Numerically stable `log(1 + exp(x))`

Computes \(\log(1 + \exp(x))\) accurately for any real `x`, avoiding overflow as `x -> +Inf` and catastrophic cancellation as `x -> -Inf`.

Usage

log1pexp(x, c0 = -37, c1 = 18, c2 = 33.3)

Arguments

x

Numeric vector. `NA` values are preserved.

c0, c1, c2

Numeric scalars defining the switch points between four asymptotically optimal formulas. Defaults (-37, 18, 33.3) are from Mächler (2012) and should not normally be changed.

Value

A numeric vector the same length as `x` with \(\log(1 + \exp(x))\).

References

Mächler, M. (2012). *Accurately Computing log(1 − exp(− |a|)).* CRAN package `copula` vignette.

See also

log1mexp, log1p, expm1

Examples

x <- seq(-40, 40, by = 10)
cbind(x, log1p(exp(x)), log1pexp(x))
#>         x                          
#>  [1,] -40 4.248354e-18 4.248354e-18
#>  [2,] -30 9.357623e-14 9.357623e-14
#>  [3,] -20 2.061154e-09 2.061154e-09
#>  [4,] -10 4.539890e-05 4.539890e-05
#>  [5,]   0 6.931472e-01 6.931472e-01
#>  [6,]  10 1.000005e+01 1.000005e+01
#>  [7,]  20 2.000000e+01 2.000000e+01
#>  [8,]  30 3.000000e+01 3.000000e+01
#>  [9,]  40 4.000000e+01 4.000000e+01