Hi! This application is probably very common for some people, but it is the very first time I really needed high precision computation (BigInt and BigFloat). I am implementing an algorithm for designing frozen orbits in SatelliteAnalysis.jl ( https://github.com/JuliaSpace/SatelliteAnalysis.jl/blob/…

[image] Ronis_BR: setting setprecision accordingly Got any tips for estimating how much precision is needed, given an expression with factorials and inputs? That is, assuming you do the straightforward factorials instead of cancelling terms and reordering operations to restrain the magnitude. …

You can use Stirling’s approximation to the factorial to calculate the number of decimal places needed.

Got any tips for estimating how much precision is needed, given an expression with factorials and inputs? In my case, I just use a huge number (1024 I think). I know it is correct because the difference between the values computed for an increasing degree was always decreases. That is, assuming…

You can also use Arblib.jl to see how much precision you really need (you’ll get a certified error bound); This will require a little bit of coding, as you’ll need to implement factorial using Arblib.fac!, binomial using Arblib.bin! (PRs most wellcome ;). Let me know if you need help with that …

[image] Ronis_BR: The problem is when you try using very high degrees, leading to 300! and so on. I was thinking how I could possible handle this problem, like interactively computing the terms using a nice “guess” to always divide things to reach lower numbers. In series expressions like thi…

[image] stevengj: In series expressions like this, you should almost never call the factorial function, nor should you compute the powers for each term separately. Instead, compute each term iteratively from the previous term, starting with the smallest power and the smallest factorial. Not only…

Ah, by the way, I tried to compute those factorials in each term of the summation using a “clever” approach, avoiding calculating the same thing multiple times. However, considering this approach that I do not save the factors for the next summation term, the code was almost 100x slower than calling…

@stevengj On second thoughts, it is better to optimize the code as other people might have different use cases. I followed your advice and implemented those factors interactively. It indeed decreased the computational workload by a lot: # Before julia> @btime frozen_orbit(7130.982e3, 98.410 |> deg2…

Looking at https://github.com/JuliaSpace/SatelliteAnalysis.jl/blob/32ad240d229e2869e0594d80bf127190ecace50f/src/frozen_orbits.jl#L224-L228 # where the initialization is: # # 2l! # k_0 = ─────────────────────────── ⋅ sin(i)^(l) ⋅ (-1)^{p - k} . # l! ⋅…

Is there any advantage to use binomial in this case?

And Julia keeps amazing me: high precision computation

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And Julia keeps amazing me: high precision computation

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