Docstrings, de-duplicate EAMixin/DatetimeLikeIndex __new__ code
State: closed

There's a lot of duplication in the constructors and constructor-helpers.  This starts to whittle that down, writes some docstrings long the way.

Also use `ExtensionOpsMixin` to define comparison operators on the EAMixin classes.

We determined that the DatetimeIndex._local_timestamps method had an unecessary monotonicy check, so took that out.

Labels:
name: Clean
name: ExtensionArray
description: Extending pandas with custom dtypes or arrays.

Comments:
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21926?src=pr&el=h1) Report
> Merging [#21926](https://codecov.io/gh/pandas-dev/pandas/pull/21926?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/537b65cb0fd2aa318e089c5e38f09e81d1a3fe35?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `95.65%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/21926/graphs/tree.svg?height=150&token=eZ4WkYLtcO&width=650&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/21926?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #21926      +/-   ##
==========================================
+ Coverage   91.96%   91.97%   +<.01%     
==========================================
  Files         166      166              
  Lines       50329    50297      -32     
==========================================
- Hits        46287    46261      -26     
+ Misses       4042     4036       -6
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.37% <95.65%> (ø)` | :arrow_up: |
| #single | `42.24% <72.82%> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/21926?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/arrays/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2Jhc2UucHk=) | `87.85% <ø> (ø)` | :arrow_up: |
| [pandas/core/indexes/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy90aW1lZGVsdGFzLnB5) | `91.39% <100%> (-0.14%)` | :arrow_down: |
| [pandas/core/arrays/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3BlcmlvZC5weQ==) | `91.18% <100%> (-0.17%)` | :arrow_down: |
| [pandas/tseries/frequencies.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvZnJlcXVlbmNpZXMucHk=) | `95.9% <100%> (ø)` | :arrow_up: |
| [pandas/core/arrays/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lcy5weQ==) | `96.3% <100%> (+0.17%)` | :arrow_up: |
| [pandas/core/indexes/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZWxpa2UucHk=) | `97.34% <100%> (-0.02%)` | :arrow_down: |
| [pandas/core/indexes/datetimes.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9kYXRldGltZXMucHk=) | `95.12% <100%> (-0.05%)` | :arrow_down: |
| [pandas/core/indexes/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9wZXJpb2QucHk=) | `93.2% <100%> (ø)` | :arrow_up: |
| [pandas/core/arrays/timedeltas.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3RpbWVkZWx0YXMucHk=) | `91.75% <72.72%> (+1.91%)` | :arrow_up: |
| [pandas/core/arrays/datetimelike.py](https://codecov.io/gh/pandas-dev/pandas/pull/21926/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL2RhdGV0aW1lbGlrZS5weQ==) | `94.48% <97.43%> (+0.41%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21926?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/21926?src=pr&el=footer). Last update [537b65c...6eb2f8b](https://codecov.io/gh/pandas-dev/pandas/pull/21926?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).

Thoughts?  The next step here is to deal with cached_range issues.
@jreback since we're on a roll I'd like to push this through, get started on the next steps over the weekend.  Thoughts?
sure. my comments were minor.