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.
233
questions
42
votes
2
answers
4k
views
Meaning of backtick in floating-point literal
If I compute, say, 1/3//N, Mathematica displays
0.333333
as the result.
When I copy that output to use elsewhere,
the paste ...
- 4,751
42
votes
2
answers
1k
views
Is there a difference between Divide[a,b] and a/b?
In this comment it was asserted that Divide[a,b] and a/b are different, though the documentation indicates that they are the ...
- 4,959
31
votes
8
answers
2k
views
Elegant high precision `log1p`?
Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ...
- 887
30
votes
2
answers
4k
views
Why does Mathematica results differ from C++ results within machine precision?
I am trying to wrap my head around floating-point precision. Performing the following numeric operation:
275./6.*1.03692775514337
in Mathematica and C++ and ...
- 467
26
votes
2
answers
2k
views
Different floating-point numbers equal?
Let's define two different numbers.
x = 1.
y = 1. + 2^-52 (* equivalently, 1 + $MachineEpsilon *)
Let's make sure they're different with ...
- 7,861
22
votes
2
answers
3k
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 ...
- 1,982
20
votes
1
answer
2k
views
Quadruple-precision (128 bit) arithmetic
Is it possible to force Mathematica to perform computations with hardware supported quadruple-precision? The following test suggest, that all of the computations with fixed precision, different than <...
- 3,528
19
votes
5
answers
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.]. ...
- 193
18
votes
4
answers
475
views
Does Mathematica have an equivalent of C's nextafter?
In C (and many other programming languages), there is a function
double nextafter(double x, double y)
which takes two (IEEE 754) floating-point numbers and ...
- 2,336
18
votes
2
answers
572
views
Rounding problems inside InputField
The community needs to determine if this is behavior is a bug or not. – Mr.Wizard
Consider the following InputField
...
- 6,695
17
votes
2
answers
347
views
CompiledFunction returns machine numbers smaller than $MinMachineNumber
When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
- 62.1k
15
votes
4
answers
685
views
Terrible accuracy of DawsonF
DawsonF[30.] returns 0. The correct value is 0.016676...
At least it prints a warning message,
...
- 11.5k
12
votes
1
answer
817
views
Why does 1 - Exp[-10.0^12] cause an out-of-memory error?
I would like to understand why evaluation of the expression
1 - Exp[-10.0^12]
causes an out-of-memory error and how can I prevent such errors when calculating ...
- 7,876
11
votes
2
answers
899
views
Does Mathematica have an equivalent of Python's float.as_integer_ratio?
The Python programming language has a float.as_integer_ratio(x) function which exactly converts an IEEE 754 floating-point number into a numerator/denominator pair ...
- 2,336
11
votes
2
answers
848
views
Dr. StrangeNumbers or: How I Learned to Stop Worrying and Love Floating Point Arithmetic
The following is the program.
...
- 403
11
votes
1
answer
716
views
Compilation of Total with compensated summation
I sometimes obtain an unexpected error when trying to call a compiled version of Total with compensated summation turned on. More specifically I define
...
- 1,395
11
votes
1
answer
145
views
Abnormal behavior of RealDigits[x]
In the Details of the document of RealDigits writes the following line:
RealDigits[x] normally returns a list of digits of ...
- 67.6k
10
votes
1
answer
403
views
Plot of $\sin(x^x)$ is missing from $x=143$
When plotting the graph of $\sin(x^x)$ I noticed that there is no plot from about $x=143$. I don't suppose there is a purely mathematical explanation for this?
So, why is there no graph in ...
- 2,341
10
votes
2
answers
932
views
Why is Mathematica destroying this graph?
Here I have a picture of a function I graphed:
reg[x_,y_]:=(x^2+y^2)Cos[4ArcTan[y/x]];
Plot3D[reg[x,y],{x,-2,2},{y,-2,2},AxesLabel->Automatic]
And here is ...
- 389
10
votes
3
answers
901
views
Mathematica Plot: Inconsistency when plotting large values
I am working with a function in Mathematica and I am getting some inconsistencies when I plot it. As I really need to understand were this comes from I would appreciate any help.
I am working with a ...
- 103
10
votes
2
answers
2k
views
DeleteDuplicates[] does not work as expected on floating point values
Here is my simple example, and in this case function DeleteDuplicates does not work as expected.
I want to FindRoot of my ...
- 315
10
votes
1
answer
319
views
Can Someone Please Explain Internal`$SameQTolerance?
