Description
Compute.scala is a Scala library for scientific computing with Ndimensional arrays in parallel on GPU, CPU and other devices.
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README
Compute.scala
Compute.scala is a Scala library for scientific computing with Ndimensional arrays in parallel on GPU, CPU and other devices. It will be the primary backend of the incoming DeepLearning.scala 3.0, to address performance problems we encountered in DeepLearning.scala 2.0 with ND4J.
 Compute.scala can dynamically merge multiple operators into one kernel program, which runs significantly faster when performing complex computation.
 Compute.scala manages data buffers and other native resources in a determinate approach, consuming less memory and reducing the performance impact due to garbage collection.
 All dimensional transformation operators (
permute
,broadcast
,translate
, etc) in Compute.scala are views, with no additional data buffer allocation.  Ndimensional arrays in Compute.scala can be split to JVM collections, which support higherordered functions like
map
/reduce
, and still can run on GPU.
Getting started
System Requirements
Compute.scala is based on LWJGL 3's OpenCL binding, which supports AMD, NVIDIA and Intel's GPU and CPU on Linux, Windows and macOS.
Make sure you have met the following system requirements before using Compute.scala.
 Linux, Windows or macOS
 JDK 8
 OpenCL runtime
The performance of Compute.scala varies with OpenCL runtimes. For best performance, install the OpenCL runtime according to the following table.
Linux  Windows  macOS  

NVIDIA GPU  NVIDIA GPU Driver  NVIDIA GPU Driver  macOS's builtin OpenCL SDK 
AMD GPU  AMDGPUPRO Driver  AMD OpenCL™ 2.0 Driver  macOS's builtin OpenCL SDK 
Intel or AMD CPU  POCL  POCL  POCL 
Especially, Compute.scala produces nonvectorized code, which needs POCL's autovectorization feature for best performance when running on CPU.
Project setup
The artifacts of Compute.scala is published on Maven central repository for Scala 2.11 and 2.12. Add the following settings to your build.sbt
if you are using sbt.
libraryDependencies += "com.thoughtworks.compute" %% "cpu" % "latest.release"
libraryDependencies += "com.thoughtworks.compute" %% "gpu" % "latest.release"
// LWJGL OpenCL library
libraryDependencies += "org.lwjgl" % "lwjglopencl" % "latest.release"
// Platform dependent runtime of LWJGL core library
libraryDependencies += ("org.lwjgl" % "lwjgl" % "latest.release").jar().classifier {
import scala.util.Properties._
if (isMac) {
"nativesmacos"
} else if (isLinux) {
"nativeslinux"
} else if (isWin) {
"nativeswindows"
} else {
throw new MessageOnlyException(s"lwjgl does not support $osName")
}
}
Check Compute.scala on Scaladex and LWJGL customize tool for settings for Maven, Gradle and other build tools.
Creating an Ndimensional array
Import types in gpu
or cpu
object according to the OpenCL runtime you want to use.
// For Ndimensional array on GPU
import com.thoughtworks.compute.gpu._
// For Ndimensional array on CPU
import com.thoughtworks.compute.cpu._
In Compute.scala, an Ndimensional array is typed as Tensor
, which can be created from Seq
or Array
.
val my2DArray: Tensor = Tensor(Array(Seq(1.0f, 2.0f, 3.0f), Seq(4.0f, 5.0f, 6.0f)))
If you print out my2DArray
,
println(my2DArray)
then the output should be
[[1.0,2.0,3.0],[4.0,5.0,6.0]]
You can also print the sizes of each dimension using the shape
method.
// Output 2 because my2DArray is a 2D array.
println(my2DArray.shape.length)
// Output 2 because the size of first dimension of my2DArray is 2.
println(my2DArray.shape(0)) // 2
// Output 3 because the size of second dimension of my2DArray is 3.
println(my2DArray.shape(1)) // 3
So my2DArray
is a 2D array of 2x3 size.
Scalar value
Note that a Tensor
can be a zero dimensional array, which is simply a scalar value.
val scalar = Tensor(42.0f)
println(scalar.shape.length) // 0
Elementwise operators
Elementwise operators are performed for each element of in Tensor
operands.
val plus100 = my2DArray + Tensor.fill(100.0f, Array(2, 3))
println(plus100) // Output [[101.0,102.0,103.0],[104.0,105.0,106.0]]
Design
Lazyevaluation
Tensor
s in Compute.scala are immutable and lazyevaluated. All operators that create Tensor
s are pure, which allocate zero data buffer and not execute any timeconsuming tasks. The actual computation is only performed when the final result is requested.
