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
7
votes
1
answer
268
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:
...
- 4,553
5
votes
1
answer
235
views
Compilation, square roots, and integers
After looking at this question, particularly this answer, I wrote my own performance test, using the two functions
...
- 4,209
11
votes
1
answer
143
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 ...
- 63.8k
3
votes
2
answers
122
views
Make mathematica "forget" numbers beyond the precision goal
I need Mathematica to remember only things upto two decimal places.
I'm currently using the unwieldy Floor[x*100]/100 which works but is there a better way to ...
- 259
1
vote
1
answer
569
views
How to increase the precision to get the correct roots at the boundaries?
I want to solve an equation and Plot a graph of $\delta(\tau)$, where $0<\tau,\delta<1$. In principal $\delta(0)=1,\delta(1)=0$. However, when I solve the equation, the points near $\tau=1$ can'...
- 1,725
2
votes
2
answers
978
views
Export numeric data with preset decimal places
I have a table of pairs of numbers, each with 300 decimal places, which are all important. If saved using Export["data.dat", data] and then imported back via Import["data.dat"] - then the 300 decimal ...
- 755
0
votes
1
answer
146
views
N, machine precision and expression evaluation [closed]
I should state that I am a Mathematica beginner but I checked the questions about machine vs arbitrary precision (such as: this one ) and I continue to have the following issue while trying to ...
- 39
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 ...
- 1,582
1
vote
0
answers
102
views
Odd plotting/math issue (could be a precision problem) [closed]
I've got a pretty odd error on a project I'm working on and was hoping to enlist some advice to fix it. The goal of this notebook is to show that I can eliminate the non-normalizable (blowing up part) ...
- 151
0
votes
2
answers
94
views
3
votes
1
answer
136
views
Floor inconsistent with Less for machine-precision approximate numbers
For machine-precision numbers, Mathematica uses a tolerance for comparisons, so that 1.-$MachineEpsilon==1. However, Floor does ...
- 257
10
votes
1
answer
310
views
Can Someone Please Explain Internal`$SameQTolerance?
If I input
Internal`$SameQTolerance
(* output = 0.30103 *)
which is the approximation of Log[10,2], or ...
- 505
2
votes
1
answer
232
views
Precision of LinearModelFit with Polynomials
I have a Problem regarding the fit of given points with a polynomial up to the fifth degree.
tableofvalues=Import["tableofvalues.csv"]
My polynomial is:
...
- 451
16
votes
4
answers
456
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
11
votes
2
answers
881
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
1
vote
1
answer
165
views
Why does it matter at what point I replace?
I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points.
I use (LK4 is defined below, but its shape should have nothing to do with my problem)...
- 655
11
votes
1
answer
689
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
2
votes
1
answer
295
views
0
votes
1
answer
172
views
Floating point arithmetic bug caused by Table[]
I was doing something fairly ordinary and noticed something I can't, for the life of me, explain. For context, I wanted to take make a function that takes an array of data like the one below, then an ...
- 3,002
2
votes
0
answers
161
views
Enforcing WorkingPrecision in NIntegrate
I have a very complicated 2D integral that I need to calculate repeatedly, and I'm trying to speed it up a bit, since at the moment it's taking a couple of days to complete.
One thing I've noticed is ...
- 199
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 + $MachineEpsilon *)
Let's make sure they're different with ...
- 7,801
3
votes
2
answers
1k
views
NIntegrate 2D highly oscillatory function
I am trying to integrate a function, and the error I get is greater than the result.
So I need to calculate
...
- 33
6
votes
2
answers
178
views
How can I make 1+$MachineEpsilon not look like 1?
I undarstand that 1+$MachineEpsilon is actually not equal 1. However, it persists to look like it was equal ...
- 817
6
votes
0
answers
168
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:
...
- 36k
3
votes
2
answers
332
views
WorkingPrecision causes issue in the NIntegrate
I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
- 31
1
vote
0
answers
65
views
Which operations preserve digit precision?
Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
- 2,517
2
votes
2
answers
745
views
'eps' equivalent in Mathematica
In MATLAB, there is a function named eps.
eps Spacing of floating point numbers.
D = eps(X), is the positive distance from ABS(X) to the next larger in
...
- 407
3
votes
1
answer
522
views
Reasonable choice of MachinePrecision, AccuracyGoal and PrecisionGoal for NDSolve
I am trying to use this model for later use in FindFit:
...
- 325
3
votes
4
answers
315
views
Precision problem with numerical solution of a differential equation
I want solve
$$
2\sqrt{|\gamma|}x = \int_{1}^{t} dy \sqrt{\frac{1+2|\gamma_2|y}{y^2(1-y)}}
$$
where $0<t\leq $1.
I'm using a for cycle to evaluate t, calculate the integral and the assign the $x$.
...
- 1,628
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 ...
- 3,834
1
vote
2
answers
119
views
Decimal output from a simple equation
Let
x= 0.0000000000000000036;
y = 1 - x
If i type this in Mathematica the answer of y is 1. I want the answer to be as it ...
- 105
4
votes
1
answer
176
views
How to map HoldForm?
I'm trying to compare between Sqrt[3.] and Sqrt[3]. To display the result, I mapped HoldForm to display the expressions on the left hand column (code at end), but it seems like Sqrt[3.] had been ...
- 5,061
9
votes
1
answer
167
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. ...
- 25.6k
9
votes
1
answer
770
views
Machine Epsilon
I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this:
...
- 93
0
votes
1
answer
90
views
Unexpected behavior of subtraction with approximate numbers [duplicate]
I'm using the Table command to generate a list of values:
FullForm /@ Table[10. - x, {x, 2.7, 2.8, .1}]
and I get the ...
- 1
0
votes
1
answer
2k
views
How to get more accurate orthonormal eigenvectors?
I have a matrix M with real entries in MachinePrecision. I compute its eigenvectors and construct matrix ...
6
votes
1
answer
235
views
Machine precision infinity
Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ...
- 1,587
0
votes
0
answers
70
views
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
4
votes
2
answers
2k
views
Floating point addition not associative
Can anybody explain the following behavior?
x = 0.2 + (0.3 + 0.1);
y = (0.2 + 0.3) + 0.1;
x == y (* -> True *)
But actually the variables do not exactly ...
- 637
2
votes
1
answer
2k
views
Plot periodic function from Dirac delta function [duplicate]
Sorry for my bad english.
I need to plot periodic function from dirac delta:
δT(t)=∑δ(t–n*T), where T - is a constant, and n=-20..20
And after them, plot new function fd=f(t)*δT(t) - discrete signal ...
- 21
5
votes
1
answer
2k
views
Error about limit MaxExtraPrecision
After my evaluations I have an error:
N::meprec: Internal precision limit $MaxExtraPrecision=50. reached while evaluating ...
...
- 787
6
votes
1
answer
163
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
2
votes
0
answers
568
views
how to calculate with just double floating point precision [duplicate]
I want to calculate with simple double floating point precision.
...
- 21
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
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
0
votes
1
answer
272
views
How to improve the performance of this code
I have implemented a code in Mathematica 9 to simulate a scattering problem, and I got really disappointed about its performance when compared to Matlab. Since I am a newbie in Mathematica, would ...
- 1
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 ...
- 61.5k
2
votes
2
answers
177
views
Long run time for older code that ran fast in older versions
The following code block is in Trott's Guidebook for Programming. The associated notebook says that this and a few other routines ran in a matter of seconds. I killed it after half an hour.
I am ...
- 23
4
votes
1
answer
3k
views
CompiledFunction::cfse: "Compiled expression X should be a machine-size integer
I am trying to use a compiled function in order to save time...
LegrendeTransform = Compile[{y}, MaxValue[Sin[x] - x *y , x]]
Now I want to to evaluate and ...
- 274