All aforesaid reordering schemes, such as RORC, ROBPR, and SIRO, focus on reducing the power consumption during scan-based testing. However, these reordering schemes may result in long wire length of scan paths since the con-nection of scan cells is determined by cells’ response or pattern correlations, not cells’ physical distance. In this section, we proposed a scan-cell reorder-ing scheme, named PRORO (Power and Routreorder-ing-Overhead ReOrderreorder-ing), which combines the ROBPR with routing consideration. The same idea can be applied to SIRO as well.
8.1 Detail Steps of Reordering Considering both Power and Routing Overhead In PRORO, we reorder the scan cells after the placement is done. Based on the placement result, we use the Manhattan distance between two scan cells to approximate the wire length between the two cells. When selecting the next ordered scan cell, we incorporate this approximated wire length into the cost function and hence can limit the routing overhead. In our implementation, the placement is done by a commercial back-end tool and the position of each scan cell is obtained by parsing its DEF file.
Basically, PRORO contains almost the same five steps as that of ROBPR, except some modifications to the step 2 and 3. Therefore, this subsection only shows the details of step 2 and 3. The rest of the steps all follow the steps in ROBPR.
8.1.1 Construct a Directed Multiple-Weight Graph Based on Response/
Pattern Correlations and Routing Overhead. As mentioned, the Manhattan distance between two cells is used to represent their routing overhead. In or-der to make the quantity of routing overhead compatible with the quantity of the cost function regarding scan-shift power, we normalize two cells’ routing overhead (represented by the Manhattan distance) to a value between 0 to 1, which is defined as the routing weight between the two cells. We set the longest distance between any two cells as a routing weight of 1, and the shortest dis-tance as a routing weight of 0.
The directed graph constructed in this section is a revised version of the directed graph introduced in ROBPR (step 2 in Section 6.1.2). An edge in the graph contains three weights (Wp, Wr, Wl), where Wp, Wrand Wlrepresent the pattern correlation, the response correlation, and the routing weight between the two cells, respectively. Figure 12 shows an example of constructing such a directed graph given the correlation and routing weight between three scan cells.
8.1.2 Find the Hamiltonian Path with the Minimum WTC. We use a sim-ilar greedy TSP algorithm as shown in Figure 7 except its cost function CT, which is modified as follows to control the trade-off between scan-shift power and routing overhead.
CT(Vi, Vj, n) = (1 − β) × CP(Vi, Vj, n) + β × CR(Vi, Vj). (8)
Fig. 12. Construction of the directed graph based on correlations and routing effects.
CR(Vi, Vj) represents the routing weight between cells Vi and Vj. CP(Vi, Vj, n) represents the cost function of scan-shift power when selecting the nth cell and ranges from 0 to 1 as well. The value of CP(Vi, Vj, n) is computed by the value of Cost(Vi, Vj, n) divided by the maximum value of Cost(Vi, Vj, n) between any two cells, where Cost(Vi, Vj, n) is defined in ROBPR (see Figure 7).
The parameterβ in CT(Vi, Vj, n) is call the optimization factor, which is used to control the trade-off between scan-shift power and routing overhead. The value ofβ ranges from 0 to 1. If β increases, this TSP algorithm focuses more on reducing routing overhead. Ifβ decreases, this TSP algorithm focuses more on reducing scan-shift transitions. Figure 13 shows the details of this TSP algorithm.
8.2 Experimental Results
We conduct the following experiments to compare the results of PRORO us-ing different optimization factors with the results of ROBPR and a scan-cell reordering scheme supported by a commercial back-end tool [Cadence 2006], where ROBPR only focuses on minimizing the scan-shift transitions and Cadence’s [2006] scan-cell reordering only focuses on minimizing the rout-ing overhead of scan paths after the placement is done. In the followrout-ing ex-periments, we first use ROBPR to obtain a scan-cell ordering and apply the APR tool in Cadence [2006] to get its placement. Then both PRORO and Cadence’s [2006] scan-cell reordering are performed based on this placement of ROBPR. Cadence’s [2006] scan-cell reordering is performed by using the com-mand “scanreorder” in Cadence [2006]. A TSMC 0.18μm CMOS technology with 5 metal layers is used in the experiments.
