Add log(-log(1 - x)) and 1 - exp(-exp(x)) (#56)

Author: ararslan

docs/src/index.md

@@ -28,4 +28,6 @@ logsumexp
 logsumexp!
 softmax!
 softmax
+cloglog
+cexpexp
 ```

src/LogExpFunctions.jl

@@ -11,7 +11,7 @@ import LinearAlgebra
 
 export xlogx, xlogy, xlog1py, xexpx, xexpy, logistic, logit, log1psq, log1pexp, log1mexp, log2mexp, logexpm1,
     softplus, invsoftplus, log1pmx, logmxp1, logaddexp, logsubexp, logsumexp, logsumexp!, softmax,
-    softmax!, logcosh
+    softmax!, logcosh, cloglog, cexpexp
 
 include("basicfuns.jl")
 include("logsumexp.jl")

src/basicfuns.jl

@@ -407,3 +407,17 @@ function _softmax!(r, x, dims)
     end
     return r
 end
+
+"""
+$(SIGNATURES)
+
+Compute the complementary log-log, `log(-log(1 - x))`.
+"""
+cloglog(x) = log(-log1p(-x))
+
+"""
+$(SIGNATURES)
+
+Compute the complementary double exponential, `1 - exp(-exp(x))`.
+"""
+cexpexp(x) = -expm1(-exp(x))

src/chainrules.jl

@@ -163,3 +163,6 @@ function ChainRulesCore.rrule(::typeof(softmax), x::AbstractArray{<:Real}; dims=
     end
     return Ω, softmax_pullback
 end
+
+ChainRulesCore.@scalar_rule(cloglog(x), (-inv((1 - x) * log1p(-x)),))
+ChainRulesCore.@scalar_rule(cexpexp(x), (-xexpx(-exp(x)),))

src/inverse.jl

@@ -7,3 +7,6 @@ InverseFunctions.inverse(::typeof(log2mexp)) = log2mexp
 
 InverseFunctions.inverse(::typeof(logit)) = logistic
 InverseFunctions.inverse(::typeof(logistic)) = logit
+
+InverseFunctions.inverse(::typeof(cloglog)) = cexpexp
+InverseFunctions.inverse(::typeof(cexpexp)) = cloglog

test/basicfuns.jl

@@ -410,3 +410,27 @@ end
     @test axes(s, 1) == OffsetArrays.IdOffsetRange(-2:0)
     @test collect(s) ≈ softmax(1:3)
 end
+
+@testset "cloglog and cexpexp" begin
+    cloglog_big(x::T) where {T} = T(log(-log(1 - BigFloat(x))))
+    cexpexp_big(x::T) where {T} = 1 - exp(-exp(BigFloat(x)))
+
+    for x in 0.1:0.1:0.9
+        @test cloglog(x) ≈ cloglog_big(x)
+        @test cexpexp(x) ≈ cexpexp_big(x)
+    end
+    for _ in 1:10
+        randf = rand(Float64)
+        @test cloglog(randf) ≈ cloglog_big(randf)
+        randi = rand(Int)
+        @test cexpexp(randi) ≈ cexpexp_big(randi)
+    end
+
+    @test cloglog(0) == -Inf
+    @test cloglog(1) == Inf
+    @test cloglog((ℯ - 1) / ℯ) == 0
+
+    @test cexpexp(Inf) == 1.0
+    @test cexpexp(-Inf) == 0.0
+    @test cexpexp(0) == (ℯ - 1) / ℯ
+end

test/chainrules.jl

@@ -112,4 +112,8 @@
             test_rrule(softmax, x; fkwargs=(dims=dims,))
         end
     end
+
+    test_scalar(cloglog, rand())
+
+    test_scalar(cexpexp, rand())
 end

test/inverse.jl

@@ -8,4 +8,7 @@
 
     InverseFunctions.test_inverse(logistic, randn())
     InverseFunctions.test_inverse(logit, rand())
+
+    InverseFunctions.test_inverse(cloglog, rand())
+    InverseFunctions.test_inverse(cexpexp, rand())
 end