Regression testing is any type of software testing that seeks to uncover software errors by partially retesting a modified program. The intent of regression testing is to assure that a bug fix has been successfully corrected based on the error that was found, while providing a general assurance that no other errors were introduced in the process of fixing the original problem. Regression is commonly used to efficiently test bug fixes by systematically selecting the appropriate minimum test suite needed to adequately cover the affected software code/requirements change. Common methods of regression testing include rerunning previously run tests and checking whether previously fixed faults have re-emerged.
"One of the main reasons for regression testing is that it's often extremely difficult for a programmer to figure out how a change in one part of the software will echo in other parts of the software."
Uses

Regression testing can be used not only for testing the correctness of a program, but often also for tracking the quality of its output. For instance, in the design of a compiler, regression testing should track the code size, simulation time and time of the test suite cases.

    "Also as a consequence of the introduction of new bugs, program maintenance requires far more system testing per statement written than any other programming. Theoretically, after each fix one must run the entire batch of test cases previously run against the system, to ensure that it has not been damaged in an obscure way. In practice, such regression testing must indeed approximate this theoretical idea, and it is very costly."

    Fred Brooks, The Mythical Man Month, p 122

Regression tests can be broadly categorized as functional tests or unit tests. Functional tests exercise the complete program with various inputs. Unit tests exercise individual functions, subroutines, or object methods. Both functional testing tools and unit testing tools tend to be third party products that are not part of the compiler suite, and both tend to be automated. Functional tests may be a scripted series of program inputs, possibly even an automated mechanism for controlling mouse movements. Unit tests may be separate functions within the code itself, or driver layer that links to the code without altering the code being tested. Unit testing tools include open source tools like CppUnit and CppTest as well as commercial products like Sword.

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