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Benchmark Protocol
The benchmarking strategy from version 1 was vanilla flavored brute force: (8 WorkGroups)* (12 ThreadTiles)* (4 NumLoadsCoalescedAs)* (4 NumLoadsCoalescedBs)* (3 LoopUnrolls)* (5 BranchTypes)* ...*(1024 ProblemSizes)=23,592,960 is a multiplicative series which grows very quickly. Adding one more boolean parameter doubles the number of kernel enqueues of the benchmark.
Tensile version 2 allows the user to manually interrupt the multiplicative series with "additions" instead of "multiplies", i.e., (8 WorkGroups)* (12 ThreadTiles)+ (4 NumLoadsCoalescedAs)* (4 NumLoadsCoalescedBs)* (3 LoopUnrolls)+ (5 BranchTypes)* ...+(1024 ProblemSizes)=1,151 is a dramatically smaller number of enqueues. Now, adding one more boolean parameter may only add on 2 more enqueues.
To make the Tensile's programability more manageable for the user and developer, the benchmarking protocol has been split up into several steps encoded in a config.yaml file. The below sections reference the following config.yaml. Note that this config.yaml has been created to be a simple illustration and doesn't represent an actual good benchmark protocol. See the configs included in the repository (/Tensile/Configs) for examples of good benchmarking configs.
BenchmarkProblems:
- # sgemm
- # Problem Type
OperationType: GEMM
Batched: True
- # Benchmark Size-Group
InitialSolutionParameters:
- WorkGroup: [ [ 16, 16, 1 ] ]
- NumLoadsCoalescedA: [ 1 ]
- NumLoadsCoalescedB: [ 1 ]
- ThreadTile: [ [ 4, 4 ] ]
BenchmarkCommonParameters:
- ProblemSizes:
- Range: [ [512], [512], [1], [512] ]
- EdgeType: ["Branch", "ShiftPtr"]
PrefetchGlobalRead: [False, True]
ForkParameters:
- WorkGroup: [ [8, 32, 1], [16, 16, 1], [32, 8, 1] ]
ThreadTile: [ [2, 8], [4, 4], [8, 2] ]
BenchmarkForkParameters:
- ProblemSizes:
- Exact: [ 2880, 2880, 1, 2880 ]
- NumLoadsCoalescedA: [ 1, 2, 4, 8 ]
- NumLoadsCoalescedB: [ 1, 2, 4, 8 ]
JoinParameters:
- MacroTile
BenchmarkJoinParameters:
- LoopUnroll: [8, 16]
BenchmarkFinalParameters:
- ProblemSizes:
- Range: [ [16, 128], [16, 128], [1], [256] ]
A Solution is comprised of ~20 parameters, and all are needed to create a kernel. Therefore, during the first benchmark which determines which WorkGroupShape is fastest, what are the other 19 solution parameters which are used to describe the kernels that we benchmark? That's what InitialSolutionParameters are for. The solution used for benchmarking WorkGroupShape will use the parameters from InitialSolutionParameters. The user must choose good default solution parameters in order to correctly identify subsequent optimal parameters.
Each step of the benchmark can override what problem sizes will be benchmarked. A ProblemSizes entry of type Range is a list whose length is the number of indices in the ProblemType. A GEMM ProblemSizes must have 3 elements while a batched-GEMM ProblemSizes must have 4 elements. So, for a ProblemType of C[ij] = Sum[k] A[ik]*B[jk], the ProblemSizes elements represent [SizeI, SizeJ, SizeK]. For each index, there are 5 ways of specifying the sizes of that index:
- [1968]
- Benchmark only size 1968; n = 1.
- [16, 1920]
- Benchmark sizes 16 to 1968 using the default step size (=16); n = 123.
- [16, 32, 1968]
- Benchmark sizes 16 to 1968 using a step size of 32; n = 61.
- [64, 32, 16, 1968]
- Benchmark sizes from 64 to 1968 with a step size of 32. Also, increase the step size by 16 each iteration.
- This causes fewer sizes to be benchmarked when the sizes are large, and more benchmarks where the sizes are small; this is typically desired behavior.
- n = 16 (64, 96, 144, 208, 288, 384, 496, 624, 768, 928, 1104, 1296, 1504, 1728, 1968). The stride at the beginning is 32, but the stride at the end is 256.
- 0
- The size of this index is just whatever size index 0 is. For a 3-dimensional ProblemType, this allows benchmarking only a 2-dimensional or 1-dimensional slice of problem sizes.
Here are a few examples of valid ProblemSizes for 3D (Batched) GEMMs:
Range: [ [16, 128], [16, 128], [1], [16, 128] ] # n = 512
Range: [ [16, 128], 0, [1], 0] # n = 8
Range: [ [16, 16, 16, 5760], 0, [1], [1024, 1024, 4096] ] # n = 108During this first phase of benchmarking, we examine parameters which will be the same for all solutions for this ProblemType. During each step of benchmarking, there is only 1 winner. In the above example we are benchmarking the dictionary {EdgeType: [ Branch, ShiftPtr], PrefetchGlobalRead: [False, True]}.; therefore, this benchmark step generates 4 solution candidates, and the winner will be the fastest EdgeType/PrefetchGlobalRead combination. Assuming the winner is ET=SP and PGR=T, then all solutions for this ProblemType will have ET=SP and PGR=T. Also, once a parameter has been determined, all subsequent benchmarking steps will use this determined parameter rather than pulling values from InitialSolutionParameters. Because the common parameters will apply to all kernels, they are typically the parameters which are compiler-dependent or hardware-dependent rather than being tile-dependent.
If we continued to determine every parameter in the above manner, we'd end up with a single fastest solution for the specified ProblemSizes; we usually desire multiple different solutions with varying parameters which may be fastest for different groups of ProblemSizes. One simple example of this is small tiles sizes are fastest for small problem sizes, and large tiles are fastest for large tile sizes.
Therefore, we allow "forking" parameters; this means keeping multiple winners after each benchmark steps. In the above example we fork {WorkGroup: [...], ThreadTile: [...]}. This means that in subsequent benchmarking steps, rather than having one winning parameter, we'll have one winning parameter per fork permutation; we'll have 9 winners.
When we benchmark the fork parameters, we retain one winner per permutation. Therefore, we first determine the fastest NumLoadsCoalescedA for each of the WG,TT permutations, then we determine the fastest NumLoadsCoalescedB for each permutation.
After determining fastest parameters for all the forked solution permutations, we have the option of reducing the number of winning solutions. When a parameter is listed in the JoinParameters section, that means that of the kept winning solutions, each will have a different value for that parameter. Listing more parameters to join results in more winners being kept, while having a JoinParameters section with no parameters listed results on only 1 fastest solution.
In our example we join over the MacroTile (work-group x thread-tile). After forking tiles, there were 9 solutions that we kept. After joining MacroTile, we'll only keep six: 16x256, 32x128, 64x64, 128x32 and 256x16. The solutions that are kept are based on their performance during the last BenchmarkForkParameters benchmark, or, if there weren't any, JoinParameters will conduct a benchmark of all solution candidates then choose the fastest.
After narrowing the list of fastest solutions through joining, you can continue to benchmark parameters, keeping one winning parameter per solution permutation.
After all the parameter benchmarking has been completed and the final list of fastest solution has been assembled, we can benchmark all the solution over a large set of ProblemSizes. This benchmark represent the final output of benchmarking; it outputs a .csv file where the rows are all the problem sizes and the columns are all the solutions. This is the information which gets analysed to produce the library logic.