Noc QoR measurement

.gitignore

@@ -38,6 +38,19 @@ vtr_flow/benchmarks/titan_blif/titan23
 vtr_flow/benchmarks/titan_blif/titan_new
 
 
+#
+# NoC MLP benchmarks
+#
+#   We ignore blif and vqm files because of thier large size.
+#   We also ignore symbolic links to traffic flow and blif files.
+#
+vtr_flow/benchmarks/noc/Large_Designs/MLP/**/*.vqm
+vtr_flow/benchmarks/noc/Large_Designs/MLP/**/*.blif
+vtr_flow/benchmarks/noc/Large_Designs/MLP/blif_files/*
+vtr_flow/benchmarks/noc/Large_Designs/MLP/traffic_flow_files/*
+MLP_Benchmark_Netlist_Files_blif.tar.gz
+MLP_Benchmark_Netlist_Files_vqm_blif.tar.gz
+
 #
 # ISPD benchmarks
 #

CMakeLists.txt

@@ -341,6 +341,14 @@ add_custom_target(get_titan_benchmarks
     WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}
     COMMENT "Downloading (~1GB) and extracting Titan benchmarks (~10GB) into VTR source tree.")
 
+#
+# NoC MLP Benchmarks
+#
+add_custom_target(get_noc_mlp_benchmarks
+        COMMAND ./vtr_flow/scripts/download_noc_mlp.py --vtr_flow_dir ./vtr_flow
+        WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}
+        COMMENT "Downloading (~100MB) and extracting NoC MLP benchmarks (~3.2GB) into VTR source tree.")
+
 #
 # ISPD Benchmarks
 #

README.developers.md

@@ -386,17 +386,21 @@ The following are key QoR metrics which should be used to evaluate the impact of
 
 Implementation Quality Metrics:
 
-| Metric                      | Meaning                                                                  | Sensitivity |
-|-----------------------------|--------------------------------------------------------------------------|-------------|
-| num_pre_packed_blocks       | Number of primitive netlist blocks (after tech. mapping, before packing) | Low         |
-| num_post_packed_blocks      | Number of Clustered Blocks (after packing)                               | Medium      |
-| device_grid_tiles           | FPGA size in grid tiles                                                  | Low-Medium  |
-| min_chan_width              | The minimum routable channel width                                       | Medium\*    |
-| crit_path_routed_wirelength | The routed wirelength at the relaxed channel width                       | Medium      |
-| critical_path_delay         | The critical path delay at the relaxed channel width                     | Medium-High |
+| Metric                          | Meaning                                                                      | Sensitivity |
+|---------------------------------|------------------------------------------------------------------------------|-------------|
+| num_pre_packed_blocks           | Number of primitive netlist blocks (after tech. mapping, before packing)     | Low         |
+| num_post_packed_blocks          | Number of Clustered Blocks (after packing)                                   | Medium      |
+| device_grid_tiles               | FPGA size in grid tiles                                                      | Low-Medium  |
+| min_chan_width                  | The minimum routable channel width                                           | Medium\*    |
+| crit_path_routed_wirelength     | The routed wirelength at the relaxed channel width                           | Medium      |
+| NoC_agg_bandwidth\**            | The total link bandwidth utilized by all traffic flows                       | Low         |
+| NoC_latency\**                  | The total time of traffic flow data transfer (summed over all traffic flows) | Low         |
+| NoC_latency_constraints_cost\** | The total number of traffic flow latency constraints                         | Low           |
 
 \* By default, VPR attempts to find the minimum routable channel width; it then performs routing at a relaxed (e.g. 1.3x minimum) channel width. At minimum channel width routing congestion can distort the true timing/wirelength characteristics. Combined with the fact that most FPGA architectures are built with an abundance of routing, post-routing metrics are usually only evaluated at the relaxed channel width.
 
