Avoid allocations for interpolator evaluation

Description

using OrdinaryDiffEq
using BenchmarkTools

function f1(du, u, p, t)
  du[1] = u[1]
end
prob1 = ODEProblem{true}(f1, ones(1), (0.0, 1.0), nothing)
sol1 = solve(prob1, Tsit5())

f2(u, p, t) = u
prob2 = ODEProblem{false}(f2, 1.0, (0.0, 1.0), nothing)
sol2 = solve(prob2, Tsit5())

out = zeros(1)

julia> @btime $sol1(0.1)
  1.181 μs (18 allocations: 416 bytes)
1-element Array{Float64,1}:
 1.1051709180988993

julia> @btime $sol1($out, 0.1)
  1.143 μs (17 allocations: 320 bytes)
1-element Array{Float64,1}:
 1.1051709180988993

julia> @btime $sol2(0.1)
  1.267 μs (25 allocations: 1.33 KiB)
1.1051709180988993

julia> @btime $sol2($out, 0.1)
  1.185 μs (24 allocations: 1.31 KiB)
1-element Array{Float64,1}:
 1.1051709180988993

Contributor guide

Tech stack

None

Domain

performancebackend

Issue type

performance

DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.

4

Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.

1-2 days

Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.

fresh

ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.

clear

Prerequisites

Julia programmingBenchmarkTools.jlOrdinaryDiffEq usage

Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.

30

Research direction

The issue is to reduce allocations during solution interpolation in OrdinaryDiffEq. Start by examining the interpolation code in the repository, likely in src/interpolation.jl or similar files. Replicate the benchmark provided using BenchmarkTools to measure allocations. Then, profile the code to identify the source of allocations. Consider using pre allocated output arrays or in place operations to avoid allocations. Look for any existing comments or linked PRs that may offer additional context or prior attempts.