Fast Relative Comparisons of Floating Point Numbers in 'C++'.

cppdoubles

Fast Relative Comparisons of Floating Point Numbers in C++

You can install cppdoubles using the below code.

remotes::install_github("NicChr/cppdoubles")

Comparing equality of 2 double vectors

library(cppdoubles)

### Basic usage ###

# Standard equality operator
sqrt(2)^2 == 2
#> [1] FALSE

# approximate equality operator
sqrt(2)^2 %~==% 2
#> [1] TRUE

Other approximate equality operators

sqrt(2)^2 %~>=% 2
#> [1] TRUE
sqrt(2)^2 %~<=% 2
#> [1] TRUE
sqrt(2)^2 %~>% 2
#> [1] FALSE
sqrt(2)^2 %~<% 2
#> [1] FALSE

# Alternatively
double_equal(2, sqrt(2)^2)
#> [1] TRUE
double_gte(2, sqrt(2)^2)
#> [1] TRUE
double_lte(2, sqrt(2)^2)
#> [1] TRUE
double_gt(2, sqrt(2)^2)
#> [1] FALSE
double_lt(2, sqrt(2)^2)
#> [1] FALSE

All comparisons are vectorised and recycled

double_equal(sqrt(1:10),
             sqrt(1:5),
             tol = c(-Inf, 1e-10, Inf))
#>  [1] FALSE  TRUE  TRUE FALSE  TRUE  TRUE FALSE FALSE  TRUE FALSE

One can check if a double is a whole number like so

# One can check for whole numbers like so
whole_number <- function(x, tol = getOption("cppdoubles.tolerance", sqrt(.Machine$double.eps))){
  double_equal(x, round(x), tol = tol)
}
x <- seq(-5, 5, by = 0.2)
whole_nums <- x[whole_number(x)]
whole_nums
#>  [1] -5 -4 -3 -2 -1  0  1  2  3  4  5

all_equal as an alternative to base R all.equal.numeric

x <- seq(0, 10, 2)
y <- sqrt(x)^2

all_equal(x, y)
#> [1] TRUE
all_equal(x, 1)
#> [1] FALSE
all_equal(x, NA)
#> [1] NA
isTRUE(all_equal(x, NA))
#> [1] FALSE

Benchmark against all.equal.numeric

library(bench)
x <- abs(rnorm(10^7))
y <- sqrt(x)^2
z <- x^2

# 2 approximately equal vectors
mean(rel_diff(x, y))
#> [1] 7.761826e-17
mark(base = isTRUE(all.equal(x, y)),
     cppdoubles = all_equal(x, y))
#> # A tibble: 2 × 6
#>   expression      min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr> <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 base          259ms    264ms      3.79     437MB     13.3
#> 2 cppdoubles    164ms    164ms      6.08        0B      0

# 2 significantly different vectors
mean(rel_diff(x, z))
#> [1] 0.4627246
mark(base = isTRUE(all.equal(x, z)),
     cppdoubles = all_equal(x, z))
#> # A tibble: 2 × 6
#>   expression      min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr> <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 base        178.6ms  183.6ms      5.39     343MB     10.8
#> 2 cppdoubles    2.1µs    2.3µs 403385.          0B      0

Benchmark against using absolute differences

mark(double_equal(x, y),
     abs_diff(x, y) < sqrt(.Machine$double.eps))
#> # A tibble: 2 × 6
#>   expression                             min median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>                         <bch:t> <bch:>     <dbl> <bch:byt>    <dbl>
#> 1 double_equal(x, y)                 177.5ms  178ms      5.59    38.1MB      0  
#> 2 abs_diff(x, y) < sqrt(.Machine$do…  40.5ms   44ms     22.4    114.4MB     39.2