generic log1pexp

src/basicfuns.jl

@@ -152,9 +152,39 @@ Return `log(1+exp(x))` evaluated carefully for largish `x`.
 
 This is also called the ["softplus"](https://en.wikipedia.org/wiki/Rectifier_(neural_networks))
 transformation, being a smooth approximation to `max(0,x)`. Its inverse is [`logexpm1`](@ref).
+
+Uses a fast implementation for floats based on Mächler (2012), available at:
+https://cran.r-project.org/web/packages/Rmpfr/vignettes/log1mexp-note.pdf.
 """
-log1pexp(x::Real) = x ≤ -37 ? exp(x) : x ≤ 18 ? log1p(exp(x)) : x ≤ 33.3 ? x + exp(-x) : float(x)
-log1pexp(x::Float32) = x < 9f0 ? log1p(exp(x)) : x < 16f0 ? x + exp(-x) : oftype(exp(-x), x)
+function log1pexp(x::Real)
+    t = log1p(exp(-abs(x)))
+    return x ≤ 0 ? t : t + x
+end
+
+function log1pexp(x::Union{Float16,Float32,Float64})
+	a, b, c = _log1pexp_branch_bounds(x)
+    if x ≤ a
+        return exp(x)
+    elseif x ≤ b
+        return log1p(exp(x))
+    elseif x ≤ c
+        return x + exp(-x)
+    else
+        return x
+    end
+end
+
+#=
+Given the `approx` used in a branch of log1pexp(x) above, we find the first `x` (from above
+or below) that is a root of
+
+    T(log1pexp(big(x))) - approx(T(x))
+
+This determines the branch bounds below.
+=#
+_log1pexp_branch_bounds(::Float64) = (-37, 18, 33.3)
+_log1pexp_branch_bounds(::Float32) = (-15, 9, 14.5)
+_log1pexp_branch_bounds(::Float16) = (-7, 3, 5.7)
 
 """
 $(SIGNATURES)

test/basicfuns.jl

@@ -110,10 +110,19 @@ end
 # log1pexp, log1mexp, log2mexp & logexpm1
 
 @testset "log1pexp" begin
-    # test every branch
-    for x in (0, 1, 2, 10, 20, 40), T in (Int, Float32, Float64)
-        @test (@inferred log1pexp(-T(x))) ≈ log1p(exp(big(-x)))
-        @test (@inferred log1pexp(+T(x))) ≈ log1p(exp(big(+x)))
+    # generic method
+    @test (@inferred log1pexp(big(0))) ≈ log(big(2))
+    for x in 1:10, s in (-1, 1)
+        @test (@inferred log1pexp(log(big(x)))) ≈ log(big(1 + x))
+        @test (@inferred log1pexp(-log(big(x)))) ≈ log(big(1 + 1//x))
+        @test (@inferred log1pexp(big(x))) ≈ log(1 + exp(big(x)))
+        @test (@inferred log1pexp(-big(x))) ≈ log(1 + exp(-big(x)))
+    end
+
+    # test branches of specialized approximations
+    for x in (0, 1, 2, 10, 15, 20, 40), T in (Float16, Float32, Float64)
+        @test (@inferred log1pexp(-T(x))) ≈ T(log1pexp(big(-x)))
+        @test (@inferred log1pexp(+T(x))) ≈ T(log1pexp(big(+x)))
     end
 
     # large arguments

test/chainrules.jl

@@ -57,14 +57,11 @@
         test_rrule(logcosh, x)
     end
 
-    # test all branches of `log1pexp`
-    for x in (-20.9, 15.4, 41.5)
-        test_frule(log1pexp, x)
-        test_rrule(log1pexp, x)
-    end
-    for x in (8.3f0, 12.5f0, 21.2f0)
-        test_frule(log1pexp, x; rtol=1f-3, atol=1f-3)
-        test_rrule(log1pexp, x; rtol=1f-3, atol=1f-3)
+    @testset "log1pexp" begin
+        for x in (0, 1, 2, 10, 15, 20, 40), s in (-1, 1)
+            test_scalar(log1pexp, Float64(s * x))
+            test_scalar(log1pexp, Float32(s * x); rtol=1f-3, atol=1f-3)
+        end
     end
 
     for x in (-10.2, -3.3, -0.3)