From 3bbedcad3575a3193eccec067b98e19a38a21edf Mon Sep 17 00:00:00 2001
From: Simon Byrne <simonbyrne@gmail.com>
Date: Thu, 5 Nov 2020 13:41:26 -0800
Subject: [PATCH] Fix overflow for hypot in Float16

Fixes #38311
---
 base/math.jl | 15 +++++++++------
 1 file changed, 9 insertions(+), 6 deletions(-)

diff --git a/base/math.jl b/base/math.jl
index a9f259e854ee85..22c6a65d1c4bd0 100644
--- a/base/math.jl
+++ b/base/math.jl
@@ -661,12 +661,15 @@ function _hypot(x, y)
     end
 
     # Operands do not vary widely
-    scale = eps(typeof(ax))*sqrt(floatmin(ax))  #Rescaling constant
-    if ax > sqrt(floatmax(ax)/2)
-        ax = ax*scale
-        ay = ay*scale
-        scale = inv(scale)
-    elseif ay < sqrt(floatmin(ax))
+    L = sqrt(floatmin(ax))/2 # a power of 2, so inv(L) is exact
+    if ax > inv(L)
+        ax = ax*L
+        ay = ay*L
+        scale = inv(L) 
+    elseif ay < L
+        scale = L*eps(typeof(ax))
+        # inv(scale) would underflow in Float16
+        # is a power of 2, so should be optimized to a multplication by the compiler for other types
         ax = ax/scale
         ay = ay/scale
     else