# Tag Info

### Why does SetPrecision not apply to 0?

If you have a value $x$ with an absolute uncertainty $dx$ the precision of $x$ is by definition: $$\text{Precision}(x) = - \log_{10}(dx/x)$$ That is why for $x=0$ the precision is always infinity. ...
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### Why does 1 - Exp[-10.0^12] cause an out-of-memory error?

Actually this is not a duplicate. The prior question is about underflows that require massive bignums to represent at machine precision, and that much is present here as well. So what @J.M notes is ...
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### Really understanding precision

Here are my thoughts: Q1 Machine numbers: For machine numbers, what you describe is correct. I would just add that you can use InputForm or FullForm to see all the digits if desired: ...
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### Fast integer square-root

Sqrt is using exact methods in an effort to pull out "small" squares. This is going to take time. A direct approach, as already noted, would do the square root ...
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### How are Accuracy and Precision related Mathematica for a given operation?

Precision is the principal representation of numerical error Except for numbers that are equal to zero, error in arbitrary-precision numbers is stored internally as its precision. For numbers equal ...
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### How to force Mathematica to do infinite-precision calculations?

Mathematica will perform exact arithmetic only so long as all quantities are expressed as exact numbers. 90.12 is an inexact number with machine precision (i.e. ...
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### Machine-Precision and Arbitrary Precision

This is not an answer. But I don't believe we should close this question as "easily found in the documentation". Numerics in Mathematica is an extremely complicated and mostly undocumented subject, ...

### Fast integer square-root

Not directly addressing the question about GMP library, but you can get a Sqrt much faster starting with an extended precision float. ...
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### $N[a,50]-N[a,10]=0$ why? and what's the rationale behind?

The problem with using N to generate arbitrary precision numbers is that is it will generate more digits of accuracy than asked for: ...
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### How to disable roundoff error tracking in arbitrary precision arithmetic?

There are a few reasonable ways. I'll illustrate with an example of Newton iterations for square roots, take from this MathGroup post ...
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### Why do I get number with Precision larger than error estimate?

Consider any numerical integration method $I^*(f,a,b)$ that approximates the exact integral $I$ of a function $f$ over an interval $[a,b]$. It will be implemented by a computation represented by, say, ...
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### Arbitrary-Precision Arithmetic behaves unexpectedly

This is at best a partial answer. I don't know in full detail what is going on with FullForm or InputForm but I will venture to ...

### Elegant high precision log1p?

LogLogPlot[{InternalLog1p[x], Log[1 + x]}, {x, 1*^-17, 1*^-14}] ps：Of course,maybe you need InternalExpm1,too.
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### How are Accuracy and Precision related Mathematica for a given operation?

Accuracy and Precision are related though RealExponent The relation between ...
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### Error and uncertainty propagation: Is using Precision/Accuracy a sound strategy?

Your problem is similar to a wave spectra problem and a regression problem, and I have both types of problems going on at work right now which is why I've thought about your problem a bit. Here is an ...
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### plot of polynomial expression failed

$Version (* "11.2.0 for Mac OS X x86 (64-bit) (September 11, 2017)" *)$HistoryLength = 0; (* for comparing timings *) expr[a_] = <your expression> The ...
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WRI Support solved my precision issue by using $Pre to SetPrecision on all MachineNumberQ ... • 42.3k 8 votes Accepted ### Why does N not upgrade precision? N can only lower precision, it cannot raise precision. N[1.34, 10] //Precision 4. Since ... • 131k 7 votes ### How do I convert an inexact number smaller than$MinMachineNumber to machine-precision?

number = 5.80373641176129118633405301544668516*^-400; number + 0. (* 0. *) N makes arbitrary precision numbers when either ...
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### What is wrong with importing Real32 or Real64?

I don't think there's a problem. It's a question of output-formatting, connected with the fact that there are single-precision binary fractions that cannot be represented in decimal form in 17 digits ...
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