Some groups of added/deleted lines in diffs can be slid up or down,
because lines at the edges of the group are not unique. Picking good
shifts for such groups is not a matter of correctness but definitely has
a big effect on aesthetics. For example, consider the following two
diffs. The first is what standard Git emits:

    --- a/9c572b21dd090a1e5c5bb397053bf8043ffe7fb4:git-send-email.perl
    +++ b/6dcfa306f2b67b733a7eb2d7ded1bc9987809edb:git-send-email.perl
    @@ -231,6 +231,9 @@ if (!defined $initial_reply_to && $prompting) {
     }

     if (!$smtp_server) {
    +       $smtp_server = $repo->config('sendemail.smtpserver');
    +}
    +if (!$smtp_server) {
            foreach (qw( /usr/sbin/sendmail /usr/lib/sendmail )) {
                    if (-x $_) {
                            $smtp_server = $_;

The following diff is equivalent, but is obviously preferable from an
aesthetic point of view:

    --- a/9c572b21dd090a1e5c5bb397053bf8043ffe7fb4:git-send-email.perl
    +++ b/6dcfa306f2b67b733a7eb2d7ded1bc9987809edb:git-send-email.perl
    @@ -230,6 +230,9 @@ if (!defined $initial_reply_to && $prompting) {
            $initial_reply_to =~ s/(^\s+|\s+$)//g;
     }

    +if (!$smtp_server) {
    +       $smtp_server = $repo->config('sendemail.smtpserver');
    +}
     if (!$smtp_server) {
            foreach (qw( /usr/sbin/sendmail /usr/lib/sendmail )) {
                    if (-x $_) {

This patch teaches Git to pick better positions for such "diff sliders"
using heuristics that take the positions of nearby blank lines and the
indentation of nearby lines into account.

The existing Git code basically always shifts such "sliders" as far down
in the file as possible. The only exception is when the slider can be
aligned with a group of changed lines in the other file, in which case
Git favors depicting the change as one add+delete block rather than one
add and a slightly offset delete block. This naive algorithm often
yields ugly diffs.

Commit d634d61ed6 improved the situation somewhat by preferring to
position add/delete groups to make their last line a blank line, when
that is possible. This heuristic does more good than harm, but (1) it
can only help if there are blank lines in the right places, and (2)
always picks the last blank line, even if there are others that might be
better. The end result is that it makes perhaps 1/3 as many errors as
the default Git algorithm, but that still leaves a lot of ugly diffs.

This commit implements a new and much better heuristic for picking
optimal "slider" positions using the following approach: First observe
that each hypothetical positioning of a diff slider introduces two
splits: one between the context lines preceding the group and the first
added/deleted line, and the other between the last added/deleted line
and the first line of context following it. It tries to find the
positioning that creates the least bad splits.

Splits are evaluated based only on the presence and locations of nearby
blank lines, and the indentation of lines near the split. Basically, it
prefers to introduce splits adjacent to blank lines, between lines that
are indented less, and between lines with the same level of indentation.
In more detail:

1. It measures the following characteristics of a proposed splitting
   position in a `struct split_measurement`:

   * the number of blank lines above the proposed split
   * whether the line directly after the split is blank
   * the number of blank lines following that line
   * the indentation of the nearest non-blank line above the split
   * the indentation of the line directly below the split
   * the indentation of the nearest non-blank line after that line

2. It combines the measured attributes using a bunch of
   empirically-optimized weighting factors to derive a `struct
   split_score` that measures the "badness" of splitting the text at
   that position.

3. It combines the `split_score` for the top and the bottom of the
   slider at each of its possible positions, and selects the position
   that has the best `split_score`.

I determined the initial set of weighting factors by collecting a corpus
of Git histories from 29 open-source software projects in various
programming languages. I generated many diffs from this corpus, and
determined the best positioning "by eye" for about 6600 diff sliders. I
used about half of the repositories in the corpus (corresponding to
about 2/3 of the sliders) as a training set, and optimized the weights
against this corpus using a crude automated search of the parameter
space to get the best agreement with the manually-determined values.
Then I tested the resulting heuristic against the full corpus. The
results are summarized in the following table, in column `indent-1`:

