Test Suite Generation with CBMC
A Small Tutorial with a Case Study
We assume that CBMC is installed on your system. If not, follow these instructions.
CBMC can be used to automatically generate test cases that satisfy a certain code coverage criteria. Common coverage criteria include branch coverage, condition coverage and Modified Condition/Decision Coverage (MC/DC). Among others, MC/DC is required by several avionics software development guidelines to ensure adequate testing of safety critical software. Briefly, in order to satisfy MC/DC, for every conditional statement containing boolean decisions, each Boolean variable should be evaluated one time to “true” and one time to “false”, in a way that affects the outcome of the decision.
In the following, we are going to demonstrate how to apply the test suite generation functionality in CBMC, by means of a case study. The following program is an excerpt from a real-time embedded benchmark PapaBench, and implements part of a fly-by-wire autopilot for an Unmanned Aerial Vehicle (UAV). We have adjusted it slightly for our purposes.
The aim of function climb_pid_run is to control the vertical climb of the UAV. Details on the theory behind this operation are documented in the wiki for the Paparazzi UAV project. The behavior of this simple controller, supposing that the desired speed is 0.5 meters per second, is plotted in the figure below.
01: // CONSTANTS:
02: #define MAX_CLIMB_SUM_ERR 10
03: #define MAX_CLIMB 1
04:
05: #define CLOCK 16
06: #define MAX_PPRZ (CLOCK*600)
07:
08: #define CLIMB_LEVEL_GAZ 0.31
09: #define CLIMB_GAZ_OF_CLIMB 0.75
10: #define CLIMB_PITCH_OF_VZ_PGAIN 0.05
11: #define CLIMB_PGAIN -0.03
12: #define CLIMB_IGAIN 0.1
13:
14: const float pitch_of_vz_pgain=CLIMB_PITCH_OF_VZ_PGAIN;
15: const float climb_pgain=CLIMB_PGAIN;
16: const float climb_igain=CLIMB_IGAIN;
17: const float nav_pitch=0;
18:
19: /** PID function INPUTS */
20: // The user input: target speed in vertical direction
21: float desired_climb;
22: // Vertical speed of the UAV detected by GPS sensor
23: float estimator_z_dot;
24:
25: /** PID function OUTPUTS */
26: float desired_gaz;
27: float desired_pitch;
28:
29: /** The state variable: accumulated error in the control */
30: float climb_sum_err=0;
31:
32: /** Computes desired_gaz and desired_pitch */
33: void climb_pid_run()
34: {
35:
36: float err=estimator_z_dot-desired_climb;
37:
38: float fgaz=climb_pgain*(err+climb_igain*climb_sum_err)+CLIMB_LEVEL_GAZ+CLIMB_GAZ_OF_CLIMB*desired_climb;
39:
40: float pprz=fgaz*MAX_PPRZ;
41: desired_gaz=((pprz>=0 && pprz<=MAX_PPRZ) ? pprz : (pprz>MAX_PPRZ ? MAX_PPRZ : 0));
42:
43: /** pitch offset for climb */
44: float pitch_of_vz=(desired_climb>0) ? desired_climb*pitch_of_vz_pgain : 0;
45: desired_pitch=nav_pitch+pitch_of_vz;
46:
47: climb_sum_err=err+climb_sum_err;
48: if (climb_sum_err>MAX_CLIMB_SUM_ERR) climb_sum_err=MAX_CLIMB_SUM_ERR;
49: if (climb_sum_err<-MAX_CLIMB_SUM_ERR) climb_sum_err=-MAX_CLIMB_SUM_ERR;
50:
51: }
52:
53: int main()
54: {
55:
56: while(1)
57: {
58: /** Non-deterministic input values */
59: desired_climb=nondet_float();
60: estimator_z_dot=nondet_float();
61:
62: /** Range of input values */
63: __CPROVER_assume(desired_climb>=-MAX_CLIMB && desired_climb<=MAX_CLIMB);
64: __CPROVER_assume(estimator_z_dot>=-MAX_CLIMB && estimator_z_dot<=MAX_CLIMB);
65:
66: __CPROVER_input("desired_climb", desired_climb);
67: __CPROVER_input("estimator_z_dot", estimator_z_dot);
68:
69: climb_pid_run();
70:
71: __CPROVER_output("desired_gaz", desired_gaz);
72: __CPROVER_output("desired_pitch", desired_pitch);
73:
74: }
75:
76: return 0;
77: }
To test the PID controller, we construct a main control loop, which repeatedly invokes the function climb_pid_run (line 69). This PID function has two input variables: the desired speed desired_climb and the estimated speed estimated_z_dot. In the beginning of each loop iteration, values of the inputs are assigned non-deterministically. Subsequently, the __CPROVER_assume statement in lines 63 and 64 guarantees that both values are bounded within a valid range. The __CPROVER_input and __CPROVER_output will help clarify the inputs and outputs of interest for generating test suites.
