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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

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.