[MXNET-1426] Fix the wrong result of sum, mean, argmin, argmax when inputs contain inf or nan

[wkcn]

Description

Hi, there.
I fix the wrong result of sum(inf, inf) and mean(inf, inf).

Test Case:

import mxnet as mx
import numpy as np

def test(x):
    print('data', x.asnumpy())
    print('mean/sum', mx.nd.mean(x).asnumpy(), mx.nd.sum(x).asnumpy())
    print('argmin/argmax', mx.nd.argmin(x).asnumpy(), mx.nd.argmax(x).asnumpy())
    print('min/max', mx.nd.min(x).asnumpy(), mx.nd.max(x).asnumpy())
    print('-----')

x = mx.nd.array([np.inf, np.inf, 1])
test(x)

x = mx.nd.array([-np.inf, -np.inf, 1])
test(x)

x = mx.nd.array([np.inf, -np.inf, 1])
test(x)

x = mx.nd.array([np.nan, -np.inf, 1])
test(x)

x = mx.nd.array([np.nan, np.nan])
test(x)

x = mx.nd.array([np.nan, 1])
test(x)

The wrong result in mxnet_mkl-1.6.0b20191015-py2.py3-none-manylinux1_x86_64

data [inf inf  1.]
mean/sum [nan] [nan]
argmin/argmax [2.] [0.]
min/max [1.] [inf]
-----
data [-inf -inf   1.]
mean/sum [nan] [nan]
argmin/argmax [0.] [2.]
min/max [-inf] [1.]
-----
data [ inf -inf   1.]
mean/sum [nan] [nan]
argmin/argmax [1.] [0.]
min/max [-inf] [inf]
-----
data [ nan -inf   1.]
mean/sum [nan] [nan]
argmin/argmax [1.] [2.]
min/max [-inf] [1.]
-----
data [nan nan]
mean/sum [nan] [nan]
argmin/argmax [0.] [0.]
min/max [inf] [-inf]
-----
data [nan  1.]
mean/sum [nan] [nan]
argmin/argmax [1.] [1.]
min/max [1.] [1.]

The correct result in this PR:

data [inf inf  1.]
mean/sum [inf] [inf]
argmin/argmax [2.] [0.]
min/max [1.] [inf]
-----
data [-inf -inf   1.]
mean/sum [-inf] [-inf]
argmin/argmax [0.] [2.]
min/max [-inf] [1.]
-----
data [ inf -inf   1.]
mean/sum [nan] [nan]
argmin/argmax [1.] [0.]
min/max [-inf] [inf]
-----
data [ nan -inf   1.]
mean/sum [nan] [nan]
argmin/argmax [0.] [0.]
min/max [nan] [nan]
-----
data [nan nan]
mean/sum [nan] [nan]
argmin/argmax [0.] [0.]
min/max [nan] [nan]
-----
data [nan  1.]
mean/sum [nan] [nan]
argmin/argmax [0.] [0.]
min/max [nan] [nan]

If we modify the test function,

def test(x):
    x = x.asnumpy()
    print('data', x)
    print('mean/sum', np.mean(x), np.sum(x))
    print('argmin/argmax', np.argmin(x), np.argmax(x))
    print('min/max', np.min(x), np.max(x))
    print('-----')

Here is the result of NumPy.

data [inf inf  1.]
mean/sum inf inf
argmin/argmax 2 0
min/max 1.0 inf
-----
data [-inf -inf   1.]
mean/sum -inf -inf
argmin/argmax 0 2
min/max -inf 1.0
-----
data [ inf -inf   1.]
mean/sum nan nan
argmin/argmax 1 0
min/max -inf inf
-----
data [ nan -inf   1.]
mean/sum nan nan
argmin/argmax 0 0
min/max nan nan
-----
data [nan nan]
mean/sum nan nan
argmin/argmax 0 0
min/max nan nan
-----
data [nan  1.]
mean/sum nan nan
argmin/argmax 0 0
min/max nan nan
-----

Checklist

Essentials

Please feel free to remove inapplicable items for your PR.

• The PR title starts with [MXNET-$JIRA_ID], where $JIRA_ID refers to the relevant JIRA issue created (except PRs with tiny changes)
• Changes are complete (i.e. I finished coding on this PR)
• All changes have test coverage:
• Unit tests are added for small changes to verify correctness (e.g. adding a new operator)
• Nightly tests are added for complicated/long-running ones (e.g. changing distributed kvstore)
• Build tests will be added for build configuration changes (e.g. adding a new build option with NCCL)
• Code is well-documented:
• For user-facing API changes, API doc string has been updated.
• For new C++ functions in header files, their functionalities and arguments are documented.
• For new examples, README.md is added to explain the what the example does, the source of the dataset, expected performance on test set and reference to the original paper if applicable
• Check the API doc at http:https://mxnet-ci-doc.s3-accelerate.dualstack.amazonaws.com/PR-$PR_ID/$BUILD_ID/index.html
• To the my best knowledge, examples are either not affected by this change, or have been fixed to be compatible with this change

Changes

• Add isnan_typed and isinf_typed in mshadow
• Remove isnan_typed in src/operator/mshadow_op.h
• Update mshadow/extension/reduce_with_axis.h to support NaN
• Add relative python testcases
• Update Julia testcase, which is consistent with Julia built-in functions argmin and argmax.

[iblislin]

The Julia part looks fine for me.

[wkcn]

Hi @marcoabreu @access2rohit , could you please help take a review?
The PR fixes the wrong result of sum, mean, argmin and argmax when inputs contain inf or NaN.
Thank you!

[wkcn]

Hi @reminisce and @haojin2 , could you please help take a review?

This PR makes the following functions consistent with NumPy.

sum, mean, argmin, argmax

Thank you!

[wkcn]

Hi @eric-haibin-lin , could you please help take a review?
It is a bug, which outputs a wrong result or an inconsistent result with that of NumPy.

Thank you so much!

[eric-haibin-lin]

Would you mind also add what is the result before this fix?

[wkcn]

Hi @eric-haibin-lin , I have updated the test result : )

[szha]

cc @reminisce

[wkcn]

Ping : )

[marcoabreu]

Can you turn these magic values into constants with documentation? While I get 0x7ffff, 0x7c00 for example, looks quite arbitrary.

[wkcn]

Hi @marcoabreu , I add two constants MSHADOW_HALF_SIGN_BIT and MSHADOW_HALF_EXPONENT_BITS in 3rdparty/mshadow/mshadow/half.h, and replace these two magic values.

[marcoabreu]

Could you elaborate why you're introducing so much branching into a test? If the results are inconsistent, we should rather improve the test instead of skipping the checks. I'd love to have more detail

[wkcn]

Hi @marcoabreu , here is the explanation.

1. So much branching
   We need to test all reduce operators, like min, max, argmin, argmax, sum, mean when the inputs contain -inf, +inf, nan.

2. Skipping the checks
   I replace the old check with a new one. : )

[marcoabreu]

I'll merge after the feedback has been addressed :) Sorry for the delay