UMBC. space and introduced backtrace. Fujiwara s FAN efficiently constrained the backtrace to speed up search and further limited the search space.

Transcription

1 ATPG Algorithms Characteristics of the three main algorithms: Roth s -Algorithm (-ALG) defined the calculus and algorithms for ATPG using -cubes. Goel s POEM used path propagation constraints to limit the ATPG search space and introduced backtrace. Fujiwara s FAN efficiently constrained the backtrace to speed up search and further limited the search space. -Calculus and -Algorithm efinitions: Singular cover: efined to be the minimal set of input signal assignments needed to represent essential prime implicants in Karnaugh map. A B C d e F AN a b d NOR d e F X 4 X 2 X 5 X 3 6 (/2/4)

2 -Calculus and -Algorithm -cube: A collapsed truth table entry. For example, combine rows 3 and of the AN gate singular cover, and express it in Roth s 5-valued algebra (row 3 is good machine). Rows 3 and 2 yield the propagation -cube: A third is. Inverting to in each of these yields the 6 -cubes for the AN gate. 3 of the NOR gate -cubes are: -intersection: efine how different -cubes can coexist for different gates in a logic circuit. = X = X = Rule: If one cube assigns a specific = X = X = signal value, the other cubes must X X = X assign either the same signal or X 2 (/2/4)

3 -Calculus and -Algorithm -intersection (cont.): For example, " X X" intersect " X X" is the empty cube (incompatible). -intersection X φ ψ ψ φ ψ ψ X X ψ ψ µ λ ψ ψ λ µ The greek symbols φ and ψ represent incompatible assignments. If the values are incompatible during propagation or implications, the assignment is called inconsistent and backtracking is necessary. Greek symbols µ and λ indicate incompatibilities if both are present in -cubes with multiple input and. For example, if only λ occurs, invert the s in the second cube and perform intersection. 3 (/2/4)

4 -Calculus and -Algorithm -contains: A cube A -contains cube B if the set of A cube vertices contains (is a superset of) the B cube vertices. Primitive -cubes of failure (PF): These model faults including: (a) SA (represented by ) (b) SA (represented by ) (c) Bridging faults (short circuits) (d) Arbitrary change in logic gate function (e.g., from AN to OR). For the AN gate, the PF for output SA is " " Here the good machine generates a when both inputs are, while the bad machine generates a. The PFs for the AN gate output SA are " X " and "X ". Note the PF are distinct from the propagation -cubes. The former models a failure at the gate. The latter models the conditions for fault effect propagation. 4 (/2/4)

5 -Calculus and -Algorithm Implication procedure: Consists of the following steps: (a) Model the fault with the appropriate PF. (b) Select propagation -cubes to propagate fault-effect to PO(s)(-drive). (c) Select singular cover cubes to justify internal circuit signals (consistency procedure). The -algorithm s main problem is that it selects cubes and singular covers arbitrarily during test generation. 5 (/2/4)

6 -ALG Start Select a fault Generate a PF Pattern More lines to justify? yes Is there or on PO? yes Select a line to justify. Propagate -cube and intersect Mark the lines to be justified Inconsistency? Inconsistency? Consistency yes Alt path for justification? yes yes yes Alt gate for propagation? -rive Backup one level select ather path Backup one level select ather path Revisiting a de? yes No pattern exists Options exhausted? yes 6 (/2/4)

7 -ALG Examples A B C Assign PF SA d e 3 Consistency Truth Table F 2 Propagate Singular Cover A B C d e F A B C F Propagation -cubes A B C d e F 7 (/2/4)

8 -ALG Examples The following procedure is carried out for d SA in the previous circuit: Step A B C d e F Type of cube PF for AN gate 2 Propagation -cube for NOR gate 3 Singular cover of NAN gate Example #2: Consistency X C g k 4 5 B f e 6 7 h A 2 SA Assign PF Propagate 3 8 (/2/4)

9 -ALG Examples Steps followed to generate test cube (tc): Step A B C e f g h k L -drive 2 3 Consistency 4 or 5 t 6 or 7 and tc -chain dies This example and table is given in Roth s paper. Several other examples are covered in the paper. Note that all implications are performed in the consistency procedure here. A later example by our authors indicates the implications are carried out after each propagation step in the -drive? 9 (/2/4)

10 -ALG Examples Example #3: E C B A Consistency F 5 SA 6 2 Assign PF 4 3 Propagate (/2/4)

11 -ALG Examples Example #4: A B e f r n d g SA 6 m k 4 p q s t 5 2 X Y C 9 h i 3 u 7 v 8 Z Assign PF Propagate Consistency (/2/4)

