Vectorized equality testing

Question

I'd be surprised if this isn't a dup, but I couldn't find a solution.

I understand the limitations of == for testing equality of floating-point numbers. One should use all.equal

0.1 + 0.2 == 0.3
# FALSE
all.equal(0.1 + 0.2, 0.3)
# TRUE

But == has the advantage of being vectorized:

set.seed(1)
Df <- data.frame(x = sample(seq(-1, 1, by = 0.1), size = 100, replace = TRUE),
                 y = 0.1)
Df[Df$x > 0 & Df$x < 0.2,]
## x   y
## 44 0.1 0.1
## 45 0.1 0.1

# yet
sum(Df$x == Df$y)
# [1] 0

I can write a (bad) function myself:

All.Equal <- function(x, y){
  stopifnot(length(x) == length(y))
  out <- logical(length(x))
  for (i in seq_along(x)){
    out[i] <- isTRUE(all.equal(x[i], y[i]))
  }
  out
}

sum(All.Equal(Df$x, Df$y))

which gives the correct answer, but still has a long way to go.

microbenchmark::microbenchmark(All.Equal(Df$x, Df$y), Df$x == Df$y)
Unit: microseconds
                  expr      min        lq        mean     median        uq        max neval cld
 All.Equal(Df$x, Df$y) 9954.986 10298.127 20382.24436 10511.5360 10798.841 915182.911   100   b
          Df$x == Df$y   16.857    19.265    29.06261    30.8535    38.529     45.151   100  a 

Another option might be:

All.equal.abs <- function(x,y){
  tol <- .Machine$double.eps ^ 0.5
  abs(x - y) < tol
}

which performs comparably to ==.

What is an existing function that performs this task?

Answer 1

Vectorize() turns out to be a slow option. As @fishtank suggests in the comment, the best solution comes from checking if the absolute difference is smaller than some tolerance value, i.e. is_equal_tol() from below.

set.seed(123)
a <- sample(1:10, size = 50, replace = T)
b <- sample(a)

is_equal_tol <- function(x, y, tol = .Machine$double.eps ^ 0.5) {
  abs(x - y) < tol
}

is_equal_vec <- Vectorize(all.equal, c("target", "current"))

is_equal_eq <- function(x, y) x == y

microbenchmark::microbenchmark(is_equal_eq(a, b),
                               is_equal_tol(a, b), 
                               isTRUE(is_equal_vec(a, b)),
                               times = 1000L)

Unit: nanoseconds
                       expr     min      lq        mean  median      uq      max neval
          is_equal_eq(a, b)       0     856    1545.797    1284    2139    14113  1000
         is_equal_tol(a, b)    1711    2567    4991.377    4278    6843    27370  1000
 isTRUE(is_equal_vec(a, b)) 2858445 3008552 3258916.503 3082964 3204204 46130260  1000