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# 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 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 ...
31 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 ...
287 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+?? ...
62 views

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

Consider the system of differential equations ...
53 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 ...
58 views

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

Why the following calculation gives Indeterminate value? ...
53 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]. ...
46 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. ...
65 views

As is well known, Mathematica changed how it handles numbers smaller than $MinMachineNumber in recent versions. I'm running Mathematica 12 on a Mac, and I cannot figure out why it's treating these ... 1answer 141 views ### Why would Evaluate[] in Plot give me warning about precision? I have a code:- Plot[Evaluate@PDF[NormalDistribution[1.6, 0.2], x], {x, -6, 6}] And then I got the warning: ... 1answer 63 views ### Number definition and approximation I run these lines: a = 0.833 SetPrecision[a, 20] and this is the output: 0.833 0.83299999999999996270 I expected to ... 2answers 154 views ### Why is Mathematica's default precision only 16 digits? [closed] I was performing some basic computations when I noticed that NumberForm[N[Zeta], {100, 100}] yields ... 2answers 292 views ### Underflow error General::munfl from E^x instead of Exp[x] In contrast to earlier versions, Mathematica 11.3 and 12.0 generate lots of underflow errors from my code, e.g. ... 0answers 34 views ### Contradictions in PositiveDefiniteQ, Det and Inverse in Mathematica A few words before the working example. Below we find 2 functions which should theoretically transform any matrix to its closest Symmetric Positive Definite (SPD) matrix: ... 1answer 97 views ### Correct syntax for working precision in functions version 12 I just recently updated from version 11.2 -> 12...there apparently are quite a few changes since 11.2.$\unicode{952}\unicode{960}$One being how version >11.3 deal with numbers that approach zero. ... 3answers 80 views ### When should one write integer numbers with a decimal? I often see different solutions where users have taken advantage of how Mathematica handles numbers differently. I.e. when is it appropriate to use a decimal point in a calculation? Can someone ... 1answer 76 views ### Drawing from InverseWishartMatrixDistribution. A machine precision error? I'm drawing from the Inverse-Wishart Distribution, but I got the following error message: ... 1answer 113 views ### How can I suppress the warning$\mathrm{\it precision\ may\ be\ lost}$? When I import data from a .dat file, V11.3 emits the message: is too small to represent as a normalized machine number; precision may be lost. How can I close the ... 1answer 216 views ### Inexact numbers as keys in Association? Can someone explain me how Mathematica's Associations behave with inexact numbers as keys: <| 0.22499999999999964 -> a |> [0.22499999999999965] and <... 1answer 87 views ### Efficient Round edition with different rounding direction As pointed out in this post, Mathematica has a special version of Round that Round rounds numbers of the form x.5 toward the nearest even integer. A comment by ... 1answer 123 views ### How to prevent Mathematica from giving inexact answers Upon doing a simple subtraction 13.725 - 13.5 both Mathematica 11.3 and 12.0 beta version are giving me 0.22499999999999964 ... 1answer 60 views ### Forcing divisions to be a machine-precision floating point divisions instead of multiplication by inverse I want to imitate machine-precision, de facto IEEE division on Mathematica. On my quick trials I find this surprisingly hard to accomplish, since Mma rewrites a / b ... 1answer 63 views ### ContourPlot showing breaks in contours I'm trying find graphically the solutions of the intersection of the following functions. ... 2answers 177 views ### Why is 0 vs 0.0 causing a precision problem? I wasn't sure what to title this Question. I tried calculating different forms of a continued fraction, and I found that I get a correct result when I set d to 0 but a wrong result (in the final two ... 0answers 62 views ### Small positive machine number calculation in Mathematica 11.3 In Mathematica version < 11.3, any positive Machine‐Precision Numbers exceeding the range [$MinMachineNumber,$MaxMachineNumber... 1answer 105 views ### Extracting binary digits of machine precision numbers Currently, I am developing an octree data structure. And I need it to be fast. To this end, I would like to have a fast way to extract the$m$binary digits "after the dot" of each entry in a matrix ... 2answers 277 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 99 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 45 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 73 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 121 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 84 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 57 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 407 views ### Terrible accuracy of DawsonF DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ... 2answers 368 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 164 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 84 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: ...
61 views

### 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 ...
70 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?
71 views

### Precision-related error in Audio

Bug introduced in 11.3 or earlier CASE:4075745 I have been experimenting with using Audio and associated functions for data acquisition using an external sound ...
132 views

### The algorithm behind InputForm for machine numbers

There are several questions on this site about implementing fast CSV/TSV export for machine numbers without loss of precision. Recently I discovered that Export ...
115 views

### Is it possible to get the original number from DecimalForm?

Bug introduced in 5.2 or earlier and persisting through 12.0 [CASE:4315787] Wrong behavior of NumberForm (DecimalForm outputs ...
1k views

### New General::munfl error and loss of precision

The latest version 11.3.0.0 of Mathematica returns Indeterminate when evaluating Log[Exp[-800.]]. I believe this was not ...
429 views

### What is wrong with importing Real32 or Real64?

Those who visit the chat might have seen the question of varkor. I'm posting it here in the hope that I have missed something. Assume you have a real number ...