oddcount <- function(x) 
{ 
  k <- 0 
  
  for (n in x) 
  { 
    if (n %% 2 == 1) k <- k+1 
  } 
  return (k)
}

formals(oddcount)
body(oddcount)

?log
?floor

log2(1000)
log2(64)
log2(63)
floor(log2(63))
ceiling(log2(63))

ll <- c(1:20)
ll2 <- 2 * ll + 1

ll
oddcount(ll)

ll2
oddcount(ll2)

factorial(ll)
factorial(20)

logSums <- function( x )
{
    fSum <- 0  # floor sum of logs to the base 2
    lSum <- 0  # log to the base 2 sum
    cSum <- 0  # ceiling sum of logs to the base 2
    
    for (i in x)
    {
       fSum <- fSum + floor(log2(i))
       lSum <- lSum + log2(i)
       cSum <- cSum + ceiling(log2(i))
    }
    return( c(fSum, lSum, cSum) )
}