As pointed out by several users, introduction of parallel operations on
vectors severely impacts solver performance on small problems, with time
consumption increasing with the number of threads.
In order to minimize overhead of trying to execute small tasks using a
large number of threads, task scheduling mechanism was changed to avoid
scheduling all tasks at once.
However, there is still a large difference in exectuion time because the
main thread always launches the next thread before starting doing the
work. This leads to several orders of magnitude slowdown when going from
a single-threaded execution (which follows a fast-forward path to a
single loop over all indices, without any synchronization involved)
to a two-thread execution:
/bin/parallel_vector_operations_benchmark
-------------------------------------------
Benchmark Time
-------------------------------------------
SetZero/128 12.8 ns
SetZeroParallel/128/1 16.6 ns
SetZeroParallel/128/2 2211 ns
In order to eliminate this effect, we limit the block-size of parallel
execution of vector operations to 2^16 elements (thus, starting parallel
execution only for vectors of at least 2^17 elements).
Threshold of 2^16 elements was choosen by evaluating thresholds from
2^10 to 2^20 (only powers of 2), with 2^14..2^20 significantly reducing
worst-case runtime degradation.
Details can be found in discussion of the issue at
https://github.com/ceres-solver/ceres-solver/issues/1016
Change-Id: I555c882d63ee53323ceb426743b970f989b65503
As pointed out by several users, introduction of parallel operations on
vectors severely impacts solver performance on small problems, with time
consumption increasing with the number of threads.
The problem is two-fold:
- Single-threaded execution is faster than multi-threaded
- Overhead of multi-threaded execution increases dramaticaly when
number of threads is increased
Supposedly, the second problem is due to ParallelInvoke scheduling
a task for each thread via ThreadPool.
When the time required to perform computations is smaller than costs of
scheduling task, runtime becomes linear in num_threads.
Moreover, main thread competes with working threads for mutex in
ConcurrentQueue.
In order to limit scheduling overhead and minimize lock contention,
each new task is scheduled from the previous one, if:
- Number of scheduled tasks is less than num_threads
- At the moment of creating the task not all work has been done
Correctness is granted by atomicity of thread_id counter.
SchedulerBenchmark mini-benchmark was added to illustrate the issue.
Each iteration of parallel loop performs change of a single value.
With the previous scheduling strategy, increasing number of threads
leads to significant increase of runtime:
-----------------------------------------------------
Benchmark Time Iterations
-----------------------------------------------------
SchedulerBenchmark/128/1 14.1 ns 49496153
SchedulerBenchmark/128/2 3965 ns 240173
SchedulerBenchmark/128/4 13162 ns 71478
SchedulerBenchmark/128/8 30643 ns 29614
SchedulerBenchmark/128/16 63694 ns 10000
SchedulerBenchmark/256/1 24.1 ns 28943598
SchedulerBenchmark/256/2 3878 ns 227498
SchedulerBenchmark/256/4 13293 ns 69817
SchedulerBenchmark/256/8 31117 ns 32640
SchedulerBenchmark/256/16 59503 ns 14910
SchedulerBenchmark/1024/1 56.7 ns 12048398
SchedulerBenchmark/1024/2 4346 ns 203140
SchedulerBenchmark/1024/4 13487 ns 66736
SchedulerBenchmark/1024/8 30982 ns 33090
SchedulerBenchmark/1024/16 63199 ns 14762
SchedulerBenchmark/4096/1 189 ns 3633540
SchedulerBenchmark/4096/2 5932 ns 131884
SchedulerBenchmark/4096/4 14784 ns 61236
SchedulerBenchmark/4096/8 35857 ns 29276
SchedulerBenchmark/4096/16 63934 ns 10000
With new scheduling strategy, increasing requested number of threads
does not result in that high increase of runtime
-----------------------------------------------------
Benchmark Time Iterations
-----------------------------------------------------
SchedulerBenchmark/128/1 14.1 ns 49323498
SchedulerBenchmark/128/2 2411 ns 362916
SchedulerBenchmark/128/4 3556 ns 243026
SchedulerBenchmark/128/8 4346 ns 200626
SchedulerBenchmark/128/16 5066 ns 169698
SchedulerBenchmark/256/1 24.2 ns 28960018
SchedulerBenchmark/256/2 2330 ns 388470
SchedulerBenchmark/256/4 3864 ns 219233
SchedulerBenchmark/256/8 4399 ns 195225
SchedulerBenchmark/256/16 5111 ns 161858
SchedulerBenchmark/1024/1 55.9 ns 12204777
SchedulerBenchmark/1024/2 2541 ns 329807
SchedulerBenchmark/1024/4 3977 ns 222628
SchedulerBenchmark/1024/8 4607 ns 193548
SchedulerBenchmark/1024/16 5031 ns 160285
SchedulerBenchmark/4096/1 188 ns 3714433
SchedulerBenchmark/4096/2 4203 ns 188284
SchedulerBenchmark/4096/4 4832 ns 171811
SchedulerBenchmark/4096/8 5605 ns 159093
SchedulerBenchmark/4096/16 6425 ns 126861
(both runs were executed on 28-core 56-thread cpu)
Change-Id: I91eca783280598997bfe6abd28019847731692e4
Sameer Agarwal