[Roxygen-commits] r176 - pkg/sandbox

[noreply at r-forge.r-project.org]

Author: pcd
Date: 2008-08-24 10:37:11 +0200 (Sun, 24 Aug 2008)
New Revision: 176

Added:
   pkg/sandbox/example-pseudoprime.R
Log:
pseudoprime example for vignette


Added: pkg/sandbox/example-pseudoprime.R
===================================================================
--- pkg/sandbox/example-pseudoprime.R	                        (rev 0)
+++ pkg/sandbox/example-pseudoprime.R	2008-08-24 08:37:11 UTC (rev 176)
@@ -0,0 +1,43 @@
+#' Test an integer for primality with Fermat's Little Theorem.
+#'
+#' Fermat's Little Theorem states that if \eqn{n} is a prime number and
+#' \eqn{a} is any positive integer less than \eqn{n}, then a raised to the
+#' \eqn{n}th power is congruent to \eqn{a modulo n}.
+#'
+#' @param n the integer to test for primality
+#' @return Whether the integer passes the Fermat test
+#' for a randomized 0 < a < n
+#' @note Can't test for primes above 15 because of loss of precision
+#' in modulus.
+#' @TODO Use the \code{gmp} library so we can test for bigger
+#' primes.
+#' @author Peter Danenberg \email{pcd@@roxygen.org}
+fermat.test <- function(n) {
+  a <- floor(runif(1, min=1, max=n))
+  isTRUE(a ^ n %% n == a)
+}
+
+#' Check an integer for pseudo-primality to an arbitrary precision.
+#'
+#' A number is pseudo-prime if it is probably prime, the basis of
+#' which is the probabilistic Fermat test; if it passes two such
+#' tests, the chances are better than 3 out of 4 that n is prime.
+#'
+#' @param n the integer to test for pseudoprimality.
+#' @param times the number of Fermat tests to perform
+#' @return Whether the number is pseudoprime
+#' @seealso \code{\link{fermat.test}}
+#' @export
+#' @examples
+#' ## Will be true most of the time
+#' is.pseudoprime(13, 4)
+#' @references Abelson, Hal; Jerry Sussman, and Julie Sussman.
+#' Structure and Interpretation of Computer Programs. Cambridge:
+#' MIT Press, 1984.
+#' @keywords pseudoprime fermat
+#' @author Peter Danenberg \email{pcd@@roxygen.org}
+is.pseudoprime <- function(n, times) {
+  if (times == 0) TRUE
+  else if (fermat.test(n)) is.fermat.prime(n, times - 1)
+  else FALSE
+}