# 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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### Equality for floats

Suppose I have two floats (e.g. {x,y} = RandomReal[{0,1},2]). Might there be a situation where all three comparisons evaluate to ...
44 views

### Numerical precision - simulating an unstable equilibrium

I was playing around with NDSolve and the following ODE s = NDSolve[{y''[x] == -Sin[y[x]], y == \[Pi], y' == 0 }, y, {x, 0, 120}] The equation and the ...
89 views

### DeleteCases with a case as float?

Might the DeleteCases have issues in matching when the list is of floats (machine precision numbers)? E.g. in this code it might fail to match correctly because ...
39 views

### Set Underflow precision in Mathematica 12 same as version 11.x [duplicate]

It seems like Mathematica version 12 sets arbitrary underflow precision depending on the function, but I would like the underflow precision to be same as what was for previous version of Mathematica ...
45 views

### FindRoot giving error in Mathematica version 12

I was using the same code in previous version of Mathematica but unfortunately I had to update Mathematica to version 12 because I upgraded MacOS to Catalina. Now when I run my code, I get this error ...
120 views

### How does Mathematica evaluate N[π, 30] == π?

I want to know how N[π, 30] == π works. The result is True. I wonder whether the exact number ...
32 views

### Changing machine precision notebook-wide leads to peculiarities

For a project of mine it is preferrable to set notebook precision globally. I have done so by using the answer in Global precision setting. The idea is to dynamically create a ...
294 views

### How to detect underflow/overflow (post 11.3)?

This old trick used to work before 11.3: SetSystemOptions["CheckMachineUnderflow" -> True] But no longer... so how can we explicitly check for this in v12+?? ...
63 views

### Allow Mathematica to solve the differential equations with larger than 16 digits parameters

Consider the system of differential equations ...
57 views

### why some parts of my curve are removed or wiped

When I try to draw the next code I get a curve with missing parts, as shown in the picture. I do not know if it is an precision problem in the Mathematica program or is some data not calculated. Or is ...
59 views

### Why this very simple problem turns to “Indeterminate”?

Why the following calculation gives Indeterminate value? ...
54 views

### Preventing Mathematica from considering small values to be equal to zero [duplicate]

In my calculations I have a variable (say z) which can be an argument of Log, say, z Log[z]. ...
48 views

