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.
229
questions
1
vote
4
answers
216
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 ...
- 854
1
vote
1
answer
110
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
...
- 183
3
votes
3
answers
762
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 ...
- 457
3
votes
1
answer
162
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 ...
- 854
0
votes
1
answer
252
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
1
answer
72
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 ...
- 343
0
votes
0
answers
94
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 ...
- 755
0
votes
0
answers
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 ...
- 431
0
votes
0
answers
351
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 ...
- 21
5
votes
1
answer
352
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 ...
- 1,580
1
vote
0
answers
74
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 ...
- 755
3
votes
1
answer
122
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 ...
- 1,580
2
votes
0
answers
54
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 ...
- 601
1
vote
0
answers
68
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
...
- 601
4
votes
0
answers
130
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 ...
- 41
1
vote
0
answers
59
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 ...
- 177
9
votes
2
answers
442
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+??
...
- 31.2k
0
votes
1
answer
88
views
Allow Mathematica to solve the differential equations with larger than 16 digits parameters
Consider the system of differential equations
...
- 4,652
1
vote
1
answer
64
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 ...
- 629
0
votes
1
answer
99
views
Why this very simple problem turns to "Indeterminate"?
Why the following calculation gives Indeterminate value?
...
- 629
0
votes
1
answer
141
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]. ...
- 629
0
votes
0
answers
72
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.
...
- 181
3
votes
1
answer
240
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 ...
- 550
2
votes
1
answer
453
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: ...
- 3,439
1
vote
1
answer
95
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 ...
- 103
3
votes
2
answers
924
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
...
- 967
5
votes
2
answers
867
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
1
answer
171
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.
...
- 2,921
1
vote
3
answers
136
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 ...
- 2,480
1
vote
1
answer
96
views
Drawing from InverseWishartMatrixDistribution. A machine precision error?
I'm drawing from the Inverse-Wishart Distribution, but I got the following error message:
...
- 2,517
1
vote
1
answer
702
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 ...
- 617
4
votes
1
answer
233
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
<...
- 8,900
2
votes
1
answer
180
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 ...
- 17k
2
votes
1
answer
140
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 ...
- 8,900
3
votes
1
answer
138
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 ...
- 18.7k
0
votes
1
answer
77
views
ContourPlot showing breaks in contours
I'm trying find graphically the solutions of the intersection of the following functions.
...
- 573
2
votes
2
answers
495
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 ...
- 4,553
5
votes
0
answers
97
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...
- 51
6
votes
1
answer
159
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 ...
- 104k
2
votes
2
answers
2k
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
...
- 45
0
votes
1
answer
62
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]]:
...
- 45
2
votes
2
answers
431
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 ...
- 2,517
0
votes
1
answer
109
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....
- 45
3
votes
1
answer
141
views
Numerical precision problem
I have this simple code:
ep = 1 - 80000000000 (-(199999/200000) + 1/E^(1/200000))
ep // N
-8.27404*10^-8
...
- 793
0
votes
0
answers
331
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 ...
- 569
3
votes
1
answer
136
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 :
...
- 17.8k
0
votes
2
answers
91
views
equal expressions give different numerical result
I have two expressions, and they are really equal:
...
- 1,121
2
votes
1
answer
158
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, ...
- 375
1
vote
1
answer
50
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 ...
- 5,490
15
votes
4
answers
672
views
Terrible accuracy of DawsonF
DawsonF[30.] returns 0. The correct value is 0.016676...
At least it prints a warning message,
...
- 11.1k