Linked Questions

1
vote
1answer
1k views

How do computers calculate the log of a value? [duplicate]

I'm not sure if this question belongs on StackOverflow or here (please let me know if the former, and i'll delete this and ask there), but I was wondering how the <...
1
vote
0answers
59 views

Calculation of logarithms [duplicate]

I understand the properties of logarithms. However I am curious if a calculator uses complex power series, slide rule program, Taylor series, or a form of an algorithm to solve for log"base"n(x).
18
votes
6answers
3k views

What is the fastest algorithm for finding the natural logarithm of a big number?

Like for $\pi$, we have an algorithm/infinite series that can give us the first 50 decimal places in about 3 terms. So if I wasn't to calculate like $ln(25551879...)$ (a really huge integer, most ...
33
votes
4answers
21k views

Calculator algorithms

Does there exist a good reference on the algorithms used by calculators, especially on the trigonometric and transcendental functions? I would still like to know how Casio generates its random ...
5
votes
4answers
2k views

Write number as a power of 10

Just to clarify, I'm not interested in Standard Form/Scientific notation. Is it possible to write a number as a power of ten, so that for example it would look like this? ...
1
vote
2answers
797 views

logarithm and exponent computation performance

Using glibc on a x86 processor, which takes more CPU time? $a\ log\ b$ or $b^a$? For which values of $a$ is one faster than the other? Optional: Does the base used matter? See also: What algorithm ...
1
vote
3answers
348 views

How is the Logarithm derived from the exponential function? (aren't they inverses?)

I've been learning logs in school, and my teacher, friend, and I are stumped on something. How does one derive the logarithmic function from the exponential function? My friend thinks Tayler Series ...
1
vote
2answers
59 views

Defining logarithms explicitly

How are logarithms defined explicitly? One way I can come up with is the following, first start by using McLaurin series representation of exponent function: $$e^x = \sum_{k=o}^{\infty}\frac{x^k}{k!}...
2
votes
0answers
96 views

How calculators compute. [duplicate]

I would like to teach a class on the "magic" behind the calculator, so I would like to generate a list of "algorithms" for how a calculator computes the things we want it to. I will get the ball ...
4
votes
0answers
72 views

Algorithm for numerically calculating $\log x$

It was while fiddling yesterday that I came up with this rather pretty approximation: $$\log x = \frac{1}{2\epsilon}(x^{\epsilon}-x^{-\epsilon})+\mathcal{O}(\epsilon^2)$$ To be more precise, $$\...
0
votes
2answers
38 views

Is it impossible to calculate any power with limited mathimatical operations?

Before I start this question, I am talking about calculating any calculatable power, with real numbers. EG: $2^{7.16}$ In the scripting language BATCH, you have access to only addition, substraction, ...