Delta Debugging CS 6340. 2 All Windows 3.1 Windows 95 Windows 98 Windows ME Windows 2000 Windows NT...

Delta Debugging

CS 6340

<td align=left valign=top><SELECT NAME="op sys" MULTIPLE SIZE=7><OPTION VALUE="All">All<OPTION VALUE="Windows 3.1">Windows 3.1<OPTION VALUE="Windows 95">Windows 95<OPTION VALUE="Windows 98">Windows 98<OPTION VALUE="Windows ME">Windows ME<OPTION VALUE="Windows 2000">Windows 2000<OPTION VALUE="Windows NT">Windows NT<OPTION VALUE="Mac System 7">Mac System 7<OPTION VALUE="Mac System 7.5">Mac System 7.5<OPTION VALUE="Mac System 7.6.1">Mac System 7.6.1<OPTION VALUE="Mac System 8.0">Mac System 8.0<OPTION VALUE="Mac System 8.5">Mac System 8.5<OPTION VALUE="Mac System 8.6">Mac System 8.6<OPTION VALUE="Mac System 9.x">Mac System 9.x<OPTION VALUE="MacOS X">MacOS X<OPTION VALUE="Linux">Linux<OPTION VALUE="BSDI">BSDI<OPTION VALUE="FreeBSD">FreeBSD<OPTION VALUE="NetBSD">NetBSD<OPTION VALUE="OpenBSD">OpenBSD<OPTION VALUE="AIX">AIX<OPTION VALUE="BeOS">BeOS<OPTION VALUE="HP-UX">HP-UX<OPTION VALUE="IRIX">IRIX<OPTION VALUE="Neutrino">Neutrino<OPTION VALUE="OpenVMS">OpenVMS<OPTION VALUE="OS/2">OS/2<OPTION VALUE="OSF/1">OSF/1<OPTION VALUE="Solaris">Solaris<OPTION VALUE="SunOS">SunOS<OPTION VALUE="other">other</SELECT></td><td align=left valign=top><SELECT NAME="priority" MULTIPLE SIZE=7><OPTION VALUE="--">--<OPTION VALUE="P1">P1<OPTION VALUE="P2">P2<OPTION VALUE="P3">P3<OPTION VALUE="P4">P4<OPTION VALUE="P5">P5</SELECT></td><td align=left valign=top><SELECT NAME="bug severity" MULTIPLE SIZE=7><OPTION VALUE="blocker">blocker<OPTION VALUE="critical">critical<OPTION VALUE="major">major<OPTION VALUE="normal">normal<OPTION VALUE="minor">minor<OPTION VALUE="trivial">trivial<OPTION VALUE="enhancement">enhancement</SELECT></tr></table>

How do we go from this ...

File Print Segmentation Fault

... to this?

Simplification

Once one has reproduced a problem, one must find out what’s relevant

– Does failure really depend on 10,000 lines of input?– Does failure really require this exact schedule?– Does failure really need this sequence of calls?

Why Simplify?

• Ease of communication: a simplified test case is easier to communicate

• Easier debugging: smaller test cases result in smaller states and shorter executions

• Identify duplicates: simplified test cases subsume several duplicates

Real-World Scenario• The Mozilla open-source web browser project receives several

dozens bug reports a day

• Each bug report has to be simplified– Eliminate all details irrelevant to producing the failure

• To facilitate debugging• To make sure it does not replicate a similar bug report

• In July 1999, Bugzilla listed more than 370 open bug reports for Mozilla– These were not even simplified– Mozilla engineers were overwhelmed with work– They created the Mozilla BugAThon: a call for volunteers to process bug

reports

Real-World Scenario• The Mozilla open-source web browser project receives several

dozens bug reports a day

• Each bug report has to be simplified– Eliminate all details irrelevant to producing the failure

• To facilitate debugging• To make sure it does not replicate a similar bug report

• In July 1999, Bugzilla listed more than 370 open bug reports for Mozilla– These were not even simplified– Mozilla engineers were overwhelmed with work– They created the Mozilla BugAThon: a call for volunteers to process bug

reports

For 5 bug reports simplified, the volunteer would be invited to the launch party; 20 bugs

would earn a T-shirt signed by the grateful engineers.

