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+Fighting regressions with git bisect
+====================================
+:Author: Christian Couder
+:Email: chriscool@tuxfamily.org
+:Date: 2009/11/08
+
+Abstract
+--------
+
+"git bisect" enables software users and developers to easily find the
+commit that introduced a regression. We show why it is important to
+have good tools to fight regressions. We describe how "git bisect"
+works from the outside and the algorithms it uses inside. Then we
+explain how to take advantage of "git bisect" to improve current
+practices. And we discuss how "git bisect" could improve in the
+future.
+
+
+Introduction to "git bisect"
+----------------------------
+
+Git is a Distributed Version Control system (DVCS) created by Linus
+Torvalds and maintained by Junio Hamano.
+
+In Git like in many other Version Control Systems (VCS), the different
+states of the data that is managed by the system are called
+commits. And, as VCS are mostly used to manage software source code,
+sometimes "interesting" changes of behavior in the software are
+introduced in some commits.
+
+In fact people are specially interested in commits that introduce a
+"bad" behavior, called a bug or a regression. They are interested in
+these commits because a commit (hopefully) contains a very small set
+of source code changes. And it's much easier to understand and
+properly fix a problem when you only need to check a very small set of
+changes, than when you don't know where look in the first place.
+
+So to help people find commits that introduce a "bad" behavior, the
+"git bisect" set of commands was invented. And it follows of course
+that in "git bisect" parlance, commits where the "interesting
+behavior" is present are called "bad" commits, while other commits are
+called "good" commits. And a commit that introduce the behavior we are
+interested in is called a "first bad commit". Note that there could be
+more than one "first bad commit" in the commit space we are searching.
+
+So "git bisect" is designed to help find a "first bad commit". And to
+be as efficient as possible, it tries to perform a binary search.
+
+
+Fighting regressions overview
+-----------------------------
+
+Regressions: a big problem
+~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Regressions are a big problem in the software industry. But it's
+difficult to put some real numbers behind that claim.
+
+There are some numbers about bugs in general, like a NIST study in
+2002 <<1>> that said:
+
+_____________
+Software bugs, or errors, are so prevalent and so detrimental that
+they cost the U.S. economy an estimated $59.5 billion annually, or
+about 0.6 percent of the gross domestic product, according to a newly
+released study commissioned by the Department of Commerce's National
+Institute of Standards and Technology (NIST). At the national level,
+over half of the costs are borne by software users and the remainder
+by software developers/vendors.  The study also found that, although
+all errors cannot be removed, more than a third of these costs, or an
+estimated $22.2 billion, could be eliminated by an improved testing
+infrastructure that enables earlier and more effective identification
+and removal of software defects. These are the savings associated with
+finding an increased percentage (but not 100 percent) of errors closer
+to the development stages in which they are introduced. Currently,
+over half of all errors are not found until "downstream" in the
+development process or during post-sale software use.
+_____________
+
+And then:
+
+_____________
+Software developers already spend approximately 80 percent of
+development costs on identifying and correcting defects, and yet few
+products of any type other than software are shipped with such high
+levels of errors.
+_____________
+
+Eventually the conclusion started with:
+
+_____________
+The path to higher software quality is significantly improved software
+testing.
+_____________
+
+There are other estimates saying that 80% of the cost related to
+software is about maintenance <<2>>.
+
+Though, according to Wikipedia <<3>>:
+
+_____________
+A common perception of maintenance is that it is merely fixing
+bugs. However, studies and surveys over the years have indicated that
+the majority, over 80%, of the maintenance effort is used for
+non-corrective actions (Pigosky 1997). This perception is perpetuated
+by users submitting problem reports that in reality are functionality
+enhancements to the system.
+_____________
+
+But we can guess that improving on existing software is very costly
+because you have to watch out for regressions. At least this would
+make the above studies consistent among themselves.
+
+Of course some kind of software is developed, then used during some
+time without being improved on much, and then finally thrown away. In
+this case, of course, regressions may not be a big problem. But on the
+other hand, there is a lot of big software that is continually
+developed and maintained during years or even tens of years by a lot
+of people. And as there are often many people who depend (sometimes
+critically) on such software, regressions are a really big problem.
+
+One such software is the linux kernel. And if we look at the linux
+kernel, we can see that a lot of time and effort is spent to fight
+regressions. The release cycle start with a 2 weeks long merge
+window. Then the first release candidate (rc) version is tagged. And
+after that about 7 or 8 more rc versions will appear with around one
+week between each of them, before the final release.
+
+The time between the first rc release and the final release is
+supposed to be used to test rc versions and fight bugs and especially
+regressions. And this time is more than 80% of the release cycle
+time. But this is not the end of the fight yet, as of course it
+continues after the release.
+
+And then this is what Ingo Molnar (a well known linux kernel
+developer) says about his use of git bisect:
+
+_____________
+I most actively use it during the merge window (when a lot of trees
+get merged upstream and when the influx of bugs is the highest) - and
+yes, there have been cases that i used it multiple times a day. My
+average is roughly once a day.
+_____________
+
+So regressions are fought all the time by developers, and indeed it is
+well known that bugs should be fixed as soon as possible, so as soon
+as they are found. That's why it is interesting to have good tools for
+this purpose.
+
+Other tools to fight regressions
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+So what are the tools used to fight regressions? They are nearly the
+same as those used to fight regular bugs. The only specific tools are
+test suites and tools similar as "git bisect".
+
+Test suites are very nice. But when they are used alone, they are
+supposed to be used so that all the tests are checked after each
+commit. This means that they are not very efficient, because many
+tests are run for no interesting result, and they suffer from
+combinational explosion.
+
+In fact the problem is that big software often has many different
+configuration options and that each test case should pass for each
+configuration after each commit. So if you have for each release: N
+configurations, M commits and T test cases, you should perform:
+
+-------------
+N * M * T tests
+-------------
+
+where N, M and T are all growing with the size your software.
