BUG: Fix rollover handling in json encoding
This is a fix attempt for issue #15716 as well as #15864.

Note that whenever the frac is incremented, there is a chance that its
value may hit the value of pow10.
please add tests for the issue you are fixing. please run ``cpplint``, see here: https://travis-ci.org/pandas-dev/pandas/jobs/217690469 # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=h1) Report
> Merging [#15865](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/d1e1ba08ef259724ba71e0953c52e8e4ad81bd17?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `n/a`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/15865/graphs/tree.svg?token=eZ4WkYLtcO&width=650&src=pr&height=150)](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #15865      +/-   ##
==========================================
- Coverage   90.98%   90.97%   -0.02%     
==========================================
  Files         143      143              
  Lines       49449    49449              
==========================================
- Hits        44993    44984       -9     
- Misses       4456     4465       +9
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `88.72% <ø> (ø)` | :arrow_up: |
| #single | `40.65% <ø> (-0.11%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.56% <0%> (-0.1%)` | :arrow_down: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15865?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/15865?src=pr&el=footer). Last update [d1e1ba0...75effb4](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments). # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=h1) Report
> Merging [#15865](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/d1e1ba08ef259724ba71e0953c52e8e4ad81bd17?src=pr&el=desc) will **decrease** coverage by `0.01%`.
> The diff coverage is `n/a`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/15865/graphs/tree.svg?src=pr&token=eZ4WkYLtcO&width=650&height=150)](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #15865      +/-   ##
==========================================
- Coverage   90.98%   90.97%   -0.02%     
==========================================
  Files         143      143              
  Lines       49449    49479      +30     
==========================================
+ Hits        44993    45012      +19     
- Misses       4456     4467      +11
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `88.73% <ø> (ø)` | :arrow_up: |
| #single | `40.63% <ø> (-0.13%)` | :arrow_down: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/io/gbq.py](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree#diff-cGFuZGFzL2lvL2dicS5weQ==) | `25% <0%> (-58.34%)` | :arrow_down: |
| [pandas/core/frame.py](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZnJhbWUucHk=) | `97.56% <0%> (-0.1%)` | :arrow_down: |
| [pandas/\_version.py](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree#diff-cGFuZGFzL192ZXJzaW9uLnB5) | `44.65% <0%> (ø)` | :arrow_up: |
| [pandas/tseries/common.py](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvY29tbW9uLnB5) | `88.09% <0%> (ø)` | :arrow_up: |
| [pandas/tseries/tdi.py](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvdGRpLnB5) | `90.37% <0%> (+0.03%)` | :arrow_up: |
| [pandas/tseries/tools.py](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvdG9vbHMucHk=) | `85.55% <0%> (+0.61%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/15865?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/15865?src=pr&el=footer). Last update [d1e1ba0...c9710ee](https://codecov.io/gh/pandas-dev/pandas/pull/15865?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments). Please take a look at the new commits where compliance to cpplinter is considered and tests are added.

If the commits are OK, I will try to squash them into one as requested in documentation.

Since I am rather green in terms of contributing to open-source project, thanks for being patient with me. can you also add the examples from both issues (you can put in test_pandas) you don't need to squash, will do that on merging.

also pls add a whatsnew note (bug fix section / I/O), you can list both issues. Whatsnew entry and more tests are added. Thanks for your kind guidance. thanks @funnycrab very nice PR!

keep em coming! Thank you! This is my pleasure. Will try to keep'em coming. : > @funnycrab 

we have daily dev builds that also test 32-bit. see [here](https://travis-ci.org/MacPython/pandas-wheels), these are on linux.

here is an 3.6/32 that fails a couple of tests: https://travis-ci.org/MacPython/pandas-wheels/jobs/218273011

I don't have an easy way to actually test / debug this. but any thoughts on how to fix? welcome to have you push a PR (once it passes main pandas we can merge and 'see' if it passes here). @jreback 

After check with [this](https://travis-ci.org/MacPython/pandas-wheels/jobs/218273008#L2381) and [that](https://travis-ci.org/MacPython/pandas-wheels/jobs/218273011#L2575), if I understand correctly, the test fails on both 32-bit version of Python (2.7 and 3.6). And in both cases, the operating systems are all 64-bit version of Linux, right?

