Chapter Summary

Chapter Summary

Key Points

• 1.

  Use Numba for tight numerical loops. @numba.njit compiles Python loops to native machine code via LLVM, achieving 50-200x speedup over pure Python. Always use nopython=True (or @njit), warm up before benchmarking, and use parallel=True with prange for multi-core scaling. @numba.vectorize creates custom ufuncs, and @numba.cuda.jit targets NVIDIA GPUs.

• 2.

  Use JAX for functional numerical computing. JAX provides composable transformations: jax.jit for XLA compilation, jax.grad for automatic differentiation, and jax.vmap for automatic vectorization. Write pure functions with jax.numpy, and compose transformations freely: jax.jit(jax.vmap(jax.grad(f))) gives a compiled, batched gradient. JAX arrays are immutable; use x.at[i].set(v) instead of x[i] = v.

• 3.

  Choose the right parallelism tool. The GIL prevents CPU-bound thread parallelism in CPython. Use multiprocessing.Pool or concurrent.futures.ProcessPoolExecutor for CPU-bound work, ThreadPoolExecutor for I/O-bound work, and joblib.Parallel for scikit-learn-style loops. Amdahl's Law sets the speedup ceiling: $S_\infty = 1/f_s$ where $f_s$ is the serial fraction.

• 4.

  Interface with C/C++ when needed. Use ctypes for quick calls to existing shared libraries (no compilation), cffi for safer C API wrapping, pybind11 for new C++ extensions with automatic NumPy conversion, and f2py for Fortran codes. Always pass contiguous arrays and batch operations to amortize FFI call overhead.