+\** NoC-related metrics are only reported when --noc option is enabled.
+
 Run-time/Memory Usage Metrics:
 
 | Metric                      | Meaning                                                                        | Sensitivity |
@@ -493,7 +497,7 @@ k6_frac_N10_frac_chain_mem32K_40nm.xml	boundtop.v        	common       	9f591f6-
 k6_frac_N10_frac_chain_mem32K_40nm.xml	ch_intrinsics.v   	common       	9f591f6-dirty	success   	     	363                	493                  	270                 	247                   	10          	10           	17     	99    	130        	1           0       	1792                 	1.86527       	-194.602            	-1.86527            	46            	1562             	13                                    	1438                       	20                               	2.4542             	-226.033 	-2.4542  	0       	0       	3.92691e+06           	1.4642e+06           	259806.                          	2598.06                             	333135.                     	3331.35                        	0.03           	0.01          	-1          	-1          	-1      	0.46     	0.31      	0.94                     	0.09                	2.59                 	62684      	8672        	32940
 ```
 
-### Example: Titan Benchmarks QoR Measurements
+### Example: Titan Benchmarks QoR Measurement
 
 The [Titan benchmarks](https://docs.verilogtorouting.org/en/latest/vtr/benchmarks/#titan-benchmarks) are a group of large benchmark circuits from a wide range of applications, which are compatible with the VTR project.
 The are typically used as post-technology mapped netlists which have been pre-synthesized with Quartus.
@@ -511,7 +515,7 @@ $ make get_titan_benchmarks
 #Move to the task directory
 $ cd vtr_flow/tasks
 
-#Run the VTR benchmarks
+#Run the Titan benchmarks
 $ ../scripts/run_vtr_task.py regression_tests/vtr_reg_nightly_test2/titan_quick_qor
 
 #Several days later... they complete
@@ -528,6 +532,44 @@ stratixiv_arch.timing.xml	stereo_vision_stratixiv_arch_timing.blif	0208312
 stratixiv_arch.timing.xml	cholesky_mc_stratixiv_arch_timing.blif  	0208312     	success   	     	140214             	108592               	67410               	5444                  	121         	90           	-1     	111   	151        	-1          -1      	5221059              	8.16972       	-454610             	-8.16972            	1518597          	15                               	0                     	0                    	2.38657e+08       	21915.3              	9.34704            	-531231     -9.34704 	0       	0       	211.12   	364.32    	490.24              	6356252    	-1          	-1
 ```
 
+### Example: NoC Benchmarks QoR Measurements
+NoC benchmarks currently include synthetic and MLP benchmarks. Synthetic benchmarks have various NoC traffic patters,
+bandwidth utilization, and latency requirements. High-quality NoC router placement solutions for these benchmarks are
+known. By comparing the known solutions with NoC router placement results, the developer can evaluate the sanity of 
+the NoC router placement algorithm. MLP benchmarks are the only realistic netlists included in this benchmark set.
+
+Based on the number of NoC routers in a synthetic benchmark, it is run on one of two different architectures. All MLP
+benchmarks are run on an FPGA architecture with 16 NoC routers. Post-technology mapped netlists (blif files)
+for synthetic benchmarks are added to the VTR project. However, MLP blif files are very large and should be downloaded
+separately.
+
+Since NoC benchmarks target different FPGA architectures, they are run as different circuits. A typical way to run all
+NoC benchmarks is to run a task list and gather QoR data form different tasks:
+
+#### Running and Integrating the NoC Benchmarks with VTR
+```shell
+#From the VTR root
+
+#Download and integrate NoC MLP benchmarks into the VTR source tree
+$ make get_noc_mlp_benchmarks
+
+#Move to the task directory
+$ cd vtr_flow
+
+#Run the VTR benchmarks
+$ scripts/run_vtr_task.py -l tasks/noc_qor/task_list.txt
+
+#Several days later... they complete
+
+#NoC benchmarks are run as several different tasks. Therefore, QoR results should be gathered from multiple directories,
+#one for each task.
+$ head -5 tasks/noc_qor/large_complex_synthetic/latest/parse_results.txt
+$ head -5 tasks/noc_qor/large_simple_synthetic/latest/parse_results.txt
+$ head -5 tasks/noc_qor/small_complex_synthetic/latest/parse_results.txt
+$ head -5 tasks/noc_qor/small_simple_synthetic/latest/parse_results.txt
+$ head -5 tasks/noc_qor/MLP/latest/parse_results.txt
+```
+
 ### Example: Koios Benchmarks QoR Measurement
 
 The [Koios benchmarks](https://github.com/verilog-to-routing/vtr-verilog-to-routing/tree/master/vtr_flow/benchmarks/verilog/koios) are a group of Deep Learning benchmark circuits distributed with the VTR project.

doc/README

@@ -4,7 +4,7 @@ Overview
 The VTR documentation is generated using sphinx, a python based documentation generator.
 