My hunch is this has something to do with the floating-point operation, maybe the conversion of Decimal object to float object is handled differently in 32-bit and 64-bit version of Python. Though I have basic understanding in how floating point is typically handled in memory and the relevant IEEE 754 standard, I have never gone this far in Python. I am willing to try to find the reason, just may I ask how I can reproduce this bug first? I have a machine running Ubuntu 16.04 64-bit OS and anaconda Python. But it seems I failed to install 32-bit version Python environment with anaconda. I followed this [solution](http://stackoverflow.com/questions/33709391/using-multiple-python-engines-32bit-64bit-and-2-7-3-5) in the attempt.
 you need to install 32-bit linux (which is not that common, but for now we support it).
then install miniconda

you can use the docker image thats in the repo (or I image some are out there find via google).
its unfortunately a PITA to actually do this (which is why I would suggest following the repo construction exactly).

There *might* be a free web service out there were you can just get a virtual box already setup for this

lmk - we can skip these tests, but ideally like to figure it out. @jreback 

I managed to set up a AWS instance to reproduce the bug and the following are my findings.
The AMI ID of the instance is **ubuntu/images/ebs/ubuntu-trusty-14.04-i386-server-20161213 (ami-01f84d61)**. The python is anaconda Python 3.6.1.

Say we take the failed test case as example (actually all the newly added test cases should fail on 32-bit Linux),
```python
pd.DataFrame([dict(a_float=0.95)]).to_json(double_precision=1)
```

On 32-bit Linux, the intermediate variables around [here](https://github.com/pandas-dev/pandas/blob/master/pandas/_libs/src/ujson/lib/ultrajsonenc.c#L817) have the following values ,
```c
    ...
    pow10 = g_pow10[enc->doublePrecision];

    whole = (unsigned long long)value;
    tmp = (value - whole) * pow10;
    frac = (unsigned long long)(tmp);
    diff = tmp - frac;

    // output 0.9499999999999999555910790149937383830547
    printf("value-whole is %.40f\n", value-whole);
    
    // output 9.5000000000000000000000000000000000000000
    printf("value*pow10 is %.40f\n", value*pow10);
    
    // output 0.5000000000000000000000000000000000000000
    printf("value*pow10-frac is %.40f\n", value*pow10-frac);

    // output 0.4999999999999995559107901499373838305473
    printf("(value-whole)*pow10-frac is %.40f\n", (value-whole)*pow10-frac);
    
    // output 9.5000000000000000000000000000000000000000
    printf("(value - whole)*pow10 is %.40f\n", (value-whole)*pow10);
    
    // output 0.9499999999999999555910790149937383830547
    printf("value %.40f\n", value);
    
    // output 10.00
    printf("pow10 %.2f\n", pow10);
    
    // output 0
    printf("whole %llu\n", whole);
    
    // output 9.5000000000000000000000000000000000000000
    printf("tmp %.40f\n", tmp);

    // output 9
    printf("frac %llu\n", frac);

    // output 9.0000000000000000000000000000000000000000
    printf("frac (convert to double) %.40f\n", (double)frac);

    // output 0.4999999999999995559107901499373838305473
    printf("diff %.40f\n", diff);

    if (diff > 0.5) {
        ++frac;
    } else if (diff == 0.5 && ((frac == 0) || (frac & 1))) {
        /* if halfway, round up if odd, OR
        if last digit is 0.  That last part is strange */
        ++frac;
    }
    ...
```

