May 11, 2006 High-Level Spectral ATPG 1

High-Level Test Generationfor Gate-level Fault Coverage

Nitin Yogi and Vishwani D. AgrawalAuburn University

Department of ECEAuburn, AL 36849

May 11, 2006 High-Level Spectral ATPG 2

Outline

• Need for High Level Testing

• Problem and Approach

• Spectral analysis and generation of test sequences

• RTL testing approach

• Experimental Results

• Conclusion

May 11, 2006 High-Level Spectral ATPG 3

Need for High Level Testing

• Motivations for high level testing:– Low testing complexity– Low testing times and costs– Early detection of testability issues during

design phase at high level or RTL– Difficulty of gate-level test generation for black

box cores with known functionality

Seems interesting !But is it feasible ?

May 11, 2006 High-Level Spectral ATPG 4

Problem and Approach

• The problem is …– Develop synthesis-independent ATPG methods using

RTL circuit description.

• And our approach is: – Implementation-independent characterization:

• RTL test generation• Characterization of RTL vectors for spectral components

and the noise level for each PI of the circuit.

– Test generation for gate-level implementation:• Generation of spectral vectors• Fault simulation and vector compaction

That’s fine !But does it work ?

May 11, 2006 High-Level Spectral ATPG 5

RTL Faults

CombinationalLogic

FF

FF

Inputs Outputs

RTL stuck-at fault sites

May 11, 2006 High-Level Spectral ATPG 6

Walsh Functions and Hadamard Spectrum

1 1 1 1 1 1 1 11 -1 1 -1 1 -1 1 -11 1 -1 -1 1 1 -1 -11 -1 -1 1 1 -1 -1 11 1 1 1 -1 -1 -1 -11 -1 1 -1 -1 1 -1 11 1 -1 -1 -1 -1 1 11 -1 -1 1 -1 1 1 -1

H8 =

w0

w1

w2

w3

w4

w5

w6

w7

Wal

sh f

unct

ions

(or

der

8)

• Walsh functions form an orthogonal and complete set of basis functions that can represent any arbitrary bit-stream.

• Walsh functions are the rows of the Hadamard matrix.

• Example of Hadamard matrix of order 8:

OK…so its just another way of representing information

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Characterizing a Bit-Stream

• A bit-stream is correlated with each row of Hadamard matrix.• Highly correlated basis Walsh functions are retained as essential

components and others are regarded as noise.

Bit stream to analyze

Correlating with Walsh functions by multiplying with Hadamard matrix.

Essential component (others noise)

Hadamard Matrix

Bit stream

Spectral coeffs.

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Test Vector Generation• Spectrum for new bit-streams consists of the essential components and

added random noise.• Essential component plus noise spectra are converted into bit-streams by

multiplying with Hadamard matrix.• Any number of bit-streams can be generated; all contain the same essential

components but differ in their noise spectrum.

Perturbation

Generation of test vectors by multiplying with Hadamard matrix

Spectral components

Essential component

retainedNew test vector

OK…so you are refining the bit stream

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RTL Testing Approach (Circuit Characterization)

• RTL test generation:– Test vectors are generated for RTL faults

(PIs, POs and inputs - outputs of flip-flops.)

• Spectral analysis:– Test sequences for each input are analyzed using Hadamard

matrix.– Essential components are currently determined by comparing

their power Hi2 with the average power per component M2.

– Condition to pick-out essential components:

where K is a constant

– The process starts with the highest magnitude component and is repeated till the criteria is not satisfied.

KM

Ηi2

2

May 11, 2006 High-Level Spectral ATPG 10

Circuit b01: Coefficient Analysis (Vectors for RTL faults obtained from delay optimized circuit)

-25

-20

-15

-10

-5

0

5

10

15

20

25

C0 C2 C4 C6 C8 C10 C12 C14 C16 C18 C20 C22 C24 C26 C28 C30

Coefficients

Mag

nit

ud

e Input 1

Input 2

Reset

Magnitudes of 32 Hadamard Coeffs. for 3 inputs of b01

Examples of essential

components

Examples of noise

components

May 11, 2006 High-Level Spectral ATPG 11

Selecting Minimal Vector Sequences Using ILP• A set of perturbation vector sequences

{V1, V2, .. , VM} are generated.• Vector sequences are fault simulated and faults detected by

each is obtained.• Compaction problem: Find minimum set of vector

sequences which cover all the detected faults.• Minimize Count{V1, … ,VM} to obtain compressed seq. {V1,… ,VC}

where {V1, … ,VC} {V1, … , VM} Count{V1, … ,VC} ≤ Count{V1, … ,VM} Fault Coverage{V1, … ,VC} = Fault Coverage{V1, … ,VM}

• Compaction problem is formulated as an Integer Linear Program (ILP) [1].

