Questions tagged [arbitrary-precision]

Questions on the arbitrary precision capabilities of Mathematica.

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Dealing with zero at high precision

I am using mathematica to deal with rational functions, $p(x)/q(x)$, where the polynomials, $p,q$ have a high degree and coefficients with high order of precision, e.g: ...
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39 views

Set Underflow precision in Mathematica 12 same as version 11.x [duplicate]

It seems like Mathematica version 12 sets arbitrary underflow precision depending on the function, but I would like the underflow precision to be same as what was for previous version of Mathematica ...
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40 views

What is the limit of digits to show in the conversion of an exact number to an Arbitrary Precision Number?

By executing something like N[π, c] what is the maximum positive integer value c can have until the output is compromised by ...
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118 views

How does Mathematica evaluate N[π, 30] == π?

I want to know how N[π, 30] == π works. The result is True. I wonder whether the exact number ...
5
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1answer
72 views

Linear Algebra in Arbitrary Precision - SLOW

I am trying to implement an arbitrary precision algorithm, but I am not very familiar with Mathematica or arbitrary precision arithmetic. I was able to implement it but surprised by how much slower it ...
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32 views

Changing machine precision notebook-wide leads to peculiarities

For a project of mine it is preferrable to set notebook precision globally. I have done so by using the answer in Global precision setting. The idea is to dynamically create a ...
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1answer
59 views

Why this very simple problem turns to “Indeterminate”?

Why the following calculation gives Indeterminate value? ...
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1answer
54 views

Preventing Mathematica from considering small values to be equal to zero [duplicate]

In my calculations I have a variable (say z) which can be an argument of Log, say, z Log[z]. ...
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1answer
78 views

Number definition and approximation

I run these lines: a = 0.833 SetPrecision[a, 20] and this is the output: 0.833 0.83299999999999996270 I expected to ...
5
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0answers
47 views

DumpSave and precision of interpolation data

Consider the following prec = 32; x = N[Range[0, 1, 1/10], prec]; f = Interpolation[Transpose@{x, x}]; Then ...
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1answer
121 views

How can I suppress the warning $\mathrm{\it precision\ may\ be\ lost}$?

When I import data from a .dat file, V11.3 emits the message: is too small to represent as a normalized machine number; precision may be lost. How can I close the ...
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2answers
318 views

Truncate a number in mathematica

I want to truncate a simple number to n decimal digits. For example, 2/3. I used f[x_, n_] := N[IntegerPart[x 10^n]/10^n] but I get ...
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1answer
56 views

How to get the correct result in a simple operation in Mathematica

I have the following values for x[[i]], y[[i]] and A[[i,j]]: ...
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1answer
46 views

Simple division with high precision in Mathematica [closed]

I want to do a simple division i.e. 0.70524/0.51824 . What I want is to find the result of the roundation of this division for precision from 1 to 19 decimal digits....
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92 views

Arbitrary Precision, Nearly-Singular Matrices, and LinearSolve

I have been trying to solve a nonlinear eigenvalue problem, $\mathbf{M}(\lambda) \mathbf{v} = 0$, in Mathematica using Newton's method. The core of the algorithm relies upon an inverse iteration, ...
5
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2answers
371 views

Why does N not upgrade precision? [duplicate]

Precision[N[1.0, 20]] Precision[N[1, 20]] MachinePrecision 20. It would be so much more intuitive and less error prone, if <...
9
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1answer
166 views

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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2answers
139 views

Early vs. late application of arbitrary precision

The following arbitrary-precision computations, in which arbitrary precision is applied early (to the inputs), both work as expected: ...
6
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1answer
447 views

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 ...
6
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1answer
220 views

Mathematica precision common problems

When I do something a little bit more complicated than standard documentation examples, I often hit precision problem. Or I accidentally disprove Riemann hypothesis Like this ...
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1answer
84 views

Interpolation function precision in multi dimentional case

I have this interpolation example ...
3
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1answer
182 views

Can NDEigensystem use arbitrary precision arithmetic?

Consider the following computation of an eigenfunction of 1D Laplacian on the interval of $[0,\pi]$: ...
8
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2answers
1k views

Fast integer square-root

I'm looking for the highest-performance method of calculating integer square roots in Mathematica of very big arbitrary-precision numbers. As an example testcase, I use: ...
2
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1answer
157 views

plot of polynomial expression failed [duplicate]

I want to plot a polynomial expression for {a,0,1}: ...
1
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1answer
79 views

Rigorous error bounds for `NIntegrate`

Suppose I want to numerically evaluate an integral of the form $$\int_{-\infty} ^\infty f(x) \mathrm{d}x $$ with error not exceeding some positive bound $\epsilon$. Is there a way to do this using <...
6
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4answers
284 views

How do I convert an inexact number smaller than $MinMachineNumber to machine-precision?

