diff --git a/build/Linux-386-GCC/Makefile b/build/Linux-386-GCC/Makefile
index faeb3972..24d9b735 100644
--- a/build/Linux-386-GCC/Makefile
+++ b/build/Linux-386-GCC/Makefile
@@ -133,6 +133,9 @@ OBJS_OTHERS = \
   s_tryPropagateNaNExtF80M$(OBJ) \
   s_invalidExtF80M$(OBJ) \
   s_normExtF80SigM$(OBJ) \
+  s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80M$(OBJ) \
+  s_canonicalizeExtF80MUI$(OBJ) \
   s_roundPackMToExtF80M$(OBJ) \
   s_normRoundPackMToExtF80M$(OBJ) \
   s_addExtF80M$(OBJ) \
diff --git a/build/Linux-386-SSE2-GCC/Makefile b/build/Linux-386-SSE2-GCC/Makefile
index ced977b6..b041561d 100644
--- a/build/Linux-386-SSE2-GCC/Makefile
+++ b/build/Linux-386-SSE2-GCC/Makefile
@@ -133,6 +133,9 @@ OBJS_OTHERS = \
   s_tryPropagateNaNExtF80M$(OBJ) \
   s_invalidExtF80M$(OBJ) \
   s_normExtF80SigM$(OBJ) \
+  s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80M$(OBJ) \
+  s_canonicalizeExtF80MUI$(OBJ) \
   s_roundPackMToExtF80M$(OBJ) \
   s_normRoundPackMToExtF80M$(OBJ) \
   s_addExtF80M$(OBJ) \
diff --git a/build/Linux-ARM-VFPv2-GCC/Makefile b/build/Linux-ARM-VFPv2-GCC/Makefile
index a1e7c830..23252179 100644
--- a/build/Linux-ARM-VFPv2-GCC/Makefile
+++ b/build/Linux-ARM-VFPv2-GCC/Makefile
@@ -131,6 +131,9 @@ OBJS_OTHERS = \
   s_tryPropagateNaNExtF80M$(OBJ) \
   s_invalidExtF80M$(OBJ) \
   s_normExtF80SigM$(OBJ) \
+  s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80M$(OBJ) \
+  s_canonicalizeExtF80MUI$(OBJ) \
   s_roundPackMToExtF80M$(OBJ) \
   s_normRoundPackMToExtF80M$(OBJ) \
   s_addExtF80M$(OBJ) \
diff --git a/build/Linux-RISCV64-GCC/Makefile b/build/Linux-RISCV64-GCC/Makefile
index 72e1f632..fa34548e 100644
--- a/build/Linux-RISCV64-GCC/Makefile
+++ b/build/Linux-RISCV64-GCC/Makefile
@@ -140,6 +140,8 @@ OBJS_OTHERS = \
   s_subMagsF64$(OBJ) \
   s_mulAddF64$(OBJ) \
   s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80$(OBJ) \
+  s_canonicalizeExtF80UI$(OBJ) \
   s_roundPackToExtF80$(OBJ) \
   s_normRoundPackToExtF80$(OBJ) \
   s_addMagsExtF80$(OBJ) \
diff --git a/build/Linux-x86_64-GCC/Makefile b/build/Linux-x86_64-GCC/Makefile
index 72f251a5..b7744aef 100644
--- a/build/Linux-x86_64-GCC/Makefile
+++ b/build/Linux-x86_64-GCC/Makefile
@@ -137,6 +137,8 @@ OBJS_OTHERS = \
   s_subMagsF64$(OBJ) \
   s_mulAddF64$(OBJ) \
   s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80$(OBJ) \
+  s_canonicalizeExtF80UI$(OBJ) \
   s_roundPackToExtF80$(OBJ) \
   s_normRoundPackToExtF80$(OBJ) \
   s_addMagsExtF80$(OBJ) \
diff --git a/build/Win32-MinGW/Makefile b/build/Win32-MinGW/Makefile
index faeb3972..24d9b735 100644
--- a/build/Win32-MinGW/Makefile
+++ b/build/Win32-MinGW/Makefile
@@ -133,6 +133,9 @@ OBJS_OTHERS = \
   s_tryPropagateNaNExtF80M$(OBJ) \
   s_invalidExtF80M$(OBJ) \
   s_normExtF80SigM$(OBJ) \
+  s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80M$(OBJ) \
+  s_canonicalizeExtF80MUI$(OBJ) \
   s_roundPackMToExtF80M$(OBJ) \
   s_normRoundPackMToExtF80M$(OBJ) \
   s_addExtF80M$(OBJ) \
diff --git a/build/Win32-SSE2-MinGW/Makefile b/build/Win32-SSE2-MinGW/Makefile
index ced977b6..b041561d 100644
--- a/build/Win32-SSE2-MinGW/Makefile
+++ b/build/Win32-SSE2-MinGW/Makefile
@@ -133,6 +133,9 @@ OBJS_OTHERS = \
   s_tryPropagateNaNExtF80M$(OBJ) \
   s_invalidExtF80M$(OBJ) \
   s_normExtF80SigM$(OBJ) \
+  s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80M$(OBJ) \
+  s_canonicalizeExtF80MUI$(OBJ) \
   s_roundPackMToExtF80M$(OBJ) \
   s_normRoundPackMToExtF80M$(OBJ) \
   s_addExtF80M$(OBJ) \
diff --git a/build/Win64-MinGW-w64/Makefile b/build/Win64-MinGW-w64/Makefile
index cc5bc0c5..d3686ccb 100644
--- a/build/Win64-MinGW-w64/Makefile
+++ b/build/Win64-MinGW-w64/Makefile
@@ -133,6 +133,8 @@ OBJS_OTHERS = \
   s_subMagsF64$(OBJ) \
   s_mulAddF64$(OBJ) \
   s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80$(OBJ) \
+  s_canonicalizeExtF80UI$(OBJ) \
   s_roundPackToExtF80$(OBJ) \
   s_normRoundPackToExtF80$(OBJ) \
   s_addMagsExtF80$(OBJ) \
diff --git a/build/template-FAST_INT64/Makefile b/build/template-FAST_INT64/Makefile