If I input
Internal`$SameQTolerance
(* output = 0.30103 *)
which is the approximation of Log[10,2], or ...
- 505
9
votes
1
answer
557
views
What explains the inaccuracies in machine-precision 'integers' with trigonometry or powers?
This Mathematica tutorial notes some strange behaviour with calculations such as Sin[10^50]:
...
- 607
9
votes
3
answers
2k
views
Very different results from evaluating same expression with different precisions
When I evalute the following expression,
...
- 749
9
votes
2
answers
462
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+??
...
- 31.7k
9
votes
2
answers
610
views
Precision differences
I run this sum and get the symbolic answer below :
Sum[ (1/(k^2 - k) - 1/k^2), {k, 2, Infinity}]
$2 - \frac{\pi^2}{6}$
I look up the sequence on OEIS and ...
- 2,360
9
votes
1
answer
318
views
IntegerPart - is this a known bug?
I'm working in Mathematica 13.0 and I type
a=0.00001;
IntegerPart[a/a]
and well, the output is 0.
Try with almost any other value of ...
- 465
9
votes
1
answer
795
views
Machine Epsilon
I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this:
...
- 93
9
votes
1
answer
1k
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
...
- 113k
9
votes
1
answer
169
views
Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?
Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
- 25.9k
9
votes
1
answer
259
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:
...
- 6,107
8
votes
2
answers
555
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
...
- 236k
8
votes
3
answers
6k
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 ...
- 1,592
8
votes
1
answer
856
views
Really understanding precision
I've been reading the documentation in Mathematica about precision, namely:
Exact and Approximate Results
Arbitrary-Precision Numbers
Arbitrary-Precision Calculations
Machine-Precision Numbers
...
- 1,111
8
votes
1
answer
945
views
Machine-Precision and Arbitrary Precision [closed]
What is meant by a machine number in the Mathematica documentation? What is the difference between machine-precision and fixed-point precision? What is arbitrary precision?
- 181
8
votes
1
answer
121
views
Unexpected behavior from CoordinateBoundingBoxArray with Into[1] and 0.41
I want to get the four corners of a Cuboid. This usually works:
CoordinateBoundingBoxArray[{-{1., 1.}, {1., 1.}}, Into@1]
gives
...
- 5,739
8
votes
2
answers
630
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 ...
- 149k
7
votes
4
answers
3k
views
Mathematica Precision
How can I set the output precision of the following statement to 10 decimal places? I was looking through the documentation, and for some reason, all I could find was ...
- 369
7
votes
3
answers
444
views
7
votes
4
answers
369
views
Definition of $MachineEpsilon
$MachineEpsilon
x = 0.0000000000000001
% + 1
% - 1
As expected the final result equals zero, since x < MachineEpsilon ($2.22045\times10^{-16}$).
However, if I ...
- 2,341
7
votes
2
answers
1k
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 ...
- 315
7
votes
1
answer
3k
views
Error about limit MaxExtraPrecision
After my evaluations I have an error:
N::meprec: Internal precision limit $MaxExtraPrecision=50. reached while evaluating ...
...
- 837
7
votes
1
answer
156
views
Using Differences on data: trouble with floats and doubles
Consider the following data set (after I have run FullForm), which is imported from a file (stored typically as 10.040):
...
- 4,969
7
votes
1
answer
271
views
Bug in ListPlot?
I want to check if this is a bug before I email WR about it.
I can't get ListPlot[] to make scatter plots over a very small area:
...
- 4,632
6
votes
4
answers
3k
views
Making a calculation with high precision
I would like to make the following calculation:
1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1
Mathematica 8 returns 0. The result is obviously not 0, but my ...
- 1,013
6
votes
4
answers
516
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 ...
- 7,182
6
votes
3
answers
837
views
A bug with high precision
Consider the following two numbers:
num1=0.0006000000000000001`;
num2=0.0006000000000000003`;
num2 appeared from ...
- 5,913
6
votes
1
answer
165
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 ...
- 87
6
votes
1
answer
358
views
Table does not give expected result with `30 but right with `40
I want Mathematica to generate a table, but I am very confused by its behaviour.
tab = Table[i, {i, 6.311, 6.312, 0.001}]
Now I get the desired result, namely {6....
6
votes
1
answer
293
views
ConvexHullMesh fails with small numbers
When I try to get the ConvexHullMesh of a List of points that are "small scale", I get errors:
...
- 1,077