+
+So very soon it will not be possible to completely test everything.
+
+And if some bugs slip through your test suite, then you can add a test
+to your test suite. But if you want to use your new improved test
+suite to find where the bug slipped in, then you will either have to
+emulate a bisection process or you will perhaps bluntly test each
+commit backward starting from the "bad" commit you have which may be
+very wasteful.
+
+"git bisect" overview
+---------------------
+
+Starting a bisection
+~~~~~~~~~~~~~~~~~~~~
+
+The first "git bisect" subcommand to use is "git bisect start" to
+start the search. Then bounds must be set to limit the commit
+space. This is done usually by giving one "bad" and at least one
+"good" commit. They can be passed in the initial call to "git bisect
+start" like this:
+
+-------------
+$ git bisect start [BAD [GOOD...]]
+-------------
+
+or they can be set using:
+
+-------------
+$ git bisect bad [COMMIT]
+-------------
+
+and:
+
+-------------
+$ git bisect good [COMMIT...]
+-------------
+
+where BAD, GOOD and COMMIT are all names that can be resolved to a
+commit.
+
+Then "git bisect" will checkout a commit of its choosing and ask the
+user to test it, like this:
+
+-------------
+$ git bisect start v2.6.27 v2.6.25
+Bisecting: 10928 revisions left to test after this (roughly 14 steps)
+[2ec65f8b89ea003c27ff7723525a2ee335a2b393] x86: clean up using max_low_pfn on 32-bit
+-------------
+
+Note that the example that we will use is really a toy example, we
+will be looking for the first commit that has a version like
+"2.6.26-something", that is the commit that has a "SUBLEVEL = 26" line
+in the top level Makefile. This is a toy example because there are
+better ways to find this commit with git than using "git bisect" (for
+example "git blame" or "git log -S<string>").
+
+Driving a bisection manually
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+At this point there are basically 2 ways to drive the search. It can
+be driven manually by the user or it can be driven automatically by a
+script or a command.
+
+If the user is driving it, then at each step of the search, the user
+will have to test the current commit and say if it is "good" or "bad"
+using the "git bisect good" or "git bisect bad" commands respectively
+that have been described above. For example:
+
+-------------
+$ git bisect bad
+Bisecting: 5480 revisions left to test after this (roughly 13 steps)
+[66c0b394f08fd89236515c1c84485ea712a157be] KVM: kill file->f_count abuse in kvm
+-------------
+
+And after a few more steps like that, "git bisect" will eventually
+find a first bad commit:
+
+-------------
+$ git bisect bad
+2ddcca36c8bcfa251724fe342c8327451988be0d is the first bad commit
+commit 2ddcca36c8bcfa251724fe342c8327451988be0d
+Author: Linus Torvalds <torvalds@linux-foundation.org>
+Date:   Sat May 3 11:59:44 2008 -0700
+
+    Linux 2.6.26-rc1
+
+:100644 100644 5cf8258195331a4dbdddff08b8d68642638eea57 4492984efc09ab72ff6219a7bc21fb6a957c4cd5 M      Makefile
+-------------
+
+At this point we can see what the commit does, check it out (if it's
+not already checked out) or tinker with it, for example:
+
+-------------
+$ git show HEAD
+commit 2ddcca36c8bcfa251724fe342c8327451988be0d
+Author: Linus Torvalds <torvalds@linux-foundation.org>
+Date:   Sat May 3 11:59:44 2008 -0700
+
+    Linux 2.6.26-rc1
+
+diff --git a/Makefile b/Makefile
+index 5cf8258..4492984 100644
+--- a/Makefile
++++ b/Makefile
+@@ -1,7 +1,7 @@
+ VERSION = 2
+ PATCHLEVEL = 6
+-SUBLEVEL = 25
+-EXTRAVERSION =
++SUBLEVEL = 26
++EXTRAVERSION = -rc1
+ NAME = Funky Weasel is Jiggy wit it
+
+ # *DOCUMENTATION*
+-------------
+
+And when we are finished we can use "git bisect reset" to go back to
+the branch we were in before we started bisecting:
+
+-------------
+$ git bisect reset
+Checking out files: 100% (21549/21549), done.
+Previous HEAD position was 2ddcca3... Linux 2.6.26-rc1
+Switched to branch 'master'
+-------------
+
+Driving a bisection automatically
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The other way to drive the bisection process is to tell "git bisect"
+to launch a script or command at each bisection step to know if the
+current commit is "good" or "bad". To do that, we use the "git bisect
+run" command. For example:
+
+-------------
+$ git bisect start v2.6.27 v2.6.25
+Bisecting: 10928 revisions left to test after this (roughly 14 steps)
+[2ec65f8b89ea003c27ff7723525a2ee335a2b393] x86: clean up using max_low_pfn on 32-bit
+$
+$ git bisect run grep '^SUBLEVEL = 25' Makefile
+running grep ^SUBLEVEL = 25 Makefile
+Bisecting: 5480 revisions left to test after this (roughly 13 steps)
+[66c0b394f08fd89236515c1c84485ea712a157be] KVM: kill file->f_count abuse in kvm
+running grep ^SUBLEVEL = 25 Makefile
+SUBLEVEL = 25
+Bisecting: 2740 revisions left to test after this (roughly 12 steps)
+[671294719628f1671faefd4882764886f8ad08cb] V4L/DVB(7879): Adding cx18 Support for mxl5005s
+...
+...
