Backward integration does not step to the first occuring callback

[dcourteville]

Describe the bug 🐞

When multiple distinct callbacks occur in an single time step during backward integration, the integrator will step to the last occurring callback (in the integration direction) instead of the first.

This is caused by this date comparison that doesn't account for integration direction :

https://github.com/SciML/DiffEqBase.jl/blob/2ff29cc394503da446f50127c31cc2b889b12b8f/src/callbacks.jl#L143C1-L143C68

I will open a pull request with the fix.

Minimal Reproducible Example 👇

using OrdinaryDiffEq, Test

cb = ContinuousCallback(
    (u, t, integrator) -> t - 0e-8,
    (integrator) -> push!(record, 0)
)

vcb = VectorContinuousCallback(
    (out, u, t, integrator) -> out .= (t - 1e-8, t - 2e-8),
    (integrator, event_index) -> push!(record, event_index),
    2
)

f(u, p, t) = 1.0
u0 = 0.0

# Forward propagation with successive events
record = []
tspan = (-1.0, 1.0)
prob = ODEProblem(f, u0, tspan)
sol = solve(prob, Tsit5(), dt=2.0, callback=CallbackSet(cb, vcb))
@test record == [0,1,2]

# Backward propagation with successive events
record = []
tspan = (1.0, -1.0)
prob = ODEProblem(f, u0, tspan)
sol = solve(prob, Tsit5(), dt=2.0, callback=CallbackSet(cb, vcb))
@test record == [2,1,0] # Fail

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

[1dea7af3] OrdinaryDiffEq v6.104.0

[ChrisRackauckas]

I meant it should be in the downstream folder here