OK…I got that…..What about the RESULTS !!!

[1] P. Drineas and Y. Makris, “Independent Test Sequence Compaction through Integer Programming," Proc. ICCD’03, pp. 380-386.

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Experimental Results• RTL Spectral ATPG technique applied to the following benchmarks:

– three ITC’99 high level RTL circuits– four ISCAS’89 circuits.– PARWAN processor (Z. Navabi, VHDL: Analysis and Modeling of Digital Systems, McGraw-Hill, 1993.)

• Characteristics of benchmark circuits:

• ATPG for RTL faults and fault simulation performed using commercial sequential ATPG tool Mentor Graphics FlexTest.

• Results obtained on Sun Ultra 5 machines with 256MB RAM.

Circuit benchmark PIs POs FFs

b01 ITC’99 2 2 5

b09 ITC’99 1 1 28

b11 ITC’99 7 6 31

b14 ITC’99 34 54 239

s1488 ISCAS’89 8 19 6

s5378 ISCAS’89 36 49 179

s9234 ISCAS’89 37 39 211

s35932 ISCAS’89 36 320 1728

PARWAN processor 11 23 53

May 11, 2006 High-Level Spectral ATPG 13

Results for b11-A

No. of RTL faults

Number of Vectors

RTL test cov. (%)

CPU* seconds

No. of spec. components

Gate level test cov. (%) of RTL vecs.

240 224 76.16 530 256 74.09

* Sun Ultra 5, 256MB RAM

No. of gate-level faults

RTL ATPG

Spectral Test SetsGate-level ATPG

Gate level cov.

(%)

Number of vectors

CPU* seconds

Gate level cov. (%)

Number of vectors

CPU* seconds

2380 88.84 768 737 84.62 468 1866

RTL characterization:

RTL-ATPG results:

May 11, 2006 High-Level Spectral ATPG 14

b11-A Circuit

0

10

20

30

40

50

60

70

80

90

100

1 10 100 1000 10000

Number of Vectors

Te

st

Co

ve

rag

e (

%)

RTL spectralATPG

Gate-levelATPG

Randomvectors

RTL faultvectors

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PARWAN processor

0

10

20

30

40

50

60

70

80

90

100

1 10 100 1000 10000

No. of Vectors

Tes

t co

vera

ge

(%) RTL spectral

ATPG

Gate-levelATPG

Randomvectors

RTL faultvectors

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ResultsCircuit name

No. of gate-level faults

RTL-ATPG spectral tests Gate-level ATPG Random inputs

Cov. (%)

No. of vectors

CPU (secs)

Cov. (%)

No. of vectors

CPU (secs)

No. of vectors

Cov (%)

b01-A 228 99.57 128 19 99.77 75 1 640 97.78

b01-D 290 98.77 128 19 99.77 91 1 640 95.80

b09-A 882 84.68 640 730 84.56 436 384 3840 11.71

b09-D 1048 84.21 768 815 78.82 555 575 7680 6.09

b11-A 2380 88.84 768 737 84.62 468 1866 3840 45.29

b11-D 3070 89.25 1024 987 86.16 365 3076 3840 41.42

b14 25894 85.09 6656 5436 68.78 500 6574 12800 74.61

s1488 4184 95.65 512 103 98.42 470 131 1600 67.47

s5378 15584 76.49 2432 2088 76.79 835 4439 3840 67.10

s5378* 15944 73.59 1399 718 73.31 332 22567 2880 62.77

s9234 28976 17.36 64 721 20.14 6967 18241 160 15.44

s9234* 29400 49.47 832 2734 48.74 12365 4119 2176 33.06

s35932 103204 95.70 256 1801 95.99 744 3192 320 50.70

PARWAN 5380 89.11 1344 1006 87.11 718 3626 6400 76.63* Reset input added.

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Conclusion• Spectral RTL ATPG technique applied to three ITC’99

and four ISCAS’89 benchmarks, and a processor circuit.• Results indicate promise in further development of the

Spectral RTL ATPG technique.• Test generation using Spectral RTL ATPG brings with it

all the benefits of high level testing • Techniques that will enhance Spectral ATPG are:

– Efficient RTL ATPG– Accurate determination and use of noise components– Better compaction algorithms

• Future work: Spectral characterization of functional vectors.

May 11, 2006 High-Level Spectral ATPG 18

Thank You !

Questions ?