Chapter 6 Testability Analysis
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1 電機系 Chapter 6 Testability Analysis 可測度分析法
2 2 Outline Introduction SCOAP COP High-level Testability
3 Testability Analysis Applications To give early warnings about the test problems Guide the selection of test points to improve testability. Automate the Design for Testability problem To provide guidance in ATPG For example, determine the hardest & easiest inputs in backtrace of PODEM Complexity should be simpler than ATPG and fault simulation Need to be linear or almost linear in terms of circuit size Topology analysis Only the structure of the circuit is analyzed No test vectors are involved Only an approximation reconvergent fanouts cause inaccuracy 3
4 4 Testability Measures Controllability The difficulty of setting a particular logic signal to or. Observability The difficulty of observing the logic state of a signal.
5 5 SCOAP Sandia Controllability/Observability Analysis Program Goldstein, DAC 98 SCOAP computes 6 numbers for each node N. - controllability - controllability Observability Combinational CC (N) CC (N) CO(N) Sequential SC (N) SC (N) SO(N)
6 Combinational SCOAP Measures Combinational controllability CC (N), CC (N) Related to the minimum number of combinational node (PI or gate output) assignments required to justify a or on a node N. Combinational observability CO(N) Related to the number of gates between N and PO s, and the minimum number of PI assignments required to propagate the logical value on node N to a primary output. 6
7 7 CC (N) & CC (N) CC (y) CC (y) x x 2 y min[cc (x ),CC (x 2 )] + CC (x ) + CC (x 2 ) + x x 2 y CC (x ) + CC (x 2 ) + min[cc (x ),CC (x 2 )] + x x 2 x y y min[cc (x ) + CC (x 2 ), CC (x ) + CC (x 2 )] + min[cc (x ) + CC (x 2 ), + CC (x) + CC (x) + CC (x ) + CC (x 2 )] Primary inputs
8 8 CO(N) CO(x ) x x 2 x x 2 y y CO(y) + CC (x 2 ) + CO(y) + CC (x 2 ) + x x 2 x y y CO(y) + min[cc (x 2 ),CC (x 2 )] + CO(y) + y x y 2 min[co(y ),CO(y 2 )] Primary outputs
9 9 An Example Controllability CC /CC / a / / 3/5 4 2/6 / b 2/7 6 5/7 x c / / 2 2/2 2/2 / 3 3/5 3/5 5 2/7 2/7 3/5 y z
10 An Example Observability CC /CC a b c / 4 / 6 / 4 / 4 2 2/2 3 2/2 3 / / / /5 3/ / /6 3 2/7 2/ /7 2/7 3/5 x y z
11 Sequential SCOAP Measures Sequential controllability SC (N), SC (N) Estimate the minimum number of sequential node (FF output) assignments required to justify a or on a node N. Sequential observability SO(N) Related to the number of FF s between N and PO s, and the minimum number of FF assignments required to propagate the logical value on node N to a primary output.
12 2 Computing the Sequential SCOAP Measures Computation of SC (N), SC (N), and SO(N) is similar to that of CC (N), CC (N), and CO(N). The differences are One increments the sequential measures by only when signals propagate from FF inputs to Q or Q, or backwards. Several iterations may be required for the controllability numbers to converge.
13 3 Computing SC (N) and SC (N) SC (y) SC (y) x x 2 y min[sc (x ),SC (x 2 )] SC (x ) + SC (x 2 ) x x 2 y SC (x ) + SC (x 2 ) min[sc (x ),SC (x 2 )] x x 2 y min[sc (x ) + SC (x 2 ), SC (x ) + SC (x 2 )] min[sc (x ) + SC (x 2 ), SC (x ) + SC (x 2 )] x y SC (x) SC (x) Primary inputs
14 4 SO(N) SO(x ) x x 2 x x 2 y y SO(y) + SC (x 2 ) SO(y) + SC (x 2 ) x x 2 x y y SO(y) + min[sc (x 2 ),SC (x 2 )] SO(y) y x y 2 min[so(y ),SO(y 2 )] Primary outputs
15 5 Flip-Flop D CLK R D Q CLK RST Q Q CC (Q) = CC (D) + CC (CLK) + CC (CLK) + CC (R) SC (Q) = SC (D) + SC (CLK) + SC (CLK) + SC (R) + CC (Q) = min[cc (R) + CC (CLK), CC (D) + CC (CLK) + CC (CLK) + CC (R)] SC (Q) = min[sc (R) + SC (CLK), SC (D) + SC (CLK) + SC (CLK) + SC (R)] +
16 6 D CLK R D Q CLK RST Q Q CO(D) = CO(Q) + CC (CLK) + CC (CLK) + CC (R) SO(D) = SO(Q) + SC (CLK) + SC (CLK) + SC (R) +
17 7 Computing Testability Measures for Sequential Circuits. For all PI s, set CC = CC = and SC = SC =. 2. For all other nodes, set CC = CC = and SC = SC =. 3. Propagate controllability measures from PI s to PO s. Iterate until the controllability numbers stabilize. 4. For all PO s, set CO = SO =. 5. For all other nodes, set CO = SO =. 6. Propagate observability from PO s to PI s.
