# 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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### 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: ...
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### Compilation, square roots, and integers

After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ...
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### 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 ...
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### 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 ...
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1 vote
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### 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'...
978 views

### 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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### 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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### Machine precision near zero: not fulfilled?

I am puzzled by the behavior of Mathematica machine precision with numbers approaching zero. This manifests itself, e.g., with FixedPoint and the like. In the ...
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1 vote
102 views

### 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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### 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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### 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: ...
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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 ...
1 vote
65 views

### Which operations preserve digit precision?

Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
745 views

### 'eps' equivalent in Mathematica

In MATLAB, there is a function named eps. eps Spacing of floating point numbers. D = eps(X), is the positive distance from ABS(X) to the next larger in ...
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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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### Precision problem with numerical solution of a differential equation

I want solve $$2\sqrt{|\gamma|}x = \int_{1}^{t} dy \sqrt{\frac{1+2|\gamma_2|y}{y^2(1-y)}}$$ where $0<t\leq$1. I'm using a for cycle to evaluate t, calculate the integral and the assign the $x$. ...
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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 ...
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1 vote
119 views

### 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 ...
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### Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?

Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
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### Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
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### Unexpected behavior of subtraction with approximate numbers [duplicate]

I'm using the Table command to generate a list of values: FullForm /@ Table[10. - x, {x, 2.7, 2.8, .1}] and I get the ...
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### How to get more accurate orthonormal eigenvectors?

I have a matrix M with real entries in MachinePrecision. I compute its eigenvectors and construct matrix ...
235 views

### 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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### Number precision in a list [duplicate]

I have list with elements: ...
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### The precision of the number

I have problem in Mathematica with unnecessary rounding which is caused by high precision. For example I have value a = 2.052685846*10^-1865, when I make ...
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### Floating point addition not associative

Can anybody explain the following behavior? x = 0.2 + (0.3 + 0.1); y = (0.2 + 0.3) + 0.1; x == y (* -> True *) But actually the variables do not exactly ...
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### Plot periodic function from Dirac delta function [duplicate]

Sorry for my bad english. I need to plot periodic function from dirac delta: δT(t)=∑δ(t–n*T), where T - is a constant, and n=-20..20 And after them, plot new function fd=f(t)*δT(t) - discrete signal ...
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I'm attempting to add $MachineEpsilon to numbers I am pulling from the domains of 3 interpolating functions. I pulled 3 numbers, and for one of these numbers adding ... • 87 2 votes 0 answers 568 views ### how to calculate with just double floating point precision [duplicate] I want to calculate with simple double floating point precision. ... 42 votes 2 answers 1k views ### Is there a difference between Divide[a,b] and a/b? In this comment it was asserted that Divide[a,b] and a/b are different, though the documentation indicates that they are the ... • 4,939 31 votes 8 answers 2k views ### Elegant high precision log1p`? Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ... • 877 0 votes 1 answer 272 views ### How to improve the performance of this code I have implemented a code in Mathematica 9 to simulate a scattering problem, and I got really disappointed about its performance when compared to Matlab. Since I am a newbie in Mathematica, would ... • 1 17 votes 2 answers 343 views ### CompiledFunction returns machine numbers smaller than$MinMachineNumber

When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
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