In vb.net
In fact, I snip the watch window
10^-8 is correct 1e-8
Yet there is something with .1^8 or even .1^2
Why?
For an experiment, I tried with .1*.1 and 1/100 and 1/(10^8). Some produce correct results and some don't. I wonder why.
My guess is 10^-1, which is mathematically equivalent with .1 can be coded exactly. They are stored differently than .1. I don't exactly know how. I think they have the same mantisa and then they just have -1 as exponent.
Notice that 10^-120 seems to show up as exact
Problems only start after 10^-309
10^-308 is still accurate.
I wonder how they represent it? in ieee754
Related
I am new to LabVIEW and I am trying to read a code written in LabVIEW. The block diagram is this:
This is the program to input x and y functions into the voltage input. It is meant to give an input voltage in different forms (sine, heartshape , etc.) into the fast-steering mirror or galvano mirror x and y axises.
x and y function controls are for inputting a formula for a function, and then we use "evaluation single value" function to input into a daq assistant.
I understand that { 2*(|-Mpi|)/N }*i + -Mpi*pi goes into the x value. However, I dont understand why we use this kind of formula. Why we need to assign a negative value and then do the absolute value of -M*pi. Also, I don`t understand why we need to divide to N and then multiply by i. And finally, why need to add -Mpi again? If you provide any hints about this I would really appreciate it.
This is just a complicated way to write the code/formula. Given what the code looks like (unnecessary wire bends, duplicate loop-input-tunnels, hidden wires, unnecessary coercion dots, failure to use appropriate built-in 'negate' function) not much care has been given in writing it. So while it probably yields the correct results you should not expect it to do so in the most readable way.
To answer you specific questions:
Why we need to assign a negative value and then do the absolute value
We don't. We can just move the negation immediately before the last addition or change that to a subtraction:
{ 2*(|Mpi|)/N }*i - Mpi*pi
And as #yair pointed out: We are not assigning a value here, we are basically flipping the sign of whatever value the user entered.
Why we need to divide to N and then multiply by i
This gives you a fraction between 0 and 1, no matter how many steps you do in your for-loop. Think of N as a sampling rate. I.e. your mirrors will always do the same movement, but a larger N just produces more steps in between.
Why need to add -Mpi again
I would strongly assume this is some kind of quick-and-dirty workaround for a bug that has not been fixed properly. Looking at the code it seems this +Mpi*pi has been added later on in the development process. And while I don't know what the expected values are I would believe that multiplying only one of the summands by Pi is probably wrong.
I would like to proceduraly generate 2D caves. I already tried out using some 1D simplex noise to determine the terrain of the floor, which is basically everything you can change in a sidescroller, but it turned out rather unimpressive.
I would like to have an interesting terrain for my cave/dungeon and if possible some alternative paths.
I couldn't come up with any ideas for this kind of terrain and I also could not find any promising ways to do this kind of stuff on the internet.
Assuming you've tried something like abs(simplex) > 0.1 ? nocave : cave, maybe the problem you're running into is that it's too connected, and that there are no dead-ends anywhere. You could extend this by doing the following simplex1*simplex1 > threshold(simplex2) where threshold(t)=a*t/(t+b) where a roughly controls the max threshold (cave opening size) and b roughly controls how much of the underground is caves vs not. The function looks like this, and the fact that it quickly rushes to zero is supposed to make dead ends look more rounded and less pointy. Working with the squared noise value is also for this purpose.
Have you tried Perlin Noise? Seems to be the standard way of doing this sort of thing.
I was reviewing some code from a library for Arduino and saw the following if statement in the main loop:
draw_state++;
if ( draw_state >= 14*8 )
draw_state = 0;
draw_state is a uint8_t.
Why is 14*8 written here instead of 112? I initially thought this was done to save space, as 14 and 8 can both be represented by a single byte, but then so can 112.
I can't see why a compiler wouldn't optimize this to 112, since otherwise it would mean a multiplication has to be done every iteration instead of the lookup of a value. This looks to me like there is some form of memory and processing tradeoff.
Does anyone have a suggestion as to why this was done?
Note: I had a hard time coming up with a clear title, so suggestions are welcome.
Probably to explicitly show where the number 112 came from. For example, it could be number of bits in 14 bytes (but of course I don't know the context of the code, so I could be wrong). It would then be more obvious to humans where the value came from, than wiriting just 112.
And as you pointed out, the compiler will probably optimize it, so there will be no multiplication in the machine code.
I do something like this to get:
bMRes += MatrixXd(n, n).setZero()
.selfadjointView<Eigen::Upper>().rankUpdate(bM);
This gets me an incrementation of bMRes by bM * bM.transpose() but twice as fast.
Note that bMRes and bM are of type Map<MatrixXd>.
To optimize things further, I would like to skip the copy (and incrementation) of the Lower part.
In other words, I would like to compute and write only the Upper part.
Again, in other words, I would like to have my result in the Upper part and 0's in the Lower part.
If it is not clear enough, feel free to ask questions.
Thanks in advance.
Florian
If your bMRes is self-adjoint originally, you could use the following code, which only updates the upper half of bMRes.
bMRes.selfadjointView<Eigen::Upper>().rankUpdate(bM);
If not, I think you have to accept that .selfadjointView<>() will always copy the other half when assigned to a MatrixXd.
Compared to A*A.transpose() or .rankUpdate(A), the cost of copying half of A can be ignored when A is reasonably large. So I guess you don't need to optimize your code further.
If you just want to evaluate the difference, you could use low-level BLAS APIs. A*A.transpose() is equivalent to gemm(), and .rankUpdate(A) is equivalent to syrk(), but syrk() don't copy the other half automatically.
I am trying to do the simplest of constrained optimizations in Mathematica but it just wont work and I dont know what I am doing wrong.
I just want max ln[x]+ln[y] subject to 10=x+y. This can simply be done by hand but Mathematica keeps spitting this out:
NMaximize::nrnum: The function value -2.19476-3.14159 I is not a real number at {x,y} = {10.8291,-0.829053}. >>
General::stop: Further output of NMaximize::nrnum will be suppressed during this calculation. >>
What's going on? Why cant it solve for the optimal x and y values?
Thanks