diff: Absolute and relative difference

In cppdoubles: Fast Relative Comparisons of Floating Point Numbers in 'C++'

Absolute and relative difference

Description

Calculate absolute differences with abs_diff() and relative differences with rel_diff()

Usage

rel_diff(x, y, scale = NA_real_)

abs_diff(x, y)

Arguments

x	A double vector.
y	A double vector.
scale	A double vector. When NA, the scale is calculated as max(abs(x), abs(y)).

Details

Relative difference

The relative difference in this package is calculated as abs_diff(x / scale, y / scale) except in the case that both x and y are approximately 0 which results in 0.

The scale is calculated as max(abs(x), abs(y)) by default when scale is NA. This has the nice property of making rel_diff() a commutative function in which the order of the arguments doesn't matter. You can of course supply your own scale.

For info, an R way to calculate the relative difference is as follows

  r_rel_diff <- function(x, y){
    ax <- abs(x)
    ay <- abs(y)
    scale <- pmax(ax, ay)
    ifelse(
      ax < sqrt(.Machine$double.eps) & ay < sqrt(.Machine$double.eps),
      0,
      abs_diff(x / scale, y / scale)
    )
  }

This is much slower than the C++ written rel_diff.

Comparison with all.equal()

As mentioned above, unlike base::all.equal(), rel_diff() is commutative. To match the relative difference calculation used by all.equal(), simply set scale = x.

Therefore, to make a vectorised binary version of all.equal(), we can write for example the following:

  all.equal2 <- \(x, y, tol = get_tolerance()) rel_diff(x, y, scale = x) < tol

Value

A numeric vector.

cppdoubles documentation built on June 9, 2025, 5:09 p.m.