diff --git a/core/math/integers/integers-tests.factor b/core/math/integers/integers-tests.factor
index b477b00a2f..1204e5b929 100644
--- a/core/math/integers/integers-tests.factor
+++ b/core/math/integers/integers-tests.factor
@@ -226,6 +226,29 @@ unit-test
 [ -0x1.0p55 ] [ -0x7f,ffff,ffff,ffff >bignum 1 /f ] unit-test
 [ -0x1.0p55 ] [ 0x7f,ffff,ffff,ffff >bignum -1 /f ] unit-test
 
+[ 0x1.0000,0000,0000,0p56 ] [ 0x100,0000,0000,0007 >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,0p56 ] [ -0x100,0000,0000,0007 >bignum -1 /f ] unit-test
+[ 0x1.0000,0000,0000,0p120 ] [ 0x100,0000,0000,0007,FFFF,FFFF,FFFF,FFFF >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,0p120 ] [ -0x100,0000,0000,0007,FFFF,FFFF,FFFF,FFFF >bignum -1 /f ] unit-test
+[ 0x1.0000,0000,0000,0p56 ] [ 0x100,0000,0000,0008 >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,0p56 ] [ -0x100,0000,0000,0008 >bignum -1 /f ] unit-test
+[ 0x1.0000,0000,0000,1p56 ] [ 0x100,0000,0000,0009 >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,1p56 ] [ -0x100,0000,0000,0009 >bignum -1 /f ] unit-test
+[ 0x1.0000,0000,0000,1p120 ] [ 0x100,0000,0000,0008,0000,0000,0000,0001 >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,1p120 ] [ -0x100,0000,0000,0008,0000,0000,0000,0001 >bignum -1 /f ] unit-test
+
+! Ensure that /f rounds to even on tie
+[ 0x1.0000,0000,0000,1p56 ] [ 0x100,0000,0000,0017 >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,1p56 ] [ -0x100,0000,0000,0017 >bignum -1 /f ] unit-test
+[ 0x1.0000,0000,0000,1p120 ] [ 0x100,0000,0000,0017,FFFF,FFFF,FFFF,FFFF >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,1p120 ] [ -0x100,0000,0000,0017,FFFF,FFFF,FFFF,FFFF >bignum -1 /f ] unit-test
+[ 0x1.0000,0000,0000,2p56 ] [ 0x100,0000,0000,0018 >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,2p56 ] [ -0x100,0000,0000,0018 >bignum -1 /f ] unit-test
+[ 0x1.0000,0000,0000,2p56 ] [ 0x100,0000,0000,0019 >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,2p56 ] [ -0x100,0000,0000,0019 >bignum -1 /f ] unit-test
+[ 0x1.0000,0000,0000,2p120 ] [ 0x100,0000,0000,0018,0000,0000,0000,0001 >bignum 1 /f ] unit-test
+[ 0x1.0000,0000,0000,2p120 ] [ -0x100,0000,0000,0018,0000,0000,0000,0001 >bignum -1 /f ] unit-test
+
 [ 17 ] [ 17 >bignum 5 max ] unit-test
 [ 5 ] [ 17 >bignum 5 min ] unit-test
 
diff --git a/core/math/parser/parser-tests.factor b/core/math/parser/parser-tests.factor
index 80270923cc..ad396555ac 100644
--- a/core/math/parser/parser-tests.factor
+++ b/core/math/parser/parser-tests.factor
@@ -289,3 +289,47 @@ unit-test
 ! #372
 ! hex float requires exponent
 [ f ] [ "0x1.0" string>number ] unit-test
+
+! hex float rounds to even on half
+[ 0x1.0000,0000,0000,0p0 ] [ "0x1.0000,0000,0000,0,8p0" string>number ] unit-test
