3. High-Level Fault Grading 3
Motivation
Gate-level fault simulation is
computationally infeasible for large
circuits
RTL design available early in the design
cycle for fault grading of available
(validation or legacy) test vectors
It would be nice if fault analysis could
be done at RTL level but the results
closely approximated gate-level
coverage.
4. High-Level Fault Grading 4
Basic Idea
Inject stuck-type faults on all PIs,
internal signals, and their fanouts using
RTL constructs.
Use an RTL fault simulator (e.g.
Verifault for Verilog) for fault grading at
the RTL level
Verify the closeness of approximation
against gate-level fault coverage.
11. High-Level Fault Grading 11
Critique
Technique works well only when the circuit is
simulated at low-level RTL
Errors arise because of:
Differences in fanouts at the two levels
Most signal fanout lot more at the RTL level (exception:
Reset signal)
Complex blocks with only I/O visibility
The last shortcoming is addressed in the
stratified sampling approach of Thaker,
Agrawal, and Zaghloul that we consider next.
12. Stratified Sampling for Fault
Coverage of VLSI Systems
Vishwani D. Agrawal
Auburn University
Collaborators: Pradip Thaker and Mona Zaghloul
13. High-Level Fault Grading 14
Problem
Accurately estimate the gate-level fault
coverage for a VLSI system at the RT-level
Advantages:
Improve test
Improve design
Avoid expensive design changes
Previous approaches do not accurately
represent gate-level fault coverage (function
errors, mutation, statement faults, branch
faults, etc.)
14. High-Level Fault Grading 15
Solution
Model faults as representative sample
of the targeted (gate-level stuck-at)
faults.
Treat the coverage in an RTL module as
a statistical sampling estimate.
For a multi-module VLSI system,
combine module coverages according to
the stratified sampling technique.
15. High-Level Fault Grading 17
Fault Sampling
A randomly selected subset (sample) of
faults is simulated.
Measured coverage in the sample is
used to estimate fault coverage in the
entire circuit.
Advantage: Saving in computing
resources (CPU time and memory.)
Disadvantage: Limited data on
undetected faults.
16. High-Level Fault Grading 20
Sampling Error Bounds
C (1 - C )
| x - C | = 3 [ -------------- ] 1/2
Ns
Solving the quadratic equation for C, we get the 3-sigma
(99.8% confidence) estimate (Agrawal-Kato, 1990):
4.5
C 3s = x ------- [1 + 0.44 Ns x (1 - x )]1/2
Ns
Where Ns is sample size and x is the measured fault
coverage in the sample.
Example: A circuit with 39,096 faults has an actual
fault coverage of 87.1%. The measured coverage in
a random sample of 1,000 faults is 88.7%. The above
formula gives an estimate of 88.7% 3%. CPU time for
sample simulation was about 10% of that for all faults.
Millot, 1923
17. High-Level Fault Grading 21
An RTL Fault Model
(ITC-2000)
Language operators are assumed to be fault-free
Variables (map onto signal lines) contain faults
stuck-at-0
stuck-at-1
Only one fault is applied at a time (single fault
assumption)
18. High-Level Fault Grading 22
RTL Fault Injection
Not affected by faults:
Synthetic operators + - * >= <= == !=
Boolean operators & | ^ ~
Logical operators && || !
Sequential elements (flip-flops & latches)
Faults introduced in signal variables (stems and
fan-outs)
Separate faults for bits of data words
19. High-Level Fault Grading 23
Fault Modeling for Boolean
Operators
module mux(c, a, b, s);
assign d = a & s;
assign e = s1 & b;
assign s1 = !s;
assign c = d | e;
endmodule
RTL Description Symbolic Description
a
s
b
d
e
c
s1
20. High-Level Fault Grading 24
Stem and Fan-out Fault Modeling
RTL fan-out faults: if(X) then Z=Y; else Z=!Y;
Unique RTL fault is placed on each fan-out of each bit of a
variable
Unique RTL fault on each stem
(a)
module
(b)
module
21. High-Level Fault Grading 25
More RTL Faults
b [1 ]
b [0 ]
a [ 1 ]
d [1 ]
c [ 0 ]
c [ 1 ]
a [ 0 ]
d [0 ]
+
-
*
f [2 :0 ]
e [ 3 : 0 ]
g [2 :0 ]
<
f [2 :0 ]
>
e [3 :0 ]
e [3 :0 ]
g [ 2 :0 ]
f [2 :0 ]
=
h
j
i
M
U
X
c lk
r e s e t _
v
w
k
o u t_ si g 1
o u t_ s ig 2
g [2 :0 ]
22. High-Level Fault Grading 26
Observations and Assumption: RTL Faults
RTL faults may have detection probability
distribution similar to that of collapsed gate-level
faults
Statistically, an RTL fault-list approximates a
random sample from the gate-level fault-list
Number of RTL faults vs. gate-level faults depends
on
Level of RTL description
Synthesis procedure used to convert RTL to gate level
23. High-Level Fault Grading 27
RTL Fault Simulation
Analogous to gate-level approach
Faults injected in RTL code of the design
description by a C++ parser; a logic buffer
element inserted at fault site (technique
identical to Mao & Gulati’s).
