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Summer of Math Exposition 3 - How does a computer/calculator compute logarithms?

Vibe coding a Mandelbrot renderer Spent today “vibe coding” with Claude, just describing what I wanted and letting it drive, to see how far that gets you on a small self-contained project. The result is fractalPy, a small Numba-accelerated Mandelbrot set renderer. It started as a single script — render the set to a PNG, colour it, done — using @njit(parallel=True, fastmath=True, cache=True) to JIT-compile the escape-time kernel so it’s fast enough to iterate on interactively:

In recent months, there has been some encouraging progress in Clojure’s story for signal processing. A lot of that is work-in-progress and will be made more visible soon: updates to the Fastmath 3 li...

thanks for the suggestion. TIL that -Ofast enables `-ffast-math` flag. I removed `-ffast-math` and set -O3: g++ -Wall -Wextra -O3 -march=native -mtune=native -std=c++23 select_elements.cpp the elapsed time is `0.58802 s ± 0.01281 s`, so it is slower than Rust version now. Interesting. But I still wonder why is numba then produces quite fast code (even if I explicitly turn off fast math)? In [3]: @jit(fastmath=False) ...: def sum_selected(v: np.ndarray): ...: res_sum = np.float64(0.0) ...: for i in v: ...: if i > 0.5: ...: res_sum += i ...: return res_sum ...: In [4]: v = np.random.rand(100000000) In [5]: %timeit sum_selected(v) 163 ms ± 888 μs per loop (mean ± std. dev. of 7 runs, 1 loop each)

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