lecture_03_GPU_computing.jl

### A Pluto.jl notebook ###
# v0.20.18

#> [frontmatter]
#> title = "Lecture 03"

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    #! format: off
    return quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
    #! format: on
end

# ╔═╡ f695f3c2-9215-11f0-1eb1-fde5e8318217
begin
	using PlutoUI, PlutoTeachingTools
	using PlutoUI: Slider
	PlutoUI.TableOfContents(; depth=4)
end

# ╔═╡ 778871eb-7387-4046-afb2-eefe4bfd453f
begin
	using CairoMakie
	set_theme!(theme_latexfonts();
			   fontsize = 16,
			   Lines = (linewidth = 2,),
			   markersize = 16)
end

# ╔═╡ 4661f37a-a116-4f40-99fe-cf4314cfeeff
using LinearAlgebra, Random

# ╔═╡ 7379af68-0afd-4e26-b9f5-e239f677657d
using KernelAbstractions, BenchmarkTools

# ╔═╡ 910c0f4a-caa7-4482-ad03-a6224e8df409
using Atomix: @atomic, @atomicswap, @atomicreplace

# ╔═╡ cbdc2dc8-8246-4377-9d12-0bf748d3a158
using GPUArraysCore

# ╔═╡ 918f7bfe-dc80-418c-9ddf-99ff8907ff61
md"""
## Accessing the GPU node

Getting onto the remote server

1. User name `juliaXX`
2. `ssh juliaxx@licca-li-02.rz.uni-augsburg.de`
3. Jump to `ssh licca047`
4. `git clone https://github.com/hpsc-lab/spp2256-software-dev`
5. `cd spp2256-software-dev`
5. `./start_notebook.sh`


You will see something like:
```
On your local machine run
    ssh -f -N licca-li-02.rz.uni-augsburg.de -L 1729:localhost:1729
```

And later:
```
┌ Info:
│ Go to http://localhost:1729/?secret=XXXXXX in your browser to start writing ~ have fun!
```
"""

# ╔═╡ ef309337-b906-4f77-9eb7-c373238e051e
md"""
# Accelerated Computing
"""

# ╔═╡ c656f4aa-697f-4a07-b8a4-242218c29a9d
md"""
A GPU has many "lightweight" threads
"""

# ╔═╡ b723a980-8e5c-4e96-9a9b-88e25857b651
md"""
#### CPU die shot

$(RobustLocalResource("https://s3.amazonaws.com/media-p.slid.es/uploads/779853/images/4399827/800px-coffee_lake_die__quad_core___annotated_.png", "quad_core.png"))
"""

# ╔═╡ 1a15dc6e-e190-4b83-89e0-45d62e131930
md"""
#### GPU block-diagram

$(RobustLocalResource("https://devblogs.nvidia.com/parallelforall/wp-content/uploads/2016/04/gp100_block_diagram-1-624x368.png", "p100.png"))
"""

# ╔═╡ 51d23938-fdef-414f-8912-2d9cc5c19dc6
md"""
#### Bottlenecks

$(RobustLocalResource("https://s3.amazonaws.com/media-p.slid.es/uploads/779853/images/4399848/pasted-from-clipboard.png", "gpu_system.png"))
"""

# ╔═╡ af917e4b-d13b-4477-bdda-df10eb0a01c7
md"""
#### Composable infrastructure

##### Core
- GPUCompiler.jl: Takes native Julia code and compiles it directly to GPUs
- GPUArrays.jl: High-level array based common functionality
- KerneAbstractions.jl: Vendor-agnostic kernel programming language
- Adapt.jl: Translate complex structs across the host-device boundary

##### Vendor specific
- CUDA.jl
- AMDGPU.jl
- oneAPI.jl
- Metal.jl

"""

# ╔═╡ 5db16d40-b38b-4f02-bfa5-9c54de107fff
md"""
#### Different layers of abstraction

##### Vendor-specific
```julia
using CUDA

function saxpy!(a,X,Y)
	i = (blockIdx().x - 1) * blockDim().x + threadIdx().x
	if i <= length(Y)
		@inbounds Y[i] = a * X[i] + Y[i]
	end
	return nothing
end

@cuda threads=32 blocks=cld(length(Y), 32) saxpy!(a, X, Y)
```