To demonstrate the automatic test suite generation in CBMC, we call the following command:
cbmc pid.c --cover mcdc --show-test-suite --unwind 6 --xml-ui
We’ll describe those command line options one by one. The option --cover mcdc specifies the code coverage criterion, and –show-test-suite requests that a test suite be printed. There are four conditional statements in the PID function: in lines 41, 44, 48, and 49. To satisfy MC/DC, the test suite has to meet multiple requirements. For instance, each conditional statement needs to evaluate to true and false. Consider the condition "pprz>=0 && pprz<=MAX_PPRZ" in line 41. CBMC instruments three coverage goals to control the respective evaluated results of "pprz>=0" and "pprz<=MAX_PPRZ". They satisfy the MC/DC rules.
!(pprz >= (float)0) && pprz <= (float)(16 * 600) id="climb_pid_run.coverage.1" pprz >= (float)0 && !(pprz <= (float)(16 * 600)) id="climb_pid_run.coverage.2" pprz >= (float)0 && pprz <= (float)(16 * 600) id="climb_pid_run.coverage.3"
Note that MAX_PPRZ is defined as 16 * 600 in line 06 of the program.
The “id” of each coverage goal is automatically assigned by CBMC. For every coverage goal, a test suite (if there exists) that satisfies such a goal is printed out in XML format, as the parameter --xml-ui is given. Multiple coverage goals can share a test suite, when the corresponding execution of the program satisfies all these goals at the same time.
In the end, the following test suites are automatically generated for testing the PID controller. A test suite consists of a sequence of input parameters that are passed to the PID function climb_pid_run at each loop iteration. For example, Test 1 covers the MC/DC goal with id=“climb_pid_run.coverage.1”. The complete output from CBMC is in pid\_test\_suites.xml, where every test suite and the coverage goals it is for are clearly described.
Test suite: Test 1. (iteration 1) desired_climb=-1.000000f, estimator_z_dot=1.000000f Test 2. (iteration 1) desired_climb=-1.000000f, estimator_z_dot=1.000000f (iteration 2) desired_climb=1.000000f, estimator_z_dot=-1.000000f Test 3. (iteration 1) desired_climb=0.000000f, estimator_z_dot=-1.000000f (iteration 2) desired_climb=1.000000f, estimator_z_dot=-1.000000f Test 4. (iteration 1) desired_climb=1.000000f, estimator_z_dot=-1.000000f (iteration 2) desired_climb=1.000000f, estimator_z_dot=-1.000000f (iteration 3) desired_climb=1.000000f, estimator_z_dot=-1.000000f (iteration 4) desired_climb=1.000000f, estimator_z_dot=-1.000000f (iteration 5) desired_climb=0.000000f, estimator_z_dot=-1.000000f (iteration 6) desired_climb=1.000000f, estimator_z_dot=-1.000000f Test 5. (iteration 1) desired_climb=-1.000000f, estimator_z_dot=1.000000f (iteration 2) desired_climb=-1.000000f, estimator_z_dot=1.000000f (iteration 3) desired_climb=-1.000000f, estimator_z_dot=1.000000f (iteration 4) desired_climb=-1.000000f, estimator_z_dot=1.000000f (iteration 5) desired_climb=-1.000000f, estimator_z_dot=1.000000f (iteration 6) desired_climb=-1.000000f, estimator_z_dot=1.000000f
The option --unwind 6 unwinds the loop inside the main function body six times. To achieve complete coverage on all the instrumented goals in the PID function climb_pid_run, the loop must be unwound enough times. For example, climb_pid_run needs to be called at least six times for evaluating the condition climb_sum_err>MAX_CLIMB_SUM_ERR in line 48 to true. This corresponds to Test 5. To learn more about loop unwinding take a look at Understanding Loop Unwinding.
In this tutorial, we present the automatic test suite generation functionality of CBMC, by applying the MC/DC code coverage criterion to a PID controller case study. In addition to --cover mcdc, other coverage criteria such as branch, decision, and path are also available when calling CBMC.
Coverage Criteria
The table below summarizes the coverage criteria that CBMC supports.
| Criterion | Definition |
|---|---|
| assertion | For every assertion, generate a test that reaches it |
| assume | For every assume, generate tests before and after the assume statement to indicate coverage before and after it |
| location | For every location, generate a test that reaches it |
| branch | Generate a test for every branch outcome |
| decision | Generate a test for both outcomes of every Boolean expression that is not an operand of a propositional connective |
| condition | Generate a test for both outcomes of every Boolean expression |
| mcdc | Modified Condition/Decision Coverage (MC/DC) |
| path | Bounded path coverage |
| cover | Generate a test for every __CPROVER_cover statement |
Last modified: 2024-11-12 09:30:37 +0200