Fault report contains statistics on detected
and undetected RTL faults
Cadence’s Verifault-XL used as RTL fault
simulator
24. High-Level Fault Grading 28
Estimation Error for
Module Fault Coverage
RTL fault coverage assumed to be an
estimate of the collapsed gate-fault coverage
within statistical bound [Agrawal and Kato,
D&T, 1990]:
2
2
1 4 1 2
k
N
Nc c k
( )/
a = 3.00 for confidence probability of 99.8%
c = ratio of detected to total number of RTL faults
M = number of gate faults
N = number of RTL faults, k = 1 - N/M
26. High-Level Fault Grading 30
RTL Faults and VLSI System
Coverage
Experimental results demonstrate RTL fault
coverage of a module to be a good statistical
estimate of the gate-level fault coverage
A VLSI system consists of many
interconnected modules
Overall RTL fault-list of a VLSI system does
not constitute a representative sample of the
gate-level fault-list
27. High-Level Fault Grading 31
Error at System Level
RTL Coverage = (0.91 x 100 + 0.39 x 100) / 200 = 65%
Gate Coverage = (0.90 x 150 + 0.40 x 400) / 550 = 54%
A correct estimation of gate-level fault coverage from RTL
coverage:
91 x (150 / 550) + 39 x (400 / 550) = 53%
M2
100 faults
39% cov.
M1
100 faults
91% cov.
M1
150 faults
90% cov.
M2
400 faults
40% cov.
RTL Gate-
level
28. High-Level Fault Grading 32
Application of Stratified Sampling
Fault population of a VLSI system divided into
strata according to RTL module boundaries
RTL faults in each module are considered a
sample of corresponding gate-level faults
The stratified RTL coverage is an estimate of
the gate-level coverage:
Wm = stratum weight of mth module = Gm/G
cm = RTL fault coverage of mth module
Gm = number of gate-level faults in mth module
G = number of all gate-level faults in the system
M = number of RTL modules in the system
M
C = S Wmcm
m=1
29. High-Level Fault Grading 33
Application of Stratified Sampling
Range of
coverage,
where,
rm = number of RTL faults in mth module
t = value from tables of normal distribution
The technique requires knowledge of stratum weights
and not absolute values of Gm and G
s2
= cm(1 cm)
S
Wm
rm 1
m=1
M
C + t s
30. High-Level Fault Grading 34
Stratum Weight Extraction
Techniques
Logic synthesis based weight extraction
Wm = Gm/G
Floor-planning based weight extraction
Wm = Am/A
Entropy-measure based weight extraction
31. High-Level Fault Grading 35
Experimental Procedure
Technology-dependent weight extraction
Several unique gate-level netlists obtained by logic synthesis from
the same RTL code
Each synthesis run performed using a different set of constraints,
e.g., area optimization (netlist 1), speed optimization (netlist 2), or
combined area and speed optimizations (netlists 3 and 4)
Strata weights calculated using gate-level fault lists of various
synthesized netlists
Technology-independent weight extraction
Stratum weights calculated using area distribution among modules
Each set of stratum weights used to calculate RTL fault
coverage and error bounds
Impact of estimation error investigated
37. High-Level Fault Grading 41
Conclusion
Main ideas of RTL fault modeling
A small or high-level RTL module contributes few RTL faults,
but large statistical tolerance gives a correct coverage
estimate
Stratified sampling accounts for varying module sizes and for
different RTL details that may be used
Stratum weights appear to be insensitive to specific details
of synthesis
Advantages of the proposed RTL fault model
High-level test generation and evaluation
Early identification of hard-to-test RTL architectures
Potential for significantly reducing run-time penalty of the
gate-level fault simulation
38. High-Level Fault Grading 42
References - 1
V. D. Agrawal, “Sampling Techniques for Determining Fault
Coverage in LSI Circuits,” J. Digital Systems, vol. V, no. 3, pp.
189-202, 1981.
V. D. Agrawal and H. Kato, “Fault Sampling Revisited,” IEEE
Design & Test of Computers, vol. 7, no. 4, pp. 32-35, Aug. 1990.
P. A. Thaker, M. E. Zaghloul, and M. B. Amin, “Study of
Correlation of Testability Aspects of RTL Description and Resulting
Structural Implementation,” Proc. 12th Int. Conf. VLSI Design,
Jan. 1999, pp. 256-259.
P. A. Thaker, V. D. Agrawal, and M. E. Zaghloul, “Validation Vector
Grade (VVG): A New Coverage Metric for Validation and Test,”
Proc. 17th IEEE VLSI Test Symp., Apr. 1999, pp. 182-188.
39. High-Level Fault Grading 43
References - 2
P. A. Thaker, Register-Transfer Level Fault Modeling
and Evaluation Techniques, PhD Thesis, George
Washington University, Washington, D.C., May 2000.
P. A. Thaker, V. D. Agrawal, and M. E. Zaghloul,
“Register-Transfer Level Fault Modeling and Test
Evaluation Techniques for VLSI Circuits,” Proc. Int. Test
Conf., Oct. 2000, pp. 940-949.
This presentation is available from the website
http://cm.bell-labs.com/cm/cs/who/va
40. High-Level Fault Grading 44
Other Related Papers
1. OCCOM: Fallah et al., IEEE TCAD, Aug.
2001, pp. 1003-1015.
2. IFMB: Santos et al., ITC2001, pp. 377-
385.
3. Probabilistic Testability: Fernandes et
al., DATE04, pp. 10176-10181.
4. Kang et al., VTS07.
