r - Copy-on-modify semantic on a vector does not append in a loop. Why?

Question

This question sounds to be partially answered here but this is not enough specific to me. I would like to understand better when an object is updated by reference and when it is copied.

The simpler example is vector growing. The following code is blazingly inefficient in R because the memory is not allocated before the loop and a copy is made at each iteration.

  x = runif(10)
  y = c() 

  for(i in 2:length(x))
    y = c(y, x[i] - x[i-1])

Allocating the memory enable to reserve some memory without reallocating the memory at each iteration. Thus this code is drastically faster especially with long vectors.

  x = runif(10)
  y = numeric(length(x))

  for(i in 2:length(x))
    y[i] = x[i] - x[i-1]

And here comes my question. Actually when a vector is updated it does move. There is a copy that is made as shown below.

a = 1:10
pryr::tracemem(a)
[1] "<0xf34a268>"
a[1] <- 0L
tracemem[0xf34a268 -> 0x4ab0c3f8]:
a[3] <-0L
tracemem[0x4ab0c3f8 -> 0xf2b0a48]:  

But in a loop this copy does not occur

y = numeric(length(x))
for(i in 2:length(x))
{
   y[i] = x[i] - x[i-1]
   print(address(y))
}

Gives

[1] "0xe849dc0"
[1] "0xe849dc0"
[1] "0xe849dc0"
[1] "0xe849dc0"
[1] "0xe849dc0"
[1] "0xe849dc0"
[1] "0xe849dc0"
[1] "0xe849dc0"
[1] "0xe849dc0" 

I understand why a code is slow or fast as a function of the memory allocations but I don't understand the R logic. Why and how, for the same statement, in a case the update is made by reference and in the other case the update in made by copy. In the general case how can we know what will happen.

Answer 1

This is covered in Hadley's Advanced R book. In it he says (paraphrasing here) that whenever 2 or more variables point to the same object, R will make a copy and then modify that copy. Before going into examples, one important note which is also mentioned in Hadley's book is that when you're using RStudio

the environment browser makes a reference to every object you create on the command line.

Given your observed behavior, I'm assuming you're using RStudio which we will see will explain why there are actually 2 variables pointing to a instead of 1 like you might expect.

The function we'll use to check how many variables are pointing to an object is refs(). In the first example you posted you can see:

library(pryr)
a = 1:10
refs(x)
#[1] 2

This suggests (which is what you found) that 2 variables are pointing to a and thus any modification to a will result in R copying it, then modifying that copy.

Checking the for loop we can see that y always has the same address and that refs(y) = 1 in the for loop. y is not copied because there are no other references pointing to y in your function y[i] = x[i] - x[i-1]:

for(i in 2:length(x))
{
  y[i] = x[i] - x[i-1]
  print(c(address(y), refs(y)))
}

#[1] "0x19c3a230" "1"         
#[1] "0x19c3a230" "1"         
#[1] "0x19c3a230" "1"         
#[1] "0x19c3a230" "1"         
#[1] "0x19c3a230" "1"         
#[1] "0x19c3a230" "1"         
#[1] "0x19c3a230" "1"         
#[1] "0x19c3a230" "1"         
#[1] "0x19c3a230" "1" 

On the other hand if introduce a non-primitive function of y in your for loop you would see that address of y changes each time which is more in line with what we would expect:

is.primitive(lag)
#[1] FALSE

for(i in 2:length(x))
{
  y[i] = lag(y)[i]
  print(c(address(y), refs(y)))
}

#[1] "0x19b31600" "1"         
#[1] "0x19b31948" "1"         
#[1] "0x19b2f4a8" "1"         
#[1] "0x19b2d2f8" "1"         
#[1] "0x19b299d0" "1"         
#[1] "0x19b1bf58" "1"         
#[1] "0x19ae2370" "1"         
#[1] "0x19a649e8" "1"         
#[1] "0x198cccf0" "1"  

Note the emphasis on non-primitive. If your function of y is primitive such as - like: y[i] = y[i] - y[i-1] R can optimize this to avoid copying.

Credit to @duckmayr for helping explain the behavior inside the for loop.