Rmpfr (version 0.9-5)

factorialMpfr: Factorial 'n!' in Arbitrary Precision

Description

Efficiently compute \(n!\) in arbitrary precision, using the MPFR-internal implementation. This is mathematically (but not numerically) the same as \(\Gamma(n+1)\).

factorialZ (package gmp) should typically be used instead of factorialMpfr() nowadays. Hence, factorialMpfr now is somewhat deprecated.

Usage

factorialMpfr(n, precBits = max(2, ceiling(lgamma(n+1)/log(2))),
              rnd.mode = c("N","D","U","Z","A"))

Value

a number of (S4) class mpfr.

Arguments

n

non-negative integer (vector).

precBits

desired precision in bits (“binary digits”); the default sets the precision high enough for the result to be exact.

rnd.mode

a 1-letter string specifying how rounding should happen at C-level conversion to MPFR, see mpfr.

See Also

factorial and gamma in base R.

factorialZ (package gmp), to replace factorialMpfr, see above.

chooseMpfr() and pochMpfr() (on the same page).

Examples

factorialMpfr(200)

n <- 1000:1010
f1000 <- factorialMpfr(n)
stopifnot(1e-15 > abs(as.numeric(1 - lfactorial(n)/log(f1000))))

## Note that---astonishingly--- measurements show only
## *small* efficiency gain of ~ 10% : over using the previous "technique"
system.time(replicate(8, f1e4 <- factorialMpfr(10000)))
system.time(replicate(8, f.1e4 <- factorial(mpfr(10000,
                            prec=1+lfactorial(10000)/log(2)))))