parallel arrays and sorting
Norm Rubin
nrubin at nvidia.com
Fri Apr 19 05:58:14 PDT 2013
Histograms are looking like a good collection of examples for experimenting with ParallelJS
Here are some histogram options
1) dense histograms where some bins have a zero entry and
2) sparse histograms where only the non-zero bins are stored
Sometimes you know the number of bins beforehand but in general, you need to look at the data to find the min and max
For example given the data set [2 1 0 0 2 2 1 1 1 1 4] contains 2 zeros, 5 ones, and 3 twos and 1 four, is[2 5 3 0 1]
using the dense method and[(0,2), (1,5), (2,3), (4,1)] using the sparse method. Since there are no threes, the sparse histogram representation does not contain a bin for that value
One way to store the sparse histogram is as two separate arrays one of keys and one of bin counts
[0 1 2 4] and [2 5 3 1] (The soa format )
If the number of bins is relatively small compared to the input size, then binary search based dense might be the best performing while if the number of bins is near the input size then the sparse version might be better
If I just add prims, here are two ways to calculate histograms
Dense
Sort the data
Find the number of bins, equal to max value plus one
Allocate the space to hold the histogram, and fill it with 0,1,2,3.. max value
Initially set each histogram bin to upperbound
Upper bound is a useful prim
Given a sorted array, and a set of values use binary search to find the last position in the sorted array where each data value could be inserted, all the binary search ops happen in parallel
(I'm not sure if there is a nice way to express this op in ParallelArrays)
n At this point we have a vector of positions the pair hist[i], hist[i+1] are the indexes in the sorted data that go into bin i
In parallel do all the adds, no need for atomics
Your alternative -
find the max
Allocate the bins
Scatter each element to the bin number, handle collisions by an add, works but I suspect it will be a lot slower, because each add has to be atomic and will need synchronization
Another alternative for dense histograms would require knowing a lot of machine details
If you knew you were on a cpu not a gpu, you could form a partial histogram per core and then serially combine the results but on a gpu with massive parallelism, the space for all the partial histograms would be problematic so you would need to lay this out carefully - like share some of the partial histograms over blocks of threads
Sparse
Sort the data
Need to find the number of bins, which is the number of unique values
Reduce using sum ( Map if data [i] = data[j] then 0, else 1) - counts the number of values that are different from the prior
Allocate two arrays keys and counts
Reduce by key - this is a generalization of reduce, Reduce each element with the same key returning the set of keys and the reduced results which sets up both arrays, (another tricky prim to express)
From: Herhut, Stephan A [mailto:stephan.a.herhut at intel.com]
Sent: Friday, April 19, 2013 12:45 AM
To: Norm Rubin; es-discuss at mozilla.org
Cc: dev-tech-js-engine-rivertrail at lists.mozilla.org
Subject: RE: parallel arrays and sorting
Thanks for the overview of thrust. I had completely missed the issue of stability before. This needs careful consideration and I have not yet made up my mind. I understand the desire to have unstable sort for performance reasons, but it also introduces a form of non-determinism.
Histogram can also be expressed using scatter in out API. Assuming some array A of color values, you can do
A.map((v) => 1).scatter(A.map((v) => bucket(v)), 0, (a,b) => a+b, numberOfBuckets)
So, essentially create a vector of 1's and then scatter those to your buckets based on their bucket value, using addition as the conflict resolution. Sorting the scatter indices indeed makes a lot of sense and an implementation would be free to first sort the vector of scatter indices to reduce synchronization cost. I also thought about an explicit version directly using sort and some other primitives of our API but I could not come up with a formulation that would benefit from sorting.
The array of structures (AoS) vs. structures of arrays (SoA) transformation is problematic in JavaScript. In C like languages one has a lot of structural information, in particular the fields and types of a structure are statically known and homogeneous across an array. In JavaScript, on the other hand, objects can be used like structures but in general there may be a lot more dynamism: Arrays may contain objects with varying labels, properties may have different types and, probably worst of all, the programmer can add new properties to objects at any time. So even though a structure may start out as a homogeneous array, this can change during its lifetime. Analyzing these data structures and tracking the 'anomalies' seems not straight forward to me and I am not convinced that this can be implemented efficiently.
However, there is also good news. The binary data proposal (see http://wiki.ecmascript.org/doku.php?id=harmony:binary_data) brings C like data types, including arrays of structures, to JavaScript and we have proposed an extension to Parallel JavaScript that makes use of binary data as storage format (see http://wiki.ecmascript.org/doku.php?id=strawman:data_parallelism#support_for_binary_data). In such a setting, doing automatic AoS to SoA transformations is possible and our programming model does not preclude this.
Stephan
From: Norm Rubin [mailto:nrubin at nvidia.com]
Sent: Thursday, April 11, 2013 11:36 AM
To: Herhut, Stephan A; es-discuss at mozilla.org<mailto:es-discuss at mozilla.org>
Cc: dev-tech-js-engine-rivertrail at lists.mozilla.org<mailto:dev-tech-js-engine-rivertrail at lists.mozilla.org>
Subject: RE: parallel arrays and sorting
Good set of questions about sort, thanks for looking at this carefully. You guys have been great about responding to my emails.
