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 = get_tolerance()){
  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)
set.seed(100)
x <- abs(rnorm(10^7))
y <- sqrt(x)^2
z <- x^2

# 2 approximately equal vectors
mean(rel_diff(x, y))
#> [1] 7.532799e-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        326.8ms  328.4ms      3.05     437MB     10.7
#> 2 cppdoubles   75.4ms   85.3ms     11.7         0B      0

# 2 significantly different vectors
mean(rel_diff(x, z))
#> [1] 0.4627377
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        199.5ms  213.3ms      4.57     343MB     10.7
#> 2 cppdoubles    1.6µs    1.9µs 467277.          0B      0

Benchmark against using absolute differences

mark(double_equal(x, y),
     abs_diff(x, y) < sqrt(.Machine$double.eps))
#> # A tibble: 2 × 6
#>   expression                             min median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>                          <bch:> <bch:>     <dbl> <bch:byt>    <dbl>
#> 1 double_equal(x, y)                  83.8ms 86.3ms      11.5    38.1MB     5.75
#> 2 abs_diff(x, y) < sqrt(.Machine$dou… 49.7ms 53.8ms      17.4   114.4MB    10.4