`expect_near_rel` behaves weirdly for values around 1e-8

Developers
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Disclaimer: I just taught myself some numerics in the past few months, I might easily be very wrong

I’ve been thinking a bit about this, and now I most like to make the tolerance depend on the average as:

auto avg = 0.5 * (fabs(x1) + fabs(x2));
tol_final = max(tol_min, tol * avg);
EXPECT_NEAR(0, x1 - x2, tol_final);

here both tol and tol_min can be set by the user and the default for tol_min is tol_rel ^ 2.

The proposed approach gives the same relative tolerance as the current approach when avg >= tol, but then increases the tolerance more gradually.

Graphically, the relative tolerance implied by the current and the proposed approach when tol = 1e-8 looks like this:

image
image776×220 14.5 KB

The code I’ve written for my recent pull request passes this more stringent standard, but some other tests fail - I am not sure if this is cause for concern or simply means that the tolerances need to be better adjusted.

Does that make sense as a recommended practice? Or am I missing something obvious?

Code for the plot 
library(ggplot2)

x <- 10^(seq(-15,5, length.out = 100))
tol_current <- ifelse(x < 1e-8, 1e-8, x* 1e-8)
tol_proposed <- pmax(x*1e-8,1e-16)
df = rbind(
  data.frame(x = x, type = "current", tol = tol_current),
  data.frame(x = x, type = "proposed", tol = tol_proposed))
df$relative_tol = df$tol / df$x

ggplot(df, aes(x = x, y = relative_tol, color = type)) + geom_line() + scale_x_log10("0.5 * (fabs(x1) + fabs(x2))")+ scale_y_log10()
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