Short circuiting mod1 to speed offsetc

[kbarros]

For systems with very simple interactions, wrapping indices to the system's periodic boundaries can absorb a significant chunk of the total simulation time. The culprit is the modulo operation (used as mod1 in Julia). In the common case, the index will already be in-bounds, so no wrapping is needed. If this situation is detected, we can short-circuit the mod1 operation and immediately return the original index. Doing so reduces the overhead for index-wrapping from 16% to about 8% of the total run-time in the dynamics benchmark below. It should also provide speedups for the LocalSampler use-case.

using Sunny, Random, BenchmarkTools

# Simple model on square lattice
latvecs = lattice_vectors(1, 1, 10, 90, 90, 90)
cryst = Crystal(latvecs, [[0,0,0]])
sys = System(cryst, (10,10,1), [SpinInfo(1, S=1, g=2)], :dipole; seed=1)
J = -1.0
set_exchange!(sys, J, Bond(1, 1, (1, 0, 0)))

Random.seed!(0)
randomize_spins!(sys)

Δt = 0.1
integrator = ImplicitMidpoint(Δt)

function f(sys, integrator)
    for _ in 1:100_000
        step!(sys, integrator)
    end
end

@btime f(sys, integrator)

# Before PR: 4.31s
# After PR:  4.02s

@profview f(sys, integrator)

# Before PR: 16% in offsetc
# After PR:  8% in offsetc

[kbarros]

Note that we previously avoided mod1 operations through a nested closure scheme involving a custom variant of the CartesianIndices iterator. That code was removed in #176. However, the shifted CartesianIndices scheme was not very effective. On Sunny@0.5.4 (with the shifted CartesianIndices) I find that the benchmark posted above takes 4.29s. So with the current PR, there is now a significant boost over all previous Sunny versions.