# 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.

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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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Let's define two different numbers. x = 1. y = 1. + 2^-52 (* equivalently, 1 + $MachineEpsilon *) Let's make sure they're different with ... 21 votes 2 answers 2k views ### New General::munfl error and loss of precision The latest version 11.3.0.0 of Mathematica returns Indeterminate when evaluating Log[Exp[-800.]]. I believe this was not ... 20 votes 1 answer 1k views ### Quadruple-precision (128 bit) arithmetic Is it possible to force Mathematica to perform computations with hardware supported quadruple-precision? The following test suggest, that all of the computations with fixed precision, different than <... 19 votes 5 answers 4k views ### Numerical underflow for a scaled error function I calculate a scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ... 18 votes 2 answers 562 views ### Rounding problems inside InputField The community needs to determine if this is behavior is a bug or not. – Mr.Wizard Consider the following InputField ... 17 votes 2 answers 343 views ### CompiledFunction returns machine numbers smaller than$MinMachineNumber

When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
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### 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 ...
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### Terrible accuracy of DawsonF

DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ...
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### 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 ...
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### 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 ...
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### Dr. StrangeNumbers or: How I Learned to Stop Worrying and Love Floating Point Arithmetic

The following is the program. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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]: ...
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### Very different results from evaluating same expression with different precisions

When I evalute the following expression, ...
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### 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+?? ...
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### 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 ...
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### 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 ...
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### Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
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### 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. ...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### Unexpected behavior from CoordinateBoundingBoxArray with Into and 0.41

I want to get the four corners of a Cuboid. This usually works: CoordinateBoundingBoxArray[{-{1., 1.}, {1., 1.}}, Into@1] gives ...
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### 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 ...
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### 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 ...
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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 ...
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When I do: ...
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### 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 ...
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### 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): ...
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### 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: ...
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### 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 ...