index e04c2160..867674a0 100644
--- a/build/template-FAST_INT64/Makefile
+++ b/build/template-FAST_INT64/Makefile
@@ -136,6 +136,8 @@ OBJS_OTHERS = \
   s_subMagsF64$(OBJ) \
   s_mulAddF64$(OBJ) \
   s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80$(OBJ) \
+  s_canonicalizeExtF80UI$(OBJ) \
   s_roundPackToExtF80$(OBJ) \
   s_normRoundPackToExtF80$(OBJ) \
   s_addMagsExtF80$(OBJ) \
diff --git a/build/template-not-FAST_INT64/Makefile b/build/template-not-FAST_INT64/Makefile
index 48b2cd6b..33d79759 100644
--- a/build/template-not-FAST_INT64/Makefile
+++ b/build/template-not-FAST_INT64/Makefile
@@ -133,6 +133,9 @@ OBJS_OTHERS = \
   s_tryPropagateNaNExtF80M$(OBJ) \
   s_invalidExtF80M$(OBJ) \
   s_normExtF80SigM$(OBJ) \
+  s_normSubnormalExtF80Sig$(OBJ) \
+  s_canonicalizeExtF80M$(OBJ) \
+  s_canonicalizeExtF80MUI$(OBJ) \
   s_roundPackMToExtF80M$(OBJ) \
   s_normRoundPackMToExtF80M$(OBJ) \
   s_addExtF80M$(OBJ) \
diff --git a/source/extF80M_eq.c b/source/extF80M_eq.c
index 24800371..533c28eb 100644
--- a/source/extF80M_eq.c
+++ b/source/extF80M_eq.c
@@ -70,6 +70,8 @@ bool extF80M_eq( const extFloat80_t *aPtr, const extFloat80_t *bPtr )
     uiA0  = aSPtr->signif;
     uiB64 = bSPtr->signExp;
     uiB0  = bSPtr->signif;
+    softfloat_canonicalizeExtF80MUI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80MUI( &uiB64, &uiB0 );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( isNaNExtF80UI( uiA64, uiA0 ) || isNaNExtF80UI( uiB64, uiB0 ) ) {
diff --git a/source/extF80M_eq_signaling.c b/source/extF80M_eq_signaling.c
index 785eba1e..81b31ab9 100644
--- a/source/extF80M_eq_signaling.c
+++ b/source/extF80M_eq_signaling.c
@@ -69,6 +69,8 @@ bool extF80M_eq_signaling( const extFloat80_t *aPtr, const extFloat80_t *bPtr )
     uiA0  = aSPtr->signif;
     uiB64 = bSPtr->signExp;
     uiB0  = bSPtr->signif;
+    softfloat_canonicalizeExtF80MUI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80MUI( &uiB64, &uiB0 );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( isNaNExtF80UI( uiA64, uiA0 ) || isNaNExtF80UI( uiB64, uiB0 ) ) {
diff --git a/source/extF80M_le.c b/source/extF80M_le.c
index 24edae87..a164f97b 100644
--- a/source/extF80M_le.c
+++ b/source/extF80M_le.c
@@ -70,6 +70,8 @@ bool extF80M_le( const extFloat80_t *aPtr, const extFloat80_t *bPtr )
     uiA0  = aSPtr->signif;
     uiB64 = bSPtr->signExp;
     uiB0  = bSPtr->signif;
+    softfloat_canonicalizeExtF80MUI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80MUI( &uiB64, &uiB0 );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( isNaNExtF80UI( uiA64, uiA0 ) || isNaNExtF80UI( uiB64, uiB0 ) ) {
diff --git a/source/extF80M_le_quiet.c b/source/extF80M_le_quiet.c
index 3880e36d..16e4ee4c 100644
--- a/source/extF80M_le_quiet.c
+++ b/source/extF80M_le_quiet.c
@@ -71,6 +71,8 @@ bool extF80M_le_quiet( const extFloat80_t *aPtr, const extFloat80_t *bPtr )
     uiA0  = aSPtr->signif;
     uiB64 = bSPtr->signExp;
     uiB0  = bSPtr->signif;
+    softfloat_canonicalizeExtF80MUI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80MUI( &uiB64, &uiB0 );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( isNaNExtF80UI( uiA64, uiA0 ) || isNaNExtF80UI( uiB64, uiB0 ) ) {
diff --git a/source/extF80M_lt.c b/source/extF80M_lt.c
index 70fa8f05..ec9a33a6 100644
--- a/source/extF80M_lt.c
+++ b/source/extF80M_lt.c
@@ -70,6 +70,8 @@ bool extF80M_lt( const extFloat80_t *aPtr, const extFloat80_t *bPtr )
     uiA0  = aSPtr->signif;
     uiB64 = bSPtr->signExp;
     uiB0  = bSPtr->signif;
+    softfloat_canonicalizeExtF80MUI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80MUI( &uiB64, &uiB0 );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( isNaNExtF80UI( uiA64, uiA0 ) || isNaNExtF80UI( uiB64, uiB0 ) ) {
diff --git a/source/extF80M_lt_quiet.c b/source/extF80M_lt_quiet.c
index b119af30..385e358c 100644
--- a/source/extF80M_lt_quiet.c
+++ b/source/extF80M_lt_quiet.c
@@ -71,6 +71,8 @@ bool extF80M_lt_quiet( const extFloat80_t *aPtr, const extFloat80_t *bPtr )
