API: consistency with .ix and .loc for getitem operations (GH8613)
closes #8613 

```
In [1]:      df = DataFrame(np.random.randn(5,4), columns=list('ABCD'), index=date_range('20130101',periods=5))

In [2]:      df
Out[2]: 
                   A         B         C         D
2013-01-01 -1.380065  1.221596  0.279703 -0.119258
2013-01-02  1.684202 -0.202251 -0.961145 -1.595015
2013-01-03 -0.623634 -2.377577 -3.024554 -0.298809
2013-01-04 -1.251699  0.456356  1.257002  1.465878
2013-01-05  0.687818 -2.125079  1.454911  1.914207

In [5]:      s = Series(range(5),[-2,-1,1,2,3])

In [6]:      s
Out[6]: 
-2    0
-1    1
 1    2
 2    3
 3    4
dtype: int64

In [7]:      df.loc['2013-01-02':'2013-01-10']
Out[7]: 
                   A         B         C         D
2013-01-02  1.684202 -0.202251 -0.961145 -1.595015
2013-01-03 -0.623634 -2.377577 -3.024554 -0.298809
2013-01-04 -1.251699  0.456356  1.257002  1.465878
2013-01-05  0.687818 -2.125079  1.454911  1.914207

In [9]:      s.loc[-10:3]
Out[9]: 
-2    0
-1    1
 1    2
 2    3
 3    4
dtype: int64
```

```
# this used to be a KeyError
In [15]: df.loc[2:3]
TypeError: Cannot index datetime64 with <type 'int'> keys
```

Slicing with float indexers; now works for ix (loc worked before)

```
In [3]: s.loc[-1.0:2]
Out[3]: 
-1    1
 1    2
 2    3
dtype: int64

In [4]: s.ix[-1.0:2]
Out[4]: 
-1    1
 1    2
 2    3
dtype: int64

# [] raises
In [5]: s[-1.0:2]
TypeError: cannot do slice start value indexing on <class 'pandas.core.index.Int64Index'> with these indexers [-1.0] of <type 'float'>
```

cc @immerrr 
@jorisvandenbossche 
@shoyer 

I think this should resolve things and make `.loc` strict, while matching `.ix` (notably in that `.ix` tries for positional access when it _can_, but `.loc` will refuse to guess).
 First of all, big thanks for working on this, @jreback!

However, I don't think we need to enforce distinctions between float and int for slice bounds, because there is no ambiguity in the ordering between integers and floats (whereas the ordering with respect to strings, for example, is indeed problematic). Users shouldn't have to check the type of their index (if they know it's numeric) before doing indexing.

In particular:
1. I think it should be OK to index an `Int64Index` with floats, like `.loc[0.5:2.5]` or `.loc[-1.0:2]`.
2. I think it should be OK to index a `Float64Index` with integers, like `.loc[0:10]`. (Of course, these are still to be interpreted as labels, not integer positions)

The binary search logic for determining slice bound locations should already work for both of these cases.
 To give a more concrete example from my experience: an index corresponding to a variable like `longitude` might variously consist of integer (e.g., if it's in multiples of whole degrees) or as floating point numbers (e.g., if it's in multiples of half degrees). It's a bad user experience to need to cast their slice bounds to the type of index. Code like `s.loc[min_lon:max_lon]` should work regardless of dtypes.
 @shoyer 

I added in these checks, mainly because numpy is deprecating float indexers (IIRC it has a warning now), and we have been warning on it.

Its easy to take out, but I think that indexing with a float on an integer index is really not in the `.loc` domain. This is moving back to the `.ix` functionaility (which actually doesn't work in 0.15.2 or atm), though `.loc` did (which is odd).

though it IS convenient. 

currently we don't allow this for `[],.ix` (but allow for `.loc` in 0.15.2.

simple example from 0.15.2

```
In [1]: s = Series(range(5))

In [2]: s[1.5:3]
TypeError: the slice start value [1.5] is not a proper indexer for this index type (Int64Index)

In [3]: s.ix[1.5:3]
TypeError: the slice start value [1.5] is not a proper indexer for this index type (Int64Index)

In [4]: s.loc[1.5:3]
Out[4]: 
2    2
3    3
dtype: int64
```

These all fail  with
`TypeError: cannot do slice start value indexing on <class 'pandas.core.index.Int64Index'> with these indexers [1.5] of <type 'float'>` in master/0.16.0
 @jorisvandenbossche what do you think?
 I agree that using float indexers is a based idea for _position_ based indexing (`.iloc`). Position based indexing should always use integers. We should be consistent with numpy for this.