+running grep ^SUBLEVEL = 25 Makefile
+Bisecting: 0 revisions left to test after this (roughly 0 steps)
+[2ddcca36c8bcfa251724fe342c8327451988be0d] Linux 2.6.26-rc1
+running grep ^SUBLEVEL = 25 Makefile
+2ddcca36c8bcfa251724fe342c8327451988be0d is the first bad commit
+commit 2ddcca36c8bcfa251724fe342c8327451988be0d
+Author: Linus Torvalds <torvalds@linux-foundation.org>
+Date:   Sat May 3 11:59:44 2008 -0700
+
+    Linux 2.6.26-rc1
+
+:100644 100644 5cf8258195331a4dbdddff08b8d68642638eea57 4492984efc09ab72ff6219a7bc21fb6a957c4cd5 M      Makefile
+bisect run success
+-------------
+
+In this example, we passed "grep '^SUBLEVEL = 25' Makefile" as
+parameter to "git bisect run". This means that at each step, the grep
+command we passed will be launched. And if it exits with code 0 (that
+means success) then git bisect will mark the current state as
+"good". If it exits with code 1 (or any code between 1 and 127
+included, except the special code 125), then the current state will be
+marked as "bad".
+
+Exit code between 128 and 255 are special to "git bisect run". They
+make it stop immediately the bisection process. This is useful for
+example if the command passed takes too long to complete, because you
+can kill it with a signal and it will stop the bisection process.
+
+It can also be useful in scripts passed to "git bisect run" to "exit
+255" if some very abnormal situation is detected.
+
+Avoiding untestable commits
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Sometimes it happens that the current state cannot be tested, for
+example if it does not compile because there was a bug preventing it
+at that time. This is what the special exit code 125 is for. It tells
+"git bisect run" that the current commit should be marked as
+untestable and that another one should be chosen and checked out.
+
+If the bisection process is driven manually, you can use "git bisect
+skip" to do the same thing. (In fact the special exit code 125 makes
+"git bisect run" use "git bisect skip" in the background.)
+
+Or if you want more control, you can inspect the current state using
+for example "git bisect visualize". It will launch gitk (or "git log"
+if the DISPLAY environment variable is not set) to help you find a
+better bisection point.
+
+Either way, if you have a string of untestable commits, it might
+happen that the regression you are looking for has been introduced by
+one of these untestable commits. In this case it's not possible to
+tell for sure which commit introduced the regression.
+
+So if you used "git bisect skip" (or the run script exited with
+special code 125) you could get a result like this:
+
+-------------
+There are only 'skip'ped commits left to test.
+The first bad commit could be any of:
+15722f2fa328eaba97022898a305ffc8172db6b1
+78e86cf3e850bd755bb71831f42e200626fbd1e0
+e15b73ad3db9b48d7d1ade32f8cd23a751fe0ace
+070eab2303024706f2924822bfec8b9847e4ac1b
+We cannot bisect more!
+-------------
+
+Saving a log and replaying it
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+If you want to show other people your bisection process, you can get a
+log using for example:
+
+-------------
+$ git bisect log > bisect_log.txt
+-------------
+
+And it is possible to replay it using:
+
+-------------
+$ git bisect replay bisect_log.txt
+-------------
+
+
+"git bisect" details
+--------------------
+
+Bisection algorithm
+~~~~~~~~~~~~~~~~~~~
+
+As the Git commits form a directed acyclic graph (DAG), finding the
+best bisection commit to test at each step is not so simple. Anyway
+Linus found and implemented a "truly stupid" algorithm, later improved
+by Junio Hamano, that works quite well.
+
+So the algorithm used by "git bisect" to find the best bisection
+commit when there are no skipped commits is the following:
+
+1) keep only the commits that:
+
+a) are ancestor of the "bad" commit (including the "bad" commit itself),
+b) are not ancestor of a "good" commit (excluding the "good" commits).
+
+This means that we get rid of the uninteresting commits in the DAG.
+
+For example if we start with a graph like this:
+
+-------------
+G-Y-G-W-W-W-X-X-X-X
+	   \ /
+	    W-W-B
+	   /
+Y---G-W---W
+ \ /   \
+Y-Y     X-X-X-X
+
+-> time goes this way ->
+-------------
+
+where B is the "bad" commit, "G" are "good" commits and W, X, and Y
+are other commits, we will get the following graph after this first
+step:
+
+-------------
+W-W-W
+     \
+      W-W-B
+     /
+W---W
+-------------
+
+So only the W and B commits will be kept. Because commits X and Y will
+have been removed by rules a) and b) respectively, and because commits
+G are removed by rule b) too.
+
+Note for git users, that it is equivalent as keeping only the commit
+given by:
+
+-------------
+git rev-list BAD --not GOOD1 GOOD2...
+-------------
+
+Also note that we don't require the commits that are kept to be
+descendants of a "good" commit. So in the following example, commits W
+and Z will be kept:
+
+-------------
+G-W-W-W-B
+   /
+Z-Z
+-------------
+
+2) starting from the "good" ends of the graph, associate to each
+commit the number of ancestors it has plus one
+
+For example with the following graph where H is the "bad" commit and A
+and D are some parents of some "good" commits:
+
+-------------
+A-B-C
+     \
+      F-G-H
+     /
+D---E
+-------------
+
+this will give:
+
+-------------
+1 2 3
+A-B-C
+     \6 7 8
+      F-G-H
+1   2/
+D---E
+-------------
+
+3) associate to each commit: min(X, N - X)
+
+where X is the value associated to the commit in step 2) and N is the
+total number of commits in the graph.
+
+In the above example we have N = 8, so this will give:
+
+-------------
+1 2 3
+A-B-C
+     \2 1 0
+      F-G-H
+1   2/
+D---E
+-------------
+
+4) the best bisection point is the commit with the highest associated
+number
+
+So in the above example the best bisection point is commit C.
+
+5) note that some shortcuts are implemented to speed up the algorithm
+
+As we know N from the beginning, we know that min(X, N - X) can't be
+greater than N/2. So during steps 2) and 3), if we would associate N/2
+to a commit, then we know this is the best bisection point. So in this
+case we can just stop processing any other commit and return the
+current commit.