     uiA0  = aSPtr->signif;
     uiB64 = bSPtr->signExp;
     uiB0  = bSPtr->signif;
+    softfloat_canonicalizeExtF80MUI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80MUI( &uiB64, &uiB0 );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( isNaNExtF80UI( uiA64, uiA0 ) || isNaNExtF80UI( uiB64, uiB0 ) ) {
diff --git a/source/extF80M_rem.c b/source/extF80M_rem.c
index 065e271a..18355e93 100644
--- a/source/extF80M_rem.c
+++ b/source/extF80M_rem.c
@@ -79,6 +79,10 @@ void
     uiA64 = aSPtr->signExp;
     expA = expExtF80UI64( uiA64 );
     expB = expExtF80UI64( bSPtr->signExp );
+    sigA = aSPtr->signif;
+    x64 = bSPtr->signif;
+    softfloat_canonicalizeExtF80M( &expA, &sigA );
+    softfloat_canonicalizeExtF80M( &expB, &x64 );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( (expA == 0x7FFF) || (expB == 0x7FFF) ) {
@@ -95,14 +99,12 @@ void
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( ! expB ) expB = 1;
-    x64 = bSPtr->signif;
     if ( ! (x64 & UINT64_C( 0x8000000000000000 )) ) {
         if ( ! x64 ) goto invalid;
         expB += softfloat_normExtF80SigM( &x64 );
     }
     signRem = signExtF80UI64( uiA64 );
     if ( ! expA ) expA = 1;
-    sigA = aSPtr->signif;
     if ( ! (sigA & UINT64_C( 0x8000000000000000 )) ) {
         if ( ! sigA ) {
             expA = 0;
diff --git a/source/extF80M_to_i32.c b/source/extF80M_to_i32.c
index c0464b13..e8b7046d 100644
--- a/source/extF80M_to_i32.c
+++ b/source/extF80M_to_i32.c
@@ -72,6 +72,7 @@ int_fast32_t
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig = aSPtr->signif;
+    softfloat_canonicalizeExtF80M( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x4032 - exp;
diff --git a/source/extF80M_to_i64.c b/source/extF80M_to_i64.c
index 2e07207a..892dba80 100644
--- a/source/extF80M_to_i64.c
+++ b/source/extF80M_to_i64.c
@@ -73,6 +73,7 @@ int_fast64_t
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig = aSPtr->signif;
+    softfloat_canonicalizeExtF80M( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x403E - exp;
diff --git a/source/extF80M_to_ui32.c b/source/extF80M_to_ui32.c
index 72579e41..9a9a01d7 100644
--- a/source/extF80M_to_ui32.c
+++ b/source/extF80M_to_ui32.c
@@ -72,6 +72,7 @@ uint_fast32_t
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig = aSPtr->signif;
+    softfloat_canonicalizeExtF80M( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x4032 - exp;
diff --git a/source/extF80M_to_ui64.c b/source/extF80M_to_ui64.c
index a7ee39fb..53bbdfb3 100644
--- a/source/extF80M_to_ui64.c
+++ b/source/extF80M_to_ui64.c
@@ -73,6 +73,7 @@ uint_fast64_t
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig = aSPtr->signif;
+    softfloat_canonicalizeExtF80M( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x403E - exp;
diff --git a/source/extF80_eq.c b/source/extF80_eq.c
index 60f29daf..e2034921 100644
--- a/source/extF80_eq.c
+++ b/source/extF80_eq.c
@@ -65,6 +65,8 @@ bool extF80_eq( extFloat80_t a, extFloat80_t b )
         }
         return false;
     }
+    softfloat_canonicalizeExtF80UI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80UI( &uiB64, &uiB0 );
     return
            (uiA0 == uiB0)
         && ((uiA64 == uiB64) || (! uiA0 && ! ((uiA64 | uiB64) & 0x7FFF)));
diff --git a/source/extF80_eq_signaling.c b/source/extF80_eq_signaling.c
index 5a0dfe4a..45d8b862 100644
--- a/source/extF80_eq_signaling.c
+++ b/source/extF80_eq_signaling.c
@@ -59,6 +59,8 @@ bool extF80_eq_signaling( extFloat80_t a, extFloat80_t b )
         softfloat_raiseFlags( softfloat_flag_invalid );
         return false;
     }
+    softfloat_canonicalizeExtF80UI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80UI( &uiB64, &uiB0 );
     return
            (uiA0 == uiB0)
         && ((uiA64 == uiB64) || (! uiA0 && ! ((uiA64 | uiB64) & 0x7FFF)));
diff --git a/source/extF80_le.c b/source/extF80_le.c
index 2a1ee60f..dd352954 100644
--- a/source/extF80_le.c
+++ b/source/extF80_le.c