However, on 64-bit Linux,
```c
    ...
    pow10 = g_pow10[enc->doublePrecision];

    whole = (unsigned long long)value;
    tmp = (value - whole) * pow10;
    frac = (unsigned long long)(tmp);
    diff = tmp - frac;

    // output 0.9499999999999999555910790149937383830547
    printf("value-whole is %.40f\n", value-whole);
    
    // output 9.5000000000000000000000000000000000000000
    printf("value*pow10 is %.40f\n", value*pow10);
    
    // output 0.5000000000000000000000000000000000000000
    printf("value*pow10-frac is %.40f\n", value*pow10-frac);

    // output 0.5000000000000000000000000000000000000000
    printf("(value-whole)*pow10-frac is %.40f\n", (value-whole)*pow10-frac);
    
    // output 9.5000000000000000000000000000000000000000
    printf("(value - whole)*pow10 is %.40f\n", (value-whole)*pow10);
    
    // output 0.9499999999999999555910790149937383830547
    printf("value %.40f\n", value);
    
    // output 10.00
    printf("pow10 %.2f\n", pow10);
    
    // output 0
    printf("whole %llu\n", whole);
    
    // output 9.5000000000000000000000000000000000000000
    printf("tmp %.40f\n", tmp);

    // output 9
    printf("frac %llu\n", frac);

    // output 9.0000000000000000000000000000000000000000
    printf("frac (convert to double) %.40f\n", (double)frac);

    // output 0.5000000000000000000000000000000000000000
    printf("diff %.40f\n", diff);

    if (diff > 0.5) {
        ++frac;
    } else if (diff == 0.5 && ((frac == 0) || (frac & 1))) {
        /* if halfway, round up if odd, OR
        if last digit is 0.  That last part is strange */
        ++frac;
    }
    ...
```

And I would like to bring your attention to the following two lines of code and their outputs,
32-bit Linux
```c
    // output 0.5000000000000000000000000000000000000000
    printf("value*pow10-frac is %.40f\n", value*pow10-frac);

    // output 0.4999999999999995559107901499373838305473
    printf("(value-whole)*pow10-frac is %.40f\n", (value-whole)*pow10-frac);
```
64-bit Linux
```c
    // output 0.5000000000000000000000000000000000000000
    printf("value*pow10-frac is %.40f\n", value*pow10-frac);

    // output 0.5000000000000000000000000000000000000000
    printf("(value-whole)*pow10-frac is %.40f\n", (value-whole)*pow10-frac);
```

Since **whole** is **0** in this case, mathematically, expression **value\*pow10-frac** and **(value-whole)\*pow10-frac** should yield exactly the same result which is not the case on 32-bit Linux. In this sense, the result produced on 32-bit Linux is kind of strange, maybe the compiler does some optimization which change the order of the evaluation and thus different rounding?

Also, even on 64-bit Linux, the two expressions give the same result, I find it difficult to understand. Since the original **value** is **0.9499999999999999555910790149937383830547**, based on what rule does the code know that it should round the value of expression **value*pow10** to **9.5000000000000000000000000000000000000000** instead of **9.4999999999999995559107901499373838305470**. Maybe it is due to the fact that the _significand_ part has reached some upper limit?

Since I don't know the exact reason, I choose not to temper with the code before you kindly shed some light on this. 

Thank you! so ``value`` and ``pow10`` are ``double``, while ``whole`` and ``frac`` are ``unsigned long long``.

maybe some casting e.g. ``value-whole`` needs a cast on whole? maybe if its explicit it will help? Yes, ```value``` and ```pow10``` are ```double```, while ```whole``` and ```frac``` are ```unsigned long long```.

Tried following, no luck.
```c
// output
// (value - (double)(whole))*pow10-frac is 0.4999999999999995559107901499373838305473
printf("(value - (double)(whole))*pow10-frac is %.40f\n", (value-(double)(whole))*pow10-frac);
```
And I believe when the data types of the two operands are different, the implicit cast should be done automatically. 

Also, I checked the size of the *unsigned long long* and *double* on 32-bit Linux, quite normal
```c
// output
// size of unsigned long long is 8
printf("size of unsigned long long is %d\n", sizeof(unsigned long long));

// output
// size of double is 8
printf("size of double is %d\n", sizeof(double));
``` https://github.com/pandas-dev/pandas/pull/15922

skipping these. (please feel free to keep digging if you want). though more interested if you want to solve other issues :>