
        [5, None, 11, 13],
        [],
        [19, 23]]
    assert awkward1.tolist(awkward1.max(array, axis=-2)) == [
        [13, 11, 5],
        [],
        [23, 19]]

    array = awkward1.Array([
        [[ True, False, True],
         [                  ],
         [False, False      ],
         [ True             ]],
        [],
        [[False,  True      ],
         [ True             ]]])

    assert awkward1.any(array) == True
    assert awkward1.tolist(awkward1.any(array, axis=-1)) == [
        [True, False, False, True],
        [],
        [True, True]]
    assert awkward1.tolist(awkward1.any(array, axis=-2)) == [
        [True, False, True],
        [],
        [True, True]]

    assert awkward1.all(array) == False
    assert awkward1.tolist(awkward1.all(array, axis=-1)) == [
        [False, True, False, True],
        [],
        [False, True]]
    assert awkward1.tolist(awkward1.all(array, axis=-2)) == [
        [False, False, True],
        [],
        [False, True]]

def test_nonreducers():
    x = awkward1.Array([[1, 2, 3, 4, 5], [1, 2, 3, 4, 5]])
    y = awkward1.Array([[1.1, 2.2, 2.9, 4.0, 5.1], [0.9, 2.1, 3.2, 4.1, 4.9]])

    assert awkward1.mean(y) == numpy.mean(awkward1.tonumpy(y))
    assert awkward1.var(y) == numpy.var(awkward1.tonumpy(y))
    assert awkward1.var(y, ddof=1) == numpy.var(awkward1.tonumpy(y), ddof=1)
    assert awkward1.std(y) == numpy.std(awkward1.tonumpy(y))
    assert awkward1.std(y, ddof=1) == numpy.std(awkward1.tonumpy(y), ddof=1)

    assert awkward1.moment(y, 1) == numpy.mean(awkward1.tonumpy(y))
    assert awkward1.moment(y - awkward1.mean(y), 2) == numpy.var(awkward1.tonumpy(y))
    assert awkward1.covar(y, y) == numpy.var(awkward1.tonumpy(y))
    assert awkward1.corr(y, y) == 1.0

    assert awkward1.corr(x, y) == pytest.approx(0.9968772535047296)
    fit = awkward1.linearfit(x, y)
    assert awkward1.tolist(fit) == pytest.approx({"intercept": 0.07999999999999773, "slope": 0.99, "intercept_error": 0.7416198487095663, "slope_error": 0.22360679774997896})

    assert awkward1.tolist(awkward1.mean(y, axis=-1)) == awkward1.tolist(numpy.mean(awkward1.tonumpy(y), axis=-1))
    assert awkward1.tolist(awkward1.var(y, axis=-1)) == awkward1.tolist(numpy.var(awkward1.tonumpy(y), axis=-1))
    assert awkward1.tolist(awkward1.var(y, axis=-1, ddof=1)) == awkward1.tolist(numpy.var(awkward1.tonumpy(y), axis=-1, ddof=1))
    assert awkward1.tolist(awkward1.std(y, axis=-1)) == awkward1.tolist(numpy.std(awkward1.tonumpy(y), axis=-1))
    assert awkward1.tolist(awkward1.std(y, axis=-1, ddof=1)) == awkward1.tolist(numpy.std(awkward1.tonumpy(y), axis=-1, ddof=1))

    assert awkward1.tolist(awkward1.moment(y, 1, axis=-1)) == awkward1.tolist(numpy.mean(awkward1.tonumpy(y), axis=-1))
    assert awkward1.tolist(awkward1.moment(y - awkward1.mean(y, axis=-1), 2, axis=-1)) == awkward1.tolist(numpy.var(awkward1.tonumpy(y), axis=-1))
    assert awkward1.tolist(awkward1.covar(y, y, axis=-1)) == awkward1.tolist(numpy.var(awkward1.tonumpy(y), axis=-1))
    assert awkward1.tolist(awkward1.corr(y, y, axis=-1)) == [1.0, 1.0]

    assert awkward1.tolist(awkward1.corr(x, y, axis=-1)) == pytest.approx([0.9975103695813371, 0.9964193240901015])
    fit = awkward1.linearfit(x, y, axis=-1)
    assert awkward1.tolist(fit[0]) == pytest.approx({"intercept": 0.11999999999999772, "slope": 0.9800000000000005, "intercept_error": 1.0488088481701516, "slope_error": 0.31622776601683794})
    assert awkward1.tolist(fit[1]) == pytest.approx({"intercept": 0.04000000000000228, "slope": 0.9999999999999994, "intercept_error": 1.0488088481701516, "slope_error": 0.31622776601683794})