Python:以高达 100 万位的精度计算正弦/余弦 [英] Python: Calculate sine/cosine with a precision of up to 1 million digits

问题描述

问题是不言自明的.我已经看到了几个 pi 的例子，但没有看到 trigo 函数的例子.也许人们可以使用泰勒级数

其中 Rn 是 拉格朗日余数

注意 Rn 在 x 远离中心 x₀ 时增长很快，所以尝试计算任意的sin(x)或cos(x)时，请小心使用麦克劳林级数(以0为中心的泰勒级数) x.

Question is pretty self-explanatory. I've seen a couple of examples for pi but not for trigo functions. Maybe one could use a Taylor series as done here but I'm not entirely sure how to implement that in python. Especially how to store so many digits. I should mention: this ideally would run on vanilla python i.e. no numpy etc.

Thanks!

Edit: as said, I know the question has been asked before but it's in java and I was looking for a python implementation :)

Edit 2: wow I wasn't aware people here can be so self-absorbed. I did try several approaches but none would work. I thought this a place you can ask for advice, guess I was wrong

last edit: For anyone who might find this useful: many angles can be calculated as a multiple of sqrt(2), sqrt(3) and Phi (1.61803..) Since those numbers are widely available with a precision up to 10mio digits, it's useful to have them in a file and read them in your program directly

解决方案

mpmath is the way:

from mpmath import mp
precision = 1000000
mp.dps = precision
mp.cos(0.1)

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If unable to install mpmath or any other module you could try polynomial approximation as suggested.

where Rn is the Lagrange Remainder

Note that Rn grows fast as soon as x moves away from the center x₀, so be careful using Maclaurin series (Taylor series centered in 0) when trying to calculate sin(x) or cos(x) of arbitrary x.

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