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

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

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.

Value

a number of (S4) class 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

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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)))))

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