I was trying to convert some arbitrary-precision numbers to machine-precision numbers using N[myNumber,MachinePrecision]. But, although my test number did lose some ...
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0answers
57 views

Arbitrary precision calculation makes my computer hang

I have this code list = Accumulate@Tan[N[Range[10^8]]]; // AbsoluteTiming and the timing is slightly more than two seconds. Now if I try to compute this ...
18
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2answers
768 views

Error and uncertainty propagation: Is using Precision/Accuracy a sound strategy?

Questions What are the available resources to deal with experimental error and uncertainty propagation in Mathematica? Given that Mathematica already uses linearized model of error propagation on ...
18
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2answers
1k views

How are Accuracy and Precision related Mathematica for a given operation?

The common understanding for Accuracy and Precision in English language is given by this figure. Inspired by this question I have a follow up question relating ...
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1answer
621 views

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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1answer
82 views

Simple precision issue [closed]

Considering binomial expansion $1 = (p+(1-p))^n = \sum_{k=0}^n p^n (1-p)^{n-k},$ which is true for any real value of $p$, I'm getting diverging results when I numerically evaluate the above even ...
3
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1answer
59 views

Constructing a List from a Decimal Number

I am trying to get from a number such as $12.345$ to a list $\{1,2,3,4,5\}$. My best attempt so far has been: First[RealDigits[12.345]] however this of course ...
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0answers
72 views

Buggy behavior of EllipticK with arbitrary precision input and $MinPrecision

I have encountered weird buggy behavior of EllipticK with arbitrary precision input and when $MinPrecision is set. Consider the following code: ...
15
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2answers
443 views

Why does SetPrecision not apply to 0?

Is there a rationale why SetPrecision works on integers except for 0? SetPrecision[1,5] 1.0000 ...
12
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1answer
711 views

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 ...
3
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1answer
76 views

Why does SetPrecision drop “unknown” digits if precision requested is Infinity but retain them if it's finite?

I was trying to reset the imprecision record of a number like 0.0076022266122755632`1.025 by calling SetPrecision with second ...
13
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0answers
225 views

Bug? Numerical calculation error with FullSimplify and arbitrary precision

Bug introduced after 5.2, fixed in 8.0, reintroduced in 9.0 and persisting through 11.3 Is this a bug? If I do FullSimplify[n E^(0``10 n)] then it returns <...
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2answers
275 views

Integrate over sharp peak [closed]

Hi I have a function that has a sharp spike. I need to NIntegrate over the peak but it seems that NIntegrate does not handle it well. Actually as far as I can tell, even the evaluation of the ...
3
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0answers
120 views

Does Mathematica implement its own methods of tracking precision? [closed]

I know that for arbitrary precision arithmetic Mathematica uses GMP. But apart from just providing arbitrary precision, Mathematica also does precision tracking for its arbitrary-precision numbers, so ...
8
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1answer
191 views

Arbitrary-Precision Arithmetic behaves unexpectedly

I want to understand how small numerical errors propagate through a computation and may drastically change the final result. To this end, I consider a toy world in which every number is limited to ...
1
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1answer
83 views

Finding the probability of one or more very unlikely successes in an enormous number of Bernoulli trials

I'm trying to find an upper bound on the complexity of a self-replicating matter pattern in order for it to be at all probable for it to spontaneously occur in the universe. The idea being, if some ...
1
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1answer
151 views

Specify a decimal value as exact

I would like to specify that a number is exact, even though it contains a decimal point. For example, I would like to be able to write some variation of 3.4 and ...
4
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1answer
213 views

How to disable roundoff error tracking in arbitrary precision arithmetic?

In my calculations I need some larger precision. But due to the fact that I iteratively refine the results to compensate for rounding errors accumulated in previous iteration, Mathematica's arbitraty ...
2
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0answers
71 views

Why is distributing the definitions of a list of arbitrary precision numbers so slow?

For a parallel application I need to make a large list of numbers available to the parallel kernels, which I do using DistributeDefinitions. I have noticed that this is much slower when the numbers ...
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0answers
74 views
4
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2answers
150 views

Why do I get number with Precision larger than error estimate?

I'm trying to integrate a large function like this ...
3
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1answer
127 views

Why does this expression involving HypergeometricU and $MinPrecision crash?

Bug introduced in 10.0 and fixed in 11.0 Can somebody help me understand why the following code snippet cause the Mathematica kernel to crash (without producing any further error messages)? ...
6
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2answers
208 views

$N[a,50]-N[a,10]=0$ why? and what's the rationale behind?

Let $a=\sqrt{3}$. What's the point of having In[102]:= N[Sqrt[3],100]-N[Sqrt[3],10] Out[102]= 0.*10^-10 ? Let's imagine I wanted to get the difference between ...
9
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1answer
160 views

Has “faster arbitrary precision computation of elementary functions” been incorporated into Mathematica?

In this Wolfram Conference talk from last year, "Faster Arbitrary Precision Computation of Elementary Functions", they talk about R&D for algorithms to numerically evaluate elementary functions ...
2
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2answers
109 views

Mathematics arbitrary precision evaluation [duplicate]

I am trying to solve a simple expression: where a = 77617, and b = 33096. Wolfram|Alpha returns a correct result, using ...