# Questions tagged [machine-precision]

For questions on the use of machine-precision real numbers (also known as floats), the numbers that can be directly manipulated through the underlying numerical capabilities of your computer system.

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### How to use Working Precision to get good result and plot?

I have a function f(x) which I would like to see going up for very low values of x: from an asymptotic study, I expect it to go to Infinity for low x; however, I can see an elbow and many oscillations....
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### Unpredictable behavior of numerical error

A comparison of float calculation and exact expression for NumberForm[0.3^2 - (3/10)^2, 18] gives an exact zero for $0.3$. However, ...
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### Precision of integers vs. Precision of floating numbers

It seems that Mathematica can handle very big integers accurately, but cannot do the same for floating numbers. See the following code: ...
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### Why does 1 - Exp[-10.0^12] cause an out-of-memory error?

I would like to understand why evaluation of the expression 1 - Exp[-10.0^12] causes an out-of-memory error and how can I prevent such errors when calculating ...
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### How to use a higher precision?

Below is my code. If I set W to $10^{55}$, it breaks down and the result is wrong. What do I need to do to use W as large as $10^{200}$? ...
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### Treating a bad conditioned covariance matrix

I am trying to detect outliers in a big dataset using the Mahalanobys distance method. To calculate the Mahalanobys distance for a given vector $x$ from a mean vector $\mu$ you have to compute the ...
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### Chop intermediate results of NDSolve after each step [closed]

Using NDSolve for a set of three ordinary differential equations, I ran into the problem that intermediate results quickly develop negligible imaginary parts. I get ...
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### Unexpected behavior from CoordinateBoundingBoxArray with Into and 0.41

I want to get the four corners of a Cuboid. This usually works: CoordinateBoundingBoxArray[{-{1., 1.}, {1., 1.}}, Into@1] gives ...
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### Why does this rounding happen at machine precision?

Clearly, dividing by two in a binary number shifts the decimal point like this: BaseForm[InputForm, 2] BaseForm[InputForm[7/2 // N], 2] It gives: 2^^111 and 2^...
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### What happens at the end of MachinePrecision? Is the remainder discarded or rounded?

What happens at the end of MachinePrecision? Is the remainder discarded or rounded? This code suggests it is discarded; is that conclusion correct? Why is it not rounded? ...
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### Showing what happens with a number beyond machineprecision

I want to play around a bit in Mathematica to understand how floating-point precision, rounding and truncation actually works. I understand that Machineprecision is $2^{-52}$. First of all I would ...
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### problem in matching two sets of particles

I have been trying to simulate a simple system in which there are two set of particles. One kind of particles are localized on the boundary of a circle (shown in purple below), whereas the second kind ...
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### ConvexHullMesh fails with small numbers

When I try to get the ConvexHullMesh of a List of points that are "small scale", I get errors: ...
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### A simple syntax does not work

The code below does not work. Can anyone tell me why? Thanks! ...
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### Machine-Precision and Arbitrary Precision [closed]

What is meant by a machine number in the Mathematica documentation? What is the difference between machine-precision and fixed-point precision? What is arbitrary precision?
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### Precision of LinearModelFit with Polynomials

I have a Problem regarding the fit of given points with a polynomial up to the fifth degree. tableofvalues=Import["tableofvalues.csv"] My polynomial is: ...
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### Does Mathematica have an equivalent of C's nextafter?

In C (and many other programming languages), there is a function double nextafter(double x, double y) which takes two (IEEE 754) floating-point numbers and ...
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### Does Mathematica have an equivalent of Python's float.as_integer_ratio?

The Python programming language has a float.as_integer_ratio(x) function which exactly converts an IEEE 754 floating-point number into a numerator/denominator pair ...
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### Why does it matter at what point I replace?

I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points. I use (LK4 is defined below, but its shape should have nothing to do with my problem)...
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### Compilation of Total with compensated summation

I sometimes obtain an unexpected error when trying to call a compiled version of Total with compensated summation turned on. More specifically I define ...
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### Floating point arithmetic bug caused by Table[]

I was doing something fairly ordinary and noticed something I can't, for the life of me, explain. For context, I wanted to take make a function that takes an array of data like the one below, then an ...