How to deal with floating point errors in R

Question

Consider the following R function

is.sqrt <- function(x, y){
  if(x^2 == y) TRUE
  else FALSE
}

which answers whether x is the square ro

Answer 1

you can use all.equal in your function, which "tests if two objects are 'nearly' equal"

is.sqrt <- function(x, y){
    isTRUE(all.equal(x^2,y)
}


 is.sqrt(sqrt(2), 2)
 # TRUE

 is.sqrt(sqrt(2), 3)
 # FALSE

Answer 2

You can use the near function from dplyr, it has a built-in tolerance.

is.sqrt <- function(x, y) {
  near(x^2, y)
}

is.sqrt(sqrt(2), 2)

> TRUE

Answer 3

Another option could be to use all.equal.numeric itself.

Option-A)

is.sqrt <- function(x, y){
  isTRUE(all.equal.numeric(x^2, y))
}

#> is.sqrt(sqrt(2),2)
#[1] TRUE

Option-B)

Using tolerance limit double precision. Optionally one can use .Machine.double.eps but I had preferred to use a fixed value as 1e-8.

is.sqrt_abs_tol<- function(x, y){
  tol <- 1e-8   # OR .Machine$double.eps can be used
  abs(x^2 - y) <= tol
}

#> is.sqrt_abs_tol(sqrt(2), 2)
#[1] TRUE

As agreed with @docendodiscimus, I thought do some performance analysis about these options.

library(microbenchmark)
library(dplyr)

is.sqrt_Dan <- function(x, y){
  isTRUE(all.equal(x^2,y))
}

is.sqrt_MKR <- function(x, y){
  isTRUE(all.equal.numeric(x^2, y))
}

is.sqrt_Leon <- function(x, y) {
  near(x^2, y)
}

is.sqrt_abs_tol<- function(x, y){
  tol <- 1e-5
  abs(x^2 - y) <= tol
}

microbenchmark(
  is.sqrt_Leon(sqrt(2), 2),
  is.sqrt_Dan(sqrt(2), 2),
  is.sqrt_MKR(sqrt(2), 2),
  is.sqrt_abs_tol(sqrt(2), 2),
  times=1000L  
)

                        expr   min    lq      mean median    uq     max neval
    is.sqrt_Leon(sqrt(2), 2)  2369  3948  4736.816   4737  5132   60001  1000
     is.sqrt_Dan(sqrt(2), 2) 36711 38291 44590.051  39474 41844 2750542  1000
     is.sqrt_MKR(sqrt(2), 2) 32369 33949 38130.556  35133 37501  211975  1000
 is.sqrt_abs_tol(sqrt(2), 2)   395  1185  4571.833   1579  1580 3107387  1000

Few observations from the analysis above:

• Surprisingly near function from dplyr is faster than all.equal variants.
• all.equal.numeric is slightly faster than all.equal
• The custom version using abs and tolerance is super-fast.