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.

learn more… | top users | synonyms

3
votes
1answer
127 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?
14
votes
4answers
295 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 ...
3
votes
1answer
58 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: ...
0
votes
1answer
1k views
10
votes
2answers
745 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 ...
2
votes
2answers
54 views

How do I overcome an Overflow?

I'm trying to calculate entropies for an absolutely giant system by counting states, and this means I have to use some obscenely large numbers. I'm running ...
2
votes
1answer
118 views

Mathematica Precisions vs Doubles in C/C++

I'm having a bit of an issue regarding numerical precision and I'm not sure how to deal with it. I have a certain randomly generated matrix, say $M$, that I wish to compute the eigenvalues. The ...
4
votes
1answer
351 views

How to calculate accurate answer in Mathematica?

I accidentally discovered for myself, that Mathematica outputs inaccurate answer. For instance, if I take $\sin(2 \cdot \pi \cdot 0.5) = 0 $, then in Mathematica it is: But if I calculate it on ...
3
votes
1answer
50 views
2
votes
1answer
79 views

How to tell Mathematica to treat all numbers (including those in decimal form) as arbitrary precision numbers

I have code that is essentially numerical. It uses functions like NDSolve and NIntegrate. But in most interesting cases, the ...
9
votes
2answers
452 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 ...
10
votes
2answers
253 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 ...
3
votes
0answers
101 views
1
vote
1answer
70 views

Wrong Limit[…] for inexact expressions

I noticed that Limit can return nonsense when using inexact parameters. In the following code, a is my (exact/inexact) parameter,...
6
votes
1answer
152 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
104 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
101 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 ...
0
votes
0answers
34 views

Handling a matrix with components greater than machine precision

I have four quantities stemming from a 4th order differential equation. I can represent these as a vector which is a product of a 4X4 matrix $$ M=\left\{v,\frac{\partial v}{\partial x},\frac{\partial ...
11
votes
1answer
115 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 ...
3
votes
2answers
67 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 ...
1
vote
1answer
97 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'...
15
votes
2answers
203 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 ...
1
vote
2answers
87 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 ...
0
votes
1answer
60 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 ...
3
votes
2answers
149 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 "...
10
votes
1answer
192 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
vote
0answers
74 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) ...
0
votes
2answers
75 views

Varying results from the Round function

My problem is simple. Consider the following. ...
3
votes
2answers
161 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 ...
21
votes
7answers
779 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 ...
1
vote
0answers
69 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 ...
5
votes
1answer
85 views

Can Someone Please Explain Internal`$SameQTolerance?

If I input Internal`$SameQTolerance (* output = 0.30103 *) which is the approximation of Log[10,2], or ...
2
votes
1answer
115 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: ...
4
votes
2answers
349 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 ...
10
votes
2answers
474 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 ...
19
votes
2answers
608 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 ...
1
vote
1answer
144 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)...
0
votes
1answer
98 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 ...
2
votes
0answers
70 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 ...
2
votes
2answers
424 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 ...
0
votes
0answers
26 views

why i cannot get appropriate number with my custom precision? [duplicate]

why i cannot get appropriate number with my custom precision? In[25]:= N[(1 + Exp[-30])/(1 + Exp[-29.9]), 1000] Out[25]= 1. I expect to see a few digits after 1....
6
votes
1answer
114 views

Machine precision infinity

Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ...
5
votes
0answers
51 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: ...
1
vote
0answers
50 views

Which operations preserve digit precision?

Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
2
votes
1answer
275 views
2
votes
4answers
181 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 $x$. ...
5
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. ...
1
vote
1answer
254 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 ...