[R] : Ramanujan and the accuracy of floating point computations - using Rmpfr in R

[RK]

Also when I try the following with Rmpfr, it works jut fine.

> exp(sqrt(mpfr(163, 120)) * Const("pi", 120))
1 'mpfr' number of precision  120   bits 
[1] 262537412640768743.99999999999925007601

and

> exp(sqrt(mpfr(163, 400)) * Const("pi", 400))
1 'mpfr' number of precision  400   bits 
[1] 
262537412640768743.99999999999925007259719818568887935385633733699086270
753741037821064791011860731295118134618606450419548

Which compares very nicely with the following:

In[10]:= N[Exp[Sqrt[163] Pi], 125]

Out[10]= 
2.6253741264076874399999999999925007259719818568887935385633733699086270
753741037821064791011860731295118134618606450419308389*10^17


In the multiprecision business, you can never be too certain that you 
are using the right precision throughout your calculations.


Nordlund, Dan (DSHS/RDA <NordlDJ <at> dshs.wa.gov> writes:

> 
> Ravi,
> 
> Take a look at the following link.  
> 
> https://code.google.com/p/r-bc/
> 
> I followed the instructions to get a Windows version of the 'nix 
utility program , bc (a high precision
> calculator), and the source for an R to bc interface.  After 
installing them, I executed
> 
> exp(sqrt(bc(163))*4*atan(bc(1)))
> 
> in R and got this result
> 
> 
"262537412640768743.9999999999992500725971981856888793538563373369908627
075374103782106479101186073116295306145602054347"
> 
> I don't know if this is helpful, but ...
> 
> Dan
> 
> Daniel Nordlund, PhD
> Research and Data Analysis Division
> Services & Enterprise Support Administration
> Washington State Department of Social and Health Services
>