### How to resolve underflow occurrences?

I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve. ...
76 views

As is well known, Mathematica changed how it handles numbers smaller than $MinMachineNumber in recent versions. I'm running Mathematica 12 on a Mac, and I cannot figure out why it's treating these ... 1answer 159 views ### Why would Evaluate[] in Plot give me warning about precision? I have a code:- Plot[Evaluate@PDF[NormalDistribution[1.6, 0.2], x], {x, -6, 6}] And then I got the warning: ... 1answer 86 views ### Number definition and approximation I run these lines: a = 0.833 SetPrecision[a, 20] and this is the output: 0.833 0.83299999999999996270 I expected to ... 2answers 168 views ### Why is Mathematica's default precision only 16 digits? [closed] I was performing some basic computations when I noticed that NumberForm[N[Zeta], {100, 100}] yields ... 2answers 343 views ### Underflow error General::munfl from E^x instead of Exp[x] In contrast to earlier versions, Mathematica 11.3 and 12.0 generate lots of underflow errors from my code, e.g. ... 0answers 35 views ### Contradictions in PositiveDefiniteQ, Det and Inverse in Mathematica A few words before the working example. Below we find 2 functions which should theoretically transform any matrix to its closest Symmetric Positive Definite (SPD) matrix: ... 1answer 108 views ### Correct syntax for working precision in functions version 12 I just recently updated from version 11.2 -> 12...there apparently are quite a few changes since 11.2.$\unicode{952}\unicode{960}$One being how version >11.3 deal with numbers that approach zero. ... 3answers 83 views ### When should one write integer numbers with a decimal? I often see different solutions where users have taken advantage of how Mathematica handles numbers differently. I.e. when is it appropriate to use a decimal point in a calculation? Can someone ... 1answer 77 views ### Drawing from InverseWishartMatrixDistribution. A machine precision error? I'm drawing from the Inverse-Wishart Distribution, but I got the following error message: ... 1answer 143 views ### How can I suppress the warning$\mathrm{\it precision\ may\ be\ lost}$? When I import data from a .dat file, V11.3 emits the message: is too small to represent as a normalized machine number; precision may be lost. How can I close the ... 1answer 218 views ### Inexact numbers as keys in Association? Can someone explain me how Mathematica's Associations behave with inexact numbers as keys: <| 0.22499999999999964 -> a |> [0.22499999999999965] and <... 1answer 91 views ### Efficient Round edition with different rounding direction As pointed out in this post, Mathematica has a special version of Round that Round rounds numbers of the form x.5 toward the nearest even integer. A comment by ... 1answer 124 views ### How to prevent Mathematica from giving inexact answers Upon doing a simple subtraction 13.725 - 13.5 both Mathematica 11.3 and 12.0 beta version are giving me 0.22499999999999964 ... 1answer 62 views ### Forcing divisions to be a machine-precision floating point divisions instead of multiplication by inverse I want to imitate machine-precision, de facto IEEE division on Mathematica. On my quick trials I find this surprisingly hard to accomplish, since Mma rewrites a / b ... 1answer 64 views ### ContourPlot showing breaks in contours I'm trying find graphically the solutions of the intersection of the following functions. ... 2answers 212 views ### Why is 0 vs 0.0 causing a precision problem? I wasn't sure what to title this Question. I tried calculating different forms of a continued fraction, and I found that I get a correct result when I set d to 0 but a wrong result (in the final two ... 0answers 66 views ### Small positive machine number calculation in Mathematica 11.3 In Mathematica version < 11.3, any positive Machine‐Precision Numbers exceeding the range [$MinMachineNumber,$MaxMachineNumber... 1answer 106 views ### Extracting binary digits of machine precision numbers Currently, I am developing an octree data structure. And I need it to be fast. To this end, I would like to have a fast way to extract the$m$binary digits "after the dot" of each entry in a matrix ... 2answers 395 views ### Truncate a number in mathematica I want to truncate a simple number to n decimal digits. For example, 2/3. I used f[x_, n_] := N[IntegerPart[x 10^n]/10^n] but I get ... 1answer 56 views ### How to get the correct result in a simple operation in Mathematica I have the following values for x[[i]], y[[i]] and A[[i,j]]: ... 2answers 110 views ### What's the smallest positive real allowed in mathematica? This question may be a bit strange, but in this question, one of the answers suggests substituting some negatives values in a matrix by the smallest positive real number allowed. So, I was wondering ... 1answer 46 views ### Simple division with high precision in Mathematica [closed] I want to do a simple division i.e. 0.70524/0.51824 . What I want is to find the result of the roundation of this division for precision from 1 to 19 decimal digits.... 1answer 74 views ### Numerical precision problem I have this simple code: ep = 1 - 80000000000 (-(199999/200000) + 1/E^(1/200000)) ep // N -8.27404*10^-8 ... 0answers 138 views ### Plot a function with very small values, close to zero I want to plot a function with very small values, close to zero, but even though the limit is -3/2 as x->0, I can't get any ... 1answer 87 views ### Copy-paste with annoying trailing 0s When one copies an output containing machine-precision numbers to a input, many trailing 0s appears. For example : Evaluate the following expression : ... 2answers 72 views ### equal expressions give different numerical result I have two expressions, and they are really equal: ... 1answer 61 views ### Working Precision warnings for ParametricPlot I wish to plot a series of parametric curves for the following function called poly that has five parameters (Γ, ... 1answer 41 views ### How to choose elements of a matrix with internally generated variables and rank them with real coefficients I have a Code (a long one), part of it is below. The following piece basically multiplies an adjacency matrix with a vector of equilibrium values. Then tries to pick non-zero elements to be used in ... 4answers 424 views ### Terrible accuracy of DawsonF DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ... 2answers 375 views ### Why does N not upgrade precision? [duplicate] Precision[N[1.0, 20]] Precision[N[1, 20]] MachinePrecision 20. It would be so much more intuitive and less error prone, if <... 1answer 168 views ### Plot3D discrepancy between MMA 10 and 11.3 - possible small numbers issue I'm having some troubles with the following code I wrote in MMA 10 some time ago: ... 1answer 92 views ### Machine Epsilon is not equal to$MachineEpsilon

I try to wrap my head around machine precision calculations in Mathematica (11.2, Linux). I do not understand the following behavior: ...
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### NIntegrate numerical accuracy and errors

I have the following 3x3 matrix M = {{-I*ω + Γ/2, I*g1, 0}, {I*g1, -I*ω + κ1/2, I*g2}, {0, I*g2, -I*ω + κ2/2}}; Finding the eigenvalues and eigenvectors ...
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### Performance Tuning - How can I make Mathematica to use less than certain digits number?

I would like to know if there is a way to make Mathematica to use at most certain digit number. For example, Suppose I want to calculate 2*Pi. x=N[Pi] y=2*x ...
77 views

### Getting max precision limit overflow for a very simple calculation

I've never seen this error on such a simple calculation. Does anybody know how to fix this annoying error?