 BUG: don't mangle NaN-float-values and pd.NaT (GH 22295) 
it is more or less the clean-up after PR #21904 and PR #22207, the underlying hash-map handles all cases correctly out-of-the box and thus no special handling is needed.

As a collateral, the mangling of NaNs and NaT is fixed.

- [x] closes #22295 
- [x] closes #22332
- [x] tests added / passed
- [x] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

Performance tests:

`asv continuous -f 1.01 upstream/master HEAD -b ^series_methods -b ^algorithms -b ^categorial`

<details>

```
· Creating environments
· Discovering benchmarks
·· Uninstalling from conda-py3.6-Cython-matplotlib-numexpr-numpy-openpyxl-pytables-pytest-scipy-sqlalchemy-xlrd-xlsxwriter-xlwt
·· Installing into conda-py3.6-Cython-matplotlib-numexpr-numpy-openpyxl-pytables-pytest-scipy-sqlalchemy-xlrd-xlsxwriter-xlwt..
· Running 66 total benchmarks (2 commits * 1 environments * 33 benchmarks)
[  0.00%] · For pandas commit hash e14fd992:
[  0.00%] ·· Building for conda-py3.6-Cython-matplotlib-numexpr-numpy-openpyxl-pytables-pytest-scipy-sqlalchemy-xlrd-xlsxwriter-xlwt...
[  0.00%] ·· Benchmarking conda-py3.6-Cython-matplotlib-numexpr-numpy-openpyxl-pytables-pytest-scipy-sqlalchemy-xlrd-xlsxwriter-xlwt
[  0.00%] ··· Running benchmarks............................
[  0.00%] ··· Setting up algorithms.py:95
[  0.00%] ··· Running benchmarks.........
[  1.52%] ··· algorithms.Duplicated.time_duplicated_float                                                    19.1±1ms;...
[  3.03%] ··· algorithms.Duplicated.time_duplicated_int                                                    10.5±0.9ms;...
[  4.55%] ··· algorithms.Duplicated.time_duplicated_string                                                 11.0±0.2μs;...
[  6.06%] ··· algorithms.DuplicatedUniqueIndex.time_duplicated_unique_int                                      31.5±0.2μs
[  7.58%] ··· algorithms.Factorize.time_factorize_float                                                      67.7±8ms;...
[  9.09%] ··· algorithms.Factorize.time_factorize_int                                                        23.1±4ms;...
[ 10.61%] ··· algorithms.Factorize.time_factorize_string                                                     162±20ms;...
[ 12.12%] ··· algorithms.Match.time_match_string                                                                  376±4μs
[ 13.64%] ··· series_methods.Clip.time_clip                                                                       126±3μs
[ 15.15%] ··· series_methods.Dir.time_dir_strings                                                             2.06±0.03ms
[ 16.67%] ··· series_methods.Dropna.time_dropna                                                           2.85±0.08ms;...
[ 18.18%] ··· series_methods.IsIn.time_isin                                                               1.67±0.05ms;...
[ 19.70%] ··· series_methods.IsInFloat64.time_isin_few_different                                                 39.5±2ms
[ 21.21%] ··· series_methods.IsInFloat64.time_isin_many_different                                                48.9±9ms
[ 22.73%] ··· series_methods.IsInFloat64.time_isin_nan_values                                                  38.8±0.3ms
[ 24.24%] ··· series_methods.IsInForObjects.time_isin_long_series_long_values                                  3.62±0.1ms
[ 25.76%] ··· series_methods.IsInForObjects.time_isin_long_series_long_values_floats                          6.46±0.09ms
[ 27.27%] ··· series_methods.IsInForObjects.time_isin_long_series_short_values                                2.37±0.05ms
[ 28.79%] ··· series_methods.IsInForObjects.time_isin_nans                                                       717±40μs
[ 30.30%] ··· series_methods.IsInForObjects.time_isin_short_series_long_values                                 1.41±0.1ms
[ 31.82%] ··· series_methods.Map.time_map                                                                 1.10±0.05ms;...
[ 33.33%] ··· series_methods.NSort.time_nlargest                                                           2.89±0.1ms;...
[ 34.85%] ··· series_methods.NSort.time_nsmallest                                                         2.42±0.07ms;...
[ 36.36%] ··· series_methods.SeriesConstructor.time_constructor                                               163±3μs;...
[ 37.88%] ··· series_methods.SeriesGetattr.time_series_datetimeindex_repr                                     3.19±0.09μs
[ 39.39%] ··· series_methods.ValueCounts.time_value_counts                                                 2.19±0.3ms;...
[ 40.91%] ··· algorithms.Hashing.time_frame                                                                    22.5±0.6ms
[ 42.42%] ··· algorithms.Hashing.time_series_categorical                                                       5.35±0.1ms
[ 43.94%] ··· algorithms.Hashing.time_series_dates                                                            3.56±0.03ms
[ 45.45%] ··· algorithms.Hashing.time_series_float                                                            3.59±0.05ms
