# Special Functions (Elliptic.jl) and arbitrary precision
**URL:** https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658
**Category:** General Usage
**Created:** [May 3, 2020, 9:28am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658 "2020-05-03T09:28:00Z")
**Posts on this page:** 10
**Page:** 1
### Author:  [@StarecZosima](https://discourse.julialang.org/u/StarecZosima)
#### Post date: [May 3, 2020, 9:28am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/1 "2020-05-03T09:28:00Z")
I do not understand how to work in arbitrary precision in Julia.
I encountered the problem when using a function from the Elliptic.jl package
```
K(1-10^-23)
```
returns
Inf
while for example Mathematica accurately computes a value of approx- 30.168, using 200 digits of working precision.
If my understanding is right, the BigFloat type shoud allow arbitrary precision computations in Julia.
I tried
```
setprecision(500)
a = BigFloat(1-10^-23)
K(a)
```
but still obtain Inf as a result. As a matter of fact
```
BigFloat(1-10^-23) == 1
```
returns True.
Could somebody please explain what is that I am doing wrong? Thanks a lot
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [May 3, 2020, 9:39am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/2 "2020-05-03T09:39:38Z")
You identify the source of the problem correctly: precision is lost _before_ converting to `BigFloat`.
You should convert something to `BigFloat` _before_ performing that calculation, eg make
```julia
a = 1 - BigFloat(10)^-23
```
or similar.
---
### Author:  [@StarecZosima](https://discourse.julialang.org/u/StarecZosima)
#### Post date: [May 3, 2020, 9:45am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/3 "2020-05-03T09:45:18Z")
Thanks for your reply, but I did try that one too
```
a = 1 -BigFloat(10)^-23
```
and while I now noticed that indeed, a =! 1
still
```
K(a)
```
diverges.
At least now I can define the argument correctly. Could it be something to do with the function itself?
Thanks
---
### Author:  [@EHBaozi](https://discourse.julialang.org/u/EHBaozi)
#### Post date: [May 3, 2020, 11:07am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/4 "2020-05-03T11:07:50Z")
This is probably a problem with the package? I see [here](https://github.com/nolta/Elliptic.jl/blob/master/src/Elliptic.jl#L100) that `K` converts everything to `Float64`.
---
### Author:  [@EHBaozi](https://discourse.julialang.org/u/EHBaozi)
#### Post date: [May 3, 2020, 11:18am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/5 "2020-05-03T11:18:56Z")
As an alternative, the `DoubleFloats` package exports the `ellipk` function, but it seems to give a different answer than Mathematica:
```julia-repl
julia> using DoubleFloats; ellipk(1-Double64(10)^(-23))
27.866022930551416
```
---
### Author:  [@ettersi](https://discourse.julialang.org/u/ettersi)
#### Post date: [May 3, 2020, 11:36am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/6 "2020-05-03T11:36:15Z")
Another alternative: [SpecialFunctions.jl/elliptic.jl at 37e5999c5fe0f778f2de2e41b6beeff339a21cb8 · JuliaMath/SpecialFunctions.jl · GitHub](https://github.com/JuliaMath/SpecialFunctions.jl/blob/37e5999c5fe0f778f2de2e41b6beeff339a21cb8/src/elliptic.jl)
---
### Author:  [@jishnub](https://discourse.julialang.org/u/jishnub)
#### Post date: [May 3, 2020, 11:37am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/7 "2020-05-03T11:37:53Z")
This precision loss appears to be [a known issue](https://github.com/nolta/Elliptic.jl/issues/11) with the package, but it has not been addressed in two-and-a-half years.
---
### Author:  [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [May 3, 2020, 11:42am UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/8 "2020-05-03T11:42:36Z")
```julia
julia> using ArbNumerics
julia> setextrabits(64); setprecision(ArbFloat, bits=256);
julia> x = 1 - ArbFloat(10)^(-23)
0.99999999999999999999999
julia> elliptic_k(x)
27.866022930551415985041433136843867902103629991741788896439319076571988943551
```
---
### Author:  [@EHBaozi](https://discourse.julialang.org/u/EHBaozi)
#### Post date: [May 3, 2020, 12:13pm UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/9 "2020-05-03T12:13:26Z")
Nice! This should be the one then.
Also, @StarecZosima could you kindly check whether your Mathematica is doing something strange? Mine gives the same answer of ~27.866.
---
### Author:  [@StarecZosima](https://discourse.julialang.org/u/StarecZosima)
#### Post date: [May 3, 2020, 6:43pm UTC](https://discourse.julialang.org/t/special-functions-elliptic-jl-and-arbitrary-precision/38658/10 "2020-05-03T18:43:46Z")
Thanks to all very much, I got it working now, good to learn about these additional packages.
@EHBaozi, I inadvertendly typed 10^-25 and not 10^-23 when checking. Indeed in Mathemica
```
EllipticK [1-10^-23] = 27.866022930551415985
```
so matching what you got and Julia’s ArbNumerics.
Thanks once more