##### KernelAbstractions

```julia
using KernelAbstractions
using CUDA

@kernel function saxpy!(a, @Const(X), Y)
    I = @index(Global)
    @inbounds Y[I] = a * X[I] + Y[I]
end

saxpy!(CUDABackend())(a, X, Y, ndrange=length(Y))
```

##### Array abstractions

```julia
Y .= a .* X .+ Y
```

"""

# ╔═╡ f9d99731-b26f-467b-8e09-215b35da978a
md"""
#### Asynchronous operations

!!! warn
    GPU operations are asynchronous with regards to the host! They are **ordered** with respect to each other, but special care must be taken when using Julia's task based programming together with GPU programming.

The JuliaGPU ecosystem **synchronizes** the GPU on access, so when you move data from and to the GPU we wait for all the kernels to finish!

See the exercise "Introduction to KernelAbstractions" for more details on how to measure GPU kernels and performance.
"""

# ╔═╡ 7efdca23-1543-42bb-b9d4-56bc99e0239a
md"""
#### How to use KernelAbstractions

- Use `@kernel function mykernel(args...) end` to write a GPU-style program
- Instantiate kernel for a backend `kernel = mykernel(backend)`
- Backends come from Vendor specific libraries
- `KA.allocate(backend, ...)` to obtain memory
- Launch kernel `kernel(args..., ndrange=...)` while specifying the grid to execute over.
"""

# ╔═╡ 59e7ab7d-57e2-4a5f-9d30-0a569b188b36
TwoColumn(
md"""
```julia
function vadd(a, b, c)
	for i in eachindex(c)
		c[i] = a[i] + b[i]
	end
end



a = rand(N)
b = rand(N)
c = similar(a)

	
vadd(a, b, c)
```
""",
md"""
```julia
import KernelAbstractions as KA
	
@kernel function vadd(a, b, c)
	i = @index(Global)
	c[i] = a[i] + b[i]
end

backend = CUDABackend()
a = KA.allocate(backend, Float32, N)
b = KA.allocate(backend, Float32, N)
c = similar(a)

vadd_kernel = vadd(backend)
vadd_kernel(a, b, c; ndrange=size(c))
```
""")

# ╔═╡ fa761189-630c-405e-88e3-c7eb727a3c45
md"""
!!! note
	GPU execution is asynchronous! We will discuss the details in the later GPU lecture. When benchmarking you need to synchronize the device!

	```julia
		@benchmark begin 
			vadd_kernel(a, b, c; ndrange=size(c))
			KA.synchronize(backend)
		end
	```
	Otherwise you are only measuring the **launch** of the kernel.
"""

# ╔═╡ 87024a8a-2a31-48d7-b601-d7b49956165a
md"""
#### High-level array based programming

Julia and GPUArrays.jl provide support for an efficient GPU programming environment build around array abstractions and higher-order functions.

- **Vocabulary of operations**: `map`, `broadcast`, `scan`, `reduce`, ... 
  Map naturally onto GPU execution models
- **Compiled to efficient code**: multiple dispatch, specialization
  Write generic, reusable applications
- BLAS (matrix-multiply, ...), and other libraries like FFT
"""

# ╔═╡ 6fdf71ca-a0b5-4031-8e03-1d11292bf0c8
md"""
Array types -- **where** memory resides and **how** code is executed.

|  |  |
| --- | --- |
|  `A = Matrix{Float64}(undef, 64, 32)`   | CPU   |
|  `A = CuMatrix{Float64}(undef, 64, 32)`   | Nvidia GPU   |
|  `A = ROCMatrix{Float64}(undef, 64, 32)`   | AMD GPU   |

!!! info
    Data movement is explicit.
"""

# ╔═╡ b9556ad1-0bf8-4cb1-b7aa-86238aefb60b
md"""
### What makes an application portable?

1. Can I **run** it on a different compute architecture
    1. Different CPU architectures
    2. We live in a mult GPU vendor world
2. Does it **compute** the same thing?
    1. Can I develop on one platform and move to another later?
3. Does it achieve the same **performance**?
4. Can I take advantage of platform **specific** capabilities?
"""

