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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9
votes
2answers
280 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+?? ...
1
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0answers
29 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 ...
2
votes
2answers
148 views

Why is Mathematica's default precision only 16 digits? [closed]

I was performing some basic computations when I noticed that NumberForm[N[Zeta[3]], {100, 100}] yields ...
7
votes
2answers
671 views

Accurately evaluating the hypergeometric function

As part of another problem, I am working to evaluate hypergeometric functions such as Hypergeometric2F1[1, 1, n, -1] for large $n$. I am hoping to obtain at ...
1
vote
1answer
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 ...
0
votes
1answer
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]. ...
0
votes
1answer
57 views

Why this very simple problem turns to “Indeterminate”?

Why the following calculation gives Indeterminate value? ...
0
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0answers
44 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. ...
3
votes
1answer
56 views

Setting precision and machine underflow

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 ...
3
votes
0answers
114 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 ...
1
vote
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 ...
19
votes
5answers
4k views

Numerical underflow for a scaled error function

I calculate a scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ...
2
votes
1answer
138 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: ...
4
votes
2answers
279 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. ...
0
votes
0answers
33 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: ...
2
votes
1answer
96 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. ...
8
votes
2answers
284 views

how to get single, and quad Precision out of Mathematica which match Fortran result

by default, if a number has decimal . after it, then Mathematica will do computation using machine Precision, which on my PC (intel hardware) running windows 7 64 ...
1
vote
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 ...
1
vote
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: ...
4
votes
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 <...
1
vote
1answer
108 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 ...
2
votes
1answer
85 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 ...
2
votes
1answer
122 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 ...
3
votes
1answer
59 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 ...
0
votes
1answer
63 views

ContourPlot showing breaks in contours

I'm trying find graphically the solutions of the intersection of the following functions. ...
6
votes
1answer
104 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 ...
6
votes
2answers
167 views

How can I make 1+$MachineEpsilon not look like 1?

I undarstand that 1+$MachineEpsilon is actually not equal 1. However, it persists to look like it was equal ...
2
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2answers
164 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 ...
5
votes
0answers
61 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...
1
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2answers
245 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 ...
0
votes
1answer
53 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]]: ...
2
votes
2answers
97 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 ...
0
votes
0answers
120 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 ...
0
votes
1answer
44 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....
3
votes
1answer
71 views

Numerical precision problem

I have this simple code: ep = 1 - 80000000000 (-(199999/200000) + 1/E^(1/200000)) ep // N -8.27404*10^-8 ...
1
vote
1answer
82 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 : ...
17
votes
2answers
997 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 ...
0
votes
2answers
71 views

equal expressions give different numerical result

I have two expressions, and they are really equal: ...
6
votes
4answers
264 views

How do I convert an inexact number smaller than $MinMachineNumber to machine-precision?

I was trying to convert some arbitrary-precision numbers to machine-precision numbers using N[myNumber,MachinePrecision]. But, although my test number did lose some ...
1
vote
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 ...
2
votes
1answer
55 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, ...
14
votes
4answers
396 views

Terrible accuracy of DawsonF

DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ...
8
votes
3answers
3k views

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 ...
5
votes
2answers
366 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 <...
8
votes
1answer
157 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: ...
3
votes
1answer
75 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: ...
0
votes
2answers
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 ...
7
votes
2answers
458 views

Dealing with numbers too large for machine precision in Graphics

Graphics only supports machine precision numbers (i.e. number that can be converted to machine precision). Take for example ...
1
vote
1answer
100 views

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 ...