add logabstanh

src/LogExpFunctions.jl

@@ -8,7 +8,7 @@ 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, logabssinh, cloglog, cexpexp,
+    softmax!, logcosh, logabssinh, logabstanh, cloglog, cexpexp,
     loglogistic, logitexp, log1mlogistic, logit1mexp
 
 # expm1(::Float16) is not defined in older Julia versions,

src/basicfuns.jl

@@ -149,6 +149,31 @@ end
 """
 $(SIGNATURES)
 
+Return `log(abs(tanh(x)))`, carefully evaluated without intermediate calculation of `tanh(x)`.
+
+The implementation ensures `logabstanh(-x) = logabstanh(x)`.
+"""
+function logabstanh(x::Real)
+    return log1p(-2/(exp(2*abs(x))+1))
+end
+function logabstanh(x::Float32)
+    abs_x = abs(x)
+    if abs_x < 0.0625f0
+        return log(abs_x) - x^2/3
+    end
+    return log1p(-2/(exp(2*abs_x)+1))
+end
+function logabstanh(x::Float64)
+    abs_x = abs(x)
+    if abs_x < 0x1p-5
+        return log(abs_x) + evalpoly(x*x, (0, -1/3, 7/90, -62/2835))
+    end
+    return log1p(-2/(exp(2*abs_x)+1))
+end
+
+"""
+$(SIGNATURES)
+
 Return `log(1+x^2)` evaluated carefully for `abs(x)` very small or very large.
 """
 log1psq(x::Real) = log1p(abs2(x))