## Copyright (c) 2016, James P. Howard, II <jh@jameshoward.us>
##
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##
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#' @name division
#' @rdname division
#'
#' @title Algorithms for divisions
#'
#' @description
#' Algorithms for division that provide a quotient and remainder.
#'
#' @param m the dividend
#' @param n the divisor
#'
#' @details
#' The \code{naivediv} divides \code{m} by \code{n} by using repeated
#' division. The \code{longdiv} function uses the long division
#' algorithm in binary.
#'
#' @return the quotient and remainder as a list
#'
#' @family algebra
#'
#' @examples
#' a <- floor(runif(1, 1, 1000))
#' b <- floor(runif(1, 1, 100))
#' naivediv(a, b)
#' longdiv(a, b)
#'
#' @export
naivediv <- function(m, n) {
quot <- 0
r <- m
if(n == 0)
stop("Attempted division by 0")
while(r >= n) {
quot <- quot + 1
r <- r - n
}
return(list(quotient = quot, remainder = r))
}
#' @rdname division
#' @export
longdiv <- function(m, n) {
quot <- 0
r <- 0
if(n == 0)
stop("Attempted division by 0")
for(i in 31:0) {
r <- bitwShiftL(r, 1)
r <- r + bitwAnd(bitwShiftR(m, i), 1)
if(r >= n) {
r <- r - n
quot <- quot + bitwShiftL(1, i)
}
}
return(list(quotient = quot, remainder = r))
}
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