 The documentation itself is written in re-structured text (files ending in .rst), which
-is a lightwieght mark-up language for text documents.
+is a lightweight mark-up language for text documents.
 
 Currently VTR's documenation is automatically built by https://readthedocs.org/projects/vtr/ and is served at:
 
@@ -36,7 +36,7 @@ from the main documentation directory (i.e. <vtr_root>/doc).
 
 This will produce the output html in the _build directory.
 
-You can then view the resulting documention with the web-browser of your choice.
+You can then view the resulting documentation with the web-browser of your choice.
 For instance:
 
     $ firefox _build/html/index.html

doc/src/vtr/benchmarks.rst

@@ -191,7 +191,20 @@ The SymbiFlow benchmarks can be downloaded and extracted by running the followin
     cd $VTR_ROOT
     make get_symbiflow_benchmarks
 
-Once downloaded and extracted, benchmarks are provided as post-synthesized eblif files under: ::
+Once downloaded and extracted, benchmarks are provided as post-synthesized blif files under: ::
 
     $VTR_ROOT/vtr_flow/benchmarks/symbiflow
 
+.. _noc_benchmarks:
+
+NoC Benchmarks
+----------------
+NoC benchmarks are composed of synthetic and MLP benchmarks and target NoC-enhanced FPGA architectures. Synthetic
+benchmarks include a wide variety of traffic flow patters and are divided into two groups: 1) simple and 2) complex
+benchmarks. As their names imply, simple benchmarks use very simple and small logic modules connected to NoC routers,
+while complex benchmarks implement more complicated functionalities like encryption. These benchmarks do not come from
+real application domains. On the other hand, MLP benchmarks include modules that perform matrix-vector multiplication
+and move data. Pre-synthesized netlists for the synthetic benchmarks are added to VTR project, but MLP netlists should
+be downloaded separately.
+
+.. note:: The NoC MLP benchmarks are not included with the VTR release (due to their size). However they can be downloaded and extracted by running ``make get_noc_mlp_benchmarks`` from the root of the VTR tree.  They can also be `downloaded manually <https://www.eecg.utoronto.ca/~vaughn/titan/>`_.

vtr_flow/benchmarks/noc/Large_Designs/MLP/Readme.txt

@@ -12,15 +12,17 @@ Benchmark Structure:
 		|---<Benchmark>.flows - Is the NoC traffic flows file associated with the given benchmark
 					(A benchmark can have multiple traffic flows files)
 		|---verilog	      - Contains design files needed to generate the netlist file for the benchmark
-	|---shared_verilog	      - Contains design files needed by all benchmarks to generate thier netlist files
+	|---shared_verilog	      - Contains design files needed by all benchmarks to generate their netlist files
+	|---blif_files	          - Contains symbolic links to all .blif files that exist in this directory
+    |---flow_files	          - Contains symbolic links to all .flow files that exist in this directory
 
 Running the benchmarks:
 	Pre-requisite
 		- Ensure VPR is built (refer to 'https://docs.verilogtorouting.org/en/latest/' for build instructions)
 		- Set 'VTR_ROOT' as environment variable pointing to the location of the VTR source tree
 		- Ensure python version 3.6.9 or higher is installed
 		- Copy over the netlist files from 'https://drive.google.com/drive/folders/135QhmfgUaGnK2ZEfbfEXtdm1BfS7YoG7?usp=sharing'.
-	          The file structure in the previous link is similiar to structure found in '$VTR_ROOT/vtr_flow/benchmarks/noc/Large_Designs/MLP'.
+	          The file structure in the previous link is similar to structure found in '$VTR_ROOT/vtr_flow/benchmarks/noc/Large_Designs/MLP'.
 		  Place the netlist files in the appropriate folder locations.
 