But indexing with `.loc` uses _labels_. Here (e.g., with `searchsorted`), numpy is more flexible -- the important thing is that there is a well defined sort order.
 this should then also work for `.ix/[]`? 
 To elaborate:

There is never a good reason to use floats for position based indexing. Numpy warns and/or raises because using a float is an indication that your code probably has a bug.

In contrast, there certainly are good reasons to use floats for label based indexing, because the labels might include floats themselves (or might not, depending on dtypes).
 `.ix` and `[]` are an unpredictable mess! We hadn't even written down the rules for exactly how indexing with `[]` works last time I checked.

If I had my way, we would make some hard choices and deprecate/remove fall-back indexing all together (#9213). In the mean-time, I suspect the best approach is to simply try to break/change as little existing code as possible.
 ok, [here](https://github.com/pydata/pandas/commit/4f761995b1231fb55577a681b48a9ad6d3b4e827) is the change (plus making some testing more robust)

```
In [3]:  index = tm.makeIntIndex()
In [4]:  s = Series(np.arange(len(index))+10,index+5)
In [5]: s
Out[5]: 
5     10
6     11
7     12
8     13
9     14
10    15
11    16
12    17
13    18
14    19
dtype: int64

In [6]: s.loc[6.0:8.5]
Out[6]: 
6    11
7    12
8    13
dtype: int64

In [7]: s.loc[5.5:8.5]
Out[7]: 
6    11
7    12
8    13
dtype: int64

In [8]: s.loc[5.5:8.0]
Out[8]: 
6    11
7    12
8    13
dtype: int64
```

I _could_ enable for `[]/ix`, but then would `s[5.0:8.0]` become a fallback scenario (yes I think)
so what would `s[5.5,8.5]` do (non-fallback I think), so they become very sensitive to the actual values, hence bad
 I agree with the logic of allowing float indexers for integer indexes _when using `loc`_ (so as you now implemented)

Ideally, I think it should also work for `ix` (to keep `ix` as much as possible to the logic of `try: s.loc[]; except: s.iloc[]`. In principle , we say that for an integer index axis, we do _never_ integer location fallback (http://pandas.pydata.org/pandas-docs/stable/indexing.html#different-choices-for-indexing), so following the `loc` behaviour should not be ambiguous in this case I think.

For `[]`, it is something else. For that, we should first have a better documented overview of it behaviour (I started with that last week, will try to put it up as a PR)
 ok, I added the .ix support for float indexers on an Int index. It is trivial to make this work for `[]`. I am thinking that this should have the same semantics as `.ix` (e.g. label based with an int index). It works the same.
 But for `[]` slicing is 'integer-location' based (an exception on the other types of slicing), so this should follow the semantics of `iloc` in this case, disallowing floats.
 Example:

```
In [46]: s = Series(range(4), index=[-1,0,1,2])

In [47]: s
Out[47]:
-1    0
 0    1
 1    2
 2    3
dtype: int64

In [48]: s[0:2]    # <--- slicing = integer location based
Out[48]:
-1    0
 0    1
dtype: int64

In [49]: s[0]    # <--- single label = label based
Out[49]: 1
```
 ok, is updated, any more comments
@jorisvandenbossche @shoyer 
 Generally seems fine by me.
 indexing is such a rabbit hole :)

I cleaned up `_convert_slice_indexer` a bit. I tried to use `_maybe_cast_slice_bound` directly there (I added the `kind` argument which is the type of indexing, e.g. `ix/loc/iloc/getitem`). But so many cases are handled that its really hard to get this right. Because the different kinds are handled in different places 

its tricky because you have the kinds of indexers (ix/loc/iloc/getitem) x index_types (Index,Float,Int,Datetime....) x kinds of indexing (slice/scalar)

So its _better_  (meaning slightly cleaner), with the semantics we discussed above.
 Thanks a lot for this!
 Indeed, greatly appreciated!
 That's great that you guys (and especially @jreback) actually went through this :+1: 
 trying to make indexing slightly less of a rabbit hole :)