# ╔═╡ ea0e9ceb-9aca-4c14-9c42-0da50b2d1e74
md"""
### Adapt.jl

[Adapt.jl](https://github.com/JuliaGPU/Adapt.jl) is a lightweight dependency that you can use to convert complex structures from CPU to GPU.

```julia
using Adapt
adapt(CuArray, ::Adjoint{Array})::Adjoint{CuArray}
```

```julia
struct Model{T<:Number, AT<:AbstractArray{T}}
   data::AT
end

Adapt.adapt_structure(to, x::Model) = Model(adapt(to, x.data))


cpu = Model(rand(64, 64));
using CUDA

gpu = adapt(CuArray, cpu)
Model{Float64, CuArray{Float64, 2, CUDA.Mem.DeviceBuffer}}(...)
```
"""

# ╔═╡ 29f82a24-f8d8-408e-bbad-843f6cf52f15
md"""
## Putting it all together
"""

# ╔═╡ 94f1380b-a40a-468d-adbd-c105c08485b6
md"""
!!! note "An old example from Discourse"
	[https://discourse.julialang.org/t/types-and-gradients-including-forward-gradient/946](https://discourse.julialang.org/t/types-and-gradients-including-forward-gradient/946)
"""

# ╔═╡ ad35943f-e323-45b1-a474-6274030a22ab
md"""
```julia
using LinearAlgebra
loss(w,b,x,y) = sum(abs2, y - (w*x .+ b)) / size(y,2)
loss∇w(w, b, x, y) = ...
lossdb(w, b, x, y) = ...
function train(w, b, x, y ; lr=.1)
   w -= lmul!(lr, loss∇w(w, b, x, y))
   b -= lr * lossdb(w, b, x, y)
   return w, b
end
n = 100
p = 10
x = randn(n,p)'
y = sum(x[1:5,:]; dims=1) .+ randn(n)'*0.1
w = 0.0001*randn(1,p)
b = 0.0
for i=1:50
   w, b = train(w, b, x, y)
end
```
"""

# ╔═╡ 47963ca4-e499-4065-a2cb-f3d8842a5bdc
md"""
How to execute it on the GPU?
"""

# ╔═╡ d6e1d716-d8a2-4448-9270-354184239fec
TwoColumn(md"""
```julia
x = CuArray(x)
y = CuArray(y)
w = CuArray(w)
```
""",
md"""
```julia
x = adapt(backend, x)
y = adapt(backend, y)
w = adapt(backend, w)
```
""")

# ╔═╡ 72b43b54-b7a6-4f1c-a647-7907fe913474
md"""
!!! info "Composability: reuse of libraries"
    `loss∇w` & `lossdb` can be implemented with any of the autodiff libraries provided in Julia. AD and GPU accelerations are orthogonal problems.
"""

# ╔═╡ 96aa8dd9-8179-4b06-a496-ad76f04823fb
begin
	import CUDA
	import Metal
	# Work around <https://github.com/JuliaGPU/oneAPI.jl/issues/445>.
	ENV["SYCL_PI_LEVEL_ZERO_BATCH_SIZE"] = "1"
	import oneAPI
	
	# **sigh** Currently crashes inside Pluto
	# import AMDGPU
end;

# ╔═╡ 570a6da5-0658-4500-a6e6-c1e32534f47b
md"""
Choose your own backend:
"""

# ╔═╡ c8ec8997-1009-4c7e-a24d-3945195db964
let
    available_backends = KernelAbstractions.Backend[CPU()]
    CI = get(ENV, "GITHUB_ACTIONS", "false") == "true"
	# Always shows all backend when rendering the notebook on GitHub Actions,
	# notebooks will be static anyway.
	if CUDA.functional() || CI
		push!(available_backends, CUDA.CUDABackend())
	end
	if oneAPI.functional() || CI
		push!(available_backends, oneAPI.oneAPIBackend())
	end
	if Metal.functional() || CI
		push!(available_backends, Metal.MetalBackend())
	end
	# if AMDGPU.functional() || CI
	# 	push!(available_backends, AMDGPU.ROCBackend())
	# end
	@bind backend Select(available_backends)
end

# ╔═╡ 7dfb12da-a68c-497b-973f-72cad14be7a4
md"""
The below code implements a custom eigenvalue solver. We are interested in implementing porting it to the GPU.