@@ -61,6 +61,8 @@ bool extF80_le( extFloat80_t a, extFloat80_t b )
         softfloat_raiseFlags( softfloat_flag_invalid );
         return false;
     }
+    softfloat_canonicalizeExtF80UI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80UI( &uiB64, &uiB0 );
     signA = signExtF80UI64( uiA64 );
     signB = signExtF80UI64( uiB64 );
     return
diff --git a/source/extF80_le_quiet.c b/source/extF80_le_quiet.c
index 5d0c3ae7..62309bad 100644
--- a/source/extF80_le_quiet.c
+++ b/source/extF80_le_quiet.c
@@ -66,6 +66,8 @@ bool extF80_le_quiet( extFloat80_t a, extFloat80_t b )
         }
         return false;
     }
+    softfloat_canonicalizeExtF80UI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80UI( &uiB64, &uiB0 );
     signA = signExtF80UI64( uiA64 );
     signB = signExtF80UI64( uiB64 );
     return
diff --git a/source/extF80_lt.c b/source/extF80_lt.c
index 9560d8ec..400ce084 100644
--- a/source/extF80_lt.c
+++ b/source/extF80_lt.c
@@ -61,6 +61,8 @@ bool extF80_lt( extFloat80_t a, extFloat80_t b )
         softfloat_raiseFlags( softfloat_flag_invalid );
         return false;
     }
+    softfloat_canonicalizeExtF80UI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80UI( &uiB64, &uiB0 );
     signA = signExtF80UI64( uiA64 );
     signB = signExtF80UI64( uiB64 );
     return
diff --git a/source/extF80_lt_quiet.c b/source/extF80_lt_quiet.c
index 711652c7..d37c6a73 100644
--- a/source/extF80_lt_quiet.c
+++ b/source/extF80_lt_quiet.c
@@ -66,6 +66,8 @@ bool extF80_lt_quiet( extFloat80_t a, extFloat80_t b )
         }
         return false;
     }
+    softfloat_canonicalizeExtF80UI( &uiA64, &uiA0 );
+    softfloat_canonicalizeExtF80UI( &uiB64, &uiB0 );
     signA = signExtF80UI64( uiA64 );
     signB = signExtF80UI64( uiB64 );
     return
diff --git a/source/extF80_mul.c b/source/extF80_mul.c
index c0c50a6c..06b48c77 100644
--- a/source/extF80_mul.c
+++ b/source/extF80_mul.c
@@ -56,7 +56,6 @@ extFloat80_t extF80_mul( extFloat80_t a, extFloat80_t b )
     int_fast32_t expB;
     uint_fast64_t sigB;
     bool signZ;
-    uint_fast64_t magBits;
     struct exp32_sig64 normExpSig;
     int_fast32_t expZ;
     struct uint128 sig128Z, uiZ;
@@ -88,13 +87,13 @@ extFloat80_t extF80_mul( extFloat80_t a, extFloat80_t b )
         ) {
             goto propagateNaN;
         }
-        magBits = expB | sigB;
-        goto infArg;
+        if ( (expB != 0x7FFF) && ! sigB ) goto invalid;
+        goto infinity;
     }
     if ( expB == 0x7FFF ) {
         if ( sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) goto propagateNaN;
-        magBits = expA | sigA;
-        goto infArg;
+        if ( ! sigA ) goto invalid;
+        goto infinity;
     }
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
@@ -134,15 +133,16 @@ extFloat80_t extF80_mul( extFloat80_t a, extFloat80_t b )
     goto uiZ;
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
- infArg:
-    if ( ! magBits ) {
-        softfloat_raiseFlags( softfloat_flag_invalid );
-        uiZ64 = defaultNaNExtF80UI64;
-        uiZ0  = defaultNaNExtF80UI0;
-    } else {
-        uiZ64 = packToExtF80UI64( signZ, 0x7FFF );
-        uiZ0  = UINT64_C( 0x8000000000000000 );
-    }
+ invalid:
+    softfloat_raiseFlags( softfloat_flag_invalid );
+    uiZ64 = defaultNaNExtF80UI64;
+    uiZ0  = defaultNaNExtF80UI0;
+    goto uiZ;
+    /*------------------------------------------------------------------------
+    *------------------------------------------------------------------------*/
+ infinity:
+    uiZ64 = packToExtF80UI64( signZ, 0x7FFF );
+    uiZ0  = UINT64_C( 0x8000000000000000 );
     goto uiZ;
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
diff --git a/source/extF80_rem.c b/source/extF80_rem.c
index a2ebaad8..85f2310c 100644
--- a/source/extF80_rem.c
+++ b/source/extF80_rem.c
@@ -97,6 +97,7 @@ extFloat80_t extF80_rem( extFloat80_t a, extFloat80_t b )
         | that `expDiff' later is less than -1, which will result in returning
         | a canonicalized version of argument a.