+
+Bisection algorithm debugging
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+For any commit graph, you can see the number associated with each
+commit using "git rev-list --bisect-all".
+
+For example, for the above graph, a command like:
+
+-------------
+$ git rev-list --bisect-all BAD --not GOOD1 GOOD2
+-------------
+
+would output something like:
+
+-------------
+e15b73ad3db9b48d7d1ade32f8cd23a751fe0ace (dist=3)
+15722f2fa328eaba97022898a305ffc8172db6b1 (dist=2)
+78e86cf3e850bd755bb71831f42e200626fbd1e0 (dist=2)
+a1939d9a142de972094af4dde9a544e577ddef0e (dist=2)
+070eab2303024706f2924822bfec8b9847e4ac1b (dist=1)
+a3864d4f32a3bf5ed177ddef598490a08760b70d (dist=1)
+a41baa717dd74f1180abf55e9341bc7a0bb9d556 (dist=1)
+9e622a6dad403b71c40979743bb9d5be17b16bd6 (dist=0)
+-------------
+
+Bisection algorithm discussed
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+First let's define "best bisection point". We will say that a commit X
+is a best bisection point or a best bisection commit if knowing its
+state ("good" or "bad") gives as much information as possible whether
+the state of the commit happens to be "good" or "bad".
+
+This means that the best bisection commits are the commits where the
+following function is maximum:
+
+-------------
+f(X) = min(information_if_good(X), information_if_bad(X))
+-------------
+
+where information_if_good(X) is the information we get if X is good
+and information_if_bad(X) is the information we get if X is bad.
+
+Now we will suppose that there is only one "first bad commit". This
+means that all its descendants are "bad" and all the other commits are
+"good". And we will suppose that all commits have an equal probability
+of being good or bad, or of being the first bad commit, so knowing the
+state of c commits gives always the same amount of information
+wherever these c commits are on the graph and whatever c is. (So we
+suppose that these commits being for example on a branch or near a
+good or a bad commit does not give more or less information).
+
+Let's also suppose that we have a cleaned up graph like one after step
+1) in the bisection algorithm above. This means that we can measure
+the information we get in terms of number of commit we can remove from
+the graph..
+
+And let's take a commit X in the graph.
+
+If X is found to be "good", then we know that its ancestors are all
+"good", so we want to say that:
+
+-------------
+information_if_good(X) = number_of_ancestors(X)  (TRUE)
+-------------
+
+And this is true because at step 1) b) we remove the ancestors of the
+"good" commits.
+
+If X is found to be "bad", then we know that its descendants are all
+"bad", so we want to say that:
+
+-------------
+information_if_bad(X) = number_of_descendants(X)  (WRONG)
+-------------
+
+But this is wrong because at step 1) a) we keep only the ancestors of
+the bad commit. So we get more information when a commit is marked as
+"bad", because we also know that the ancestors of the previous "bad"
+commit that are not ancestors of the new "bad" commit are not the
+first bad commit. We don't know if they are good or bad, but we know
+that they are not the first bad commit because they are not ancestor
+of the new "bad" commit.
+
+So when a commit is marked as "bad" we know we can remove all the
+commits in the graph except those that are ancestors of the new "bad"
+commit. This means that:
+
+-------------
+information_if_bad(X) = N - number_of_ancestors(X)  (TRUE)
+-------------
+
+where N is the number of commits in the (cleaned up) graph.
+
+So in the end this means that to find the best bisection commits we
+should maximize the function:
+
+-------------
+f(X) = min(number_of_ancestors(X), N - number_of_ancestors(X))
+-------------
+
+And this is nice because at step 2) we compute number_of_ancestors(X)
+and so at step 3) we compute f(X).
+
+Let's take the following graph as an example:
+
+-------------
+	    G-H-I-J
+	   /       \
+A-B-C-D-E-F         O
+	   \       /
+	    K-L-M-N
+-------------
+
+If we compute the following non optimal function on it:
+
+-------------
+g(X) = min(number_of_ancestors(X), number_of_descendants(X))
+-------------
+
+we get:
+
+-------------
+	    4 3 2 1
+	    G-H-I-J
+1 2 3 4 5 6/       \0
+A-B-C-D-E-F         O
+	   \       /
+	    K-L-M-N
+	    4 3 2 1
+-------------
+
+but with the algorithm used by git bisect we get:
+
+-------------
+	    7 7 6 5
+	    G-H-I-J
+1 2 3 4 5 6/       \0
+A-B-C-D-E-F         O
+	   \       /
+	    K-L-M-N
+	    7 7 6 5
+-------------
+
+So we chose G, H, K or L as the best bisection point, which is better
+than F. Because if for example L is bad, then we will know not only
+that L, M and N are bad but also that G, H, I and J are not the first
+bad commit (since we suppose that there is only one first bad commit
+and it must be an ancestor of L).
+
+So the current algorithm seems to be the best possible given what we
+initially supposed.
+
+Skip algorithm
+~~~~~~~~~~~~~~
+
+When some commits have been skipped (using "git bisect skip"), then
+the bisection algorithm is the same for step 1) to 3). But then we use
+roughly the following steps:
+
+6) sort the commit by decreasing associated value
+
+7) if the first commit has not been skipped, we can return it and stop
+here
+
+8) otherwise filter out all the skipped commits in the sorted list
+
+9) use a pseudo random number generator (PRNG) to generate a random
+number between 0 and 1
+
+10) multiply this random number with its square root to bias it toward
+0
+
+11) multiply the result by the number of commits in the filtered list
+to get an index into this list
+
+12) return the commit at the computed index
+
+Skip algorithm discussed
+~~~~~~~~~~~~~~~~~~~~~~~~
+
+After step 7) (in the skip algorithm), we could check if the second
+commit has been skipped and return it if it is not the case. And in
+fact that was the algorithm we used from when "git bisect skip" was
+developed in git version 1.5.4 (released on February 1st 2008) until
+git version 1.6.4 (released July 29th 2009).