For a momement let's forget about `GPUArrays` and all the high-level primitives it provides.
"""

# ╔═╡ da0a4612-f532-4bc0-8c84-38c7a8afc127
md"""
```
f(A::MyMatrix)  = λ ->  1 + mapreduce((v) -> v^2 / (v - λ)  , +, A.v)
f′(A::MyMatrix) = λ ->      mapreduce((v) -> v^2 / (v - λ)^2, +, A.v)

function LinearAlgebra.eigmax(A::MyMatrix; tol = eps(2.0), debug = false)
    x0 = maximum(A.v) + maximum(A.v)^2
    δ = f(A)(x0)/f′(A)(x0)
    while abs(δ) > x0 * tol               
        x0 -= δ
        δ = f(A)(x0)/f′(A)(x0) 
        debug && println("x = $x0, δ = $δ") # Debugging
    end
    x0
end
```
"""

# ╔═╡ a40309cb-f5c1-4a51-8a8a-ffc33b07cf10
question_box(md"""
1. What fundamental operations do we need to implement?
2. Is there a synchronization point within this code?
""")

# ╔═╡ ce193fd6-637b-436f-9656-17397b788ddc
hint(md"""
1. `maximum(v)` can also be written as `reduce(max, v, init=typemin(eltype(v)))`
2. `reduce(op, v)` can also be written as `mapreduce(identity, op, f)`

So the only operation we need to implement is a `mapreduce`! 

Yes, there are several synchronization points, most notably both `f` and `f′` have to wait for the GPU kernel to finish to return a scalar GPU value. An interesting optimization might be to better pipeline this code and try to avoid a bubble between `f` and `f′`. Or perhaps write a fully custom kernel!
""")

# ╔═╡ 961aac99-5370-416e-b4cd-40e8234de32b
md"""
We can only communicate with the GPU through Global Memory. A GPU kernel does not return anything. Thus we allocate a single "value" storage array.

!!! note "Shared Virtual Memory / Unified Virtual Memory"
    SVM/UVM make memory on the GPU/CPU mutually accesibly, we could thus not use an array, but perhaps a `RefValue`, though this is not portable and would mean we miss the implicit syncronization semantics. 

For our custom eigenvalue solver we need `mapreduce`, but for now let's just implement a non-generic `sum`.
"""

# ╔═╡ 4406606f-8098-4e32-8c57-f9bf698a7706
@kernel function naive_sum(val, data)
	I = @index(Global)
	x = data[I]
	val[1] += x
end

# ╔═╡ ad9430ac-dcb6-4d08-8b26-bd0275ca5f46
data = KernelAbstractions.ones(backend, Int, 1024^2);

# ╔═╡ 41cf381c-485a-4ebf-b06b-d8be83d60e6f
sum(data)

# ╔═╡ b3ef6ecf-1530-4b30-85fd-f3f5790b646b
let
	x = KernelAbstractions.zeros(backend, eltype(data), 1)
	naive_sum(backend)(x, data, ndrange=length(data))
	Array(x)[1]
end

# ╔═╡ 14085825-4990-4251-8810-aa05d96bead0
md"""
!!! note "Data-race"
    This looks similar to our issues from earlier! Data races galore!
	Let's use Atomix avoid these issues.
"""

# ╔═╡ b00d9c81-6584-4d47-9b0c-d7e2d4df901b
@kernel function naive_atomic_sum(val, data)
	I = @index(Global)
	x = data[I]
	@atomic val[1] += x
end

# ╔═╡ 61ceb3fc-c617-4ce8-8902-a8767187d1b2
let
	x = KernelAbstractions.zeros(backend, eltype(data), 1) # oops I used similar here...
	naive_atomic_sum(backend)(x, data, ndrange=length(data))
	Array(x)[1]
end

