Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

# 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).

107 questions
Filter by
Sorted by
Tagged with
474 views

### Implementing std::nextafter: Should denormals-are-zero mode affect it? If so, how?

This might be the wrong stackexchange site for this question. math.SE, cs.SE, programmers.SE, and of course stackoverflow are all possibilities. I'm hoping to reach an audience that might actually ...
544 views

### Hardware performance, floating point functions

First of all, hope I've found the right forum for this question, if I haven't please pass me on to a one which would fit better. Out of curiosity from an argument with someone who may or may not be ...
438 views

262 views

### Why should I renormalize physical variables?

I am working with legacy physical codes and I develop new ones based on the output of them. They all use their own internal normalization of variables (for example all distances are divided by the ...
3k views

### How to avoid catastrophic cancellation in python function?

I am having trouble implementing a function numerically. It suffers from the fact that at large input values the result is a very large number times a very small number. I am not sure if catastrophic ...
23 views

I need a numerically stable way to compute the following ratio: $$\frac{_{2}F_{1}(a+1,b;c;x)}{_{2}F_{1}(a,b;c;x)}$$ All the parameters are real positive numbers, with $0 < a,b,c$ and $0 < x &... 2answers 910 views ### Choosing epsilons Most numerical algorithms require an epsilon to be chosen in order to be robust and provide meaningful results. Choosing machine epsilon is usually too aggressive. Barring any special knowledge ... 1answer 171 views ### Compute hypergeometric function ratio:$\frac{_{2}F_{1}(a+1,b;c;x)}{_{2}F_{1}(a,b;c;x)}$? I need a numerically stable way to compute the following ratio: $$\frac{_{2}F_{1}(a+1,b;c;x)}{_{2}F_{1}(a,b;c;x)}$$ All the parameters are real numbers, with$a< 0$,$\ b,c > 0$and$0<x&...
74 views

After studying the process of Gradual Underflow, I'm left a little curious as to why machines don't implement Gradual Overflow; where numbers exceeding the overflow level would be stored as un-...
721 views

### Overcoming floating point issues when Inverse does not exist but determinant provides nonzero result

I have an expression (let's say determinant of matrix A) expressed in symbolic form in terms of 2 decision variables x1, x2 and 2 parameters q1 and q2. I'm minimizing this using fmincon for different ...
692 views

### Accurate Polynomial Evaluation in Floating Point

What are the most accurate algorithms for evaluating a polynomial using floating point arithmetic? The internet seems to suggest that Horner's method is commonly used. In particular I have a cubic ...
62k views

### How to determine the amount of FLOPs my computer is capable of

I would like to determine the theoretical number of FLOPs (Floating Point Operations) that my computer can do. Can someone please help me with this. (I would like to compare my computer to some ...
5k views

### Which algorithm is more accurate for computing the sum of a sorted array of numbers?

Given is an increasing finite sequence of positive numbers $z_{1} ,z_{2},.....z_{n}$. Which of the following two algorithms is better for computing the sum of the numbers? ...
109 views

### Re-scaling array of floats so that all items are approximately integer

I have an array of floating point values $F$. I want to input my array into an algorithm that only takes integer values. How can I efficiently determine the smallest multiplier $m$ such that all ...
209 views

### 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 ...
3k views

### 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. ...
5k views

### 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 ...
1k views

### 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 ...
10k views

### 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 ...
616 views

### Relevance of fixed-point and arbitrary precision computations

I see very few non-floating point computing libraries/packages around. Given the various inaccuracies of floating point representation, the question arises why there aren't at least some fields where ...
1k views

### cancellation problem in float-point numbers

In http://en.wikipedia.org/wiki/Floating_point#Addition_and_subtraction, it gives an example about cancellation problem in float-point numbers, see I don't understand why it is written : ...
245 views

### Are there Improved ways of computing $p \log(p)$?

Most math libraries have a number of versions of logarithm functions. Most of the time we assume them to be perfect, but actually quite a lot of them just offer a certain number of digits of precision....
2k views

### Need for quad precision in scientific computing?

Even if quad precision is not directly supported by most CPUs, many Compilers (GNU, Intel) support them. Also some software packages allow to compile with quad precision, e.g. PETSc. But is there ...
264 views

### Krylov subspace iterative methods in floating point arithmetic

Is there any work that considers Krylov subspace iterative methods in floating point arithmetic? I'm especially interested in how rounding errors influence the convergence and the accuracy of the ...
336 views

### Catastrophic cancellation in logsum

I'm trying to implement the following function in double-precision floating point with low relative error: $$\mathrm{logsum}(x,y) = \log(\exp(x) + \exp(y))$$ This is used extensively in statistical ...
1k views

### Relative comparison of floating point numbers

I have a numerical function f(x, y) returning a double floating point number that implements some formula and I want to check that it is correct against analytic ...
618 views

### transitive floating point comparison with (absolute) tolerance

I want to compare two floating point numbers for equality relative to a known absolute tolerance. However, this is inside an algorithm I wrote quite some time ago, and I believe the logic of that ...
478 views

### In floating point arithmetic, why does numerical imprecision result from adding a small term to a difference of large terms?

I have been reading the book Computer Simulation of Liquids by Allen and Tildesley. Starting on page 71, the authors discuss the various algorithms that are used to integrate Newton's equations of ...
569 views

### What algorithm for solving a set of stiff ODEs would be easiest to port to high precision floating point arithmetic?

I want to solve a relatively small system of stiff ODEs (< 10 first-order equations) using high precision floating point arithmetic (using MPFR or alike). What would be the easiest algorithm to ...
A very common problem in Markov Chain Monte Carlo involves computing probabilities that are sum of large exponential terms, $e^{a_1} + e^{a_2} + ...$ where the components of $a$ can range from ...