Merge pull request #99 from nsajko/logit_accuracy

fix accuracy of `logit`

Author: tpapp

src/basicfuns.jl

@@ -120,7 +120,13 @@ for ``0 < x < 1``.
 
 Its inverse is the [`logistic`](@ref) function.
 """
-logit(x::Real) = log(x / (one(x) - x))
+function logit(x::Real)
+    if 4 * x < 1
+        -log(inv(x) - 1)
+    else
+        2 * atanh(2*x - 1)
+    end
+end
 
 """
 $(SIGNATURES)

test/basicfuns.jl

@@ -86,6 +86,11 @@ end
     @test logistic(+750.0) === 1.0
     @test iszero(logit(0.5))
     @test logit(logistic(2)) ≈ 2.0
+    @testset "accuracy of `logit`" begin
+        for t in (Float16, Float32, Float64)
+            @test 2 * ulp_error_maximum(logit, range(start = t(0), stop = t(1), length = 500)) < 3
+        end
+    end
 end
 
 @testset "logcosh and logabssinh" begin