# factorialZ

0th

Percentile

##### Factorial and Binomial Coefficient as Big Integer

Efficiently compute the factorial $n!$ or a binomial coefficient $choose(n, k)$ as big integer (class bigz).

Keywords
arith
##### Usage
factorialZ(n)
chooseZ(n, k)
##### Arguments
n
non-negative integer (vector), for factorialZ. For chooseZ, may be a bigz big integer, also negative.
k
non-negative integer vector.
##### Value

a vector of big integers, i.e., of class bigz.

factorial and gamma in base R;

• factorialZ
• chooseZ
##### Examples
factorialZ(0:10)# 1 1 2 6 ... 3628800
factorialZ(0:40)# larger
factorialZ(200)

n <- 1000
f1000 <- factorialZ(n)
stopifnot(1e-15 > abs(as.numeric(1 - lfactorial(n)/log(f1000))))

system.time(replicate(8, f1e4 <<- factorialZ(10000)))
nchar(as.character(f1e4))# 35660 ... (too many to even look at ..)

chooseZ(1000, 100:102)# vectorizes
chooseZ(as.bigz(2)^120, 10)
n <- c(50,80,100)
k <- c(20,30,40)
## currently with an undesirable warning: % from methods/src/eval.c  _FIXME_
stopifnot(chooseZ(n,k) == factorialZ(n) / (factorialZ(k)*factorialZ(n-k)))

Documentation reproduced from package gmp, version 0.5-13, License: GPL

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