"which.just.above" <- 
function(x, reference, strict = T)
{
	# output[k] will be index of smallest value in reference vector
	# larger than x[k].  If strict=F, replace 'larger than' by
	# 'larger than or equal to'.
	# We should allow NA's in x (but we don't). NA's in reference
	# should not be allowed.
	if(any(is.na(x)) || any(is.na(reference))) stop("NA's in input")
	if(strict)
		i <- c(rep(T, length(reference)), rep(F, length(x)))[order(
			c(reference, x))]
	else i <- c(rep(F, length(x)), rep(T, length(reference)))[order(c(
			x, reference))]
	i <- cumsum(i)[!i] + 1.
	i[i > length(reference)] <- NA
	# i is length of x and has values in range 1:length(reference) or NA
	# following needed if reference is not sorted 
	i <- order(reference)[i]
	# following needed if x is not sorted
	i[order(order(x))]
}

"which.just.below" <- 
function(x, reference, strict = T)
{
	# output[k] will be index of largest value in reference vector
	# less than x[k].  If strict=F, replace 'less than' by
	# 'less than or equal to'.  Neither x nor reference need be
	# sorted, although they should not have NA's (in theory, NA's
	# in x are ok, but not in reference).
	if(any(is.na(x)) || any(is.na(reference))) stop("NA's in input")
	if(!strict)
		i <- c(rep(T, length(reference)), rep(F, length(x)))[order(
			c(reference, x))]
	else i <- c(rep(F, length(x)), rep(T, length(reference)))[order(c(
			x, reference))]
	i <- cumsum(i)[!i]
	i[i <= 0] <- NA
	# i is length of x and has values in range 1:length(reference) or NA
	# following needed if reference is not sorted 
	i <- order(reference)[i]
	# following needed if x is not sorted
	i[order(order(x))]
}

test <- function(x, ref) {
   data.frame(
         belowStrict=ref[which.just.below(x,ref,strict=T)],
         belowNonstrict= ref[which.just.below(x,ref,strict=F)],
         x=x,
         aboveNonstrict= ref[which.just.above(x,ref,strict=F)],
         aboveStrict=ref[which.just.above(x,ref,strict=T)]
   )[order(x),]
}
ref <- 11:14
x <- c(10.5, 11, 11.5, 12, 12.5, 13, 13.5, 14, 14.5)
print(test(x,ref))
times<-as.POSIXct("2009-05-22") + seq(0, 5 * 24*60*60, len=15)
reftimes<-as.POSIXct("2009-05-23") + seq(0, 4 * 24*60*60, by=24*60*60)
print(test(times,reftimes))