diff --git a/src/Quadmath.jl b/src/Quadmath.jl
index ca5fed3..0d2b8d7 100644
--- a/src/Quadmath.jl
+++ b/src/Quadmath.jl
@@ -465,7 +465,7 @@ end
 
 Float128(::Irrational{:π}) =  reinterpret(Float128, 0x4000921fb54442d18469898cc51701b8)
 Float128(::Irrational{:ℯ}) =  reinterpret(Float128, 0x40005bf0a8b1457695355fb8ac404e7a)
-Float128(x::Irrational{T}) where {T} = Float128(BigFloat(x))
+Float128(x::AbstractIrrational) = Float128(BigFloat(x; precision=128))
 
 import Base.MPFR
 
diff --git a/test/runtests.jl b/test/runtests.jl
index 49c81ac..4d60ead 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -202,11 +202,23 @@ end
     @test parse(Float128,"3.0") == Float128(3.0)
 end
 
+struct TwoPi <: AbstractIrrational
+end
+Base.BigFloat(::TwoPi; precision=precision(BigFloat)) =
+    setprecision(() -> 2 * big(π), BigFloat, precision)
+Base.Float64(x::TwoPi) = Float64(big(x))
+
 @testset "irrationals" begin
     tiny = 2eps(Float128(1))
-    @test abs(cos(Float128(pi)) + 1) < tiny
-    @test abs(log(Float128(ℯ)) - 1) < tiny
-    @test abs((2*Float128(MathConstants.golden) - 1)^2 - 5) < 5 * tiny
+    default = precision(BigFloat)
+    for prec in (default, 16)
+        setprecision(BigFloat, prec)
+        @test abs(cos(Float128(pi)) + 1) < tiny
+        @test abs(log(Float128(ℯ)) - 1) < tiny
+        @test abs((2*Float128(MathConstants.golden) - 1)^2 - 5) < 5 * tiny
+        @test abs(cos(Float128(TwoPi())) - 1) < tiny
+    end
+    setprecision(default)
 end
 
 @testset "rationals" begin