Table XIV first lists the total number of scan-shift transitions generated by different scan-cell reordering schemes. For the convenience of result compar-ison, Table XIV normalizes the total number of scan-shift transitions of each reordering scheme by dividing it with the total number of scan-shift transitions of ROBPR, which is supposed to be the reordering scheme generating the least scan-shift transitions in this experiment.
Table XV lists the estimated wire length of the scan paths (inμm) generated by different scan-cell reordering schemes. This estimated wire length of scan paths is measured by the summation of the Manhattan distance between any two adjacent scan cells. Similar to Table XIV, Table XV also normalizes the
Scan-Cell Reordering for Minimizing Scan-Shift Power
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10: 25Fig. 13. The proposed algorithm for finding a Hamiltonian path optimizing power and routing overhead in PRORO.
Table XIV. Comparisons of Scan-Shift Transitions Generated by Different Scan-Cell Reordering Schemes
circuit method ROBPR PRORO [Cadence 2006]
β = 0.25 β = 0.5 β = 0.75 reordering s13207 total trans. 3,665,027 3,895,618 4,074,157 4,324,338 8,490,452
normalized 1.00 1.06 1.11 1.18 2.32
s15850 total trans. 2,994,375 3,034,897 3,533,745 3,729,978 7,013,465
normalized 1.00 1.02 1.19 1.25 2.36
s35932 total trans. 7,329,830 7,491,731 8,165,155 9,500,240 16,994,567
normalized 1.00 1.02 1.12 1.30 2.32
s38417 total trans. 39,396,985 40,505,086 41,866,409 43,820,365 82,459,089
normalized 1.00 1.03 1.07 1.12 2.10
s38584 total trans. 37,493,542 37,527,256 38,305,451 39,692,049 60,049,467
normalized 1.00 1.00 1.02 1.06 1.60
b17 total trans. 63,096,447 64,846,104 68,542,710 84,217,531 295,180,622
normalized 1.00 1.03 1.09 1.34 4.70
b20 total trans. 8,357,887 8,913,037 9,275,721 11,098,671 16,092,439
normalized 1.00 1.07 1.11 1.33 1.93
b21 total trans. 7,887,930 9,169,859 9,383,991 10,140,868 17,417,163
normalized 1.00 1.16 1.19 1.29 2.21
b22 total trans. 16,878,768 18,206,365 19,318,666 22,159,697 34,902,204
normalized 1.00 1.08 1.15 1.32 2.07
avg. normalized 1.00 1.05 1.12 1.24 2.40
Table XV. Comparisons of Scan Path’s Wire Length (μm) after Global Route Generated by Different Scan-Cell Reordering Schemes
circuit method ROBPR PRORO [Cadence 2006]
β = 0.25 β = 0.5 β = 0.75 reordering s13207 scan wire length 23,494 20,366 20,240 17,939 8,769
normalized 2.68 2.32 2.31 2.05 1.00
s15850 scan wire length 20,628 17,235 16,787 15,017 8,204
normalized 2.51 2.10 2.05 1.83 1.00
s35932 scan wire length 174,595 115,435 81,122 64,720 24,551
normalized 7.11 4.70 3.30 2.64 1.00
s38417 scan wire length 65,372 57,655 49,622 47,316 22,605
normalized 2.89 2.55 2.20 2.09 1.00
s38584 scan wire length 91,460 64,784 56,182 54,412 21,361
normalized 4.28 3.03 2.63 2.55 1.00
b17 scan wire length 60,729 56,566 54,437 51,740 23,657
normalized 2.57 2.39 2.30 2.19 1.00
b20 scan wire length 20,838 19,821 18,599 18,278 8,814
normalized 2.36 2.25 2.11 2.07 1.00
b21 scan wire length 21,032 20,502 17,915 16,812 8,371
normalized 2.51 2.45 2.14 2.01 1.00
b22 scan wire length 36,080 31,928 30,083 28,120 13,139
normalized 2.75 2.43 2.29 2.14 1.00
avg. normalized 3.30 2.69 2.37 2.17 1.00
Table XVI. Comparisons of Total Wire Length (μm) after Detailed Route Generated by Different Scan-Cell Reordering Schemes
circuit method ROBPR PRORO [Cadence 2006]
β = 0.25 β = 0.5 β = 0.75 reordering s13207 total wire length 179,304 150,990 140,076 132,945 132,240
normalized 1.35 1.14 1.06 1.01 1.00
s15850 total wire length 166,007 148,994 140,033 144,092 132,585
normalized 1.25 1.12 1.06 1.09 1.00
s35932 total wire length 822,755 533,494 513,903 481,645 398,855
normalized 2.06 1.34 1.29 1.21 1.00
s38417 total wire length 493,421 429,109 432,452 409,148 397,568
normalized 1.24 1.08 1.09 1.03 1.00
s38584 total wire length 786,806 656,511 673,550 667,683 658,329
normalized 1.20 1.00 1.02 1.01 1.00
b17 total wire length 1,269,029 1,245,434 1,239,651 1,255,198 1,245,979
normalized 1.02 1.00 0.99 1.01 1.00
b20 total wire length 376,651 371,546 378,538 375,255 358,385
