Allow large array operation in MXNet

[apeforest]

This change is a dependency for the integer overflow issue in MXNet where a large ND array is created and converted to numpy.

An earlier PR was reviewed but it makes too significant change to mshadow module and is not necessary. This PR is a new one and it has been verified in the MXNet issue filed above.

[apeforest]

@eric-haibin-lin @tqchen @piiswrong Please review this PR for large array support in MXNet. Thx.

[piiswrong]

If we are going to change this we should change it to signed int64_t instead of unsigned size_t.

Although there could be pitfalls. @tqchen any thoughts?

[tqchen]

int64_t is a better choice than size_t

[apeforest]

@tqchen Could you elaborate a little more on the advantage of using int64_t over size_t here? Curious to learn. Thanks!

[tqchen]

The main reason is that int64_t is used by default by DLPack and a few other frameworks. It also allows introducing -1 as some special placeholder when necessary.

size_t is usually not preferred in data-structure members, because it has a cross-platform issue(size_t can be 32 bit in 32bit platforms). I have explained the reason to favor int64_t over uint64_t

[apeforest]

@tqchen Thanks for your explanation. I have change to use int64_t as type for the tensor dimension. For the completeness of this change, instead of only changing return type of the size() function, I updated the type definition of index_t from unsigned to int64_t.

I have written simple example to check runtime impact to softmax and relu operators in MXNet and did not see noticeable difference. Any other suggestion on performance test is appreciated.

import mxnet as mx
from mxnet.test_utils import check_speed

NUM_ITER = 1000

def check_softmax_cpu():
    data_shape=(1,10000)
    data = mx.sym.Variable(name='data',shape=data_shape)
    ctx=mx.cpu(0)
    avg_runtime = 0
    for iter in range(NUM_ITER):
        x = mx.nd.random.normal(0, 1.0, shape=data_shape, ctx=ctx)
        net = mx.sym.softmax(data=data)
        avg_runtime += check_speed(sym=net, location={'data': x}, ctx=ctx, N=10, grad_req='null', typ='forward') * 1000
    avg_runtime /= NUM_ITER
    print('runtime of softmax: ' + str(avg_runtime))

def check_relu_cpu():
    data_shape=(1,10000)
    data = mx.sym.Variable(name='data',shape=data_shape)
    ctx=mx.cpu(0)
    avg_runtime = 0
    for iter in range(NUM_ITER):
        x = mx.nd.random.normal(0, 1.0, shape=data_shape, ctx=ctx)
        net = mx.sym.relu(data=data)
        avg_runtime += check_speed(sym=net, location={'data': x}, ctx=ctx, N=10, grad_req='null', typ='forward') * 1000
    avg_runtime /= NUM_ITER
    print('runtime of relu: ' + str(avg_runtime))

check_softmax_cpu()
check_relu_cpu()

[apeforest]

@tqchen I will appreciate if you could help to review this at your convenience or relay to other reviewers for me. We have another PR (apache/mxnet#11742) dependent on this. Thanks!

[apeforest]

@piiswrong @tqchen Would appreciate if you could help review this at your earliest convenience. There is a MXNet issue depending on this. Thanks!