+
+But Ingo Molnar and H. Peter Anvin (another well known linux kernel
+developer) both complained that sometimes the best bisection points
+all happened to be in an area where all the commits are
+untestable. And in this case the user was asked to test many
+untestable commits, which could be very inefficient.
+
+Indeed untestable commits are often untestable because a breakage was
+introduced at one time, and that breakage was fixed only after many
+other commits were introduced.
+
+This breakage is of course most of the time unrelated to the breakage
+we are trying to locate in the commit graph. But it prevents us to
+know if the interesting "bad behavior" is present or not.
+
+So it is a fact that commits near an untestable commit have a high
+probability of being untestable themselves. And the best bisection
+commits are often found together too (due to the bisection algorithm).
+
+This is why it is a bad idea to just chose the next best unskipped
+bisection commit when the first one has been skipped.
+
+We found that most commits on the graph may give quite a lot of
+information when they are tested. And the commits that will not on
+average give a lot of information are the one near the good and bad
+commits.
+
+So using a PRNG with a bias to favor commits away from the good and
+bad commits looked like a good choice.
+
+One obvious improvement to this algorithm would be to look for a
+commit that has an associated value near the one of the best bisection
+commit, and that is on another branch, before using the PRNG. Because
+if such a commit exists, then it is not very likely to be untestable
+too, so it will probably give more information than a nearly randomly
+chosen one.
+
+Checking merge bases
+~~~~~~~~~~~~~~~~~~~~
+
+There is another tweak in the bisection algorithm that has not been
+described in the "bisection algorithm" above.
+
+We supposed in the previous examples that the "good" commits were
+ancestors of the "bad" commit. But this is not a requirement of "git
+bisect".
+
+Of course the "bad" commit cannot be an ancestor of a "good" commit,
+because the ancestors of the good commits are supposed to be
+"good". And all the "good" commits must be related to the bad commit.
+They cannot be on a branch that has no link with the branch of the
+"bad" commit. But it is possible for a good commit to be related to a
+bad commit and yet not be neither one of its ancestor nor one of its
+descendants.
+
+For example, there can be a "main" branch, and a "dev" branch that was
+forked of the main branch at a commit named "D" like this:
+
+-------------
+A-B-C-D-E-F-G  <--main
+       \
+	H-I-J  <--dev
+-------------
+
+The commit "D" is called a "merge base" for branch "main" and "dev"
+because it's the best common ancestor for these branches for a merge.
+
+Now let's suppose that commit J is bad and commit G is good and that
+we apply the bisection algorithm like it has been previously
+described.
+
+As described in step 1) b) of the bisection algorithm, we remove all
+the ancestors of the good commits because they are supposed to be good
+too.
+
+So we would be left with only:
+
+-------------
+H-I-J
+-------------
+
+But what happens if the first bad commit is "B" and if it has been
+fixed in the "main" branch by commit "F"?
+
+The result of such a bisection would be that we would find that H is
+the first bad commit, when in fact it's B. So that would be wrong!
+
+And yes it can happen in practice that people working on one branch
+are not aware that people working on another branch fixed a bug! It
+could also happen that F fixed more than one bug or that it is a
+revert of some big development effort that was not ready to be
+released.
+
+In fact development teams often maintain both a development branch and
+a maintenance branch, and it would be quite easy for them if "git
+bisect" just worked when they want to bisect a regression on the
+development branch that is not on the maintenance branch. They should
+be able to start bisecting using:
+
+-------------
+$ git bisect start dev main
+-------------
+
+To enable that additional nice feature, when a bisection is started
+and when some good commits are not ancestors of the bad commit, we
+first compute the merge bases between the bad and the good commits and
+we chose these merge bases as the first commits that will be checked
+out and tested.
+
+If it happens that one merge base is bad, then the bisection process
+is stopped with a message like:
+
+-------------
+The merge base BBBBBB is bad.
+This means the bug has been fixed between BBBBBB and [GGGGGG,...].
+-------------
+
+where BBBBBB is the sha1 hash of the bad merge base and [GGGGGG,...]
+is a comma separated list of the sha1 of the good commits.
+
+If some of the merge bases are skipped, then the bisection process
+continues, but the following message is printed for each skipped merge
+base:
+
+-------------
+Warning: the merge base between BBBBBB and [GGGGGG,...] must be skipped.
+So we cannot be sure the first bad commit is between MMMMMM and BBBBBB.
+We continue anyway.
+-------------
+
+where BBBBBB is the sha1 hash of the bad commit, MMMMMM is the sha1
+hash of the merge base that is skipped and [GGGGGG,...]  is a comma
+separated list of the sha1 of the good commits.
+
+So if there is no bad merge base, the bisection process continues as
+usual after this step.
+
+Best bisecting practices
+------------------------
+
+Using test suites and git bisect together
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+If you both have a test suite and use git bisect, then it becomes less
+important to check that all tests pass after each commit. Though of
+course it is probably a good idea to have some checks to avoid
+breaking too many things because it could make bisecting other bugs
+more difficult.
+
+You can focus your efforts to check at a few points (for example rc
+and beta releases) that all the T test cases pass for all the N
+configurations. And when some tests don't pass you can use "git
+bisect" (or better "git bisect run"). So you should perform roughly:
+
+-------------
+c * N * T + b * M * log2(M) tests
+-------------
+
+where c is the number of rounds of test (so a small constant) and b is
+the ratio of bug per commit (hopefully a small constant too).
+
+So of course it's much better as it's O(N \* T) vs O(N \* T \* M) if
+you would test everything after each commit.
+
+This means that test suites are good to prevent some bugs from being
+committed and they are also quite good to tell you that you have some
+bugs. But they are not so good to tell you where some bugs have been
+introduced. To tell you that efficiently, git bisect is needed.
