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Nitpick: is that really computing 20M digits correctly? Reading the code gives me the impression that this does all float computations in 20 million digits (or 20 million-ish? If BigFloat internally is binary, it might use a bit more), but I would expect that you need to compute using a few more digits to avoid rounding errors in the last digits.

Edit: also, reading https://stackoverflow.com/a/67919533, it seems you can do

  BigFloat(π, precision=20000000)

How does that perform?

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I ran the following in my Julia REPL

julia> @time BigFloat(π, precision=20000000); 11.208211 seconds (60.53 k allocations: 2.932 GiB, 0.16% gc time)

Which is pretty good considering I ran this in WSL on my laptop and Mathematica in a different comment took 10 seconds. (Plain Windows took ~26 seconds for some reason?)

> (Plain Windows took ~26 seconds for some reason?)

Maybe the allocations were the reason?

I’m too late to update my own comment, but I now suspect BigFloat(π, precision=20000000) may allocate a Bigfloat with precision of two million digits and then store the constant π which has much lower precision in it.

What value does that print?

It definitely does calculate it otherwise it would diverge significantly at lower digits from the Gauss Legendre and Chudnovsky algorithm that I compared it to. It just defers calculation to MPFR, the C library Julia binds to for BigFloat calculations.

Also one additional comment is that you are setting precision in number of bits, not in decimal digits. It obviously runs much faster when it is only computing log2(20000000) not 20000000 digits of precision.

BigFloat internally is not binary, it uses an array because it is made for arbitrary precision. There will absolutely be small errors at the end but it’s easier to say 20M than 1.999999M digits of pi.

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