[ 46.97%] ··· algorithms.Hashing.time_series_int                                                               3.37±0.2ms
[ 48.48%] ··· algorithms.Hashing.time_series_string                                                            14.0±0.9ms
[ 50.00%] ··· algorithms.Hashing.time_series_timedeltas                                                       3.42±0.06ms
[ 50.00%] · For pandas commit hash 03707400:
[ 50.00%] ·· Building for conda-py3.6-Cython-matplotlib-numexpr-numpy-openpyxl-pytables-pytest-scipy-sqlalchemy-xlrd-xlsxwriter-xlwt...
[ 50.00%] ·· Benchmarking conda-py3.6-Cython-matplotlib-numexpr-numpy-openpyxl-pytables-pytest-scipy-sqlalchemy-xlrd-xlsxwriter-xlwt
[ 50.00%] ··· Running benchmarks............................
[ 50.00%] ··· Setting up algorithms.py:95
[ 50.00%] ··· Running benchmarks.........
[ 51.52%] ··· algorithms.Duplicated.time_duplicated_float                                                  15.5±0.3ms;...
[ 53.03%] ··· algorithms.Duplicated.time_duplicated_int                                                      11.3±2ms;...
[ 54.55%] ··· algorithms.Duplicated.time_duplicated_string                                                 10.6±0.2μs;...
[ 56.06%] ··· algorithms.DuplicatedUniqueIndex.time_duplicated_unique_int                                      31.3±0.3μs
[ 57.58%] ··· algorithms.Factorize.time_factorize_float                                                      63.8±3ms;...
[ 59.09%] ··· algorithms.Factorize.time_factorize_int                                                        22.6±3ms;...
[ 60.61%] ··· algorithms.Factorize.time_factorize_string                                                      145±6ms;...
[ 62.12%] ··· algorithms.Match.time_match_string                                                                  367±3μs
[ 63.64%] ··· series_methods.Clip.time_clip                                                                       120±2μs
[ 65.15%] ··· series_methods.Dir.time_dir_strings                                                              2.03±0.1ms
[ 66.67%] ··· series_methods.Dropna.time_dropna                                                            3.03±0.1ms;...
[ 68.18%] ··· series_methods.IsIn.time_isin                                                               1.68±0.01ms;...
[ 69.70%] ··· series_methods.IsInFloat64.time_isin_few_different                                               39.0±0.5ms
[ 71.21%] ··· series_methods.IsInFloat64.time_isin_many_different                                                43.6±7ms
[ 72.73%] ··· series_methods.IsInFloat64.time_isin_nan_values                                                  38.9±0.1ms
[ 74.24%] ··· series_methods.IsInForObjects.time_isin_long_series_long_values                                 3.55±0.05ms
[ 75.76%] ··· series_methods.IsInForObjects.time_isin_long_series_long_values_floats                           6.12±0.1ms
[ 77.27%] ··· series_methods.IsInForObjects.time_isin_long_series_short_values                                2.25±0.03ms
[ 78.79%] ··· series_methods.IsInForObjects.time_isin_nans                                                       680±10μs
[ 80.30%] ··· series_methods.IsInForObjects.time_isin_short_series_long_values                                 1.28±0.1ms
[ 81.82%] ··· series_methods.Map.time_map                                                                 1.11±0.04ms;...
[ 83.33%] ··· series_methods.NSort.time_nlargest                                                          2.94±0.06ms;...
[ 84.85%] ··· series_methods.NSort.time_nsmallest                                                         2.45±0.09ms;...
[ 86.36%] ··· series_methods.SeriesConstructor.time_constructor                                              169±10μs;...
[ 87.88%] ··· series_methods.SeriesGetattr.time_series_datetimeindex_repr                                      3.53±0.2μs
[ 89.39%] ··· series_methods.ValueCounts.time_value_counts                                                 2.17±0.2ms;...
[ 90.91%] ··· algorithms.Hashing.time_frame                                                                    21.4±0.4ms
[ 92.42%] ··· algorithms.Hashing.time_series_categorical                                                      5.31±0.09ms
[ 93.94%] ··· algorithms.Hashing.time_series_dates                                                             3.51±0.1ms
[ 95.45%] ··· algorithms.Hashing.time_series_float                                                            3.35±0.03ms
[ 96.97%] ··· algorithms.Hashing.time_series_int                                                              3.31±0.06ms
[ 98.48%] ··· algorithms.Hashing.time_series_string                                                            15.2±0.4ms
[100.00%] ··· algorithms.Hashing.time_series_timedeltas                                                       3.44±0.07ms
```
</details>
BENCHMARKS NOT SIGNIFICANTLY CHANGED.
 @jreback, @jorisvandenbossche, @mroeschke, @WillAyd wanted to ask for your advice, concerning this PR.