For example:
val a = Tensor(Seq(Seq(1.0f, 2.0f, 3.0f), Seq(4.0f, 5.0f, 6.0f)))
val b = Tensor(Seq(Seq(7.0f, 8.0f, 9.0f), Seq(10.0f, 11.0f, 12.0f)))
val c = Tensor(Seq(Seq(13.0f, 14.0f, 15.0f), Seq(16.0f, 17.0f, 18.0f)))
val result: InlineTensor = a * b + c
All the Tensor
s, including a
, b
, c
and result
are small JVM objects and no computation is performed up to now.
println(result.toString)
When result.toString
is called, the Compute.scala compiles the expression a * b + c
into one kernel program and execute it.
Both result
and the temporary variable a * b
are InlineTensor
s, indicating their computation can be inlined into a more complex kernel program. You can think of an InlineTensor
as an @inline def
method on device side.
This approach is faster than other libraries because we don't have to execute two kernels for multiplication and addition respectively.
Check the Scaladoc seeing which operators return InlineTensor
or its subtype TransformedTensor
, which can be inlined into a more complex kernel program as well.
Caching
By default, when result.toString
is called more than once, the expression a * b + c
is executed more than once.
println(result.toString)
// The computation is performed, again
println(result.toString)
Fortunately, we provides a doCache
method to eagerly allocate data buffer for a CachedTensor
.
import com.thoughtworks.future._
import com.thoughtworks.raii.asynchronous._
val Resource(cachedTensor, releaseCache) = result.doCache.acquire.blockingAwait
try {
// The cache is reused. No deviceside computation is performed.
println(cachedTensor.toString)
// The cache is reused. No deviceside computation is performed.
println(cachedTensor.toString)
val tmp: InlineTensor = exp(cachedTensor)
// The cache for cachedTensor is reused, but the exponential function is performed.
println(tmp.toString)
// The cache for cachedTensor is reused, but the exponential function is performed, again.
println(tmp.toString)
} finally {
releaseCache.blockingAwait
}
// Crash because the data buffer has been released
println(releaseCache.toString)
The data buffer allocated for cachedTensor
is kept until releaseCache
is performed.
You can think of a CachedTensor
as a lazy val
on device side.
By combining pure Tensor
s along with the impure doCache
mechanism, we achieved the following goals:
 All
Tensor
s are pure. No data buffer is allocated when creating them.  The computation of
Tensor
s can be merged together, to minimize the number of intermediate data buffers and kernel programs.  The developers can create caches for
Tensor
s, as a determinate way to manage the lifecycle of resources.
Mutable variables
Tensor
s are immutable, but you can create mutable variables of cached tensor to workaround the limitation.
var Resource(weight, releaseWeight) = Tensor.random(Array(32, 32)).doCache.acquire.blockingAwait
while (true) {
val Resource(newWeight, releaseNewWeight) = (weight * Tensor.random(Array(32, 32))).doCache.acquire.blockingAwait
releaseWeight.blockingAwait
weight = newWeight
releaseWeight = releaseNewWeight
}
Use this approach with caution. doCache
should be only used for permanent data (e.g. the weights of a neural network). doCache
is not designed for intermediate variables in a complex expression. A sophisticated Scala developer should be able to entirely avoid var
and while
in favor of recurisive functions.
Scala collection interoperability
split
A Tensor
can be split
into small Tensor
s on the direction of a specific dimension.
For example, given a 3D tensor whose shape
is 2×3×4,
val my3DTensor = Tensor((0.0f until 24.0f by 1.0f).grouped(4).toSeq.grouped(3).toSeq)
val Array(2, 3, 4) = my3DTensor.shape
when split
it at the dimension #0,
val subtensors0: Seq[Tensor] = my3DTensor.split(dimension = 0)
then the result should be a Seq
of two 3×4 tensors.
// Output: TensorSeq([[0.0,1.0,2.0,3.0],[4.0,5.0,6.0,7.0],[8.0,9.0,10.0,11.0]], [[12.0,13.0,14.0,15.0],[16.0,17.0,18.0,19.0],[20.0,21.0,22.0,23.0]])
println(subtensors0)
When split
it at the dimension #1,
val subtensors1: Seq[Tensor] = my3DTensor.split(dimension = 1)
then the result should be a Seq
of three 2×4 tensors.
// Output: TensorSeq([[0.0,1.0,2.0,3.0],[12.0,13.0,14.0,15.0]], [[4.0,5.0,6.0,7.0],[16.0,17.0,18.0,19.0]], [[8.0,9.0,10.0,11.0],[20.0,21.0,22.0,23.0]])
println(subtensors1)
Then you can use arbitrary Scala collection functions on the Seq
of subtensors.
join
Multiple Tensor
s of the same shape
can be merged into a larger Tensor
via the Tensor.join
function.
