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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28
votes
2answers
1k 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 ...
25
votes
1answer
628 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 ...
21
votes
7answers
716 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 ...
18
votes
2answers
572 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 ...
18
votes
1answer
839 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 ...
15
votes
4answers
2k views

Numerical underflow for a scaled error function

I calculate scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ...
15
votes
2answers
198 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 ...
11
votes
2answers
540 views
11
votes
2answers
256 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 ...
10
votes
2answers
455 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 ...
10
votes
1answer
151 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 ...
10
votes
1answer
173 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 ...
10
votes
3answers
711 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 ...
8
votes
2answers
449 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 ...
8
votes
1answer
376 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 ...
8
votes
1answer
108 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. ...
8
votes
1answer
104 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 ...
7
votes
2answers
368 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 ...
7
votes
3answers
381 views
7
votes
1answer
143 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): ...
6
votes
4answers
1k 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 ...
6
votes
1answer
222 views

Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
6
votes
1answer
120 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 ...
6
votes
1answer
105 views

Machine precision infinity

Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ...
6
votes
1answer
148 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: ...
5
votes
1answer
898 views

Infinite expression 1/0. encountered - caused by precision?

Planck's law dependent on frequency rho is as follows: B[T_, h_, rho_, k_, c_] := (2 h rho^3)/c^2 1/(Exp[h rho/(T k)] - 1) As you can see, the denominator can ...
5
votes
1answer
74 views

Can Someone Please Explain Internal`$SameQTolerance?

If I input Internal`$SameQTolerance (* output = 0.30103 *) which is the approximation of Log[10,2], or ...
5
votes
1answer
330 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 ...
5
votes
1answer
93 views

Compilation, square roots, and integers

After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ...
5
votes
1answer
96 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 ...
5
votes
0answers
44 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: ...
4
votes
6answers
2k 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. ...
4
votes
2answers
241 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 ...
3
votes
2answers
298 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 ...
3
votes
1answer
216 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 ...
3
votes
1answer
400 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 ...
3
votes
2answers
137 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 examples below I will use the following ...
3
votes
2answers
65 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 ...
3
votes
2answers
154 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 ...
3
votes
2answers
976 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; ...
3
votes
0answers
70 views

Classification problem using SVM methods

I am running SVM on mathematica and I a used this code with classes: ...
2
votes
2answers
156 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 ...
2
votes
4answers
173 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 $x$. ...
2
votes
1answer
248 views

How to use adaptive precision in matrix computations?

I wish to compute the pseudo inverse of rectangular (or square) matrices by the cubically method of Chebyshev given by $X_{k+1}=X_k(3I-AX_k(3I-AX_k))$ where $X_0=\frac{1}{\|A\|_F^2}A^*$. The procedure ...
2
votes
2answers
604 views

FindRoot errors

I'm trying to solve a system of two equations in two variables for some range of parameter values. I use ContourPlot to see where I should look for a solutions and ...
2
votes
1answer
110 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: ...
2
votes
1answer
90 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 ...
2
votes
2answers
332 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 ...
2
votes
1answer
221 views

Reasonable choice of MachinePrecision, AccuracyGoal and PrecisionGoal for NDSolve

I am trying to use this model for later use in FindFit: ...