How to get my function to take higher values

In R I have writing this function

ifun = function(m)  {
o=c()
for(k in 1:m) {
o[k]= prod(1:k)/ prod(2*(1:k)+1  )
}
o_sum=2*(1+sum(o)) # Final result   
print(o_sum)
}

I want the values for ifun() for high values. For example

 sprintf("%.100f",ifun(170) )

gives this output:

[1] 3.141593
[1] "3.1415926535897931159979634685441851615905761718750000000000000000000000000000000000000000000000000000"

But when I take higher values it can give me any value. For example

sprintf("%.100f",ifun(180) )

gives me this output

[1] NaN
[1] "NaN"

How can I rewrite me code so I can take ifun for larger values? Also, I use this function to approximate pi but for

> ifun(x>50)

it gives me the same result over and over again and don't make my approximation any better.

EDIT

I tried to use the method on Macin series as well I wrote this in R

mac = function(m, approx=TRUE){   
o1 = as.bigq(NULL)   
o2 = as.bigq(NULL)
for(k in 1:m) {
k <- as.bigq(k)
     o1 = c(o1, 1/((2*k+1)*5^(2*k+1))  *(-1)^k)
     o2 = c(o2, 1/((2*k+1)*239^(2*k+1))  *(-1)^k)

   }   
  o_sum = 16*(1/5+sum(o1)) -4*(1/239+sum(o2))   
  if(approx){
     as.numeric(o_sum)   
  } else{
     o_sum   } }

 library(Rmpfr)  x <- mac(250, approx=FALSE)  mpfr(x,256)

This gives me a strange output namely

> 1 'mpfr' number of precision  256   bits  [1]
> 3.1415926535897934 18913264129286527160857809883357101405

It only gives me the first 16 correct digits, it can't give me more. What can be the reason for this?

Solution

Use gmp. It can give the exact result as a rational number if you want.

library(gmp)

ifun = function(m, approx=TRUE){
  o = as.bigq(NULL)
  for(k in 1:m) {
    r <- as.bigz(1:k)
    o = c(o, prod(r)/ prod(2*r+1 ))
  }
  o_sum = 2*(1+sum(o)) 
  if(approx){
    as.numeric(o_sum)
  }else{
    o_sum
  }
}

> ifun(4, approx=FALSE)
Big Rational ('bigq') :
[1] 976/315
> ifun(180)
[1] 3.141593

Edit

Actually to convert the exact rational number to a decimal number, it is better to use the Rmpfr library:

> library(Rmpfr)
> x <- ifun(250, approx=FALSE)
> mpfr(x,256)
1 'mpfr' number of precision  256   bits 
[1] 3.14159265358979323846264338327950288419716939937510582097494459230781640628613