| repository            | count |      Git 2.9.0 |     compaction | compaction-fixed |       indent-1 |       indent-2 |
| --------------------- | ----- | -------------- | -------------- | ---------------- | -------------- | -------------- |
| afnetworking          |   109 |    89  (81.7%) |    37  (33.9%) |      37  (33.9%) |     2   (1.8%) |     2   (1.8%) |
| alamofire             |    30 |    18  (60.0%) |    14  (46.7%) |      15  (50.0%) |     0   (0.0%) |     0   (0.0%) |
| angular               |   184 |   127  (69.0%) |    39  (21.2%) |      23  (12.5%) |     5   (2.7%) |     5   (2.7%) |
| animate               |   313 |     2   (0.6%) |     2   (0.6%) |       2   (0.6%) |     2   (0.6%) |     2   (0.6%) |
| ant                   |   380 |   356  (93.7%) |   152  (40.0%) |     148  (38.9%) |    15   (3.9%) |    15   (3.9%) | *
| bugzilla              |   306 |   263  (85.9%) |   109  (35.6%) |      99  (32.4%) |    14   (4.6%) |    15   (4.9%) | *
| corefx                |   126 |    91  (72.2%) |    22  (17.5%) |      21  (16.7%) |     6   (4.8%) |     6   (4.8%) |
| couchdb               |    78 |    44  (56.4%) |    26  (33.3%) |      28  (35.9%) |     6   (7.7%) |     6   (7.7%) | *
| cpython               |   937 |   158  (16.9%) |    50   (5.3%) |      49   (5.2%) |     5   (0.5%) |     5   (0.5%) | *
| discourse             |   160 |    95  (59.4%) |    42  (26.2%) |      36  (22.5%) |    18  (11.2%) |    13   (8.1%) |
| docker                |   307 |   194  (63.2%) |   198  (64.5%) |     253  (82.4%) |     8   (2.6%) |     8   (2.6%) | *
| electron              |   163 |   132  (81.0%) |    38  (23.3%) |      39  (23.9%) |     6   (3.7%) |     6   (3.7%) |
| git                   |   536 |   470  (87.7%) |    73  (13.6%) |      78  (14.6%) |    16   (3.0%) |    16   (3.0%) | *
| gitflow               |   127 |     0   (0.0%) |     0   (0.0%) |       0   (0.0%) |     0   (0.0%) |     0   (0.0%) |
| ionic                 |   133 |    89  (66.9%) |    29  (21.8%) |      38  (28.6%) |     1   (0.8%) |     1   (0.8%) |
| ipython               |   482 |   362  (75.1%) |   167  (34.6%) |     169  (35.1%) |    11   (2.3%) |    11   (2.3%) | *
| junit                 |   161 |   147  (91.3%) |    67  (41.6%) |      66  (41.0%) |     1   (0.6%) |     1   (0.6%) | *
| lighttable            |    15 |     5  (33.3%) |     0   (0.0%) |       2  (13.3%) |     0   (0.0%) |     0   (0.0%) |
| magit                 |    88 |    75  (85.2%) |    11  (12.5%) |       9  (10.2%) |     1   (1.1%) |     0   (0.0%) |
| neural-style          |    28 |     0   (0.0%) |     0   (0.0%) |       0   (0.0%) |     0   (0.0%) |     0   (0.0%) |
| nodejs                |   781 |   649  (83.1%) |   118  (15.1%) |     111  (14.2%) |     4   (0.5%) |     5   (0.6%) | *
| phpmyadmin            |   491 |   481  (98.0%) |    75  (15.3%) |      48   (9.8%) |     2   (0.4%) |     2   (0.4%) | *
| react-native          |   168 |   130  (77.4%) |    79  (47.0%) |      81  (48.2%) |     0   (0.0%) |     0   (0.0%) |
| rust                  |   171 |   128  (74.9%) |    30  (17.5%) |      27  (15.8%) |    16   (9.4%) |    14   (8.2%) |
| spark                 |   186 |   149  (80.1%) |    52  (28.0%) |      52  (28.0%) |     2   (1.1%) |     2   (1.1%) |
| tensorflow            |   115 |    66  (57.4%) |    48  (41.7%) |      48  (41.7%) |     5   (4.3%) |     5   (4.3%) |
| test-more             |    19 |    15  (78.9%) |     2  (10.5%) |       2  (10.5%) |     1   (5.3%) |     1   (5.3%) | *
| test-unit             |    51 |    34  (66.7%) |    14  (27.5%) |       8  (15.7%) |     2   (3.9%) |     2   (3.9%) | *
| xmonad                |    23 |    22  (95.7%) |     2   (8.7%) |       2   (8.7%) |     1   (4.3%) |     1   (4.3%) | *
| --------------------- | ----- | -------------- | -------------- | ---------------- | -------------- | -------------- |
| totals                |  6668 |  4391  (65.9%) |  1496  (22.4%) |    1491  (22.4%) |   150   (2.2%) |   144   (2.2%) |
| totals (training set) |  4552 |  3195  (70.2%) |  1053  (23.1%) |    1061  (23.3%) |    86   (1.9%) |    88   (1.9%) |
| totals (test set)     |  2116 |  1196  (56.5%) |   443  (20.9%) |     430  (20.3%) |    64   (3.0%) |    56   (2.6%) |

In this table, the numbers are the count and percentage of human-rated
sliders that the corresponding algorithm got *wrong*. The columns are

* "repository" - the name of the repository used. I used the diffs
  between successive non-merge commits on the HEAD branch of the
  corresponding repository.

* "count" - the number of sliders that were human-rated. I chose most,
  but not all, sliders to rate from those among which the various
  algorithms gave different answers.

* "Git 2.9.0" - the default algorithm used by `git diff` in Git 2.9.0.

* "compaction" - the heuristic used by `git diff --compaction-heuristic`
  in Git 2.9.0.

* "compaction-fixed" - the heuristic used by `git diff
  --compaction-heuristic` after the fixes from earlier in this patch
  series. Note that the results are not dramatically different than
  those for "compaction". Both produce non-ideal diffs only about 1/3 as
  often as the default `git diff`.

* "indent-1" - the new `--indent-heuristic` algorithm, using the first
  set of weighting factors, determined as described above.

* "indent-2" - the new `--indent-heuristic` algorithm, using the final
  set of weighting factors, determined as described below.

* `*` - indicates that repo was part of training set used to determine
  the first set of weighting factors.

The fact that the heuristic performed nearly as well on the test set as
on the training set in column "indent-1" is a good indication that the
heuristic was not over-trained. Given that fact, I ran a second round of
optimization, using the entire corpus as the training set. The resulting
set of weights gave the results in column "indent-2". These are the
weights included in this patch.

The final result gives consistently and significantly better results
across the whole corpus than either `git diff` or `git diff
--compaction-heuristic`. It makes only about 1/30 as many errors as the
former and about 1/10 as many errors as the latter. (And a good fraction
of the remaining errors are for diffs that involve weirdly-formatted
code, sometimes apparently machine-generated.)

The tools that were used to do this optimization and analysis, along
with the human-generated data values, are recorded in a separate project
[1].

[1] https://github.com/mhagger/diff-slider-tools

Original Git commit: 433860f3d0beb0c6f205290bd16cda413148f098