fpi <- function(expr, x = 0, k = 1000, TOL = .Machine$double.eps, print = FALSE, ...) {
  expr <- checkExpression(substitute(expr))
  
  if (length(x) != 1)
    stop("'x' should be a singular value.")

  d <- getOption("digits")
  for (i in seq(k)) {
    y <- eval(expr, envir = list(x = x), enclos = parent.frame())

    # Check to see if sequence is diverging
    if (x == Inf | y == Inf | is.nan(x) | is.nan(y))
      return("Iteration Diverged. Try another start value")

    if (print) 
      print(sprintf("%*i %.*f %.*f", 5, i, d, y, d, abs(y - x)), quote = FALSE)

    # If y is within tolerance, return it; otherwise, set it as next guess.
    if (stoppingCriteria(x = x, y = y, TOL = TOL, ...))
      return(y)

    x <- y
  }  # end for loop

  stop(paste("No solutions after", k, "iterations. Possible loop in root search."))
}  # end fpi function