Today: For 15 bug reports simplified, you get a Firefox plushie

https://developer.mozilla.org/en/Gecko_BugAThon

Your Solution

• How do you solve these problems?

• Binary search– Cut the test case in half– Iterate

• Brilliant idea: Why not automate this?

Binary Search

• Proceed by binary search. Throw away half the input and see if the output is still wrong.

• If not, go back to the previous state and discard the other half of the input.

Binary Search

Simplified input

<td align=left valign=top><SELECT NAME="op sys" MULTIPLE SIZE=7><OPTION VALUE="All">All<OPTION VALUE="Windows 3.1">Windows 3.1<OPTION VALUE="Windows 95">Windows 95<OPTION VALUE="Windows 98">Windows 98<OPTION VALUE="Windows ME">Windows ME<OPTION VALUE="Windows 2000">Windows 2000<OPTION VALUE="Windows NT">Windows NT<OPTION VALUE="Mac System 7">Mac System 7<OPTION VALUE="Mac System 7.5">Mac System 7.5<OPTION VALUE="Mac System 7.6.1">Mac System 7.6.1<OPTION VALUE="Mac System 8.0">Mac System 8.0<OPTION VALUE="Mac System 8.5">Mac System 8.5<OPTION VALUE="Mac System 8.6">Mac System 8.6<OPTION VALUE="Mac System 9.x">Mac System 9.x<OPTION VALUE="MacOS X">MacOS X<OPTION VALUE="Linux">Linux<OPTION VALUE="BSDI">BSDI<OPTION VALUE="FreeBSD">FreeBSD<OPTION VALUE="NetBSD">NetBSD<OPTION VALUE="OpenBSD">OpenBSD<OPTION VALUE="AIX">AIX<OPTION VALUE="BeOS">BeOS<OPTION VALUE="HP-UX">HP-UX<OPTION VALUE="IRIX">IRIX<OPTION VALUE="Neutrino">Neutrino<OPTION VALUE="OpenVMS">OpenVMS<OPTION VALUE="OS/2">OS/2<OPTION VALUE="OSF/1">OSF/1<OPTION VALUE="Solaris">Solaris<OPTION VALUE="SunOS">SunOS<OPTION VALUE="other">other</SELECT></td><td align=left valign=top><SELECT NAME="priority" MULTIPLE SIZE=7><OPTION VALUE="--">--<OPTION VALUE="P1">P1<OPTION VALUE="P2">P2<OPTION VALUE="P3">P3<OPTION VALUE="P4">P4<OPTION VALUE="P5">P5</SELECT></td><td align=left valign=top><SELECT NAME="bug severity" MULTIPLE SIZE=7><OPTION VALUE="blocker">blocker<OPTION VALUE="critical">critical<OPTION VALUE="major">major<OPTION VALUE="normal">normal<OPTION VALUE="minor">minor<OPTION VALUE="trivial">trivial<OPTION VALUE="enhancement">enhancement</SELECT></tr></table>

Complex Input

Simplified Input

• <SELECT NAME="priority" MULTIPLE SIZE=7>

• Simplified from 896 lines to one single line

• Required only 12 tests

Binary Search

• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>

✘✔

Binary Search

• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>

✘✔

Binary Search

What do we do if both halves pass?

✘✔

FinerGranularity of test

CoarserGranularity of test

Failure of the test case Higher Lower

Progress of the search Slower Faster

Change Granularity

FinerGranularity of test

CoarserGranularity of test

Failure of the test case Higher Lower

Progress of the search Slower Faster

Change Granularity

General Delta-Debugging Algorithm

Basic idea:

1. Start with few & large changes first

2. If all alternatives pass or are unresolved, apply more & smaller changes.

∆1∆1 ∆2∆2

∆2 ∆2 ∆1∆1

∆1∆1

∆1∆1 ∆2∆2∆2∆2 ∆3∆3

∆3∆3∆4∆4

∆4∆4∆5∆5

∆5∆5∆6∆6

∆6∆6∆7∆7

∆7∆7∆8∆8

∆8∆8

Binary Search

✘✔

Binary Search

• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>

✘✔

Binary Search

• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>

✘✔

Binary Search

• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>

✘✔

Binary Search

• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>• <SELECT NAME="priority" MULTIPLE SIZE=7>

✘✔

Inputs and Failures

• Let E be the set of possible inputs

• rP E corresponds to an input that passes

• rF E corresponds to an input that fails

Binary Search

Example of rF and rP ?