# ╔═╡ b10c2076-3c6a-4fa6-a9e3-0b891ecfaf1c
let
	x = KernelAbstractions.zeros(backend, eltype(data), 1)
	@benchmark begin
		naive_atomic_sum($backend)($x, data, ndrange=length(data))
		KernelAbstractions.synchronize($backend)
	end
end

# ╔═╡ 786a2a6b-4b70-449b-b503-2bf27be05501
@benchmark sum(data)

# ╔═╡ 8478d7f6-c3e0-404c-87ef-a7b6792dfb5b
if backend isa CUDA.CUDABackend
	CUDA.@profile sum(data)
end

# ╔═╡ 0f15901f-0825-47d1-8d11-0dc1d2d55119
md"""
Currently we have a big-bottle neck. The atomic summation on the global data!
KernelAbstraction provides a `@localmem` region that implements a memory region that is local to a work-group! So we can load all the data in parallel, then sum it up, and perform much fewer atomic stores.
"""

# ╔═╡ 6ce71f49-b55b-4102-8b27-6855ae1f1b11
@kernel function naive_shmem_sum(val, data::AbstractArray{T}) where T
	I = @index(Global)
	i = @index(Local)
	N = @uniform prod(@groupsize())
	tile = @localmem T (N,)
	tile[i] = data[I]
	@synchronize
	if i == 1
		acc = tile[1]
		for i in 2:N
			acc += tile[i]
		end	
		@atomic val[1] += acc
	end
end

# ╔═╡ c59aec82-53de-44b7-b32d-da810dff6e7b
let
	x = KernelAbstractions.zeros(backend, eltype(data), 1)
	naive_shmem_sum(backend, 64)(x, data, ndrange=length(data))
	Array(x)[1]
end

# ╔═╡ fb6a460a-9bb0-408f-affa-f8db395b584e
let
	x = KernelAbstractions.zeros(backend, eltype(data), 1)
	@benchmark begin
		naive_shmem_sum($backend, 64)($x, data, ndrange=length(data))
		KernelAbstractions.synchronize($backend)
	end
end

# ╔═╡ 3f9415e3-63a9-425b-ab3a-913bcbe29c73
md"""
!!! info
    There are improvements we can do on this algorithm! As an example one thread is doing all the "sum" work per compute-group. We probably want to share that work. In CUDA there are also shuffle operations that can be used instead of the `localmem`.
"""

# ╔═╡ 6b73a14f-9003-4b7c-bee3-3780f2e9c517
@kernel function naive_shmem_mapsum(val, data::AbstractArray{T}, f::F) where {T, F}
	I = @index(Global)
	i = @index(Local)
	N = @uniform prod(@groupsize())
	tile = @localmem T (N,)
	tile[i] = f(data[I])
	@synchronize
	if i == 1
		acc = tile[1]
		for i in 2:N
			acc += tile[i]
		end
		@atomic val[1] += acc
	end
end

# ╔═╡ 7383854f-f450-4fd5-b887-147a80c7c141
function my_mapsum(f, data)
	backend = get_backend(data)
	x = KernelAbstractions.zeros(backend, eltype(data), 1)
	naive_shmem_mapsum(backend, 64)(x, data, f, ndrange=length(data))
	GPUArraysCore.@allowscalar x[1]
end

# ╔═╡ 3164fb87-abbf-43c2-b154-ec22a5e6a757
my_mapsum(x->x^2, data)

# ╔═╡ fde79fb3-ab64-4b9c-93a5-31cbf58cebb4
mapreduce(x->x^2, +, data)

# ╔═╡ 0aff06d4-b207-432f-83e3-e9d8b97ee70c
@benchmark my_mapsum(x->x^2, $data)

# ╔═╡ 9ff55bd8-ab93-442b-af87-1c1765b8b453
@benchmark mapreduce(x->x^2, +, $data)

# ╔═╡ a9379ce2-b2ab-4e3c-b4b7-8df15e98226c
backend

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Atomix = "a9b6321e-bd34-4604-b9c9-b65b8de01458"
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Metal = "dde4c033-4e86-420c-a63e-0dd931031962"
PlutoTeachingTools = "661c6b06-c737-4d37-b85c-46df65de6f69"
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Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
oneAPI = "8f75cd03-7ff8-4ecb-9b8f-daf728133b1b"

