1. Sufficient Mutant Operators Offutt, Rothermel, Lee, Untch, and Zapf TOSEM, April 1996 Slide text copyright Robert W. Hasker, 2006 Material (and figures) from Determination of Sufficient Mutant Operators, ACM Transactions on Software Engineering and Methodology, Vol. 5, No. 2 (April 1996) http://portal.acm.org/citation.cfm?id=227610&coll=ACM&dl=GUIDE&CFID=73501362&CFTOKEN=28660440

2. Testing Programs by Random Changes Mutation testing: randomly change code, run against test suite Mutation testing: randomly change code, run against test suite For example, change For example, change int min(int a, int b) { int result = a; if ( b < a ) result = b; return result;} into into int min(int a, int b) { int result = b; if ( b < a ) result = b; return result; } Now: min(6, 1) gives 1, but min(1, 6) gives 6 Now: min(6, 1) gives 1, but min(1, 6) gives 6

3. What does this tell us? If new program produces same output on all test data, then either If new program produces same output on all test data, then either –Test data not sufficient to capture all error –Program contains dead code –New program equivalent to the old Thus: tool tests the test suite Thus: tool tests the test suite –Similar to structural coverage Problem: potentially an infinite number of mutants! Problem: potentially an infinite number of mutants!

4. Other Versions of min Changing : Changing : int min(int a, int b) { int result = a; int result = a; if ( b > a ) result = b; if ( b > a ) result = b; return result; return result;} Replacing a by result (equivalent mutant): Replacing a by result (equivalent mutant): int min(int a, int b) { int result = a; int result = a; if ( b < result ) result = b; if ( b < result ) result = b; return result; return result;} –Note this mutant could be eliminated by definition-use analysis

5. So why is mutation testing helpful? Structural coverage is a very minimal criterion Structural coverage is a very minimal criterion Consider Consider int max(int xs[], int len) { int res = -1; int res = -1; for(int i = 0; i < len; ++i) for(int i = 0; i < len; ++i) if ( xs[i] > res ) res = xs[i]; if ( xs[i] > res ) res = xs[i]; return res; return res; } –with int nums[3] = {-9, 5, 0}; –Get coverage with max(nums, 3); –Fails: max(nums, 1);

6. Mutation Testing, Described Competent programmer hypothesis Competent programmer hypothesis –Assumption: if program to be tested isnt correct, it contains at most a few small errors Plan: generate code, generate tests, generate non-equivalent mutants, add to tests until all mutants killed Plan: generate code, generate tests, generate non-equivalent mutants, add to tests until all mutants killed What operators for generating mutants? What operators for generating mutants? Mothra: system developed in 90s which used 22 operators Mothra: system developed in 90s which used 22 operators –Are all of these operators necessary? –In general: do we need a huge number of operators to make this work?

7. Set of Mutant Operators (in Mothra) (for Fortran – C would be similar) AARarray reference for array reference replacement ABSabsolute value insertion ACRArray reference for constant replacement AORArithmetic operator replacement ASRArray reference for scalar variable replacement CARConstant for array reference replacement CNRComparable array name replacement CRPConstant replacement CSRConstant for scalar variable replacement DERDO statement end replacement

8. Mutant Operators, Continued DSADATA statement alterations GLRGOTO label replacement LCRLogical connector replacement RORRelational operator replacement RSRRETURN statement replacement SANStatement analysis - replace statements by traps, return, goto SARScalar variable for array reference replacement SCRScalar for constant replacement SDLStatement deletion SRCSource constant replacement SVRScalar variable replacement UOIUnary operator insertion

9. Musing on Mutant Operators 22 operators too many mutants! 22 operators too many mutants! But note some operators produce more mutants than others: But note some operators produce more mutants than others: ~18% by SVR, ~13% by ASR; ~60% by top five ~18% by SVR, ~13% by ASR; ~60% by top five Can we find a useful subset? Can we find a useful subset?

10. An experiment 10 Fortran programs (or subroutines): 10 Fortran programs (or subroutines): ProgramDescriptionStmtsMutants BankerDeadlock avoidance482765 BubBubble sort over ints11338 CalDays between 2 dates293010 EuclidGreatest common divisor11196 FindPartition array281022 InsertInsertion sort over ints14460 MidMedian of three ints16183 QuadReal roots of quadratic eqn10359 TritypTriangle classification28951 WarshallTransitive closure of matrix11305

11. Experiment, contd. Use tool to generate test data sets Use tool to generate test data sets Augmented these with hand-generated data sets to kill remaining incorrect mutants Augmented these with hand-generated data sets to kill remaining incorrect mutants –Small number of hand-generated cases compared to total test cases –Also tried completely random data; results similar Generated 5 sets of test cases for each program Generated 5 sets of test cases for each program –Each set is then able to kill all non-equivalent mutants Then scored each set of test cases against all mutants Then scored each set of test cases against all mutants –The result: percentage of total mutants that are killed –Any mutant killed by same test set is redundant!

12. Results Tried different sets, found best results with five operators Tried different sets, found best results with five operators –ABS, AOR, LCR, ROR, UOI Each test set generated using these mutant operators resulted in killing 98.5% (and an average of 99.5%) of all mutants: Each test set generated using these mutant operators resulted in killing 98.5% (and an average of 99.5%) of all mutants: Conclusion: these operators sufficient Conclusion: these operators sufficient

13. Results, Continued Removing UOI, AOR, ABS would clearly weaken tests Removing UOI, AOR, ABS would clearly weaken tests Evidence for removing LCR is weak; few such connectives in sample programs Evidence for removing LCR is weak; few such connectives in sample programs ROR provides branch coverage and so hard to justify removing ROR provides branch coverage and so hard to justify removing

14. Minimum Set of Operators (for Fortran) ABS: insert calls to an absolute value function ABS: insert calls to an absolute value function AOR: replace all arithmetic ops by every syntactically legal alternatives AOR: replace all arithmetic ops by every syntactically legal alternatives LCR: replaces AND, OR by all logical connectors LCR: replaces AND, OR by all logical connectors ROR: replace (modify) relational operators ROR: replace (modify) relational operators UOI: insert unary operators UOI: insert unary operators

15. Conclusion Five operators, responsible for ~17% of all mutants, sufficient for 10 test programs Five operators, responsible for ~17% of all mutants, sufficient for 10 test programs In general: get O(Lines + References) mutants In general: get O(Lines + References) mutants Constant for O is large! Constant for O is large! Above 10 programs (200 lines): 231,972 mutants Above 10 programs (200 lines): 231,972 mutants Result: a testing method with minimal user input: Result: a testing method with minimal user input: 1. Write code 2. Write tests, possibly using a tool to generate cases 3. Evaluate tests using mutants; if some non-equivalent mutant not killed, extend test set Would probably focus on critical routines (unit testing) Would probably focus on critical routines (unit testing)