✘✔

Binary Search

Example of rF and rP ?

rF = <SELECT NALE SIZE=7>

rP = <SELECT NAME="priori

✘✔

✘✘

Changes

• We can go from one input to another by changes

• A change is a mapping : E E which takes one input and changes it to another input

• Example: ’ = insert ME="priori at appropriate position r1 = <SELECT NAty" MULTIPLE SIZE=7> What is ’(r1)?

Decomposing Changes

• A change can be decomposed to a number of elementary changes 1, 2, ..., n where = 1 o 2 o ... o n and (i o j)(r) = i(j(r))

• For example, deleting a part of the input file can be decomposed to deleting characters one be one from the file – in other words: by composing deleting of single characters,

we can get a change that deletes part of the input file

’ = insert ME="priori ’ = 1 o 2 o 3 o 4 o 5 o 6 o 7 o 8 o 9 o 10

– 1 = insert M– 2 = insert E– …

Summary

• We have an input without failure: rP

• We have an input with failure: rF

• We have a set of changes cF = {1, 2, ..., n } such that:

rF = (1 o 2 o ... o n )(rP)

• Each subset c of cF is a test case

Testing Test Cases

• Given a test case c, we would like to know if input generated by applying changes in c to rP causes a failure

• We define the following function:

test: Powerset(cF) {P, F, ?}

such that, given c = {1, 2, ..., m} cF

test(c) = F iff (1 o 2 o ... o m )(rP) is a failing input

Minimizing Test Cases

• Now the question is: Can we find the minimal test case c such that test(c) = F?

• A test case c cF is called the global minimum of cF if:

for all c’ cF , |c’| < |c| test(c’) F

• Global minimum is the smallest set of changes which will make the program fail

• Finding the global minimum may require us to perform exponential number of tests

Search for 1-minimal Input

• Different problem formulation: Find a set of changes that cause the failure, but removing any change causes the failure to go away

• This is 1-minimality

Minimizing Test Cases

• A test case c cF is called a local minimum of cF if:

for all c’ c. test(c’) F

• A test case c cF is n-minimal if:

for all c’ c. |c| |c’| n test(c’) F

• A test case is 1-minimal if:

for all i c. test(c – {i}) F

Naïve Algorithm

• To find a 1-minimal subset of c:

• If for all i c. test(c – {i}) F, then c is 1-minimal

• Else recurse on c – {} for some c. test(c – {}) = F

Analysis

• In the worst case, – We remove one element from the set per iteration– After trying every other element

• Work is potentially N + (N-1) + (N-2) + …

• This is O(N2)

Work Smarter, Not Harder

• We can often do better

• Silly to start out removing 1 element at a time– Try dividing change set in 2 initially– Increase # of subsets if we can’t make progress– If we get lucky, search will converge quickly

Minimization Algorithm

• The delta debugging algorithm finds a 1-minimal test case

• It partitions the set cF to 1, 2, ... n – 1, 2, ... n

are pairwise disjoint– cF = 1 2 ... n

• Define the complement of i as i = cF i

• Start with n = 2

• Tests each test case defined by partition and their complements

• Reduce test case if a smaller failure inducing set is found– otherwise refine the partition, i.e. n = n*2

Steps of the Minimization AlgorithmLet n = 2

(A) Start with as test set

(B) Test each 1, 2, ... n and each 1, 2, ..., n

(C) There are four possible outcomes:1. Some i causes failure

– Go to step (A) with = i and n = 22. Some i causes failure

– Go to step (A) with = i and n = n 13. No test causes failure

– Refine granularity: Go to (A) with = and n = 2n4. The granularity can no longer be refined

