How to get natural constant/Euler's number?

Using Swift
1

I guess this is as much a mathematics and computer science question as it is a Swift question.

I came across the need for 𝑒 today while writing a function that calculates continuously compounding interest using the formula interest = 𝑒 interest rate Γ— number of compounding periods. Surprisingly, despite its importance and usefulness, I wasn't able to find 𝑒 in the standard library, Numerics package, or Foundation. So, what are some ways to computing or approximating 𝑒, with what's available in Swift?

2

You don't need the value itself, just use exp(interestRate * numberOfCompoundingPeriods)

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3

The exponential function is part of the Numerics package:

import Numerics // or RealModule

let interest = Double.exp(...)
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4

And if you do need the actual constant, for some reason, it's .exp(1).

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5

Thanks @Nickolas_Pohilets, @Martin, and @scanon! I misinterpreted exp as the equivalent to the ^ operator in some other languages.

6

What's the justification for not defining the constant itself as .e?

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7

Is e useful for any operation other than exp and log?

8

Yes

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9

I admit I skimmed the Wikipedia article, but for the benefit of everyone can you please point out where it describes a use of e that isn’t as the base of an exponentiation or a logarithm?

10

It arises in probability. E.g. randomly select a number between 1 to n, n times. What's the probability a particular number, 1 say, never comes up? as n gets larger and larger the probability tends to 1 / e

11

1/e, aka exp(-1)?

12

No one has ever asked for it. It comes up occasionally not as the base of an exponential or logarithm, but it’s pretty infrequent by comparison.

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13

Well, yes. But if you were asked to calculate 1 / e, in maths or computing, you would not normally reach for exp(). You could also reformulate the problem so the answer is e.

14

If your goal is to compute e, then having an .e constant doesn’t do you much good.

If the only practical use of .e would be to reimplement exp() or log(), I’d rather use Steve’s high-quality implementations of those functions.