C+B Coverage

software-engineering testing

Definition

Condition/Decision Coverage

Condition/Decision Coverage (or C+B) is a strong white-box testing metric that combines the requirements of both condition coverage and branch coverage.

To satisfy this metric, a test suite must ensure:

1. Every atomic condition in a decision has taken all possible outcomes (True and False).
2. Every decision (branch) has taken all possible outcomes (True and False).

$$C+B=\frac{\text{Executed Branches}+\text{Executed Condition Values}}{\text{Total Branches}+\text{Total Condition Values}}\times 100\%$$

Concept

Since condition coverage and branch coverage are independent (one does not imply the other), C+B Coverage serves as a union of both metrics to close the testing gaps.

• Gap Closed: It prevents the scenario where atomic conditions are tested (condition coverage) but the code only ever takes the “True” path (0% branch coverage).
• Limitation: It still does not test how the combinations of conditions affect the outcome (e.g., it doesn’t require testing $A=True$ specifically when $B=False$). For that, DC is used.

Example

Consider the following code snippet and its CFG:

if (A || B) {   // BB_1 (Decision)
    // True     // BB_2
} else {
    // False    // BB_3
}

graph TD
    Entry((Entry)) --> Dec{"BB<sub>1</sub>:  b<sub>1</sub> = A || B"}
    Dec -- "b<sub>1</sub>" --> TrueBlock["BB<sub>2</sub>:  True Branch"]
    Dec -- "&not; b<sub>1</sub>" --> FalseBlock["BB<sub>3</sub>:  False Branch"]

Test Suite:

1. T1: $A=True,B=False$ $⟹$ Result: True ($B{B}_1\to B{B}_2$)
2. T2: $A=False,B=True$ $⟹$ Result: True ($B{B}_1\to B{B}_2$)
3. T3: $A=False,B=False$ $⟹$ Result: False ($B{B}_1\to B{B}_3$)

Analysis:

• Conditions:
  • $A$: True (T1), False (T2/T3). $⟹$ Covered.
  • $B$: True (T2), False (T1/T3). $⟹$ Covered.
• Branches:
  • Result True (T1/T2). $⟹$ Covered.
  • Result False (T3). $⟹$ Covered.
• Conclusion: 100% C+B Coverage.

Strategy

1. Denominator (Total Targets):

$$D=(2\times \text{Decisions})+(2\times \text{Conditions})$$

2. Numerator (Executed Targets): Run the trace (minding short-circuits).

$$N=\text{Unique Branches Taken}+\text{Unique Conditions Evaluated}$$

3. Result:

$$N/D$$

Example: The Short-Circuit Gap

Code: if (A || B)

• Denominator: 2 Decisions + 4 Conditions = 6.

Test Case: A=True

1. Conditions: A is True. B is skipped. (Hits: 1)
2. Branches: Decision is True. (Hits: 1)
3. Result: $(1+1)/6=33\%$.