seed <- 12345
set.seed(seed)

ni <- 0:1000
m <- 100000
nr <- floor(runif(m, min=-500, max=1500)) + (2*runif(m) - 1)^7 # concentrates near integers
min.err <- Inf # minimum inexact result for integer n
max.err <- 0 # maximum error for real n
xi <- rep(1, times=length(ni)) # exact values (Pascal triangle)
xr <- rep(1, times=length(nr)) # R level computed values
for (k in 0:200) {
	if (k %% 10 == 0)
		cat("k <=", k, "max err =", max.err, "\n")
	# check integer n
	yi <- choose(ni + k, k)
	min.err <- min(min.err, xi[xi != yi])
	xi <- cumsum(xi) # prepare for the next k
	# check real n
	yr <- choose(nr, k)
	ind <- yr != 0 | xr != 0
	max.err <- max(max.err, pmax(yr[ind]/xr[ind], xr[ind]/yr[ind]) - 1)
	xr <- xr*(nr - k)/(k + 1) # prepare for the next k
}

cat("minimum log2() of a wrong result for integer n :", log2(min.err), "\n")
cat("maximum error for real n :", max.err, "\n")