12 -ALG Examples Example #5: e f n 7 FAIL (backtrack) r X A B d g 3 m k 4 h i p 5 q s SA u t 2 6 v Y C Z Assign PF Propagate Implications The B = choice is eventually discovered as a bad choice. One backtrack to step 2, which sets B = and leads to the successful generation of a test. Note here that implications carried out before the -drive is completed. 2 (/2/4)

13 POEM In late 7s, IBM introduced error correction and translation (ECAT) to their RAM to increase reliability. 4 -ALG fails on attempts to generate tests for these circuits because the search is t directed. A H SA B 6 C E F G FAIL j k l m 3 choice 2 3 p n R 5 q choice The only valid tests require that these are opposite. -ALG will eventually determine that n = q is t realizable by this circuit. 3 (/2/4)

14 POEM POEM (Path-Oriented ecision-making) introduced several standard ATPG concepts: POEM expands the binary decision tree around the PIs and t around all circuit signals. This reduces the size of the tree from 2 n to 2 num_pis. -ALG tended to continue intersecting -cubes even when the -frontier disappeared. POEM introduced a subroutine to test if -frontier still existed. POEM introduced objectives and realized that choosing PIs to set was important in efficiently realizing objectives. Backtracing was used to obtain a PI assignment given an initial objective. POEM considered the length of the path between the objective and the POs and used controllability measures to guide the ATPG algorithm. 4 (/2/4)

15 POEM POEM starts at the PIs instead of at faulty line like -ALG. Start Assign a binary value to an unassigned PI etermine implications of all PIs Is there a or on any PO? Test possible with additional assigned PIs? Is there any untried combo on assigned PIs? yes Pattern maybe No Pattern exists Involves choosing objectives and performing backtrace. yes Set untried combo on assigned PIs. 5 (/2/4)

16 FAN Fujiwara and Shimo introduced several vel concepts to further limit the ATPG search space and accelerate backtracing: Immediate Implications: POEM misses opportunities to immediately assign values that are uniquely determined to signals. A B C E A B C E g h k j Given objective L =, POEM would backtrace and assign k=, g= and B=. This is unfortunate since B= => h= and j= which prevents objective. g h k j L FAN instead sets j, k and E to since they must all be set to justify L=. L= This leads to unique A and B=, C=. 6 (/2/4)

17 FAN and Other Advanced ATPG Algorithms Test book describes other vel features of the FAN algorithm. ominator ATPG Programs: TOPS (Kirkland and Mercer) Learning ATPG Programs: SOCRATES (Schulz et al.) EST (Giraldi and Bushnell) Recursive Learning (Kunz and Pradhan) Implication Graph ATPG Algorithms: NNATPG (Chakradhar et al.) TRAN (Chakradhar et al.) GRASP NEMESIS TEGUS A program by Tafertshofer et al. B-Based ATPG Algorithms (performance poor on multipliers): CATAPULT (Gaede at al.) TSUNAMI (Stanion Bhattacharya) 7 (/2/4)

18 Test Generation Systems An ATPG system may contain: Fault generator/collapsing program RPG program Fault simulator ATPG program Test compactor Performance criteria include: Fault coverage Fault coverage Fault efficiency Fault efficiency Vector set size CPU time = = Number of detected faults Total number of faults Number of detected faults Total number of faults Number of undetectable faults 8 (/2/4)

19 Test Generation Systems SOCRATES: Starts with RPG (optionally with weighted pattern probabilities), concurrent fault simulation and fault dropping. 32 random patterns are generated in parallel and one concurrent fault simulation is carried out. The process terminates when faults are detected after 64 random patterns have been tried. This is followed with several passes of ATPG. Pass one is done usually with only backtracks allowed per fault. Each pattern is then fault simulated against all remaining faults and detected faults are dropped. Later passes increase the number of backtracks to 5, and finally,. This process outputs a test vector file, a list of undetected faults, a list of redundant faults, a list of aborted faults and a backtrack distribution file. 9 (/2/4)

20 Test Compaction Many ATPG systems use RPG to get 6% fault coverage, followed by ATPG. However, many of the RPG patterns may t be as effective at providing "high" fault coverage. At the end of ATPG, all patterns are fault simulated in reverse order of their generation. Once fault coverage reaches %, the remaining RPG patterns are discarded. This type of compaction greatly reduces the size of the test set. An additional static compaction method is suitable for the ATPG generated patterns, where unassigned inputs are left at X. Two patterns can be combined if they are compatible, as defined by the - intersection operator given earlier. 2 (/2/4)

21 Test Compaction The degree of compaction possible depends on the order in which the vectors are processed. t = X t 2 = X t 3 = X t 4 = X t 3 = t 24 = Optimal static compaction algorithms are impractical, so heuristic algorithms are used. ynamic compaction immediately assigns s and s to the unassigned PIs after the ATPG program generates them. The secondary faults detected allows additional fault dropping. 2 (/2/4)