logarithm

Edit: In the initial question had a wrong formula and the algorithm tried was doing something completely different than what was intended. I apologise and I decided to rewrite the question to eliminate all the confusion. I need to compute at compile time (the result will be used as a non-type template parameter) the minimum number of bits needed to store n different states: constexpr unsigned bitsNeeded(unsigned n); or via template The results should be: +-----------+--------+ | number of | bits | | states | needed | +-----------+--------+ | 0 | 0 | * or not defined | | | | 1 | 0 | | | | | 2 |

I am generating 2D arrays on log-spaced axes (for instance, the x pixel coordinates are generated using logspace(log10(0.95), log10(2.08), n) . I want to display the image using a plain old imshow, in its native resolution and scaling (I don't need to stretch it ; the data itself is already log scaled), but I want to add ticks, labels, lines that are in the correct place on the log axes. How do I do this? Ideally I could just use commands line axvline(1.5) and the line would be in the correct place (58% from the left), but if the only way is to manually translate between logscale coordinates

While plotting histogarm, scatterplots and other plots with axes scaled to logarithmic scale in R, how is it possible to use labels such as 10^-1 10^0 10^1 10^2 10^3 and so on instead of the axes showing just -1, 0, 1, 2, 3 etc. What parameters should be added to the commands such as hist(), plot() etc? Joris Meys Apart from the solution of ggplot2 (see gsk3's comment), I would like to add that this happens automatically in plot() as well when using the correct arguments, eg : x <- 1:10 y <- exp(1:10) plot(x,y,log="y") You can use the parameter log="x" for the X axis, or log="xy" for both. If

This question already has an answer here: Histogram with Logarithmic Scale and custom breaks 7 answers Hi I'm making histogram using R, but the number of Y axis is so large that I need to turn it into logarithmic.See below my script: hplot<-read.table("libl") hplot pdf("first_end") hist(hplot$V1, breaks=24, xlim=c(0,250000000), ylim=c(0,2000000),main="first end mapping", xlab="Coordinates") dev.off() So how should I change my script? thx You can save the histogram data to tweak it before plotting: set.seed(12345) x = rnorm(1000) hist.data = hist(x, plot=F) hist.data$counts = log10(hist.data

Is there a straightforward way to extracting the exponent from a power of 2 using bitwise operations only? EDIT: Although the question was originally about bitwise operations, the thread is a good read also if you are wondering "What's the fastest way to find X given Y = 2 X in Python ?"** I am currently trying to optimize a routine ( Rabin-Miller primality test ) that reduces an even number N in the forms 2**s * d . I can get the 2**s part by: two_power_s = N & -N but I can't find a way to extract just " s " with a bitwise operation. Workarounds I am currently testing without too much

Is there a function or any other way to calculate in C the logarithm of base x , where x is an integer variable of my program? C doesn't provide functions to compute logarithms of any bases other than e or 10 . So just use math: logarithm of x base b = log(x)/log(b) If you'll be doing the logarithms over the same base repeatedly, you can precompute 1/log(b) . I wouldn't rely on the compiler being able to do this optimization for you. 来源： https://stackoverflow.com/questions/11054740/logarithm-function-of-an-arbitrary-integer-base-in-c

In a previous problem, I showed (hopefully correctly) that f(n) = O(g(n)) implies lg(f(n)) = O(lg(g(n))) with sufficient conditions (e.g., lg(g(n)) >= 1, f(n) >= 1 , and sufficiently large n). Now, I need to prove OR disprove that f(n) = O(g(n)) implies 2^(f(n)) = O(2^g(n))) . Intuitively, this makes sense, so I figured I could prove it with help from the previous theorem. I noticed that f(n) can be rewritten as lg(2^f(n)) and that g(n) is just lg(2^g(n)) , which got me excited...this is taking the log base 2 of both sides of what I want to prove, and it simplifies things a lot! But I'm pretty

This is my first course in data structures and every lecture / TA lecture , we talk about O(log(n)) . This is probably a dumb question but I'd appreciate if someone can explain to me exactly what does it mean !? It means that the thing in question (usually running time) scales in a manner that is consistent with the logarithm of its input size. Big-O notation doesn't mean an exact equation, but rather a bound . For instance, the output of the following functions is all O(n): f(x) = 3x g(x) = 0.5x m(x) = x + 5 Because as you increase x, their outputs all increase linearly - if there's a 6:1