[compat]
Atomix = "~1.1.2"
BenchmarkTools = "~1.6.0"
CUDA = "~5.8.3"
CairoMakie = "~0.15.6"
GPUArraysCore = "~0.2.0"
KernelAbstractions = "~0.9.38"
Metal = "~1.8.0"
PlutoTeachingTools = "~0.4.5"
PlutoUI = "~0.7.71"
oneAPI = "~2.2.0"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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version = "3.12.1+0"

[[deps.libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "125eedcb0a4a0bba65b657251ce1d27c8714e9d6"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.17.4+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "646634dd19587a56ee2f1199563ec056c5f228df"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.4+0"

[[deps.libigc_jll]]
deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "TOML"]
git-tree-sha1 = "7db4bac4dd5c81b694f5585c78d6e4bfc0e8f455"
uuid = "94295238-5935-5bd7-bb0f-b00942e9bdd5"
version = "2.16.0+0"

[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Zlib_jll"]
git-tree-sha1 = "07b6a107d926093898e82b3b1db657ebe33134ec"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.50+0"

[[deps.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "libpng_jll"]
git-tree-sha1 = "c1733e347283df07689d71d61e14be986e49e47a"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.5+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll"]
git-tree-sha1 = "11e1772e7f3cc987e9d3de991dd4f6b2602663a5"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.8+0"

[[deps.libwebp_jll]]
deps = ["Artifacts", "Giflib_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libglvnd_jll", "Libtiff_jll", "libpng_jll"]
git-tree-sha1 = "4e4282c4d846e11dce56d74fa8040130b7a95cb3"
uuid = "c5f90fcd-3b7e-5836-afba-fc50a0988cb2"
version = "1.6.0+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.oneAPI]]
deps = ["Adapt", "CEnum", "ExprTools", "GPUArrays", "GPUCompiler", "GPUToolbox", "KernelAbstractions", "LLVM", "Libdl", "LinearAlgebra", "NEO_jll", "Preferences", "Printf", "Random", "SPIRVIntrinsics", "SPIRV_LLVM_Translator_jll", "SPIRV_Tools_jll", "SparseArrays", "SpecialFunctions", "StaticArrays", "oneAPI_Level_Zero_Headers_jll", "oneAPI_Level_Zero_Loader_jll", "oneAPI_Support_jll"]
git-tree-sha1 = "0cc5249b9db9522af96493750c2c657add194119"
uuid = "8f75cd03-7ff8-4ecb-9b8f-daf728133b1b"
version = "2.2.0"

[[deps.oneAPI_Level_Zero_Headers_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "94613c009900974dd9296130ccd9de9886c0c3d6"
uuid = "f4bc562b-d309-54f8-9efb-476e56f0410d"
version = "1.13.0+0"

[[deps.oneAPI_Level_Zero_Loader_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "oneAPI_Level_Zero_Headers_jll"]
git-tree-sha1 = "996584b4ed4d6baed2d2946d719be1b8c65bca03"
uuid = "13eca655-d68d-5b81-8367-6d99d727ab01"
version = "1.22.4+0"

[[deps.oneAPI_Support_jll]]
deps = ["Artifacts", "Hwloc_jll", "JLLWrappers", "Libdl", "OpenCL_jll", "Pkg", "oneAPI_Level_Zero_Loader_jll"]
git-tree-sha1 = "45466284f5c38c35c77f99122f211e98962602db"
uuid = "b049733a-a71d-5ed3-8eba-7d323ac00b36"
version = "0.9.1+0"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "d5a767a3bb77135a99e433afe0eb14cd7f6914c3"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2022.0.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

[[deps.x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "14cc7083fc6dff3cc44f2bc435ee96d06ed79aa7"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "10164.0.1+0"

[[deps.x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "e7b67590c14d487e734dcb925924c5dc43ec85f3"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "4.1.0+0"
"""

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