A quick tour of R internals


This week I had a chance to make a small speed improvement to R by moving some code for the commonly used which() function from R into C. Patrick, a colleague at work, suggested the change after observing that which could become a bottleneck when dealing with vectors containing millions of elements. If you aren't familiar with R, the which function returns the indices of a logical vector that contain a TRUE value. The simplicity of which makes this a good case study for understanding the mechanism of R's internal functions, those that are coded in C instead of in R itself, and to see what's involved in moving (part of) a function from R into C.

The case for optimizing

It doesn't always make sense to move code from R into C. Adding more C code can increase the complexity of the code base and decrease the pool of potential maintainers. A function is a good candidate for becoming internal if doing so results in a significant speed gain and if the function is used in a way that this speed gain will be likely to be appreciated. Since which is a fairly low level function used in a lot of code, speed improvements could be worth while. Before going further, let's take a look at the implementation of which in R-2.10.1:

which <- function(x, arr.ind = FALSE)
        stop("argument to 'which' is not logical")
    wh <- seq_along(x)[x & !is.na(x)]
    dl <- dim(x)
    if (is.null(dl) || !arr.ind) {
        names(wh) <- names(x)[wh]
    else { ##-- return a matrix  length(wh) x rank
    ## ... omitted

The core of the function is a single line packed with vectorized goodness:

wh <- seq_along(x)[x & !is.na(x)]

This says, generate a sequence of integers from 1 to the length of x, then subset it by a logical vector consisting of the elements of x where x is not a missing (NA) value. It breaks down into these five operations:

  1. is.na(x) makes one pass through x, returning another logical vector with the same length of x indicating which elements are NA

  2. ! makes one pass through the is.na(x) result returning the logical not of each element.

  3. & makes a pass through x and !is.na(x) performing logical and

  4. seq_along(x) generates a sequence of integers from 1 to length(x). The result has length(x), but it doesn't need to read through x.

  5. [ subsetting, makes a pass through the index argument.

So four of the five operations require a full scan through the input vector and all five require an allocation of a result vector the same size as the input. Summary: we'll probably be able to speed this up by moving these operations into C code.

An implementation in C

Below is an implementation in C of the core of the which function as described above. This isn't quite what is required in order for us to wire it into R as a new .Internal call, but is a good step along the way to show how the operation can be implemented in C using R data structures.

SEXP which_core(SEXP v)
    SEXP v, v_nms, ans, ans_nms = R_NilValue;
    int i, j = 0, len, *buf;

    if (!isLogical(v))
        error(_("argument to 'which' is not logical"));
    len = length(v);
    buf = (int *) R_alloc(len, sizeof(int));

    for (i = 0; i < len; i++) {
        if (LOGICAL(v)[i] == TRUE) {
            buf[j] = i + 1;

    len = j;
    PROTECT(ans = allocVector(INTSXP, len));
    memcpy(INTEGER(ans), buf, sizeof(int) * len);

    if ((v_nms = getAttrib(v, R_NamesSymbol)) != R_NilValue) {
        PROTECT(ans_nms = allocVector(STRSXP, len));
        for (i = 0; i < len; i++) {
            SET_STRING_ELT(ans_nms, i,
                           STRING_ELT(v_nms, INTEGER(ans)[i] - 1));
        setAttrib(ans, R_NamesSymbol, ans_nms);
    return ans;

The which_core function allocates an int buffer the same length as the input, makes a single pass through the input, and then allocates an INTSXP of the appropriate length and copies over the values from the buffer. If names are present on the input, then a pass is made over the "answer" vector to add the names. Another approach is to make two passes through the input, once to determine the number of TRUE's and a second pass to fill out an answer vector. A two-pass approach involves less allocation and less memory overhead. In the tests I ran, I didn't see much difference in run time between the two approaches.

Wiring up a new .Internal function

With the core of the C implementation out of the way, the next step is to handle the details required to add a new internal function to R. At the R level, we will make the following replacement in the which code:

which <- function(x, arr.ind = FALSE)
-    if(!is.logical(x))
-       stop("argument to 'which' is not logical")
-    wh <- seq_along(x)[x & !is.na(x)]
+    wh <- .Internal(which(x))
     dl <- dim(x)
-    if (is.null(dl) || !arr.ind) {
-       names(wh) <- names(x)[wh]
-    }
-    else { ##-- return a matrix  length(wh) x rank
+    if (!is.null(dl) && arr.ind) {
+        ##-- return a matrix  length(wh) x rank

In order for .Internal(which(x)) to work, we need to add the internal function to the table of internal functions, R_FunTab, found in src/names.c. As an aside, if you are looking to find the source code for an internal R function, a good place to start grep'ing is in names.c. The entry we need to add looks like this:

{"which",  /* function name used in .Internal call in R */
do_which,  /* C entry point, by convention starts with "do_"
              and take (SEXP call, SEXP op, SEXP args, SEXP env)
0,         /* This value is passed as op when called via .Internal,
              it is used when two different R functions call the
              same internal C function and need slightly different
              behavior (e.g. return max vs min). */

11,        /* Actually three digits XYZ, 11 => 011
              X=0 => return value is visible, if x=1, effect is
              same as calling invisible(ans) at R-level

              Y=1 indicates type of function, 1 => .Internal

              Z controls argument evaluation: 1 => evaluate args
              before calling, 0 => don't evaluate (needed for
              special functions).
1,         /* This is the arity of your function */

           /* read the code for details on the rest */

Finally, we need to implement do_which. The signature looks like this:

SEXP attribute_hidden do_which(SEXP call, SEXP op, SEXP args, SEXP rho)
    SEXP v, v_nms, ans, ans_nms = R_NilValue;
    int i, j = 0, len, *buf;

    checkArity(op, args);
    v = CAR(args);

    /* rest of code here, same as which_core */

Aside from the change in arguments, there are two changes to the code when compared to the which_core version. First, the actual arguments are packaged in a pair-list in args and you can see we access the first (and only) argument via CAR(args). Second, we call the helper function checkArity that will display a standard error message if our internal function is called with the wrong number of arguments.

Measuring progress

Here is a script that checks results returned by the C version against those from the R version and does some timing comparisons. Below are the timing results for a logical vector of seven million elements as the number of TRUE elements varies between 10 and 90 percent.

pct  orig   new
0.1 0.340 0.021
0.3 0.384 0.044
0.5 0.455 0.053
0.7 0.435 0.053
0.9 0.435 0.041

As you can see, the C version is an order of magnatude faster, although it shows more variance based on the percentage of TRUE values in the input.

archived on 2010-03-14 in ,

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