JuliaDiff / JuliaDiff/ForwardDiff.jl

Allow Dual{T, SIMD.Vec, N}

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Description

Note: I have looked for issues/PR mentioning SIMD but they are all related to using SIMD to accelerate operations on the partials. Here the goal is to have the primal be SIMD, which is quite different.

I am combining explicit vectorization with SIMD.jl and AD of small functions (a few real inputs, a single real output) with ForwardDiff.

```julia

import ForwardDiff as FD
import SIMD

x = SIMD.Vec(randn(4)...)
xx = FD.Dual(x,one(x))
yy = xx/exp(xx*xx)

A typical use is computing partial derivatives of that function for each value in a large array. The above works if I commit the following type piracy:


const SVec{F,N} = SIMD.Vec{N,F}

@inline FD.can_dual(::Type{SIMD.Vec{N, F}}) where {N, F} = FD.can_dual(F)

@inline FD._mul_partial(partial::SIMD.Vec, x::SIMD.Vec) = partial * x
@inline FD._mul_partial(partial::SVec{F}, x::F) where F = partial * x
@inline FD._mul_partial(partial::F, x::SVec{F}) where F = partial * x

@inline Base.:*(x::SIMD.Vec, partials::FD.Partials) = partials*x

@inline function Base.:*(partials::FD.Partials, x::SIMD.Vec)
    return FD.Partials(FD.scale_tuple(partials.values, x))
end

@inline function FD.dual_definition_retval(::Val{T}, val::S, deriv::S, partial::FD.Partials{M,S}) where {T,F,N,M, S<:SVec{F,N}}
    return FD.Dual{T}(val, deriv*partial)   
end
@inline function FD.dual_definition_retval(::Val{T}, val::S, deriv1::S, partial1::FD.Partials{M,S}, deriv2::F, partial2::FD.Partials{M,F}) where {T,F,N,M, S<:SVec{F,N}}
    return FD.Dual{T}(val, FD._mul_partials(partial1, partial2, deriv1, deriv2))   
end
@inline function FD.dual_definition_retval(::Val{T}, val::S, deriv1::F, partial1::FD.Partials{M,F}, deriv2::S, partial2::FD.Partials{M,S}) where {T,F,N,M, S<:SVec{F,N}}
    return FD.Dual{T}(val, FD._mul_partials(partial1, partial2, deriv1, deriv2))   
end
@inline function FD.dual_definition_retval(::Val{T}, val::S, deriv1::S, partial1::FD.Partials{M,S}, deriv2::S, partial2::FD.Partials{M,S}) where {T,F,N,M, S<:SVec{F,N}}
    return FD.Dual{T}(val, FD._mul_partials(partial1, partial2, deriv1, deriv2))   
end

I also use SIMDMathFunctions to vectorize math functions cos, exp, etc. Overall this gives pretty good performance. Especially I don't have to give up SIMD when computing derivatives, which would incur a big performance hit.

If there is interest in this feature, I can work out a PR. From there I would need some guidance to implement appropriate tests.

Contributor guide

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First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start by reviewing ForwardDiff's Dual and Partials behavior alongside the SIMD-related issues and PRs mentioned in the report. Use the shown SIMD.Vec examples and SIMDMathFunctions usage as the starting case, then define appropriate tests for Dual values with SIMD primals. Done means the feature works without the proposed type piracy and its behavior is covered by tests.

Written by the indexing model from the issue text.

Assessment

Tech stack
julia
Domain
performance
Issue type
Feature
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
30/100

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