diff --git a/base/math.jl b/base/math.jl
index 3857b1b1e8c10..b972403381d2b 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -696,7 +696,20 @@ function _hypot(x, y)
     end
     return h*scale*oneunit(axu)
 end
-_hypot(x::Float16, y::Float16) = Float16(_hypot(Float32(x), Float32(y)))
+@inline function _hypot(x::Float32, y::Float32)
+    if isinf(x) || isinf(y)
+        return Inf32
+    end
+    _x, _y = Float64(x), Float64(y)
+    return Float32(sqrt(muladd(_x, _x, _y*_y)))
+end
+@inline function _hypot(x::Float16, y::Float16)
+    if isinf(x) || isinf(y)
+        return Inf16
+    end
+    _x, _y = Float32(x), Float32(y)
+    return Float16(sqrt(muladd(_x, _x, _y*_y)))
+end
 _hypot(x::ComplexF16, y::ComplexF16) = Float16(_hypot(ComplexF32(x), ComplexF32(y)))
 
 function _hypot(x...)