FTK variable resolution pattern banks TDAQ Week at SLAC – 11/18/2010 G. Volpi – INFN Frascati, MC Fellowship

Associative memory and SS size Large SS Small SS SS size optimization is an hard task, with many variables Using “large” SS the final AM bank is fully efficient with a limited number of patterns Using “small” SS, half the “large” SS, the number of patterns increase Decrease the chance a pattern fires for random hits (noise, tracks fragments, …) More patterns, more chips, more €€€ or $$$ Current estimate for the number of patterns per region is 25M for 2013, 5M for 2013-2014, up100M for 2018, 386 M after 2020 G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

SS size vs efficiency and road traffic 90% # of patterns in Amchips (barrel only, 45 f degress) 65M 500M Pattern size r-f: 24 pixel, 20 SCT 36 pix z Pattern size r-f: 12 pixel, 10 SCT 36 pix z (1.2 mm) (1.6 mm) (14 mm) (0.6 mm) (0.8 mm) (14 mm) The output is very different in a real scenario: i.e. using WHbb@3E34: <# roads/event @ 3E34> = 342k <# roads/event @ 3E34> = 40k G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

TSP and variable resolution Patterns with “large” and “small” SS could be related: One pattern with large SS contains many patterns with small SS A tree organization is natural AM is used to search the 1st step TSP processor could search within the sub-patterns TSP banks can be implemented using less expensive devices Final efficiency depends on the TSP patterns AM level TSP level G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

AM performance and TSP relation Most simple bank with AM patterns doubling the phi size of TSP pattern: 1 bit/layer Typical reduction factor 3 Most of the AM patterns have few sub-patterns (1, 2 or 3) Difference made by fake AM roads, rejected at TSP stage WH@3E34 shows a very small fraction of AM patterns are confirmed at TSP level A strategy able to reject the AM road with few kids early will have a large effect G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Variable resolution AM We can use don’t care on the least significant bit when we want to match the pattern layer @ AM resolution or use all the bits to match it @ TSP resolution TSP patterns AM pattern All patterns with 1 kid are stored at TSP precision All the layer without DC can ignore the hits in the “wrong” side of the layer DC G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

DC bits and sub-patterns distributions Single “kid” AM patterns Using DC single kid AM patterns are described using the best precision The number of DC bits in a bank peaks to 1 also for AM patterns with >1 sub-pattern The distribution shows how the sub-patterns are strongly correlated The DC bit in the AM chip increases the number of cells used to describe a pattern: from 15  16 The increase is 1/15~7%, the equivalent TSP bank is 3 times bigger G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Simulation strategy The FTK simulation was modified to include the DC bits Option A only simulation: 3 pixel layers + 4 SCT axial layers Option B test is ongoing 3 pileup scenarios were studied: 17, 40 and 75 pileup events For each pile-up scenario a different bank is chosen to try to meet chip development and LHC schedule The working point for each scenario is decided fixing the TSP size to have an efficiency >=90% and following our experience For each scenario the extracted numbers are: Number of roads/processing units at different simulation level using barrel only simulation: Final numbers assuming16 processing units G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

AM roads confirmed by DC Road flux 17.6 PE Bank studied using WHbb with 17.6 pileup events. TSP Total bank size 5 MP Average number of road at different levels per processing unit: 2020384283423 Strong reduction using DC, about 5. Most of the DC roads are confirmed by the TSP (74%) Often AM roads have more than 1 TSP roads Barrel only Median 95% of events 50% of events TSP roads AM board output AM roads confirmed at TSP level AM roads confirmed by DC G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Road flux 40 PE Barrel only Bank studied using WHbb with 40 pileup events. TSP Total bank size 100 MP The number of roads at the different levels per processing unit: 14780260015532286 The DC suppression factor 5.6 Barrel only G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Roads flux 75 PE Barrel only Bank studied using WHbb with 75 pileup events. TSP Total bank size 384 MP Number of roads at the different levels per processing unit: 21400330017702380 DC reduction factor 6.5 Barrel only G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Summary tables Average number of roads/units* AM AM w/ DC AM w/ TSP 17.6 evts 5040 959 709 1060 40 evts 37000 6500 3880 5720 75 evts 53500 8250 4430 5950 No DC in old AM chip To be compared with a limit of 8000 output roads. The 75 pileup events exceed that limit indeed at that time (2020) a more powerful chip should be used: 8L and maybe better use of DC with more bits/layer * the number are corrected x2.5 to include the traffic in the endcaps. 16 processing units are assumed G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Conclusions The use of DC bits gives the opportunity to strongly reduce the number of roads DC does most of the work of the TSP Is the TSP really necessary? Use of variable resolution patterns for option A showed promising results Further optimizations are possible The number of roads confirmed by he DC is within the required limit Variable resolution and DC are generic, test using the same algorithm in FTK option B ongoing G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Backup slides G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Combination flux Barrel only, correction factor 2.5 to apply The flux of the combinations is also largely effected the DC. The average number of combinations is (x103): 92.311.69.17.2 Barrel only, correction factor 2.5 to apply G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Combination flux Barrel only, correction factor 2.5 to apply The flux of the combinations is also largely effected the DC. The average number of combinations is (x103): 15719.912.89.58 Barrel only, correction factor 2.5 to apply G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010

Fit combinations flux The average numbers of combinations are (x103): 23728.516.312.7 AM@DC accounts for the hits in the unused part of the AM pattern. AM@ TSP can use only the standard DC mask. Could a dynamic DC mask reduce the fits’ number?e G. Volpi - FTK Variable resolution banks TDAQ@SLAC - 11/18/2010