+
+The other nice thing with test suites, is that when you have one, you
+already know how to test for bad behavior. So you can use this
+knowledge to create a new test case for "git bisect" when it appears
+that there is a regression. So it will be easier to bisect the bug and
+fix it. And then you can add the test case you just created to your
+test suite.
+
+So if you know how to create test cases and how to bisect, you will be
+subject to a virtuous circle:
+
+more tests => easier to create tests => easier to bisect => more tests
+
+So test suites and "git bisect" are complementary tools that are very
+powerful and efficient when used together.
+
+Bisecting build failures
+~~~~~~~~~~~~~~~~~~~~~~~~
+
+You can very easily automatically bisect broken builds using something
+like:
+
+-------------
+$ git bisect start BAD GOOD
+$ git bisect run make
+-------------
+
+Passing sh -c "some commands" to "git bisect run"
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+For example:
+
+-------------
+$ git bisect run sh -c "make || exit 125; ./my_app | grep 'good output'"
+-------------
+
+On the other hand if you do this often, then it can be worth having
+scripts to avoid too much typing.
+
+Finding performance regressions
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Here is an example script that comes slightly modified from a real
+world script used by Junio Hamano <<4>>.
+
+This script can be passed to "git bisect run" to find the commit that
+introduced a performance regression:
+
+-------------
+#!/bin/sh
+
+# Build errors are not what I am interested in.
+make my_app || exit 255
+
+# We are checking if it stops in a reasonable amount of time, so
+# let it run in the background...
+
+./my_app >log 2>&1 &
+
+# ... and grab its process ID.
+pid=$!
+
+# ... and then wait for sufficiently long.
+sleep $NORMAL_TIME
+
+# ... and then see if the process is still there.
+if kill -0 $pid
+then
+	# It is still running -- that is bad.
+	kill $pid; sleep 1; kill $pid;
+	exit 1
+else
+	# It has already finished (the $pid process was no more),
+	# and we are happy.
+	exit 0
+fi
+-------------
+
+Following general best practices
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+It is obviously a good idea not to have commits with changes that
+knowingly break things, even if some other commits later fix the
+breakage.
+
+It is also a good idea when using any VCS to have only one small
+logical change in each commit.
+
+The smaller the changes in your commit, the most effective "git
+bisect" will be. And you will probably need "git bisect" less in the
+first place, as small changes are easier to review even if they are
+only reviewed by the commiter.
+
+Another good idea is to have good commit messages. They can be very
+helpful to understand why some changes were made.
+
+These general best practices are very helpful if you bisect often.
+
+Avoiding bug prone merges
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+First merges by themselves can introduce some regressions even when
+the merge needs no source code conflict resolution. This is because a
+semantic change can happen in one branch while the other branch is not
+aware of it.
+
+For example one branch can change the semantic of a function while the
+other branch add more calls to the same function.
+
+This is made much worse if many files have to be fixed to resolve
+conflicts. That's why such merges are called "evil merges". They can
+make regressions very difficult to track down. It can even be
+misleading to know the first bad commit if it happens to be such a
+merge, because people might think that the bug comes from bad conflict
+resolution when it comes from a semantic change in one branch.
+
+Anyway "git rebase" can be used to linearize history. This can be used
+either to avoid merging in the first place. Or it can be used to
+bisect on a linear history instead of the non linear one, as this
+should give more information in case of a semantic change in one
+branch.
+
+Merges can be also made simpler by using smaller branches or by using
+many topic branches instead of only long version related branches.
+
+And testing can be done more often in special integration branches
+like linux-next for the linux kernel.
+
+Adapting your work-flow
+~~~~~~~~~~~~~~~~~~~~~~~
+
+A special work-flow to process regressions can give great results.
+
+Here is an example of a work-flow used by Andreas Ericsson:
+
+* write, in the test suite, a test script that exposes the regression
+* use "git bisect run" to find the commit that introduced it
+* fix the bug that is often made obvious by the previous step
+* commit both the fix and the test script (and if needed more tests)
+
+And here is what Andreas said about this work-flow <<5>>:
+
+_____________
+To give some hard figures, we used to have an average report-to-fix
+cycle of 142.6 hours (according to our somewhat weird bug-tracker
+which just measures wall-clock time). Since we moved to git, we've
+lowered that to 16.2 hours. Primarily because we can stay on top of
+the bug fixing now, and because everyone's jockeying to get to fix
+bugs (we're quite proud of how lazy we are to let git find the bugs
+for us). Each new release results in ~40% fewer bugs (almost certainly
+due to how we now feel about writing tests).
+_____________
+
+Clearly this work-flow uses the virtuous circle between test suites
+and "git bisect". In fact it makes it the standard procedure to deal
+with regression.
+
+In other messages Andreas says that they also use the "best practices"
+described above: small logical commits, topic branches, no evil
+merge,... These practices all improve the bisectability of the commit
+graph, by making it easier and more useful to bisect.
+
+So a good work-flow should be designed around the above points. That
+is making bisecting easier, more useful and standard.
+
+Involving QA people and if possible end users
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+One nice about "git bisect" is that it is not only a developer
+tool. It can effectively be used by QA people or even end users (if
+they have access to the source code or if they can get access to all
+the builds).
+
+There was a discussion at one point on the linux kernel mailing list
+of whether it was ok to always ask end user to bisect, and very good
+points were made to support the point of view that it is ok.
+
+For example David Miller wrote <<6>>:
+
+_____________
+What people don't get is that this is a situation where the "end node
+principle" applies. When you have limited resources (here: developers)
+you don't push the bulk of the burden upon them. Instead you push
+things out to the resource you have a lot of, the end nodes (here:
+users), so that the situation actually scales.
+_____________
+
+This means that it is often "cheaper" if QA people or end users can do
+it.
