Shulou(Shulou.com)05/31 Report--

This article introduces the relevant knowledge of "how to find the natural constant with high precision in python". In the operation of actual cases, many people will encounter such a dilemma, so let the editor lead you to learn how to deal with these situations. I hope you can read it carefully and be able to achieve something!

Taylor expansion and the solution of e

Do you know how to find the e in the computer?

It starts with the magical Taylor.

To put it simply, it is e, which can be expressed as:

Obviously, when n is small enough, the accuracy is already very high, and the following series is convergent and can be ignored. And this can obviously be calculated by a computer.

Python and the magical decimal

Many people are used to using python to calculate high-precision integers, because python integers are high-precision, but floating-point numbers are only 32 bits, where python provides a magical library "decimal", which allows you to specify the precision of decimals, equivalent to "high-precision decimals".

Calculate import decimalPrecision=20000decimal.getcontext (). Prec=Precision

We can set a precision for it like this.

Then it is followed by our expansion, which is generally close to the precision bit.

E=decimal.Decimal (0) nFrac=decimal.Decimal (1) for N in range (1): E+=nFrac nFrac/=Nprint (E)

The final effect is

A whole page of figures, after all, 20000 digits.

Compare

We use professional software "mathematica" to calculate the 20000 digits of e, and save it as a string and pass it to decimal. Here, we should note that we must use a string instead of directly writing the decimal, because the default decimal only 32bit will lose the remaining precision.

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