- Split SpecialFunctions files in to a separate BesselFunctions file.
In particular add:
- Modified bessel functions of the second kind k0, k1, k0e, k1e
- Bessel functions of the first kind j0, j1
- Bessel functions of the second kind y0, y1
The fixes needed are
* adding EIGEN_DEVICE_FUNC attribute to a couple of funcs (else HIPCC will error out when non-device funcs are called from global/device funcs)
* switching to using ::<math_func> instead std::<math_func> (only for HIPCC) in cases where the std::<math_func> is not recognized as a device func by HIPCC
* removing an errant "j" from a testcase (don't know how that made it in to begin with!)
* Abstracting the pointer type so that both SYCL memory and pointer can be captured.
* Converting SYCL virtual pointer to SYCL device memory in Eigen evaluator class.
* Binding SYCL placeholder accessor to command group handler by using bind method in Eigen evaluator node.
* Adding SYCL macro for controlling loop unrolling.
* Modifying the TensorDeviceSycl.h and SYCL executor method to adopt the above changes.
* Allow specifying multiple GPU architectures. E.g.:
cmake -DEIGEN_CUDA_COMPUTE_ARCH="60;70"
* Pass CUDA SDK path to clang. Without it it will default to /usr/local/cuda
which may not be the right location, if cmake was invoked with
-DCUDA_TOOLKIT_ROOT_DIR=/some/other/CUDA/path
This fixed 2 deadlocks caused by sloppiness in the EventCount logic.
Both most likely were introduced by cl/236729920 which includes the new EventCount algorithm:
01da8caf00
bug #1 (Prewait):
Prewait must not consume existing signals.
Consider the following scenario.
There are 2 thread pool threads (1 and 2) and 1 external thread (3). RunQueue is empty.
Thread 1 checks the queue, calls Prewait, checks RunQueue again and now is going to call CommitWait.
Thread 2 checks the queue and now is going to call Prewait.
Thread 3 submits 2 tasks, EventCount signals is set to 1 because only 1 waiter is registered the second signal is discarded).
Now thread 2 resumes and calls Prewait and takes away the signal.
Thread 1 resumes and calls CommitWait, there are no pending signals anymore, so it blocks.
As the result we have 2 tasks, but only 1 thread is running.
bug #2 (CancelWait):
CancelWait must not take away a signal if it's not sure that the signal was meant for this thread.
When one thread blocks and another submits a new task concurrently, the EventCount protocol guarantees only the following properties (similar to the Dekker's algorithm):
(a) the registered waiter notices presence of the new task and does not block
(b) the signaler notices presence of the waiters and wakes it
(c) both the waiter notices presence of the new task and signaler notices presence of the waiter
[it's only that both of them do not notice each other must not be possible, because it would lead to a deadlock]
CancelWait is called for cases (a) and (c). For case (c) it is OK to take the notification signal away, but it's not OK for (a) because nobody queued a signals for us and we take away a signal meant for somebody else.
Consider:
Thread 1 calls Prewait, checks RunQueue, it's empty, now it's going to call CommitWait.
Thread 3 submits 2 tasks, EventCount signals is set to 1 because only 1 waiter is registered the second signal is discarded).
Thread 2 calls Prewait, checks RunQueue, discovers the tasks, calls CancelWait and consumes the pending signal (meant for thread 1).
Now Thread 1 resumes and calls CommitWait, since there are no signals it blocks.
As the result we have 2 tasks, but only 1 thread is running.
Both deadlocks are only a problem if the tasks require parallelism. Most computational tasks do not require parallelism, i.e. a single thread will run task 1, finish it and then dequeue and run task 2.
This fix undoes some of the sloppiness in the EventCount that was meant to reduce CPU consumption by idle threads, because we now have more threads running in these corner cases. But we still don't have pthread_yield's and maybe the strictness introduced by this change will actually help to reduce tail latency because we will have threads running when we actually need them running.
B) fix deadlock in thread pool caused by RunQueue
This fixed a deadlock caused by sloppiness in the RunQueue logic.
Most likely this was introduced with the non-blocking thread pool.
The deadlock only affects workloads that require parallelism.
Most computational tasks don't require parallelism.
PopBack must not fail spuriously. If it does, it can effectively lead to single thread consuming several wake up signals.
Consider 2 worker threads are blocked.
External thread submits a task. One of the threads is woken.
It tries to steal the task, but fails due to a spurious failure in PopBack (external thread submits another task and holds the lock).
The thread executes blocking protocol again (it won't block because NonEmptyQueueIndex is precise and the thread will discover pending work, but it has called PrepareWait).
Now external thread submits another task and signals EventCount again.
The signal is consumed by the first thread again. But now we have 2 tasks pending but only 1 worker thread running.
It may be possible to fix this in a different way: make EventCount::CancelWait forward wakeup signal to a blocked thread rather then consuming it. But this looks more complex and I am not 100% that it will fix the bug.
It's also possible to have 2 versions of PopBack: one will do try_to_lock and another won't. Then worker threads could first opportunistically check all queues with try_to_lock, and only use the blocking version before blocking. But let's first fix the bug with the simpler change.
The current algorithm requires threads to commit/cancel waiting in order
they called Prewait. Spinning caused by that serialization can consume
lots of CPU time on some workloads. Restructure the algorithm to not
require that serialization and remove spin waits from Commit/CancelWait.
Note: this reduces max number of threads from 2^16 to 2^14 to leave
more space for ABA counter (which is now 22 bits).
Implementation details are explained in comments.
- cleanup noise in imaginary part of real roots
- take into account the magnitude of the derivative to check roots.
- use <= instead of < at appropriate places
