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.
62
questions
42
votes
2
answers
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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 ...
- 4,649
21
votes
2
answers
2k
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 ...
- 1,962
11
votes
2
answers
831
views
Dr. StrangeNumbers or: How I Learned to Stop Worrying and Love Floating Point Arithmetic
The following is the program.
...
- 393
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
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
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 ...
- 877
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 ...
- 4,939
9
votes
3
answers
1k
views
Very different results from evaluating same expression with different precisions
When I evalute the following expression,
...
- 739
5
votes
2
answers
845
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.
...
5
votes
2
answers
894
views
How to make the computer consider two numbers equal up to a certain precision
My problem is that I have a matrix A and the computer says is not Hermitian (self-adjoint). Then I check which elements make A ...
- 1,294
9
votes
2
answers
604
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 ...
- 2,350
18
votes
2
answers
562
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
...
- 6,635
15
votes
4
answers
661
views
Terrible accuracy of DawsonF
DawsonF[30.] returns 0. The correct value is 0.016676...
At least it prints a warning message,
...
- 11.1k
8
votes
1
answer
923
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
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 ...
- 1,572
11
votes
1
answer
681
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
2
answers
874
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 ...
- 2,306
10
votes
1
answer
306
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
752
views
Machine Epsilon
I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this:
...
- 93
7
votes
4
answers
3k
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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 ...
- 359
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 ...
- 7,801
16
votes
4
answers
455
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 ...
- 2,306
10
votes
1
answer
395
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 ...
- 2,311
5
votes
6
answers
3k
views
Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?
The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration.
...
- 2,573
10
votes
3
answers
894
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
9
votes
1
answer
249
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:
...
- 5,917
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 ...
- 993
6
votes
1
answer
134
views
Bug in floating-point number comparisons near $MachineEpsilon?
I stumbled over the following weird behavior when comparing floating-point numbers close to 1.0:
qq = 1.0 + 60.0 $MachineEpsilon;
and then
...
- 281
4
votes
0
answers
175
views
Is it possible to get the original number from DecimalForm?
Bug introduced in 5.2 or earlier and persisting through 13.1.0
[CASE:4315787]
Wrong behavior of NumberForm (DecimalForm outputs ...
- 61.3k
4
votes
2
answers
3k
views
Precision of number not maintained when saved via Export
Assume that the output of my calculation is a and is a number such as:
a = 100.1252135246354847;
...
- 5,311
3
votes
1
answer
278
views
Why to do parentheses change the results of a calculation?
I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2
<...
- 12.8k
2
votes
1
answer
292
views
2
votes
1
answer
175
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 ...
- 16.9k
2
votes
1
answer
1k
views
How to increase significant digits in Mathematica
How can I increase the number of significant digits in Mathematica?
When I import a matrix, an element like 112.5276 is rounded to 112.528. I would like to increase the number of significant digits ...
- 3,824
0
votes
1
answer
99
views
Why this very simple problem turns to "Indeterminate"?
Why the following calculation gives Indeterminate value?
...
- 629
0
votes
2
answers
240
views
The precision of the number
I have problem in Mathematica with unnecessary rounding which is caused by high precision.
For example I have value a = 2.052685846*10^-1865, when I make ...
- 787
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 ...
- 447
17
votes
2
answers
343
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 ...
- 61.3k
11
votes
1
answer
142
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 ...
- 62.8k
9
votes
1
answer
556
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
8
votes
2
answers
530
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
...
- 232k
8
votes
1
answer
810
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
...
- 1,091
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):
...
- 4,939
6
votes
4
answers
493
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 ...
- 7,102
6
votes
0
answers
167
views
Can I force Mathematica to use machine precision? [duplicate]
Some built-in functions (like Exp) give an arbitrary precision result, even when the argument is a machine precision number. Example:
...
- 35.9k
6
votes
1
answer
162
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
287
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:
...
- 1,067
5
votes
1
answer
232
views
Compilation, square roots, and integers
After looking at this question, particularly this answer, I wrote my own performance test, using the two functions
...
- 4,197
5
votes
1
answer
434
views
MachinePrecision versus $MachinePrecision in NDSolve
I'd like to understand why one of these inputs gives me an error and the other doesn't:
...
- 1,030
4
votes
1
answer
833
views
Could the PrecisionGoal for NDSolve be a negative number?
The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
- 62.8k