+
+What is interesting too is that end users that are reporting bugs (or
+QA people that reproduced a bug) have access to the environment where
+the bug happens. So they can often more easily reproduce a
+regression. And if they can bisect, then more information will be
+extracted from the environment where the bug happens, which means that
+it will be easier to understand and then fix the bug.
+
+For open source projects it can be a good way to get more useful
+contributions from end users, and to introduce them to QA and
+development activities.
+
+Using complex scripts
+~~~~~~~~~~~~~~~~~~~~~
+
+In some cases like for kernel development it can be worth developing
+complex scripts to be able to fully automate bisecting.
+
+Here is what Ingo Molnar says about that <<7>>:
+
+_____________
+i have a fully automated bootup-hang bisection script. It is based on
+"git-bisect run". I run the script, it builds and boots kernels fully
+automatically, and when the bootup fails (the script notices that via
+the serial log, which it continuously watches - or via a timeout, if
+the system does not come up within 10 minutes it's a "bad" kernel),
+the script raises my attention via a beep and i power cycle the test
+box. (yeah, i should make use of a managed power outlet to 100%
+automate it)
+_____________
+
+Combining test suites, git bisect and other systems together
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+We have seen that test suites an git bisect are very powerful when
+used together. It can be even more powerful if you can combine them
+with other systems.
+
+For example some test suites could be run automatically at night with
+some unusual (or even random) configurations. And if a regression is
+found by a test suite, then "git bisect" can be automatically
+launched, and its result can be emailed to the author of the first bad
+commit found by "git bisect", and perhaps other people too. And a new
+entry in the bug tracking system could be automatically created too.
+
+
+The future of bisecting
+-----------------------
+
+"git replace"
+~~~~~~~~~~~~~
+
+We saw earlier that "git bisect skip" is now using a PRNG to try to
+avoid areas in the commit graph where commits are untestable. The
+problem is that sometimes the first bad commit will be in an
+untestable area.
+
+To simplify the discussion we will suppose that the untestable area is
+a simple string of commits and that it was created by a breakage
+introduced by one commit (let's call it BBC for bisect breaking
+commit) and later fixed by another one (let's call it BFC for bisect
+fixing commit).
+
+For example:
+
+-------------
+...-Y-BBC-X1-X2-X3-X4-X5-X6-BFC-Z-...
+-------------
+
+where we know that Y is good and BFC is bad, and where BBC and X1 to
+X6 are untestable.
+
+In this case if you are bisecting manually, what you can do is create
+a special branch that starts just before the BBC. The first commit in
+this branch should be the BBC with the BFC squashed into it. And the
+other commits in the branch should be the commits between BBC and BFC
+rebased on the first commit of the branch and then the commit after
+BFC also rebased on.
+
+For example:
+
+-------------
+      (BBC+BFC)-X1'-X2'-X3'-X4'-X5'-X6'-Z'
+     /
+...-Y-BBC-X1-X2-X3-X4-X5-X6-BFC-Z-...
+-------------
+
+where commits quoted with ' have been rebased.
+
+You can easily create such a branch with Git using interactive rebase.
+
+For example using:
+
+-------------
+$ git rebase -i Y Z
+-------------
+
+and then moving BFC after BBC and squashing it.
+
+After that you can start bisecting as usual in the new branch and you
+should eventually find the first bad commit.
+
+For example:
+
+-------------
+$ git bisect start Z' Y
+-------------
+
+If you are using "git bisect run", you can use the same manual fix up
+as above, and then start another "git bisect run" in the special
+branch. Or as the "git bisect" man page says, the script passed to
+"git bisect run" can apply a patch before it compiles and test the
+software <<8>>. The patch should turn a current untestable commits
+into a testable one. So the testing will result in "good" or "bad" and
+"git bisect" will be able to find the first bad commit. And the script
+should not forget to remove the patch once the testing is done before
+exiting from the script.
+
+(Note that instead of a patch you can use "git cherry-pick BFC" to
+apply the fix, and in this case you should use "git reset --hard
+HEAD^" to revert the cherry-pick after testing and before returning
+from the script.)
+
+But the above ways to work around untestable areas are a little bit
+clunky. Using special branches is nice because these branches can be
+shared by developers like usual branches, but the risk is that people
+will get many such branches. And it disrupts the normal "git bisect"
+work-flow. So, if you want to use "git bisect run" completely
+automatically, you have to add special code in your script to restart
+bisection in the special branches.
+
+Anyway one can notice in the above special branch example that the Z'
+and Z commits should point to the same source code state (the same
+"tree" in git parlance). That's because Z' result from applying the
+same changes as Z just in a slightly different order.
+
+So if we could just "replace" Z by Z' when we bisect, then we would
+not need to add anything to a script. It would just work for anyone in
+the project sharing the special branches and the replacements.
+
+With the example above that would give:
+
+-------------
+      (BBC+BFC)-X1'-X2'-X3'-X4'-X5'-X6'-Z'-...
+     /
+...-Y-BBC-X1-X2-X3-X4-X5-X6-BFC-Z
+-------------
+
+That's why the "git replace" command was created. Technically it
+stores replacements "refs" in the "refs/replace/" hierarchy. These
+"refs" are like branches (that are stored in "refs/heads/") or tags
+(that are stored in "refs/tags"), and that means that they can
+automatically be shared like branches or tags among developers.
+
+"git replace" is a very powerful mechanism. It can be used to fix
+commits in already released history, for example to change the commit
+message or the author. And it can also be used instead of git "grafts"
+to link a repository with another old repository.
+
+In fact it's this last feature that "sold" it to the git community, so
+it is now in the "master" branch of git's git repository and it should
+be released in git 1.6.5 in October or November 2009.