One sorting application that I would expect is physics particle simulation, where the code might sort objects based on distance from the viewer. This could be used so that far away objects get rendered smaller.
Another might be computing a histogram over a visual image - sort the data first so nearby values will go into the same bucket, without needing atomic synchronization.
Sorting with an optional compare seems ok to me- even if implementations can only optimize for some comparisons
One interesting question you brought up as part of sorting by key is pretty tricky.
In general parallel data arrays would like to be stored in transposed order from classic cpu styles.
We usually call this array of structures or structures of arrays
Do we sort an array of objects each with multiple fields stored one object after another or do we sort multiple arrays, with all the values of field1 followed by all the values of field2 etc
I'd hope we allow implementations to reorder the data within a parallelArray as they like without needing to expose the layout to developers. Thrust, on the other hand, pushes the layout to the developer and thus has a significant set of transpose routines.
Just for a point of reference there are 8 versions of sort in the thrust library. As you can see, Thrust never aimed to be a minimal set it just gained operations as applications appeared. AMD has a similar library called bolt which uses the same interface.
Two different parallel libraries with the same routines does suggest that this set is enough to do useful work.
Internally thrust notices that the compare is < on primitive types and uses radix sort (on the gpu).
Thurst includes:
Stable and unstable forms
Ascending only or with a comparison function
Single array or a pair of keys and values
1) Sort(array) - sorts the array into ascending order, not guaranteed to be stable
2) Sort (array)- with a comparison function
3) Sort by key (keys, values) returns both the reordered keys and the reordered values, sorted by the array keys. This one is kind of confusing so here is an example
// an example of key sorting
#include <thrust/sort.h<http://docs.thrust.googlecode.com/hg/sort_8h.html>>
const int N = 6;
int keys[N] = { 1, 4, 2, 8, 5, 7};
char values[N] = {'a', 'b', 'c', 'd', 'e', 'f'};
thrust::sort_by_key<http://docs.thrust.googlecode.com/hg/group__sorting.html#ga2bb765aeef19f6a04ca8b8ba11efff24>(keys, keys + N, values, thrust::greater<int><http://docs.thrust.googlecode.com/hg/structthrust_1_1greater.html>());
// keys is now { 8, 7, 5, 4, 2, 1}
// values is now {'d', 'f', 'e', 'b', 'c', 'a'}
4) Sort by key with a comparison function
5-8 the stable forms
Based on the thrust primitives, one parallel array sort might be
Sort an array of objects
Besides the array the arguments might be
- a flag indicating if the sort must be stable
- an optional user compare function that defaulted to < on primitive types
From: Herhut, Stephan A [mailto:stephan.a.herhut at intel.com]
Sent: Thursday, April 11, 2013 1:09 PM
To: Norm Rubin; es-discuss at mozilla.org<mailto:es-discuss at mozilla.org>
Subject: RE: parallel arrays and sorting
Rick is travelling, so let me chime in.
We have discussed this back and forth but have not come to a conclusion. Generally, we agree that adding a sort primitive makes a lot of sense, in particular as the Array object in JavaScript already has a sort method. Also, as you too mentioned, implementing an efficient sort as a library function without knowing the details of the parallel hardware used is difficult, to say the least. So sort ticks all the boxes to become a primitive.
The other, and arguably more difficult question, is what a sort method should look like. If we take JavaScript's existing Array.sort, the sort method would get an (optional) comparator function. However, using a comparator would preclude the use of radix sort.
An alternative would be to implement sorting of primitive types only. This brings back more choice in sort algorithms but limits use. For such a design, we considered a function as optional argument to sort that, given a value from the ParallelArray to be sorted, returns a key used for comparison, which again needs to be a primitive. This would at least enable sorting of objects by a field and, at some runtime cost, sorting of general data.
The tradeoff between these two approaches, and probably other designs, is hard to judge without knowing what sort is used for. So we decided to wait for some good use cases before deciding on a specific design.
Sorry, no answers only further questions.
Stephan
From: es-discuss-bounces at mozilla.org<mailto:es-discuss-bounces at mozilla.org> [mailto:es-discuss-bounces at mozilla.org] On Behalf Of Norm Rubin
Sent: Monday, April 08, 2013 7:46 AM
To: es-discuss at mozilla.org<mailto:es-discuss at mozilla.org>
Subject: parallel arrays and sorting
In comparing ParallelArrays (rivertrail) to the cuda thrust library, I noticed that Sorting using parallelArrays looks like a missing primitive operation.
Sorting is special because the good (high performance) algorithm on a gpu is radix sort, while the good (high performance) algorithm on the cpu is parallel merge sort, The other way around radix sort of cpu, or parallel merge sort of a gpu is very slow and often worse than serial implementations
Sadly it is well past a jit to take the code for one flavor of sort and transform it into the other, while it would be pretty simple for a run-time to pick a good sort, if only it knew that a sort was going on. Run times would not be required to do so here since they can always pick a slow sort.
I know this is a slippery road, since once you add another prim, adding more prims becomes ever easier but sorting seems pretty important. And array already has a sort, so adding a version that works on ParallelArrays does not seem so bad.
What do you guys think?
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