– Done, found the 1-minimal subset

Delta Debugging

Asymptotic Analysis

• Worst case is still quadratic

• Subdivide until each set is of size 1– Reduced to the naïve algorithm

• Good news– For single failure, converges in log N– Binary search again

GNU C Compiler• This program (bug.c) crashes GCC

2.95.2 when optimization is enabled

• Goal: minimize this program to file a bug report

• For GCC, a passing program run is the empty input

• For sake of simplicity, model each change as insertion of a single character– r is running GCC on empty input– r means running GCC on bug.c– each change di inserts ith character

of bug.c

#define SIZE 20

double mult(double z[], int n) { int i, j;

i = 0; for (j = 0; j < n; j++) { i = i + j + 1; z[i] = z[i] * (z[0] + 1.0); } return z[n];}

void copy(double to[], double from[], int count) { int n = (count + 7) / 8; switch (count % 8) do { case 0: *to++ = *from++; case 7: *to++ = *from++; case 6: *to++ = *from++; case 5: *to++ = *from++; case 4: *to++ = *from++; case 3: *to++ = *from++; case 2: *to++ = *from++; case 1: *to++ = *from++; } while (--n > 0); return mult(to, 2);}

int main(int argc, char *argv[]) { double x[SIZE], y[SIZE]; double *px = x;

while (px < x + SIZE) *px++ = (px – x) * (SIZE + 1.0); return copy(y, x, SIZE)}

GNU C Compiler

• The test procedure:– creates the appropriate subset of bug.c– feeds it to GCC– returns if GCC crashes, otherwise

GNU C Compiler• The minimized code is:

• The test case is 1-minimal– No single character can be removed

without removing the failure– Even every superfluous whitespace

has been removed– The function name has shrunk from

mult to a single t– Program has an infinite loop, but GCC

still isn’t supposed to crash

• So where could the bug be?– We already know it is related to optimization– If we remove –O option to turn off optimization, the failure disappears

t(double z[],int n){int i,j;for(;;){i=i+j+1;z[i]=z[i]*(z[0]+0);}return z[n];}

double mult(double z[], int n) { int i, j;

i = 0; for (j = 0; j < n; j++) { i = i + j + 1; z[i] = z[i] * (z[0] + 1.0); } return z[n];}

GNU C Compiler

• The GCC documentation lists 31 options to control optimization on Linux:

• It turns out that applying all of these options causes the failure to disappear– Some option(s) prevent the failure

–ffloat-store –fno-default-inline –fno-defer-pop–fforce-mem –fforce-addr –fomit-frame-pointer–fno-inline –finline-functions –fkeep-inline-functions–fkeep-static-consts –fno-function-cse –ffast-math–fstrength-reduce –fthread-jumps –fcse-follow-jumps–fcse-skip-blocks –frerun-cse-after-loop –frerun-loop-opt–fgcse –fexpensive-optimizations –fschedule-insns–fschedule-insns2 –ffunction-sections –fdata-sections–fcaller-saves –funroll-loops –funroll-all-loops–fmove-all-movables –freduce-all-givs –fno-peephole–fstrict-aliasing

GNU C Compiler

• Use test case minimization to find the preventing option(s)– Each di stands for removing a GCC option– Having all di applied means to run GCC with no option (failing)– Having no di applied means to run GCC with all options (passing)

• After 7 tests, the single option -ffast-math is found which prevents the failure– Unfortunately, it is not a good candidate for a workaround

as it may alter program’s semantics– Thus, we remove -ffast-math from list of options and repeat– After 7 tests, we find -fforce-addr also prevents the failure– Further tests shows none other option prevents the failure

GNU C Compiler

This is what we can send to the GCC maintainers:– The minimal test case– “The failure only occurs with optimization”– “-ffast-math and -fforce-addr prevent the failure”

Case Studies

• Minimizing Mozilla input– Print the html file containing <SELECT>

• Minimizing fuzz input– Fuzzing: feed program with randomly generated

input and check if it crashes– Used delta debugging to minimize fuzz input

Another Application

• Yesterday, my program worked. Today, it does not. Why? – The new release 4.17 of GDB changed 178,000 lines– No longer integrated properly with DDD (a graphical front-end) – How to isolate the change that caused the failure?

Summary

• Delta Debugging is a technique, not a tool

• Bad News: – Probably must be re-implemented for each

significant system – To exploit knowledge of changes

• Good News: – Relatively simple algorithm, big payoff– It is worth re-implementing

Delta Debugging CS 6340. 2 All Windows 3.1 Windows 95 Windows 98 Windows ME Windows 2000 Windows NT...

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