Given a Seq
of three 2×2 Tensor
s,
val mySubtensors: Seq[Tensor] = Seq(
Tensor(Seq(Seq(1.0f, 2.0f), Seq(3.0f, 4.0f))),
Tensor(Seq(Seq(5.0f, 6.0f), Seq(7.0f, 8.0f))),
Tensor(Seq(Seq(9.0f, 10.0f), Seq(11.0f, 12.0f))),
)
when join
ing them,
val merged: Tensor = Tensor.join(mySubtensors)
then the result should be a 2x2x3 Tensor
.
// Output: [[[1.0,5.0,9.0],[2.0,6.0,10.0]],[[3.0,7.0,11.0],[4.0,8.0,12.0]]]
println(merged.toString)
Generally, when join
ing n Tensor
s of shape a0 × a1 × a2 × ⋯ × ai , the shape of the result Tensor
is a0 × a1 × a2 × ⋯ × ai × n
Case study: fast matrix multiplication via split
and join
By combining split
and join
, you can create complex computation in the following steps:
 Using
split
to createSeq
s from some of dimensions ofTensor
s.  Using Scala collection functions to manipulate
Seq
s.  Using
join
to merge transformedSeq
back toTensor
.
For example, you can implement matrix multiplication in this style.
def matrixMultiply1(matrix1: Tensor, matrix2: Tensor): Tensor = {
val columns1 = matrix1.split(1)
val columns2 = matrix2.split(1)
val resultColumns = columns2.map { column2: Tensor =>
(columns1 zip column2.split(0))
.map {
case (l: Tensor, r: Tensor) =>
l * r.broadcast(l.shape)
}
.reduce[Tensor](_ + _)
}
Tensor.join(resultColumns)
}
You can imagine the Scala collection function calls as the code generator of the kernel program, thus the loop running in Scala collection will finally become an unrolled loop in the kernel program.
The above matrixMultiply1
will create a kernel program that contains an unrolled loop of each row and column of matrix2
. Thus it runs very fast when matrix1
is big and matrix2
is small. Our benchmark shows that the above matrixMultiply1
runs even faster than ND4J's cuBLAS backend, on a Titan X GPU, when matrix1
is 65536×8 and matrix2
is 8×8.
You can also create another version of matrix multiplication, which only unrolls the loop of each row of matrix2
.
def matrixMultiply2(matrix1: Tensor, matrix2: Tensor): Tensor = {
val Array(i, j) = matrix1.shape
val Array(`j`, k) = matrix2.shape
val broadcastMatrix1 = matrix1.broadcast(Array(i, j, k))
val broadcastMatrix2 = matrix2.reshape(Array(1, j, k)).broadcast(Array(i, j, k))
val product = broadcastMatrix1 * broadcastMatrix2
product.split(1).reduce[Tensor](_ + _)
}
matrixMultiply2
will run faster than matrixMultiply1
when matrix1
is small.
A sophisticated matrix multiplication should dynamically switch the two implementations according to matrix size.
val UnrollThreshold = 4000
def matrixMultiply(matrix1: Tensor, matrix2: Tensor): Tensor = {
if (matrix1.shape.head >= UnrollThreshold) {
matrixMultiply1(matrix1, matrix2)
} else {
matrixMultiply2(matrix1, matrix2)
}
}
The final version of matrixMultiply
will have good performance for both small and big matrixes.
Benchmark
We created some benchmarks for Compute.scala and ND4J on NVIDIA and AMD GPU in an immutable style.
 Compute.scala vs ND4J on an NVIDIA Titan X GPU (source code)
 Compute.scala on an AMD RX480 GPU (source code)
Some information can be found in the benchmark result:
 Apparently, Compute.scala supports both NVIDIA GPU and AMD GPU, while ND4J does not support AMD GPU.
 Compute.scala is faster than ND4J when performing complex expressions.
 Compute.scala is faster than ND4J on large arrays.
 ND4J is faster than Compute.scala when performing one simple primary operation on small arrays.
 ND4J's
permute
andbroadcast
are extremely slow, causing very low score in the convolution benchmark.
Note that the above result of ND4J is not the same as the performance in Deeplearning4j, because Deeplearning4j uses ND4J in a mutable style (i.e. a *= b; a += c
instead of a * b + c
) and ND4J has some undocumented optimizions for permute
and broadcast
when they are invoked with some special parameters from Deeplearning4j.
Future work
Now this project is only a minimum viable product. Many important features are still under development:
 Support tensors of elements other than singleprecision floatingpoint (#104).
 Add more OpenCL math functions (#101).
 Further optimization of performance (#62, #103).
 Other backends (CUDA, Vulkan Compute).
Contribution is welcome. Check good first issues to start hacking.