normalized 1.05 1.04 1.06 1.05 1.00
b21 total wire length 397,848 380,094 375,095 380,892 364,586
normalized 1.09 1.04 1.03 1.04 1.00
b22 total wire length 579,858 566,337 562,492 550,547 549,135
normalized 1.06 1.03 1.02 1.00 1.00
avg. normalized 1.26 1.09 1.07 1.05 1.00
wire length of scan paths of each reordering scheme by dividing it with that of Cadence’s [2006] reordering scheme, which is supposed to be the reordering scheme generating the shortest wire length of scan paths in this experiment.
Table XVI further lists the total wire length (including the routing for both scan paths and CUT) generated by each reordering scheme after detailed route.
Scan-Cell Reordering for Minimizing Scan-Shift Power
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10: 27As the results show in Table XIV, if only minimizing the wire length of scan paths such as tool Cadence’s [2006] reordering scheme, 2.4 times the scan-shift transitions of ROBPR are generated, where ROBPR only minimizes scan-shift transitions. On the other hand, ROBPR requires 3.3 times the wire length of scan paths of tool Cadence’s [2006] reordering scheme as shown in Table XV. In fact, the wire length spent on CUT’s routing is much more than the wire length spent on scan paths’ routing. Thus, after detailed route, the total wire length of ROBPR is 1.26 times the total wire length of Cadence’s [2006] reordering scheme as shown in Table XVI.
Also, the experimental results in Tables XIV, XV, and XVI show that the trade-off between scan-shift transitions and scan path’s wire length can be con-trolled by PRORO with different optimization factors. Using a larger optimiza-tion factor, PRORO can reduce more wire length of scan paths but generate more scan-shift transitions. When the optimization factor equals 0.5, PRORO generates 12% more scan-shift transitions compared to ROBPR but only re-quires 7% total wire length after detailed route, which is an acceptable level of routing overhead as long as the design is not intensively routing-congested.
Another reason to sacrifice the wire length of scan paths for the scan-shift power is that the for advanced process technologies, the violation of hold-time constraints on scan paths occurs more often than the violation of setup-time constraints. Designers even intentionally increase the wire length of some scan paths to meet the hold-time constraint instead of applying a scan-cell reordering to reduce its wire length. Therefore, the motivation of reducing wire length on scan paths may not be as strong as that in the old process technologies.
9. CONCLUSIONS
In this article, we first presented a scan-cell reordering technique which can si-multaneously reduce scan-shift transitions based on the response correlations and preserve don’t-care bits in the test patterns for a later minimization of scan-in transitions using MT-fill (Section 4). Second, we considered both the re-sponse correlation and pattern correlations during the cell reordering process to further reduce the scan-in transitions generated by MT-fill (Section 6). Next, we utilized the inverse connection between scan cells to turn a low correlation into a high one and developed a corresponding scan-cell reordering scheme to consider those inverse correlations (Section 7). Last, we incorporated the rout-ing overhead of scan paths into the cost function of our scan-cell reorderrout-ing and hence the trade-off between scan path’s routing overhead and the number of scan-shift transitions can be controlled by a user-specified factor. In addition, a postprocess pattern-reordering scheme was also proposed to minimize the in-between transitions (Section 5). A series of experiments were conducted to compare the proposed schemes with a previous reordering scheme [Bonhomme et al. 2002] and a commercial tool’s reordering scheme [Cadence 2006]. The experimental results demonstrated the effectiveness and efficiency of each of the proposed scan-cell reordering schemes.
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Received February 2010; revised July 2010; accepted September 2010