diff --git a/docs/src/index.md b/docs/src/index.md
index 3c0a7f3..9454e0c 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -16,6 +16,7 @@ logistic
 logit
 logcosh
 logabssinh
+logabstanh
 log1psq
 log1pexp
 softplus
diff --git a/ext/LogExpFunctionsChainRulesCoreExt.jl b/ext/LogExpFunctionsChainRulesCoreExt.jl
index 397603a..28fe8fe 100644
--- a/ext/LogExpFunctionsChainRulesCoreExt.jl
+++ b/ext/LogExpFunctionsChainRulesCoreExt.jl
@@ -118,6 +118,7 @@ ChainRulesCore.@scalar_rule(logistic(x::Real), (Ω * (1 - Ω),))
 ChainRulesCore.@scalar_rule(logit(x::Real), (inv(x * (1 - x)),))
 ChainRulesCore.@scalar_rule(logcosh(x::Real), tanh(x))
 ChainRulesCore.@scalar_rule(logabssinh(x::Real), coth(x))
+ChainRulesCore.@scalar_rule(logabstanh(x::Real), inv(cosh(x) * sinh(x)))
 ChainRulesCore.@scalar_rule(log1psq(x::Real), (2 * x / (1 + x^2),))
 ChainRulesCore.@scalar_rule(log1pexp(x::Real), (logistic(x),))
 ChainRulesCore.@scalar_rule(log1mexp(x::Real), (-exp(x - Ω),))
diff --git a/src/LogExpFunctions.jl b/src/LogExpFunctions.jl
index 05287eb..cdb917b 100644
--- a/src/LogExpFunctions.jl
+++ b/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
 
 include("basicfuns.jl")
diff --git a/src/basicfuns.jl b/src/basicfuns.jl
index a9d7f2c..bd20aeb 100644
--- a/src/basicfuns.jl
+++ b/src/basicfuns.jl
@@ -218,6 +218,22 @@ end
 """
 $(SIGNATURES)
 
+Return `log(abs(tanh(x)))`, evaluated carefully.
+
+The implementation ensures `logabstanh(-x) = logabstanh(x)`.
+"""
+function logabstanh(x::Real)
+    a = abs(x)
+    if 8*a < 3
+        log(tanh(a))
+    else
+        log1p(-2/(exp(2*a)+1))
+    end
+end
+
+"""
+$(SIGNATURES)
+
 Return `log(1+x^2)` evaluated carefully for `abs(x)` very small or very large.
 """
 log1psq(x::Real) = log1p(abs2(x))
diff --git a/test/basicfuns.jl b/test/basicfuns.jl
index c16e2d1..cc5bccd 100644
--- a/test/basicfuns.jl
+++ b/test/basicfuns.jl
@@ -93,7 +93,7 @@ end
     end
 end
 
-@testset "logcosh and logabssinh" begin
+@testset "logcosh and logabssinh and logabstanh" begin
     for x in (randn(), randn(Float32))
         @test @inferred(logcosh(x)) isa typeof(x)
         @test logcosh(x) ≈ log(cosh(x))
@@ -101,21 +101,28 @@ end
         @test @inferred(logabssinh(x)) isa typeof(x)
         @test logabssinh(x) ≈ log(abs(sinh(x)))
         @test logabssinh(-x) == logabssinh(x)
+        @test @inferred(logabstanh(x)) isa typeof(x)
+        @test logabstanh(x) ≈ log(abs(tanh(x)))
+        @test logabstanh(-x) == logabstanh(x)
     end
 
     # special values
     for x in (-Inf, Inf, -Inf32, Inf32)
         @test @inferred(logcosh(x)) === oftype(x, Inf)
         @test @inferred(logabssinh(x)) === oftype(x, Inf)
+        @test @inferred(logabstanh(x)) === -oftype(x, 0)
     end
     for x in (NaN, NaN32)
         @test @inferred(logcosh(x)) === x
         @test @inferred(logabssinh(x)) === x
+        @test @inferred(logabstanh(x)) === x
     end
 
-    @testset "accuracy of `logcosh`" begin
+    @testset "accuracy" begin
         for t in (Float16, Float32, Float64)
-            @test ulp_error_maximum(logcosh, range(start = t(-3), stop = t(3), length = 1000)) < 3
+            ran = range(start = t(-3), stop = t(3), length = 1000)
+            @test ulp_error_maximum(logcosh, ran) < 3
+            @test ulp_error_maximum(logabstanh, ran) < 3
         end
     end
 end
diff --git a/test/chainrules.jl b/test/chainrules.jl
index f844d0b..c19ae93 100644
--- a/test/chainrules.jl
+++ b/test/chainrules.jl
@@ -64,6 +64,8 @@
         test_rrule(logcosh, x)
         test_frule(logabssinh, x)
         test_rrule(logabssinh, x)
+        test_frule(logabstanh, x)
+        test_rrule(logabstanh, x)
     end
 
     @testset "log1pexp" begin