There is currently a problem, that[ `np.unique()`](https://github.com/pandas-dev/pandas/blob/a43947283dd6dc9f9dc2742700c7fa4677d7e27a/pandas/_libs/hashtable_class_helper.pxi.in#L856) mangles `pd.NaT` and `np.nan` but not `None`:

```
 if not checknull(val) or val is None:
    ....
```

on the other hand other functions of hash_table mangle all three of them, for example [`map_locations`](https://github.com/pandas-dev/pandas/blob/a43947283dd6dc9f9dc2742700c7fa4677d7e27a/pandas/_libs/hashtable_class_helper.pxi.in#L801): 

```
if val != val or val is None:
     val = na_sentinel
....
```

Now, this leads to problems as soon as these two definition of unique meet, for example #22332, where mangling/not mangling `None` and `np.nan` is a problem.

This PR would not change the situation much: `None`+`np.nan` stays a problem,  but  the PR also demangles `np.nan` and `pd.NaT`in `pd.unique()` and thus the pair `np.nan`+`pd.NaT` becomes also a problem in situation #22332.

I see the following options:

 1. leave it as it is/do nothing
 2. mangle None with others in pd.unique(). i.e. rollback the fix for #20866
 3. go on with this PR, accept that also `[np.nan, pd.NaT]` will be a problem similar to `[None, np.nan]` for `pd.to_datetime(). Disabling/changing the one failing unit test (see related #22305, right now [`None`, pd.NaT]  is also problem, but not tested in the test-suite)
 4. Unmangle `None`, `np.nan` and `pd.NaT` everywhere. But this mangling is almost everywhere...

What would you suggest? No idea how much effort this is signing up for but option 4 imo seems to be the best and cleanest Option 4 would be very nice but as you mention would take a lot of untangling. Additionally, there's already some institutional mangling of `None` and `np.nan` when it comes to converting `None` to `np.nan` https://pandas.pydata.org/pandas-docs/stable/missing_data.html#inserting-missing-data # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22296?src=pr&el=h1) Report
> Merging [#22296](https://codecov.io/gh/pandas-dev/pandas/pull/22296?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/996f361f8e6986ea1c65ccb164a4c585e1f4a027?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/22296/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/22296?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #22296      +/-   ##
==========================================
+ Coverage   92.16%   92.16%   +<.01%     
==========================================
  Files         169      169              
  Lines       50708    50711       +3     
==========================================
+ Hits        46734    46737       +3     
  Misses       3974     3974
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.57% <100%> (ø)` | :arrow_up: |
| #single | `42.35% <80%> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/22296?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/22296/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.44% <ø> (-0.01%)` | :arrow_down: |
| [pandas/core/indexes/numeric.py](https://codecov.io/gh/pandas-dev/pandas/pull/22296/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9udW1lcmljLnB5) | `97.3% <100%> (+0.06%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22296?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/22296?src=pr&el=footer). Last update [996f361...b6459f3](https://codecov.io/gh/pandas-dev/pandas/pull/22296?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 @jreback After running asv for the whole suite and rerunning for flashing test cases, that is what is left:

```
      before           after         ratio
     [03707400]       [a6eb063c]
-        29.7±1ms       25.6±0.5ms     0.86  index_object.SetOperations.time_operation('strings', 'symmetric_difference')
-        41.0±1ms       35.2±0.5ms     0.86  index_object.SetOperations.time_operation('strings', 'intersection')
-         179±3ms          150±2ms     0.84  index_object.Indexing.time_get_loc_non_unique('String')
-      32.0±0.5ms       26.4±0.5ms     0.82  index_object.SetOperations.time_operation('date_string', 'symmetric_difference')

SOME BENCHMARKS HAVE CHANGED SIGNIFICANTLY.
```

The patch is slightly bigger than I would like, but one has to change everything at once in order not to get inconsistencies. In the end it was not as much work as expected to unmangle NA-values for object-type:

   1. Don't mangle NA-values in the hash-map and in the Base-Index
   2. Coarse NA-values to nans in Numeric-Index (to keep the current behavior), which probably makes sense.

There are probably still some hiccups, but at least the test suite doesn't show anything. @jreback pinging you to ask, whether you are Ok with the result of the performance test suite, or maybe I didn't understand your request correctly?

Btw. do I have to retrigger the CI, because there are some errors but unrelated to my changes? Hello @realead! Thanks for updating the PR.

 - There are no PEP8 issues in the file [`pandas/core/indexes/base.py`](https://github.com/realead/pandas/blob/a60864448dfa29257914c6a3faa2dbcb888f6974/pandas/core/indexes/base.py) !

 - There are no PEP8 issues in the file [`pandas/core/indexes/numeric.py`](https://github.com/realead/pandas/blob/a60864448dfa29257914c6a3faa2dbcb888f6974/pandas/core/indexes/numeric.py) !

 - There are no PEP8 issues in the file [`pandas/tests/indexes/test_base.py`](https://github.com/realead/pandas/blob/a60864448dfa29257914c6a3faa2dbcb888f6974/pandas/tests/indexes/test_base.py) !

 - There are no PEP8 issues in the file [`pandas/tests/test_algos.py`](https://github.com/realead/pandas/blob/a60864448dfa29257914c6a3faa2dbcb888f6974/pandas/tests/test_algos.py) !

 @jreback done & green. @jreback @jorisvandenbossche your remarks are adopted, PTAL. can you rebase @jreback rebased & green. thankks @realead nice!