faster hypot for Float32 and Float16 (JuliaLang#42122)

* faster hypot for Float32 and Float16

base/math.jl

@@ -702,7 +702,20 @@ 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...)