         *--------------------------------------------------------------------*/
+        sigB = UINT64_C( 0x8000000000000000 );
         expB += expB;
     }
     /*------------------------------------------------------------------------
diff --git a/source/extF80_sqrt.c b/source/extF80_sqrt.c
index 5d328a0e..0b7964ba 100644
--- a/source/extF80_sqrt.c
+++ b/source/extF80_sqrt.c
@@ -78,7 +78,11 @@ extFloat80_t extF80_sqrt( extFloat80_t a )
             uiZ0  = uiZ.v0;
             goto uiZ;
         }
-        if ( ! signA ) return a;
+        if ( ! signA ) {
+            uiZ64 = packToExtF80UI64( 0, 0x7FFF );
+            uiZ0  = UINT64_C( 0x8000000000000000 );
+            goto uiZ;
+        }
         goto invalid;
     }
     /*------------------------------------------------------------------------
diff --git a/source/extF80_to_f128.c b/source/extF80_to_f128.c
index 7fbc9cb6..a190ac9a 100644
--- a/source/extF80_to_f128.c
+++ b/source/extF80_to_f128.c
@@ -46,8 +46,8 @@ float128_t extF80_to_f128( extFloat80_t a )
     union { struct extFloat80M s; extFloat80_t f; } uA;
     uint_fast16_t uiA64;
     uint_fast64_t uiA0;
-    uint_fast16_t exp;
-    uint_fast64_t frac;
+    int_fast32_t exp;
+    uint_fast64_t sig, frac;
     struct commonNaN commonNaN;
     struct uint128 uiZ;
     bool sign;
@@ -58,7 +58,9 @@ float128_t extF80_to_f128( extFloat80_t a )
     uiA64 = uA.s.signExp;
     uiA0  = uA.s.signif;
     exp = expExtF80UI64( uiA64 );
-    frac = uiA0 & UINT64_C( 0x7FFFFFFFFFFFFFFF );
+    sig = uiA0;
+    softfloat_canonicalizeExtF80( &exp, &sig );
+    frac = sig & UINT64_C( 0x7FFFFFFFFFFFFFFF );
     if ( (exp == 0x7FFF) && frac ) {
         softfloat_extF80UIToCommonNaN( uiA64, uiA0, &commonNaN );
         uiZ = softfloat_commonNaNToF128UI( &commonNaN );
diff --git a/source/extF80_to_f16.c b/source/extF80_to_f16.c
index ca5050f4..8e410663 100644
--- a/source/extF80_to_f16.c
+++ b/source/extF80_to_f16.c
@@ -61,6 +61,7 @@ float16_t extF80_to_f16( extFloat80_t a )
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig  = uiA0;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( exp == 0x7FFF ) {
diff --git a/source/extF80_to_f32.c b/source/extF80_to_f32.c
index 357f56e9..78739441 100644
--- a/source/extF80_to_f32.c
+++ b/source/extF80_to_f32.c
@@ -61,6 +61,7 @@ float32_t extF80_to_f32( extFloat80_t a )
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig  = uiA0;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( exp == 0x7FFF ) {
diff --git a/source/extF80_to_f64.c b/source/extF80_to_f64.c
index c3873992..0716fdb5 100644
--- a/source/extF80_to_f64.c
+++ b/source/extF80_to_f64.c
@@ -61,6 +61,7 @@ float64_t extF80_to_f64( extFloat80_t a )
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig  = uiA0;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( ! (exp | sig) ) {
diff --git a/source/extF80_to_i32.c b/source/extF80_to_i32.c
index 549ca765..78ecf6ea 100644
--- a/source/extF80_to_i32.c
+++ b/source/extF80_to_i32.c
@@ -58,6 +58,7 @@ int_fast32_t
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig = uA.s.signif;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
 #if (i32_fromNaN != i32_fromPosOverflow) || (i32_fromNaN != i32_fromNegOverflow)
diff --git a/source/extF80_to_i32_r_minMag.c b/source/extF80_to_i32_r_minMag.c
index 2b7b9e2b..13d3ce04 100644
--- a/source/extF80_to_i32_r_minMag.c
+++ b/source/extF80_to_i32_r_minMag.c
@@ -57,6 +57,7 @@ int_fast32_t extF80_to_i32_r_minMag( extFloat80_t a, bool exact )
     uiA64 = uA.s.signExp;
     exp = expExtF80UI64( uiA64 );
     sig = uA.s.signif;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x403E - exp;
diff --git a/source/extF80_to_i64.c b/source/extF80_to_i64.c
index 35f55de8..9b194c36 100644
--- a/source/extF80_to_i64.c
+++ b/source/extF80_to_i64.c
@@ -60,6 +60,7 @@ int_fast64_t
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig = uA.s.signif;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x403E - exp;
diff --git a/source/extF80_to_i64_r_minMag.c b/source/extF80_to_i64_r_minMag.c
index 215876da..a12c2546 100644
--- a/source/extF80_to_i64_r_minMag.c
+++ b/source/extF80_to_i64_r_minMag.c
@@ -57,6 +57,7 @@ int_fast64_t extF80_to_i64_r_minMag( extFloat80_t a, bool exact )
     uiA64 = uA.s.signExp;
     exp = expExtF80UI64( uiA64 );
     sig = uA.s.signif;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x403E - exp;
diff --git a/source/extF80_to_ui32.c b/source/extF80_to_ui32.c
index d121c480..d193e6f0 100644
--- a/source/extF80_to_ui32.c
+++ b/source/extF80_to_ui32.c
@@ -58,6 +58,7 @@ uint_fast32_t
