使用BigFloat时DifferentialEquations.jl是否支持JIT编译？

Great question—let’s break this down clearly, especially since you’re coming from the Python/Numba pain point with arbitrary-precision floats.

The short answer: Yes, 100%. When you use BigFloat (or ArbFloat from ArbNumerics.jl) with DifferentialEquations.jl, your custom differential equation functions and the solver’s internal loops will be fully JIT-compiled to optimized machine code—no performance drop like you saw with Python/mpmath+Numba.

Here’s why this works so much better than your Python setup:

• Julia’s JIT is language-native (powered by LLVM), not an external tool like Numba. It integrates seamlessly with all Julia-native numeric types, including BigFloat. Unlike mpmath’s arbitrary-precision objects (which are dynamic Python structures Numba can’t handle in nopython mode), BigFloat is a first-class, statically typed numeric type in Julia.
• DifferentialEquations.jl is built from the ground up to leverage Julia’s type system. As long as your problem setup is type-stable (which it will be if you use BigFloat consistently for initial conditions, parameters, and time spans), the JIT compiler will generate optimized code tailored specifically for BigFloat operations—this includes your custom ODE/PDE functions and every loop inside the solver itself.

Here’s a quick example to illustrate:

using DifferentialEquations

# ODE function using BigFloat arithmetic
function ode_update(du, u, p, t)
    du[1] = -big(0.3) * u[1]  # Explicit BigFloat coefficient
end

# Initialize all components with BigFloat
u0 = big.([5.0])
tspan = (big(0.0), big(20.0))

# Set up and solve the problem
prob = ODEProblem(ode_update, u0, tspan)
sol = solve(prob, Tsit5())

In this code, ode_update gets compiled to efficient machine code for BigFloat operations, and the Tsit5 solver’s internal calculation loops are also compiled specifically for BigFloat—no slow interpreted code paths anywhere.

To contrast with your Python experience: mpmath objects are dynamic, so Numba can’t translate them to low-level code in nopython mode, forcing it to fall back to slow interpreted execution. Julia’s type system eliminates that bottleneck entirely for BigFloat and other native numeric types.

内容的提问来源于stack exchange，提问作者user5242155