xexpx, xexpy

docs/src/index.md

@@ -10,6 +10,8 @@ LogExpFunctions supports [`InverseFunctions.inverse`](https://github.com/JuliaMa
 xlogx
 xlogy
 xlog1py
+xexpx
+xexpy
 logistic
 logit
 logcosh

src/LogExpFunctions.jl

@@ -9,7 +9,7 @@ import InverseFunctions
 import IrrationalConstants
 import LinearAlgebra
 
-export xlogx, xlogy, xlog1py, logistic, logit, log1psq, log1pexp, log1mexp, log2mexp, logexpm1,
+export xlogx, xlogy, xlog1py, xexpx, xexpy, logistic, logit, log1psq, log1pexp, log1mexp, log2mexp, logexpm1,
     softplus, invsoftplus, log1pmx, logmxp1, logaddexp, logsubexp, logsumexp, softmax,
     softmax!, logcosh
 

src/basicfuns.jl

@@ -44,6 +44,31 @@ function xlog1py(x::Number, y::Number)
     return iszero(x) && !isnan(y) ? zero(result) : result
 end
 
+"""
+$(SIGNATURES)
+
+Return `x * exp(x)` for `x > -Inf`, handling `x = -Inf` by taking the downward limit.
+
+```jldoctest
+julia> xexpx(-Inf)
+0.0
+```
+"""
+xexpx(x::Real) = isfinite(x) ? x * exp(x) : exp(x)
+
+"""
+$(SIGNATURES)
+
+Return `x * exp(y)` for `y > -Inf`, handling `y = -Inf` by taking the downward limit.
+
+```jldoctest
+julia> xexpy(1.0, -Inf)
+0.0
+```
+"""
+xexpy(x::T, y::T) where {T<:Real} = isnan(x) || isfinite(y) ? x * exp(y) : exp(y)
+xexpy(x::Real, y::Real) = xexpy(promote(x, y)...)
+
 # The following bounds are precomputed versions of the following abstract
 # function, but the implicit interface for AbstractFloat doesn't uniformly
 # enforce that all floating point types implement nextfloat and prevfloat.

test/basicfuns.jl

@@ -44,6 +44,37 @@
     @test iszero(xlog1py(0 + im * 0, -1 + im * Inf))
 end
 
+@testset "xexpx" begin
+    @test iszero(xexpx(-Inf))
+    @test iszero(xexpx(0))
+    @test isnan(xexpx(NaN))
+
+    @test xexpx(1) ≈ exp(1)
+    @test xexpx(2) ≈ 2exp(2)
+
+    @inferred xexpx(0)
+    @inferred xexpx(0.)
+    @inferred xexpx(0f0)
+end
+
+@testset "xexpy" begin
+    @test iszero(xexpy(Inf, -Inf))
+
+    @test isnan(xexpy(NaN, -Inf))
+    @test isnan(xexpy(NaN, 1))
+    @test isnan(xexpy(0, NaN))
+
+    @inferred xexpy(0,-Inf)
+    @inferred xexpy(1,1)
+    @inferred xexpy(1.,-Inf)
+
+    @test xexpy(2,3) ≈ 2exp(3)
+
+    for x = -10:10, y = -10:10
+        @test xexpy(x,y) ≈ x * exp(y)
+    end
+end
+
 @testset "logistic & logit" begin
     @test logistic(2) ≈ 1.0 / (1.0 + exp(-2.0))
     @test logistic(-750.0) === 0.0