lgamma user defined function returns infinite value

Question

This calculates the log of (x-1)! to return the lgamma(x) value of an integer but my function log_gamma works only till x = 171 for x > 171 it returns Inf. How can I solve this problem?

log_gamma <- function(x){
  y <- 1
  if (x < 1)(
    return("Infinity")
  )
  if (x == 1)(
    return(0)
  )
  x <- x-1
  for (i in 1:x){
     y <- y*i
  }
    return(log(y))
}

Answer 1

Your current solution first computes 171! which is a pretty big number. Instead, use the fact that log(a*b) = log(a) + log(b) to compute this as a sum.

log_gamma <- function(x){
  y <- 1
  if (x < 1)(
    return("Infinity")
  )
  if (x == 1)(
    return(0)
  )
  x <- x-1
  for (i in 1:x){
     y <- y + log(i)
  }
    return(y)
}

log_gamma(171)
[1] 707.5731
log_gamma(172)
[1] 712.7147
log_gamma(1000)
[1] 5906.22