 	Running single instance:
@@ -48,7 +50,7 @@ Running the benchmarks:
 		  -vpr_executable $VTR_ROOT/build/vpr/vpr --device EP4SE820 -flow_file $VTR_ROOT/vtr_flow/benchmarks/noc/Large_Designs/MLP/MLP_1/mlp_1.flows \
 		  -noc_routing_algorithm xy_routing -number_of_seeds 5 -number_of_threads 1 -route
 
-	        - The above command will generate an output file in the run directory that contains all the place and route metrics. This is a txt file with a name which matches the
+	        - The above command will generate an output file in the run directory that contains all the place and route metrics. This is a txt file with a name which matches
 		  the flows file provided. So for the command shown above the output file is 'mlp_1.txt'
 
 	Special benchmarks:
@@ -64,8 +66,13 @@ Running the benchmarks:
 			  of the NoC routers needs to be locked. A 
 			- To run a single instance of this benchmark, pass in the following command line parameter and its value to the command shown above:
 			  '--fix_clusters $VTR_ROOT/vtr_flow/benchmarks/noc/Large_Designs/MLP/MLP_2_phase_optimization/MLP_2_phase_optimization_step_2/MLP_two_phase_optimization_step_two_constraints.place'
-			- To run the benchmarkusing the automated script just pass in the following command line parameter and its value to the script command above:
+			- To run the benchmarking the automated script just pass in the following command line parameter and its value to the script command above:
 			  '-fix_clusters $VTR_ROOT/vtr_flow/benchmarks/noc/Large_Designs/MLP/MLP_2_phase_optimization/MLP_2_phase_optimization_step_2/MLP_two_phase_optimization_step_two_constraints.place'
+
+	Running VTR tasks:
+        - All synthetic benchmarks can be run as VTR tasks. Example tasks are provided in vtr_flow/tasks/noc_qor
+        - Instructions on how to run VTR tasks to measure QoR for NoC benchmarks in available in VTR Developer Guide.
+
 	Expected run time:
 		- These benchmarks are quite large so the maximum expected run time for a single run is a few hours
 		- To speed up the run time with multiple VPR runs the thread count can be increased from 1. Set thread count equal to number seeds for fastest run time.

vtr_flow/benchmarks/noc/Synthetic_Designs/Readme.txt

@@ -8,7 +8,9 @@ Benchmark Structure:
 		|---<Benchmark>.flows - Is the NoC traffic flows file associated with the given benchmark
 					(A benchmark can have multiple traffic flows files)
 		|---verilog	      - Contains design files needed to generate the netlist file for the benchmark
-	|---shared_verilog	      - Contains design files needed by all benchmarks to generate thier netlist files
+	|---shared_verilog	      - Contains design files needed by all benchmarks to generate their netlist files
+	|---blif_files	          - Contains symbolic links to all .blif files that exist in this directory
+	|---flow_files	          - Contains symbolic links to all .flow files that exist in this directory
 
 Running the benchmarks:
 	Pre-requisite
@@ -42,7 +44,11 @@ Running the benchmarks:
 		  -noc_routing_algorithm xy_routing -noc_swap_percentage 40 -number_of_seeds 5 -number_of_threads 1
 
 	        - The above command will generate an output file in the run directory that contains all the place and route metrics. This is a txt file with a name which matches the
-		  the flows file provided. So for the command shown above the outout file is 'complex_2_noc_1D_chain.txt'
+		    flows file provided. So for the command shown above the output file is 'complex_2_noc_1D_chain.txt'
+
+    Running VTR tasks:
+        - All synthetic benchmarks can be run as VTR tasks. Example tasks are provided in vtr_flow/tasks/noc_qor
+        - Instructions on how to run VTR tasks to measure QoR for NoC benchmarks in available in VTR Developer Guide.
 