+[ 0x1.0000,0000,0000,2p0 ] [ "0x1.0000,0000,0000,1,8p0" string>number ] unit-test
+[ 0x1.0000,0000,0000,0p0 ] [ "0x8.0000,0000,0000,4p-3" string>number ] unit-test
+[ 0x1.0000,0000,0000,2p0 ] [ "0x8.0000,0000,0000,Cp-3" string>number ] unit-test
+
+[ -0x1.0000,0000,0000,0p0 ] [ "-0x1.0000,0000,0000,0,8p0" string>number ] unit-test
+[ -0x1.0000,0000,0000,2p0 ] [ "-0x1.0000,0000,0000,1,8p0" string>number ] unit-test
+[ -0x1.0000,0000,0000,0p0 ] [ "-0x8.0000,0000,0000,4p-3" string>number ] unit-test
+[ -0x1.0000,0000,0000,2p0 ] [ "-0x8.0000,0000,0000,Cp-3" string>number ] unit-test
+
+! hex float rounds to nearest with tiny epsilons
+[ 0x1.0000,0000,0000,0p0 ] [ "0x1.0000,0000,0000,0,4p0" string>number ] unit-test
+[ 0x1.0000,0000,0000,0p0 ] [ "0x1.0000,0000,0000,0,7Fp0" string>number ] unit-test
+[ 0x1.0000,0000,0000,0p0 ] [ "0x1.0000,0000,0000,0,7FFF,FFFF,FFFF,FFFFp0" string>number ] unit-test
+
+[ 0x1.0000,0000,0000,1p0 ] [ "0x1.0000,0000,0000,0,Cp0" string>number ] unit-test
+[ 0x1.0000,0000,0000,1p0 ] [ "0x1.0000,0000,0000,0,81p0" string>number ] unit-test
+[ 0x1.0000,0000,0000,1p0 ] [ "0x1.0000,0000,0000,0,8000,0000,0000,0001p0" string>number ] unit-test
+
+[ 0x1.0000,0000,0000,1p0 ] [ "0x1.0000,0000,0000,1,4p0" string>number ] unit-test
+[ 0x1.0000,0000,0000,1p0 ] [ "0x1.0000,0000,0000,1,7Fp0" string>number ] unit-test
+[ 0x1.0000,0000,0000,1p0 ] [ "0x1.0000,0000,0000,1,7FFF,FFFF,FFFF,FFFFp0" string>number ] unit-test
+
+[ 0x1.0000,0000,0000,2p0 ] [ "0x1.0000,0000,0000,1,Cp0" string>number ] unit-test
+[ 0x1.0000,0000,0000,2p0 ] [ "0x1.0000,0000,0000,1,81p0" string>number ] unit-test
+[ 0x1.0000,0000,0000,2p0 ] [ "0x1.0000,0000,0000,1,8000,0000,0000,0001p0" string>number ] unit-test
+
+[ -0x1.0000,0000,0000,0p0 ] [ "-0x1.0000,0000,0000,0,4p0" string>number ] unit-test
+[ -0x1.0000,0000,0000,0p0 ] [ "-0x1.0000,0000,0000,0,7Fp0" string>number ] unit-test
+[ -0x1.0000,0000,0000,0p0 ] [ "-0x1.0000,0000,0000,0,7FFF,FFFF,FFFF,FFFFp0" string>number ] unit-test
+
+[ -0x1.0000,0000,0000,1p0 ] [ "-0x1.0000,0000,0000,0,Cp0" string>number ] unit-test
+[ -0x1.0000,0000,0000,1p0 ] [ "-0x1.0000,0000,0000,0,81p0" string>number ] unit-test
+[ -0x1.0000,0000,0000,1p0 ] [ "-0x1.0000,0000,0000,0,8000,0000,0000,0001p0" string>number ] unit-test
+
+[ -0x1.0000,0000,0000,1p0 ] [ "-0x1.0000,0000,0000,1,4p0" string>number ] unit-test
+[ -0x1.0000,0000,0000,1p0 ] [ "-0x1.0000,0000,0000,1,7Fp0" string>number ] unit-test
+[ -0x1.0000,0000,0000,1p0 ] [ "-0x1.0000,0000,0000,1,7FFF,FFFF,FFFF,FFFFp0" string>number ] unit-test
+
+[ -0x1.0000,0000,0000,2p0 ] [ "-0x1.0000,0000,0000,1,Cp0" string>number ] unit-test
+[ -0x1.0000,0000,0000,2p0 ] [ "-0x1.0000,0000,0000,1,81p0" string>number ] unit-test
+[ -0x1.0000,0000,0000,2p0 ] [ "-0x1.0000,0000,0000,1,8000,0000,0000,0001p0" string>number ] unit-test