(PR#8087) NAs by integer overflow in Spearman's test p-value

Full_Name: Jan T. Kim
Version: 2.1.0 (and better)
OS: Linux
Submission from: (NULL) (139.222.3.229)


The p value in Spearman's test is NA if the length of x exceeds 46340, due to
an integer overflow, occurring if length(n) > sqrt(2^31):

   > n <- 46341;
   > set.seed(1);
   > x <- runif(n);
   > y <- runif(n);
   > cor.test(x, y, method = "spearman");

           Spearman's rank correlation rho

   data:  x and y
   S = 1.654965e+13, p-value = NA
   alternative hypothesis: true rho is not equal to 0
   sample estimates:
           rho
   0.002199426

   Warning message:
   NAs produced by integer overflow in: n * n

The integer overflow occurs in src/library/stats/R/cor.test.R, and it can be
fixed
by converting n to double appropriately (see *** fix label ***, lines 110
onwards
are shown):

               ## Use the test statistic S = sum(rank(x) - rank(y))^2
               ## and AS 89 for obtaining better p-values than via the
               ## simple normal approximation.
               ## In the case of no ties, S = (1-rho) * (n^3-n)/6.
               pspearman <- function(q, n, lower.tail = TRUE) {
                   if(n <= 1290) # n*(n^2 - 1) does not overflow
                       .C("prho",
                          as.integer(n),
                          as.double(q + 1),
                          p = double(1),
                          integer(1),
                          as.logical(lower.tail),
                          PACKAGE = "stats")$p
                   else { # for large n: aymptotic t_{n-2}
                       n <- as.double(n);  # *** fix ***
                       r <- 1 - 6 * q / (n*(n*n - 1))
                       pt(r / sqrt((1 - r^2)/(n-2)), df = n-2,
                          lower.tail= !lower.tail)
                   }
               }
               q <- round((n^3 - n) * (1 - r) / 6)
               STATISTIC <- c(S = q)
               PVAL <-
                   switch(alternative,
                          "two.sided" = {
                              p <- if(q > (n^3 - n) / 6)
                                  pspearman(q - 1, n, lower.tail = FALSE)
                              else
                                  pspearman(q, n, lower.tail = TRUE)
                              min(2 * p, 1)
                          },
                          "greater" = pspearman(q, n, lower.tail = TRUE),
                          "less" = pspearman(q - 1, n, lower.tail = FALSE))
               if(TIES)
                   warning("p-values may be incorrect due to ties")

Inserting the typecast only in the pspearman function is a minimally invasive
fix -- alternatively, replacing at line 17

   n <- length(x)

with

   n <- as.double(length(x))

achieves the same fix and may take care of other unnecessary integer overflows,
but it may also introduce new problems e.g. in .C calls etc.