 	Expected run time:
 		- These benchmarks are quite small so the maximum expected run time for a single run is ~30 minutes

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_16_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././complex_16_noc_1D_chain/complex_16_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_2_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././complex_2_noc_1D_chain/complex_2_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_32_noc_clique.blif

@@ -0,0 +1 @@
+.././complex_32_noc_clique/complex_32_noc_clique.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_32_noc_star.blif

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_noc_star.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_4_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././complex_4_noc_1D_chain/complex_4_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_64_noc_clique.blif

@@ -0,0 +1 @@
+.././complex_64_noc_clique/complex_64_noc_clique.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_64_noc_nearest_neighbor.blif

@@ -0,0 +1 @@
+.././complex_64_noc_nearest_neighbor/complex_64_noc_nearest_neighbor.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_64_noc_star.blif

@@ -0,0 +1 @@
+.././complex_64_noc_star/complex_64_noc_star.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/complex_8_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././complex_8_noc_1D_chain/complex_8_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_16_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././simple_16_noc_1D_chain/simple_16_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_2_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././simple_2_noc_1D_chain/simple_2_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_32_noc_clique.blif

@@ -0,0 +1 @@
+.././simple_32_noc_clique/simple_32_noc_clique.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_32_noc_star.blif

@@ -0,0 +1 @@
+.././simple_32_noc_star/simple_32_noc_star.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_4_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././simple_4_noc_1D_chain/simple_4_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_64_noc_2D_chain.blif

@@ -0,0 +1 @@
+.././simple_64_noc_2D_chain/simple_64_noc_2D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_64_noc_clique.blif

@@ -0,0 +1 @@
+.././simple_64_noc_clique/simple_64_noc_clique.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_64_noc_star.blif

@@ -0,0 +1 @@
+.././simple_64_noc_star/simple_64_noc_star.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/simple_8_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././simple_8_noc_1D_chain/simple_8_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/spread_2_noc_1D_chain.blif

@@ -0,0 +1 @@
+.././spread_2_noc_1D_chain/spread_2_noc_1D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/spread_32_noc_clique.blif

@@ -0,0 +1 @@
+.././spread_32_noc_clique/spread_32_noc_clique.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/spread_32_noc_star.blif

@@ -0,0 +1 @@
+.././spread_32_noc_star/spread_32_noc_star.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/spread_64_noc_2D_chain.blif

@@ -0,0 +1 @@
+.././spread_64_noc_2D_chain/spread_64_noc_2D_chain.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/spread_64_noc_clique.blif

@@ -0,0 +1 @@
+.././spread_64_noc_clique/spread_64_noc_clique.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/blif_files/spread_64_noc_star.blif

@@ -0,0 +1 @@
+.././spread_64_noc_star/spread_64_noc_star.blif

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_16_noc_1D_chain.flows

@@ -0,0 +1 @@
+.././complex_16_noc_1D_chain/complex_16_noc_1D_chain.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_2_noc_1D_chain.flows

@@ -0,0 +1 @@
+.././complex_2_noc_1D_chain/complex_2_noc_1D_chain.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_noc_clique.flows

@@ -0,0 +1 @@
+.././complex_32_noc_clique/complex_32_noc_clique.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_noc_star.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_noc_star.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_noc_star_no_constraints.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_noc_star_no_constraints.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_star_12_latency_constraints.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_star_12_latency_constraints.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_star_24_latency_constraints.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_star_24_latency_constraints.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_star_2_bandwdiths.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_star_2_bandwdiths.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_star_31_latency_constraints.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_star_31_latency_constraints.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_star_3_bandwdiths.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_star_3_bandwdiths.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_star_4_bandwdiths.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_star_4_bandwdiths.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_32_star_4_latency_constraints.flows

@@ -0,0 +1 @@
+.././complex_32_noc_star/complex_32_star_4_latency_constraints.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_4_noc_1D_chain.flows

@@ -0,0 +1 @@
+.././complex_4_noc_1D_chain/complex_4_noc_1D_chain.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_64_noc_clique.flows

@@ -0,0 +1 @@
+.././complex_64_noc_clique/complex_64_noc_clique.flows

vtr_flow/benchmarks/noc/Synthetic_Designs/traffic_flow_files/complex_64_noc_nearest_neighbor.flows

@@ -0,0 +1 @@
+.././complex_64_noc_nearest_neighbor/complex_64_noc_nearest_neighbor.flows