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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3
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1answer
59 views

Too small to represent and Chop in inaccessible algorithm

Overview I want to apply a specified Chop function to every step in an function call in Mathematica (in my case LegendreP), ...
0
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0answers
28 views

How to avoid machine underflow for plotting and integrating?

I am trying to integrate the following integrand, which I have plotted: ...
1
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0answers
169 views

General:: Exp[-717.401] is too small to represent as a normalized machine number; precision may be lost

I am solving pde. For the post processing bvp, there is solution given in output which is the solution from mathematica version 10.0.1. Output from above in mathematica 10.0.1 is, But when the similar ...
0
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0answers
24 views

Different sensitivies from LinearSolve and Eigenvalues. How to conciliate them?

I use the following functions to receive a matrix, and make it symmetric positive definite: ...
3
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1answer
47 views

Avoid MachinePrecision numbers in Message

Can I change the output of Message to not show MachinePrecision numbers? E.g. ...
1
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4answers
138 views

Can I change the default behavior so that “0.1” is interpreted as “1/10” automatically?

Consider the function f[a_] := NIntegrate[Sqrt[a + Log[x]], {x, 1, 10}, WorkingPrecision -> 30]. With this definition, I cannot call ...
0
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0answers
38 views

Inconsistent and oscillatory behavior with formula

I have the following code ...
1
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1answer
80 views

Machine-precision numbers cause loss of precision

I am trying to use the Mod function as follows. Table[ Nest[Mod[2 #, 1] &, FractionalPart[Pi], n], {n, 100}] // N ...
3
votes
3answers
374 views

How can I compute Erf of large numbers to more precision?

I would like to compute Erf[80/3] to enough precision to know the order of magnitude of 1 - Erf[80/3] How can I do that? I ...
3
votes
1answer
106 views

Why does precision decrease after increasing PrecisionGoal and WorkingPrecision on this integral?

I am trying to calculate a messy double-integral to many digits of precision. As shown below, the precision seems to increase reliably as WorkingPrecision goes from ...
0
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1answer
108 views

How to improve working precision?

I'm trying to fit the array data as follow: NonlinearModelFit[ data, s*t^r + (A/(w*(Pi/2)^0.5))*Exp[-2*((t - u)/w)^2], {s, r, A, w, u}, t]; But when ...
1
vote
1answer
32 views

How to get the output for the following code involving differentiation and integration?

I need to evaluate the following Mathematica code to get a numerical value as my output. But during compilation I get the error message NumericalMath`FixedPrecisionEvaluate::precbd: Requested ...
9
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1answer
564 views

Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
0
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0answers
65 views

Understanding Working Precision - two example equations

I am trying to understand how WorkingPrecision works, and in general how very small/large numbers are to be handled. Let me preface I probably do not have ...
6
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1answer
144 views

Issues with $MachineEpsilon

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 ...
0
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0answers
20 views

Conflicting output provided by `N[…]`

I am trying to evaluate an expression : (-((I (k2 - k1) (-1 + E^(2 I (k2 - k1) \[Pi])))/(-1 + (k2 - k1)^2))) /. {k1 -> 2, k2 -> 7} This gives ...
0
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0answers
66 views

Dealing with General::munfl errors

Edit: So, while trying to figure out a minimal exmaple, I found out that my main problem was actually unrelated to this and it just happened to be that giant pile of warnings and error messages coming ...
1
vote
1answer
276 views

How can I suppress the warning “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 ...
5
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1answer
101 views

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 ...
1
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0answers
52 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[0] == \[Pi], y'[0] == 0 }, y, {x, 0, 120}] The equation and the ...
3
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1answer
96 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 ...
1
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1answer
88 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 ...
2
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0answers
43 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 ...
1
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0answers
55 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 ...
4
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0answers
124 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 ...
9
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2answers
356 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
36 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
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2answers
250 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
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2answers
768 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
61 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
65 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
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1answer
71 views

Why this very simple problem turns to “Indeterminate”?

Why the following calculation gives Indeterminate value? ...
0
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0answers
57 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
120 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
125 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 ...
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
291 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: ...
5
votes
2answers
457 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. ...
2
votes
1answer
126 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
400 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
99 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
86 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
221 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 <...
2
votes
1answer
112 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
128 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
69 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
67 views

ContourPlot showing breaks in contours

I'm trying find graphically the solutions of the intersection of the following functions. ...
6
votes
1answer
119 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
173 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 ...