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig = uA.s.signif;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
 #if (ui32_fromNaN != ui32_fromPosOverflow) || (ui32_fromNaN != ui32_fromNegOverflow)
diff --git a/source/extF80_to_ui32_r_minMag.c b/source/extF80_to_ui32_r_minMag.c
index ad304834..fb5b1465 100644
--- a/source/extF80_to_ui32_r_minMag.c
+++ b/source/extF80_to_ui32_r_minMag.c
@@ -57,6 +57,7 @@ uint_fast32_t extF80_to_ui32_r_minMag( extFloat80_t a, bool exact )
     uiA64 = uA.s.signExp;
     exp = expExtF80UI64( uiA64 );
     sig = uA.s.signif;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x403E - exp;
diff --git a/source/extF80_to_ui64.c b/source/extF80_to_ui64.c
index a81bbd1b..191f5cde 100644
--- a/source/extF80_to_ui64.c
+++ b/source/extF80_to_ui64.c
@@ -60,6 +60,7 @@ uint_fast64_t
     sign = signExtF80UI64( uiA64 );
     exp  = expExtF80UI64( uiA64 );
     sig = uA.s.signif;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x403E - exp;
diff --git a/source/extF80_to_ui64_r_minMag.c b/source/extF80_to_ui64_r_minMag.c
index 65adfe7e..7f658790 100644
--- a/source/extF80_to_ui64_r_minMag.c
+++ b/source/extF80_to_ui64_r_minMag.c
@@ -57,6 +57,7 @@ uint_fast64_t extF80_to_ui64_r_minMag( extFloat80_t a, bool exact )
     uiA64 = uA.s.signExp;
     exp = expExtF80UI64( uiA64 );
     sig = uA.s.signif;
+    softfloat_canonicalizeExtF80( &exp, &sig );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     shiftDist = 0x403E - exp;
diff --git a/source/include/internals.h b/source/include/internals.h
index 5e6d4bd3..3bfa52ac 100644
--- a/source/include/internals.h
+++ b/source/include/internals.h
@@ -162,14 +162,23 @@ float64_t
 
 #define isNaNExtF80UI( a64, a0 ) ((((a64) & 0x7FFF) == 0x7FFF) && ((a0) & UINT64_C( 0x7FFFFFFFFFFFFFFF )))
 
+struct exp32_sig64 { int_fast32_t exp; uint64_t sig; };
+struct exp32_sig64 softfloat_normSubnormalExtF80Sig( uint_fast64_t );
+
+void
+ softfloat_canonicalizeExtF80( int_fast32_t *, uint_fast64_t * );
+void
+ softfloat_canonicalizeExtF80UI( uint_fast16_t *, uint_fast64_t * );
+void
+ softfloat_canonicalizeExtF80M( int32_t *, uint64_t * );
+void
+ softfloat_canonicalizeExtF80MUI( uint_fast16_t *, uint64_t * );
+
 #ifdef SOFTFLOAT_FAST_INT64
 
 /*----------------------------------------------------------------------------
 *----------------------------------------------------------------------------*/
 
-struct exp32_sig64 { int_fast32_t exp; uint64_t sig; };
-struct exp32_sig64 softfloat_normSubnormalExtF80Sig( uint_fast64_t );
-
 extFloat80_t
  softfloat_roundPackToExtF80(
      bool, int_fast32_t, uint_fast64_t, uint_fast64_t, uint_fast8_t );
diff --git a/source/s_addExtF80M.c b/source/s_addExtF80M.c
index f0142905..343676a8 100644
--- a/source/s_addExtF80M.c
+++ b/source/s_addExtF80M.c
@@ -53,10 +53,11 @@ void
     int32_t expA;
     uint32_t uiB64;
     int32_t expB;
+    uint64_t sigA, sigB;
     uint32_t uiZ64;
     bool signZ, signB;
     const struct extFloat80M *tempSPtr;
-    uint64_t sigZ, sigB;
+    uint64_t sigZ;
     void
      (*roundPackRoutinePtr)(
          bool, int32_t, uint32_t *, uint_fast8_t, struct extFloat80M * );
@@ -69,6 +70,12 @@ void
     expA = expExtF80UI64( uiA64 );
     uiB64 = bSPtr->signExp;
     expB = expExtF80UI64( uiB64 );
+    sigA = aSPtr->signif;
+    sigB = bSPtr->signif;
+    softfloat_canonicalizeExtF80M( &expA, &sigA );
+    softfloat_canonicalizeExtF80M( &expB, &sigB );
+    uiA64 = packToExtF80UI64( signExtF80UI64( uiA64 ), expA );
+    uiB64 = packToExtF80UI64( signExtF80UI64( uiB64 ), expB );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( (expA == 0x7FFF) || (expB == 0x7FFF) ) {
@@ -91,19 +98,21 @@ void
     signB = signExtF80UI64( uiB64 ) ^ negateB;
     negateB = (signZ != signB);
     if ( expA < expB ) {
+        int32_t tmpExp;
+        uint64_t tmpSig;
         signZ = signB;
+        tmpExp = expA;
         expA = expB;
-        expB = expExtF80UI64( uiA64 );
-        tempSPtr = aSPtr;
-        aSPtr = bSPtr;
-        bSPtr = tempSPtr;
+        expB = tmpExp;
+        tmpSig = sigA;
+        sigA = sigB;
+        sigB = tmpSig;
     }
     if ( ! expB ) {
         expB = 1;
         if ( ! expA ) expA = 1;
     }
-    sigZ = aSPtr->signif;
-    sigB = bSPtr->signif;
+    sigZ = sigA;
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     roundPackRoutinePtr = softfloat_roundPackMToExtF80M;
diff --git a/source/s_addMagsExtF80.c b/source/s_addMagsExtF80.c
index 6e7d1a6f..b4869296 100644
--- a/source/s_addMagsExtF80.c
+++ b/source/s_addMagsExtF80.c
@@ -69,6 +69,8 @@ extFloat80_t
