The domain-to-range ratio (DRR) is a ratio which describes how the number of outputs corresponds to the number of inputs of a given logical function or software component. The domain-to-range ratio is a mathematical ratio of cardinality between the set of the function's possible inputs (the domain) and the set of possible outputs (the range).[1][2] For a function defined on a domain, , and a range, , the domain-to-range ratio is given as:
It can be used to measure the risk of missing potential errors when testing the range of outputs alone.[3]
Consider the function isEven()
below, which checks the parity of an unsigned short number , any value between and , and yields a boolean value which corresponds to whether is even or odd. This solution takes advantage of the fact that integer division in programming typically rounds towards zero.
bool isEven(unsigned short x) {
return (x / 2) == ((x + 3)/2 - 1);
}
Because can be any value from to , the function's domain has a cardinality of . The function yields , if is even, or , if is odd. This is expressed as the range , which has a cardinality of . Therefore, the domain-to-range ratio of isEven()
is given by:
Here, the domain-to-range ratio indicates that this function would require a comparatively large number of tests to find errors. If a test program attempts every possible value of in order from to , the program would have to perform tests for each of the two possible outputs in order to find errors or edge cases. Because errors in functions with a high domain-to-range ratio are difficult to identify via manual testing or methods which reduce the number of tested inputs, such as orthogonal array testing or all-pairs testing, more computationally complex techniques may be used, such as fuzzing or static program analysis, to find errors.