# Questions tagged [floating-point]

A method of representing numbers by a fixed number of significant digits, and the exponent of some base number. They are characterized in the form ${(significant digits)}*base^{exponent}$. Typically, numbers are represented with respect to base = 2 (binary).

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### Where does the floating point error come from? (Finite difference using matrix multiplication versus shifts and adding.)

In Julia it appears that one picks up some error terms when doing finite differences using matrix multiplication versus shifts and addition. ...
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### Numerical computation of the complex elliptic integral $E(k)$ for medium $|k|$

I have implemented Carlson's algorithm for $E(k)$ from Numerical computation of real or complex elliptic integrals (available from ArXiv eprint, see also DLMF). It is essentially his formula (46) ...
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### Comparing two versions of the same hydrodynamic code and their error

So I have two versions of a hydrodynamic code that has the same underlying physics. Lets call them code A and B. However code B is more optimized and more object oriented. I was trying to compare the ...
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### What are the tradeoffs of using statically allocated arrays vs. pointers and dynamic allocation? [closed]

I am learning Monte Carlo simulation by C++. I begin with reading codes (from the internet and text books) of the 2D Ising model and the XY model. I find some people define spins simply by a two ...
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In going from double precision to quad (or higher) precision, roughly how much of a performance hit is taken on various architectures and frameworks. Do floating point operations take twice as much ...
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### On the cardinality of the set of numbers representable by a floating point system

I am new to numerical methods and I cannot think of a way to start solving the following problem. I know the mantissa, base and the boundaries are related when defining a number but I cannot really ...
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### Choosing epsilons

Most numerical algorithms require an epsilon to be chosen in order to be robust and provide meaningful results. Choosing machine epsilon is usually too aggressive. Barring any special knowledge ...
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### Machine epsilon does not limit relative rounding error for denormals. Is this a problem?

As we know, machine epsilon limits relative rounding error in the range of normalized floating point numbers. But it is easy to check that this is not true for denormalized numbers. My question is ...
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### range of positive mantissa in given floating-point number representation

I am a student and I came to this question while solving problems regarding the float-points. ...
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### Machine epsilon (eps)

The wiki for machine epsilon says: "Machine epsilon gives an upper bound on the relative error due to rounding in floating point arithmetic" If machine epsilon is the upper bound on the relative ...
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### How to handle floating point operations in HLSL?

I'm trying to write a perona malik anisotropic diffusion filter for the GPU. I'm basing my shader off a matlab implementation of the filter. I'm running into trouble because of what I suspect is ...
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### Do currently available GPUs support double precision floating point arithmetic?

I have run the molecular dynamics (MD) code GROMACS on a Ubuntu Linux cluster consisting of nodes containing 24 Intel Xeon CPUs. My particular point of interest turns out to be somewhat sensitive to ...