+
+One problem with "git replace" is that currently it stores all the
+replacements refs in "refs/replace/", but it would be perhaps better
+if the replacement refs that are useful only for bisecting would be in
+"refs/replace/bisect/". This way the replacement refs could be used
+only for bisecting, while other refs directly in "refs/replace/" would
+be used nearly all the time.
+
+Bisecting sporadic bugs
+~~~~~~~~~~~~~~~~~~~~~~~
+
+Another possible improvement to "git bisect" would be to optionally
+add some redundancy to the tests performed so that it would be more
+reliable when tracking sporadic bugs.
+
+This has been requested by some kernel developers because some bugs
+called sporadic bugs do not appear in all the kernel builds because
+they are very dependent on the compiler output.
+
+The idea is that every 3 test for example, "git bisect" could ask the
+user to test a commit that has already been found to be "good" or
+"bad" (because one of its descendants or one of its ancestors has been
+found to be "good" or "bad" respectively). If it happens that a commit
+has been previously incorrectly classified then the bisection can be
+aborted early, hopefully before too many mistakes have been made. Then
+the user will have to look at what happened and then restart the
+bisection using a fixed bisect log.
+
+There is already a project called BBChop created by Ealdwulf Wuffinga
+on Github that does something like that using Bayesian Search Theory
+<<9>>:
+
+_____________
+BBChop is like 'git bisect' (or equivalent), but works when your bug
+is intermittent. That is, it works in the presence of false negatives
+(when a version happens to work this time even though it contains the
+bug). It assumes that there are no false positives (in principle, the
+same approach would work, but adding it may be non-trivial).
+_____________
+
+But BBChop is independent of any VCS and it would be easier for Git
+users to have something integrated in Git.
+
+Conclusion
+----------
+
+We have seen that regressions are an important problem, and that "git
+bisect" has nice features that complement very well practices and
+other tools, especially test suites, that are generally used to fight
+regressions. But it might be needed to change some work-flows and
+(bad) habits to get the most out of it.
+
+Some improvements to the algorithms inside "git bisect" are possible
+and some new features could help in some cases, but overall "git
+bisect" works already very well, is used a lot, and is already very
+useful. To back up that last claim, let's give the final word to Ingo
+Molnar when he was asked by the author how much time does he think
+"git bisect" saves him when he uses it:
+
+_____________
+a _lot_.
+
+About ten years ago did i do my first 'bisection' of a Linux patch
+queue. That was prior the Git (and even prior the BitKeeper) days. I
+literally days spent sorting out patches, creating what in essence
+were standalone commits that i guessed to be related to that bug.
+
+It was a tool of absolute last resort. I'd rather spend days looking
+at printk output than do a manual 'patch bisection'.
+
+With Git bisect it's a breeze: in the best case i can get a ~15 step
+kernel bisection done in 20-30 minutes, in an automated way. Even with
+manual help or when bisecting multiple, overlapping bugs, it's rarely
+more than an hour.
+
+In fact it's invaluable because there are bugs i would never even
+_try_ to debug if it wasn't for git bisect. In the past there were bug
+patterns that were immediately hopeless for me to debug - at best i
+could send the crash/bug signature to lkml and hope that someone else
+can think of something.
+
+And even if a bisection fails today it tells us something valuable
+about the bug: that it's non-deterministic - timing or kernel image
+layout dependent.
+
+So git bisect is unconditional goodness - and feel free to quote that
+;-)
+_____________
+
+Acknowledgements
+----------------
+
+Many thanks to Junio Hamano for his help in reviewing this paper, for
+reviewing the patches I sent to the git mailing list, for discussing
+some ideas and helping me improve them, for improving "git bisect" a
+lot and for his awesome work in maintaining and developing Git.
+
+Many thanks to Ingo Molnar for giving me very useful information that
+appears in this paper, for commenting on this paper, for his
+suggestions to improve "git bisect" and for evangelizing "git bisect"
+on the linux kernel mailing lists.
+
+Many thanks to Linus Torvalds for inventing, developing and
+evangelizing "git bisect", Git and Linux.
+
+Many thanks to the many other great people who helped one way or
+another when I worked on git, especially to Andreas Ericsson, Johannes
+Schindelin, H. Peter Anvin, Daniel Barkalow, Bill Lear, John Hawley,
+Shawn O. Pierce, Jeff King, Sam Vilain, Jon Seymour.
+
+Many thanks to the Linux-Kongress program committee for choosing the
+author to given a talk and for publishing this paper.
+
+References
+----------
+
+- [[[1]]] http://www.nist.gov/public_affairs/releases/n02-10.htm['Software Errors Cost U.S. Economy $59.5 Billion Annually'. Nist News Release.]
+- [[[2]]] http://java.sun.com/docs/codeconv/html/CodeConventions.doc.html#16712['Code Conventions for the Java Programming Language'. Sun Microsystems.]
+- [[[3]]] http://en.wikipedia.org/wiki/Software_maintenance['Software maintenance'. Wikipedia.]
+- [[[4]]] http://article.gmane.org/gmane.comp.version-control.git/45195/[Junio C Hamano. 'Automated bisect success story'. Gmane.]
+- [[[5]]] http://lwn.net/Articles/317154/[Christian Couder. 'Fully automated bisecting with "git bisect run"'. LWN.net.]
+- [[[6]]] http://lwn.net/Articles/277872/[Jonathan Corbet. 'Bisection divides users and developers'. LWN.net.]
+- [[[7]]] http://article.gmane.org/gmane.linux.scsi/36652/[Ingo Molnar. 'Re: BUG 2.6.23-rc3 can't see sd partitions on Alpha'. Gmane.]
+- [[[8]]] http://www.kernel.org/pub/software/scm/git/docs/git-bisect.html[Junio C Hamano and the git-list. 'git-bisect(1) Manual Page'. Linux Kernel Archives.]
+- [[[9]]] http://github.com/Ealdwulf/bbchop[Ealdwulf. 'bbchop'. GitHub.]