18 8 Controllability Computation a /,/ CC /CC,SC /SC 4 2/,/ /, / 9/,/ /, / c 2 /,/ 2/2,/ /, / 3 /, / /, / /, / 3/,/ 6 /, / 7/,/ D 7 Q CLK RST Q 5 z /, / 4/,/ D 8 Q CLK RST Q /, / 5/,/ Assuming no RST can occur
19 9 Controllability Computation 2nd Iteration CC /CC,SC /SC a /,/ 4 2/4,/ 2/,/ 9/7,/2 9/,/ c 2 /,/ 2/2,/ 2/2,/ 3 /, / /6, / 3/,/ 3/9,/ 6 7/,/ 7/5,/ D 7 Q CLK RST Q 5 z 4/,/ 4/,/ D 8 Q CLK RST Q 5/,/ 5/,/2
20 2 Controllability Computation 3rd iteration CC /CC,SC /SC a /,/ 4 2/4,/ 2/4,/ 9/7,/2 9/7,/2 c 2 /,/ 2/2,/ 2/2,/ 3 /6, / 2/6,2/ 3/9,/ 3/9,/ 6 7/5,/ 7/5,/ D 7 Q CLK RST Q 5 z 4/,/ 4/27,/3 D 8 Q CLK RST Q 5/,/2 5/,/2
21 2 Observability Computation CC /CC,SC /SC 26,3 a /,/ 3,3 22,2 29,3 4 2/4,/ 9/7,/2 26,3 22,2 2 2/2,/ 25,3 2,2 3 2/6,2/ 7,2 7/5,/ 6 D 7 Q 2,2, 5,2 CLK, RST Q, 5 z 8,2 4/27,/3, 24,3 D 8 Q 8,2 CLK 3/9,/ RST Q c /,/ 5/,/2
22 22 COP [F. Brglez, 84] C x : the probability of x being. O x : the probability of x being observed at a PO. C x O a a b x C x = C a C b O a = O x C b a b x C x = - (- C a ) (- C b ) O a = O x (- C b ) x a b C x = C a = C b O x = - (- O a ) (- O b )
23 23 An Example Controllability COP values Actual contrallabilities
24 24 An Example Observability COP values 3/ /64 3/8.5 3/8 3/ * (-/4) = 3/4 *(-/4)= 3/4 Actual observabilities.5.5 /2.5 /2 /2 3/8 3/ /4 3/4
25 PODEM: Example (/3) Initial objective=(g5,). G5 is an AND gate Choose the hardest- Back-trace to (G,). G is an AND gate Choose the hardest- Arbitrarily, back-trace to (A,). A is a PI Implication G3=. A B G CY=.25 G5 / C G2 CY=.656 G7 G3 G4 G6
26 PODEM: Example (2/3) The initial objective satisfied? No! Current objective=(g5,). G5 is an AND gate Choose the hardest- Back-trace to (G,). G is an AND gate Choose the hardest- Arbitrarily, back-trace to (B,). B is a PI Implication G=, G6=. A B G CY=.25 G5 / C G2 G3 G4 CY=.656 G6 G7
27 PODEM: Example (3/3) The initial objective satisfied? No! Current objective=(g5,). The value of G is known Back-trace to (G4,). The value of G3 is known Back-trace to (G2,). A, B is known Back-trace to (C,). C is a PI Implication G2=, G4=, G5=D, G7=D. A B G CY=.25 G5 /=D C G2 CY=.656 G7 D G3 G4 G6 No backtracking!!
28 If The Backtracing Is Not Guided (/3) Initial objective=(g5,). Choose path G5-G4-G2-A A=. Implication for A= G=, G5= Backtracking to A=. Implication for A= G3=. A B G G5 / C G2 G7 G4 G6 G3
29 If The Backtracing Is Not Guided (2/3) The initial objective satisfied? No! Current objective=(g5,). Choose path G5-G4-G2-B B=. Implication for B= G=, G5= Backtracking to B=. Implication for B= G=, G6=. A B G G5 / C G2 G7 G4 G6 G3
30 If The Backtracing Is Not Guided (3/3) The initial objective satisfied? No! Current objective=(g5,). Choose path G5-G4-G2-C C=. Implication for C= G2=, G4=, G5=D, G7=D. A B C G G2 G3 G4 G5 G6 /=D G7 D A F B F C S Two times of backtracking!!
31 3 High-Level Testability Analysis Based on behavioral level circuit model. Usually part of the behavior synthesis program. To improve the testability at earlier design stage.
32 32 Data Flow Graph (DFG) Each node corresponds to a register. Each arc represents a combinational path between two registers. a b d e a b d e R R2 R3 R4 R R2 R3 R4 g + + g
33 33 A High-Level Testability Measure Sequential Depth The length of a sequential path between two nodes is the number of arcs along the path. The sequential depth between a pair of registers is the length of the shortest path between them. a b d e R R2 R3 R4 g R R : R2 R : R3 R : 2 R4 R : 2 a g : 2 b g : 3 d g : 4 e g : 4
34 34 Testability Enhancement Improve controllability and observability of registers. Whenever possible, allocate a register to at least one PI or PO. Reduce the sequential depth between a controllable and an observable registers. a b d e R R2 R3 R4 R R : R2 R : R3 R : 2 R4 R : 2 g
35 35 An Example a b d e a b d e R R2 R3 R4 R R2 R3 R4 g g + a b d e R R2 R3 R4 a b d e R R2 R3 R4 g g
36 36 a b d e R R2 R3 R4 a b d e R R2 R3 R4 g g R R : R2 R : R3 R : 2 R4 R : 2 R R2 : R2 R2 : R3 R2 : R4 R2 :
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