R version 4.4.0 beta (2024-04-09 r86391 ucrt) -- "Puppy Cup"
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Platform: x86_64-w64-mingw32/x64

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> library("matrixStats")
> 
> for (mode in c("integer", "double")) {
+   cat("mode: ", mode, "\n", sep = "")
+ 
+   # Empty vector
+   x <- 0
+   storage.mode(x) <- mode
+   y <- prod(x, na.rm = TRUE)
+   print(y)
+   z <- product(x, na.rm = TRUE)
+   print(z)
+   stopifnot(all.equal(z, y))
+ 
+   # Test negative values
+   x <- c(1, -4, 2)
+   storage.mode(x) <- mode
+   y <- prod(x, na.rm = TRUE)
+   print(y)
+   z <- product(x, na.rm = TRUE)
+   print(z)
+   stopifnot(all.equal(z, y))
+ 
+   # Test missing values
+   x <- c(1, NA, NaN, 2)
+   storage.mode(x) <- mode
+   y <- prod(x, na.rm = TRUE)
+   print(y)
+   z <- product(x, na.rm = TRUE)
+   print(z)
+   stopifnot(all.equal(z, y))
+ 
+   x <- c(1, NA, NaN, 2)
+   storage.mode(x) <- mode
+   y <- prod(x, na.rm = FALSE)
+   print(y)
+   z <- product(x, na.rm = FALSE)
+   print(z)
+   stopifnot(all(is.na(z), is.na(y)))
+ 
+   x <- c(1, NaN, 2)
+   storage.mode(x) <- mode
+   y <- prod(x, na.rm = FALSE)
+   print(y)
+   stopifnot(is.na(y))
+   z <- product(x, na.rm = FALSE)
+   print(z)
+   stopifnot(is.na(z))
+ 
+ } # for (mode ...)
mode: integer
[1] 0
[1] 0
[1] -8
[1] -8
[1] 2
[1] 2
[1] NA
[1] NA
[1] NA
[1] NA
mode: double
[1] 0
[1] 0
[1] -8
[1] -8
[1] 2
[1] 2
[1] NA
[1] NA
[1] NaN
[1] NA
> 
> 
> # NAs following 0s
> x <- c(0L, NA_integer_)
> y <- prod(x, na.rm = FALSE)
> print(y)
[1] NA
> z <- product(x, na.rm = FALSE)
> print(z)
[1] NA
> stopifnot(identical(z, y))
> 
> proc.time()
   user  system elapsed 
   0.15    0.03    0.18