# 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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### 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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### Export numeric data with preset decimal places

I have a table of pairs of numbers, each with 300 decimal places, which are all important. If saved using Export["data.dat", data] and then imported back via Import["data.dat"] - then the 300 decimal ...
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### Making a calculation with high precision

I would like to make the following calculation: 1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1 Mathematica 8 returns 0. The result is obviously not 0, but my ...
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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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### 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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### 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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### 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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### MachinePrecision versus $MachinePrecision in NDSolve I'd like to understand why one of these inputs gives me an error and the other doesn't: ... 3 votes 1 answer 3k views ### How to change machineprecision digits I am trying to compute t0: ... 10 votes 2 answers 927 views ### Why is Mathematica destroying this graph? Here I have a picture of a function I graphed: reg[x_,y_]:=(x^2+y^2)Cos[4ArcTan[y/x]]; Plot3D[reg[x,y],{x,-2,2},{y,-2,2},AxesLabel->Automatic] And here is ... 4 votes 2 answers 3k views ### How do I overcome an Overflow? I'm trying to calculate entropies for an absolutely giant system by counting states, and this means I have to use some obscenely large numbers. I'm running ... 3 votes 1 answer 645 views ### Mathematica Precisions vs Doubles in C/C++ I'm having a bit of an issue regarding numerical precision and I'm not sure how to deal with it. I have a certain randomly generated matrix, say$M$, that I wish to compute the eigenvalues. The ... 4 votes 1 answer 460 views ### How to calculate accurate answer in Mathematica? I accidentally discovered for myself, that Mathematica outputs inaccurate answer. For instance, if I take$\sin(2 \cdot \pi \cdot 0.5) = 0 $, then in Mathematica it is: But if I calculate it on site ... 4 votes 1 answer 111 views ### My NIntegrate expression returns a wildly inaccurate value I am trying to integrate a function using NIntegrate: ... 2 votes 1 answer 362 views ### How to tell Mathematica to treat all numbers (including those in decimal form) as arbitrary precision numbers I have code that is essentially numerical. It uses functions like NDSolve and NIntegrate. But in most interesting cases, the ... 10 votes 2 answers 2k views ### DeleteDuplicates[] does not work as expected on floating point values Here is my simple example, and in this case function DeleteDuplicates does not work as expected. I want to FindRoot of my ... 10 votes 1 answer 395 views ### Plot of$\sin(x^x)$is missing from$x=143$When plotting the graph of$\sin(x^x)$I noticed that there is no plot from about$x=143$. I don't suppose there is a purely mathematical explanation for this? So, why is there no graph in ... 4 votes 0 answers 244 views ### Classification problem using SVM methods I am running SVM on mathematica and I a used this code with classes: ... 1 vote 1 answer 104 views ### Wrong Limit[...] for inexact expressions I noticed that Limit can return nonsense when using inexact parameters. In the following code, a is my (exact/inexact) parameter,... 7 votes 1 answer 268 views ### Bug in ListPlot? I want to check if this is a bug before I email WR about it. I can't get ListPlot[] to make scatter plots over a very small area: ... 5 votes 1 answer 235 views ### Compilation, square roots, and integers After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ... 11 votes 1 answer 143 views ### Abnormal behavior of RealDigits[x] In the Details of the document of RealDigits writes the following line: RealDigits[x] normally returns a list of digits of ... 3 votes 2 answers 122 views ### Make mathematica "forget" numbers beyond the precision goal I need Mathematica to remember only things upto two decimal places. I'm currently using the unwieldy Floor[x*100]/100 which works but is there a better way to ... 1 vote 1 answer 569 views ### How to increase the precision to get the correct roots at the boundaries? I want to solve an equation and Plot a graph of$\delta(\tau)$, where$0<\tau,\delta<1$. In principal$\delta(0)=1,\delta(1)=0$. However, when I solve the equation, the points near$\tau=1$can'... 17 votes 2 answers 343 views ### CompiledFunction returns machine numbers smaller than$MinMachineNumber

When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
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### N, machine precision and expression evaluation [closed]

I should state that I am a Mathematica beginner but I checked the questions about machine vs arbitrary precision (such as: this one ) and I continue to have the following issue while trying to ...
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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 ...
1 vote
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### Odd plotting/math issue (could be a precision problem) [closed]

I've got a pretty odd error on a project I'm working on and was hoping to enlist some advice to fix it. The goal of this notebook is to show that I can eliminate the non-normalizable (blowing up part) ...
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### Varying results from the Round function

My problem is simple. Consider the following. ...
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### Dr. StrangeNumbers or: How I Learned to Stop Worrying and Love Floating Point Arithmetic

The following is the program. ...
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### WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
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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: ...
905 views

### How to make the computer consider two numbers equal up to a certain precision

My problem is that I have a matrix A and the computer says is not Hermitian (self-adjoint). Then I check which elements make A ...
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### Different floating-point numbers equal?

Let's define two different numbers. x = 1. y = 1. + 2^-52 (* equivalently, 1 + \$MachineEpsilon *) Let's make sure they're different with ...
1 vote
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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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### 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 ...
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### Enforcing WorkingPrecision in NIntegrate

I have a very complicated 2D integral that I need to calculate repeatedly, and I'm trying to speed it up a bit, since at the moment it's taking a couple of days to complete. One thing I've noticed is ...
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### NIntegrate 2D highly oscillatory function

I am trying to integrate a function, and the error I get is greater than the result. So I need to calculate ...
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### Machine precision infinity

Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ...
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### Can I force Mathematica to use machine precision? [duplicate]

Some built-in functions (like Exp) give an arbitrary precision result, even when the argument is a machine precision number. Example: ...
1 vote
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### Which operations preserve digit precision?

Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
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### Reasonable choice of MachinePrecision, AccuracyGoal and PrecisionGoal for NDSolve

I am trying to use this model for later use in FindFit: ...
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### How to increase significant digits in Mathematica

How can I increase the number of significant digits in Mathematica? When I import a matrix, an element like 112.5276 is rounded to 112.528. I would like to increase the number of significant digits ...
1 vote
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### Decimal output from a simple equation

Let x= 0.0000000000000000036; y = 1 - x If i type this in Mathematica the answer of y is 1. I want the answer to be as it ...
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### How to map HoldForm?

I'm trying to compare between Sqrt[3.] and Sqrt[3]. To display the result, I mapped HoldForm to display the expressions on the left hand column (code at end), but it seems like Sqrt[3.] had been ...