Safer norm

[haojin2]

Description

Resurrection of #14240 to solve #14126. With an extra argument of norm for specification of output data type.

Checklist

Essentials

Please feel free to remove inapplicable items for your PR.

• The PR title starts with [MXNET-$JIRA_ID], where $JIRA_ID refers to the relevant JIRA issue created (except PRs with tiny changes)
• Changes are complete (i.e. I finished coding on this PR)
• All changes have test coverage:
• Unit tests are added for small changes to verify correctness (e.g. adding a new operator)
• Nightly tests are added for complicated/long-running ones (e.g. changing distributed kvstore)
• Build tests will be added for build configuration changes (e.g. adding a new build option with NCCL)
• Code is well-documented:
• For user-facing API changes, API doc string has been updated.
• For new C++ functions in header files, their functionalities and arguments are documented.
• For new examples, README.md is added to explain the what the example does, the source of the dataset, expected performance on test set and reference to the original paper if applicable
• Check the API doc at http://mxnet-ci-doc.s3-accelerate.dualstack.amazonaws.com/PR-$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

• use safe accumulation for norm #14240
• out_dtype argument for norm
• Corresponding changes to backend code
• Extra test coverage for different out_dtype configurations.

Comments

@szha
Unit test passed 10000 times on GPU:

MXNET_TEST_COUNT=10000 nosetests tests/python/gpu/test_operator_gpu.py:test_norm
[INFO] Setting module np/mx/python random seeds, use MXNET_MODULE_SEED=19910248 to reproduce.
.
----------------------------------------------------------------------
Ran 1 test in 234.244s

OK

[szha]

cc @ptrendx

[piyushghai]

Thanks for your contributions @haojin2. Can you also look into the CI failures ?

@mxnet-label-bot Add [Operator, Backend]

[haojin2]

@eric-haibin-lin