     sigA = uiA0;
     expB = expExtF80UI64( uiB64 );
     sigB = uiB0;
+    softfloat_canonicalizeExtF80( &expA, &sigA );
+    softfloat_canonicalizeExtF80( &expB, &sigB );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     expDiff = expA - expB;
@@ -78,12 +80,21 @@ extFloat80_t
                 goto propagateNaN;
             }
             uiZ64 = uiA64;
-            uiZ0  = uiA0;
+            uiZ0  = UINT64_C( 0x8000000000000000 );
             goto uiZ;
         }
         sigZ = sigA + sigB;
         sigZExtra = 0;
         if ( ! expA ) {
+            if ( sigZ < sigA ) {
+                /*------------------------------------------------------------
+                | Significand addition carried (e.g., two pseudo-denormals
+                | with J=1).  Treat as effective exp=1 and fall through to
+                | `shiftRight1', which captures the carry.
+                *------------------------------------------------------------*/
+                expZ = 1;
+                goto shiftRight1;
+            }
             normExpSig = softfloat_normSubnormalExtF80Sig( sigZ );
             expZ = normExpSig.exp + 1;
             sigZ = normExpSig.sig;
@@ -98,7 +109,7 @@ extFloat80_t
         if ( expB == 0x7FFF ) {
             if ( sigB & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) goto propagateNaN;
             uiZ64 = packToExtF80UI64( signZ, 0x7FFF );
-            uiZ0  = uiB0;
+            uiZ0  = UINT64_C( 0x8000000000000000 );
             goto uiZ;
         }
         expZ = expB;
@@ -114,7 +125,7 @@ extFloat80_t
         if ( expA == 0x7FFF ) {
             if ( sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) goto propagateNaN;
             uiZ64 = uiA64;
-            uiZ0  = uiA0;
+            uiZ0  = UINT64_C( 0x8000000000000000 );
             goto uiZ;
         }
         expZ = expA;
@@ -129,6 +140,7 @@ extFloat80_t
     }
  newlyAligned:
     sigZ = sigA + sigB;
+    if ( sigZ < sigA ) goto shiftRight1;
     if ( sigZ & UINT64_C( 0x8000000000000000 ) ) goto roundAndPack;
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
diff --git a/source/s_canonicalizeExtF80.c b/source/s_canonicalizeExtF80.c
new file mode 100644
index 00000000..c4ab5481
--- /dev/null
+++ b/source/s_canonicalizeExtF80.c
@@ -0,0 +1,122 @@
+
+/*============================================================================
+
+This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
+Package, Release 3e, by John R. Hauser.  
+
+Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+ 1. Redistributions of source code must retain the above copyright notice,
+    this list of conditions, and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright notice,
+    this list of conditions, and the following disclaimer in the documentation
+    and/or other materials provided with the distribution.
+
+ 3. Neither the name of the University nor the names of its contributors may
+    be used to endorse or promote products derived from this software without
+    specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
+EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
+DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
+DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+=============================================================================*/
+
+/* This particular file was written by John Byrd. */
+
+#include <stdint.h>
+#include "platform.h"
+#include "internals.h"
+
+/*----------------------------------------------------------------------------
+| The 80-bit extended double format (extFloat80) is unique among IEEE 754
+| types in that it stores the integer bit of the significand explicitly as
+| bit 63 of the 64-bit significand field, commonly called the 'J' bit.  In
+| all other IEEE 754 binary formats, the integer bit is implicit and
+| determined solely by the exponent.  Because the J bit is stored
+| independently from the exponent in extFloat80, it is possible to construct
+| encodings where the two are inconsistent.  These inconsistent encodings
+| are called "non-canonical" or, on the 8087 through 80287, "unnormal".
+| Intel no longer generates non-canonical encodings, but the 80-bit format
+| is still defined to accept them.
+|   This function rewrites the exponent '*expPtr' and significand '*sigPtr'
+| of an extFloat80 value in place so that the encoding is canonical, i.e.,
+| the J bit is consistent with the exponent.  The mathematical value
+| represented by the encoding is preserved.  If the encoding is already
+| canonical, the values are unchanged.
