# Calculating cos(0.9528) in BigFloat
**URL:** https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489
**Category:** General Usage
**Created:** [December 4, 2017, 2:04am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489 "2017-12-04T02:04:18Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Diger](https://discourse.julialang.org/u/Diger)
#### Post date: [December 4, 2017, 2:04am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/1 "2017-12-04T02:04:19Z")
So I (incited by some others) calculated the following
```julia
setprecision(15*10^5)
x=big(9528)/10000;
y=cos(x);
ys=string(y);
ys[306890:306931]
"459423813195289597370437889596885962619893..."
```
Now this is somehow wrong…The correct sequence is:
“459423813195289597370437889596885917728725…”
In fact doing one newton-iteration with the first wrong number:
```julia
yn=y;
yn=yn+(acos(yn)-x)*sqrt(1-yn^2);
```
gives the desired result above, which I would have assumed however to be correct in the first place…
So what is going wrong here?
---
### Author:  [@Ralph\_Smith](https://discourse.julialang.org/u/Ralph_Smith)
#### Post date: [December 4, 2017, 2:53am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/2 "2017-12-04T02:53:40Z")
> [@Diger](#):
>
> x=big(9528)/10000;
is not a good way to build a `BigFloat`.
```julia
julia> x=big(9528.0)/10000;
julia> y=cos(x);
julia> ys=string(y);
julia> ys[306890:306931]
"459423813195289597370437889596885917728725"
```
Edit: Ouch, I stand corrected; promotion should work here.
---
### Author:  [@simonbyrne](https://discourse.julialang.org/u/simonbyrne)
#### Post date: [December 4, 2017, 3:29am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/3 "2017-12-04T03:29:37Z")
These should be exactly the same. If you’re using 0.6.0 (or earlier) on Windows, you might be hitting:
[https://github.com/JuliaLang/julia/issues/22758](https://github.com/JuliaLang/julia/issues/22758)
Try using 0.6.1, as this includes MPFR 3.1.5 which fixes the issue.
---
### Author:  [@simonbyrne](https://discourse.julialang.org/u/simonbyrne)
#### Post date: [December 4, 2017, 6:07am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/4 "2017-12-04T06:07:39Z")
Also, an easier way to do this is to use the `big` string macro:
```julia
x = big"0.9528"
```
---
### Author:  [@Diger](https://discourse.julialang.org/u/Diger)
#### Post date: [December 4, 2017, 11:50am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/5 "2017-12-04T11:50:37Z")
> Blockquote is not a good way to build a BigFloat.
> I first tried
> big(0.9528) but this was completely giving me the wrong number…
Actually: x=big(9528.0)/10000
like Ralph did still gives me the wrong answer…
I’m using v0.5
So I need at least v0.6.1 ? I will try…
---
### Author:  [@Tamas\_Papp](https://discourse.julialang.org/u/Tamas_Papp)
#### Post date: [December 4, 2017, 12:01pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/6 "2017-12-04T12:01:21Z")
On `v0.6.1`,
```julia
julia> big(9528.0)/10000
9.527999999999999999999999999999999999999999999999999999999999999999999999999998e-01
```
which is the same as `big"0.9528"`.
---
### Author:  [@ScottPJones](https://discourse.julialang.org/u/ScottPJones)
#### Post date: [December 4, 2017, 1:06pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/7 "2017-12-04T13:06:33Z")
You shouldn’t be doing something like `big(9528.0)`, because that first creates a `Float64` `9528.0`, which means it may have already lost information, before converting it to a `BigFloat`.
---
### Author:  [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [December 4, 2017, 1:11pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/8 "2017-12-04T13:11:09Z")
> [@ScottPJones](#):
>
> You shouldn’t be doing something like big(9528.0), because that first creates a Float64 9528.0, which means it may have already lost information, before converting it to a BigFloat.
Integers (up to 2^53) are represented exactly in floating-point arithmetic, so converting an exactly representable `Float64` like 9528.0 to `BigFloat` is perfectly safe.
---
### Author:  [@Diger](https://discourse.julialang.org/u/Diger)
#### Post date: [December 4, 2017, 1:12pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/9 "2017-12-04T13:12:15Z")
Why is big(9528)/10000 not a good way then to build a big float?
---
### Author:  [@ScottPJones](https://discourse.julialang.org/u/ScottPJones)
#### Post date: [December 4, 2017, 1:12pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/10 "2017-12-04T13:12:21Z")
In that particular case, yes. I was talking about the general case, where one shouldn’t do `big()` to create a `BigFloat`.
(I was aware that in that particular case, it didn’t lose information, but you shouldn’t be encouraging a poor programming practice, that’s confused a lot of people already)
---
### Author:  [@Ralph\_Smith](https://discourse.julialang.org/u/Ralph_Smith)
#### Post date: [December 4, 2017, 1:40pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/11 "2017-12-04T13:40:30Z")
I was wrong; `big(9528)` makes a `BigInt` and I mistakenly thought that your problem was division not done in full `BigFloat` precision.
---
### Author:  [@StefanKarpinski](https://discourse.julialang.org/u/StefanKarpinski)
#### Post date: [December 4, 2017, 5:52pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/12 "2017-12-04T17:52:12Z")
Please quote your code.
---
### Author:  [@simonbyrne](https://discourse.julialang.org/u/simonbyrne)
#### Post date: [December 4, 2017, 9:59pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/13 "2017-12-04T21:59:58Z")
Presumably they were aware of that, since they wrote `big(9528.0)/10000` instead of `big(0.9528)`
---
### Author:  [@Diger](https://discourse.julialang.org/u/Diger)
#### Post date: [December 4, 2017, 10:25pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/14 "2017-12-04T22:25:02Z")
So now that I installed 0.6.1 I tried again, but I get the same wrong answer?
Wasn’t it fixed with MPFR 3.1.5 which was implemented in 0.6.1?
---
### Author:  [@simonbyrne](https://discourse.julialang.org/u/simonbyrne)
#### Post date: [December 5, 2017, 3:43am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/15 "2017-12-05T03:43:32Z")
What does
```julia
unsafe_string(ccall((:mpfr_get_version,:libmpfr), Ptr{Cchar}, ()))
```
give?
---
### Author:  [@simonbyrne](https://discourse.julialang.org/u/simonbyrne)
#### Post date: [December 5, 2017, 5:57am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/16 "2017-12-05T05:57:06Z")
Hmm, looks like it wasn’t fixed.
---
### Author:  [@simonbyrne](https://discourse.julialang.org/u/simonbyrne)
#### Post date: [December 5, 2017, 6:07am UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/17 "2017-12-05T06:07:42Z")
Ah, never mind. It was fixed in the 3.1.6 release of MPFR. We need to upgrade…
---
### Author:  [@Diger](https://discourse.julialang.org/u/Diger)
#### Post date: [December 5, 2017, 5:17pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/18 "2017-12-05T17:17:43Z")
It gives 3.1.5
---
### Author:  [@simonbyrne](https://discourse.julialang.org/u/simonbyrne)
#### Post date: [December 5, 2017, 5:49pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/19 "2017-12-05T17:49:32Z")
Apologies: it wasn’t fixed in 3.1.5, only 3.1.6. Unfortunately, this hasn’t made it’s way into the releases yet.
---
### Author:  [@Diger](https://discourse.julialang.org/u/Diger)
#### Post date: [December 5, 2017, 5:50pm UTC](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489/20 "2017-12-05T17:50:11Z")
When will it be out?
[Next page](https://discourse.julialang.org/t/calculating-cos-0-9528-in-bigfloat/7489.md?page=2)