Numerically stable log(1 - exp(-x)) for x > 0

Computes $$\mathrm{log1mexp}(x) = \log\!\bigl(1 - e^{-x}\bigr), \qquad x > 0$$ accurately across the full range. Following Mächler (2012), the evaluation switches at \(x = \log 2\): for small \(x\) it uses \(\log(-\mathrm{expm1}(-x))\) (avoiding cancellation as \(x \to 0\)), and for larger \(x\) it uses \(\mathrm{log1p}(-e^{-x})\) (avoiding loss of precision as \(x \to \infty\)). Non-positive or non-finite inputs return NA.

Usage

hzr_log1mexp(x)

Arguments

x

Numeric vector with positive values.

Value

Numeric vector with element-wise \(\log(1 - e^{-x})\).

References

Mächler M (2012). Accurately Computing \(\log(1 - e^{-|a|})\). R package Rmpfr vignette. https://CRAN.R-project.org/package=Rmpfr/vignettes/log1mexp-note.pdf

See also

hzr_log1pexp() for the softplus \(\log(1 + e^{x})\), hzr_clamp_prob() for boundary-safe probabilities.

Examples

hzr_log1mexp(c(0.01, 0.5, 5))
#> [1] -4.610166019 -0.932752130 -0.006760749