Domain-to-range ratio

Consider the function isEven() below, which checks the parity of an unsigned short number $x$, any value between $0$ and $65,536$, and yields a boolean value which corresponds to whether $x$ 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 $x$ can be any value from $0$ to $65,535$, the function's domain has a cardinality of $65,536$. The function yields $0$, if $x$ is even, or $1$, if $x$ is odd. This is expressed as the range $\backslash \{0;1\backslash \}$, which has a cardinality of $2$. Therefore, the domain-to-range ratio of isEven() is given by:$$DRR=\{65,536\; \backslash over\; 2\}\; =\; 32,768$$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 $x$ in order from $0$ to $65,535$, the program would have to perform $32,768$ 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.

• Software testing
• Formal verification

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Category:Software metrics

Category:Software testing

Category:Set theory

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