+|   There are four classes of non-canonical encoding, each resolved as
+| follows:
+|
+|   1. Unnormals (0 < exp < 0x7FFF, J = 0).  The significand is nonzero
+|      but lacks its integer bit.  If the significand can be left-shifted
+|      to set bit 63 without driving the biased exponent below 1, the value
+|      is renormalized.  If the shift would require a biased exponent less
+|      than 1, the value is flushed to a denormal (exp = 0) with whatever
+|      significand bits survive the limited shift.  If the significand is
+|      entirely zero, the exponent is set to 0 (encoding positive or
+|      negative zero, depending on the sign bit, which is not touched here).
+|
+|   2. Pseudo-denormals (exp = 0, J = 1).  These represent the same value
+|      as a biased exponent of 1, so the exponent is set to 1 and the
+|      significand is left unchanged.
+|
+|   3. Pseudo-infinities (exp = 0x7FFF, J = 0, significand = 0).  The
+|      J bit is forced to 1, producing the canonical infinity encoding.
+|
+|   4. Pseudo-NaNs (exp = 0x7FFF, J = 0, significand != 0).  The J bit
+|      is forced to 1.  The remaining significand bits (the NaN payload)
+|      are preserved, so quiet vs. signaling status is maintained.
+|
+|   Cases 3 and 4 are handled together: when the biased exponent is
+|   0x7FFF, the J bit is unconditionally set.
+|
+|   This function does not modify the sign bit, which is not part of the
+| exponent or significand fields passed here.  It also does not raise any
+| floating-point exception flags; canonicalization is a silent rewrite of
+| the encoding only.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_canonicalizeExtF80(
+     int_fast32_t *expPtr, uint_fast64_t *sigPtr )
+{
+    int_fast32_t exp;
+    uint_fast64_t sig;
+    struct exp32_sig64 normExpSig;
+
+    exp = *expPtr;
+    sig = *sigPtr;
+    if ( exp == 0x7FFF ) {
+        *sigPtr = sig | UINT64_C( 0x8000000000000000 );
+    } else if ( exp ) {
+        if ( ! (sig & UINT64_C( 0x8000000000000000 )) ) {
+            if ( ! sig ) {
+                *expPtr = 0;
+            } else {
+                normExpSig = softfloat_normSubnormalExtF80Sig( sig );
+                if ( exp + normExpSig.exp >= 1 ) {
+                    *expPtr = exp + normExpSig.exp;
+                    *sigPtr = normExpSig.sig;
+                } else {
+                    if ( exp > 1 ) *sigPtr = sig << (exp - 1);
+                    *expPtr = 0;
+                }
+            }
+        }
+    } else {
+        if ( sig & UINT64_C( 0x8000000000000000 ) )
+            *expPtr = 1;
+    }
+
+}
diff --git a/source/s_canonicalizeExtF80M.c b/source/s_canonicalizeExtF80M.c
new file mode 100644
index 00000000..ab10f0d2
--- /dev/null
+++ b/source/s_canonicalizeExtF80M.c
@@ -0,0 +1,81 @@
+
+/*============================================================================
+
+This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
+Package, Release 3e, by John R. Hauser.
+
+Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+ 1. Redistributions of source code must retain the above copyright notice,
+    this list of conditions, and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright notice,
+    this list of conditions, and the following disclaimer in the documentation
+    and/or other materials provided with the distribution.
+
+ 3. Neither the name of the University nor the names of its contributors may
+    be used to endorse or promote products derived from this software without
+    specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
+EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
+DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
+DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+=============================================================================*/
+
+/* This particular file was written by John Byrd. */
+
+#include <stdint.h>
+#include "platform.h"
+#include "internals.h"
+
+/*----------------------------------------------------------------------------
+| Equivalent to 'softfloat_canonicalizeExtF80' (see s_canonicalizeExtF80.c
+| for the full description of extFloat80 non-canonical encodings and the
+| canonicalization rules), but using 'int32_t' and 'uint64_t' parameter
+| types to match the non-FAST_INT64 code paths.  The algorithm and behavior
+| are identical.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_canonicalizeExtF80M( int32_t *expPtr, uint64_t *sigPtr )
+{
+    int32_t exp;
+    uint64_t sig;
+    struct exp32_sig64 normExpSig;
+
+    exp = *expPtr;
+    sig = *sigPtr;
+    if ( exp == 0x7FFF ) {
+        *sigPtr = sig | UINT64_C( 0x8000000000000000 );
+    } else if ( exp ) {
+        if ( ! (sig & UINT64_C( 0x8000000000000000 )) ) {
+            if ( ! sig ) {
+                *expPtr = 0;
+            } else {
+                normExpSig = softfloat_normSubnormalExtF80Sig( sig );
+                if ( exp + normExpSig.exp >= 1 ) {
+                    *expPtr = exp + normExpSig.exp;
+                    *sigPtr = normExpSig.sig;
+                } else {
+                    if ( exp > 1 ) *sigPtr = sig << (exp - 1);
+                    *expPtr = 0;
+                }
+            }
+        }
+    } else {
+        if ( sig & UINT64_C( 0x8000000000000000 ) )
+            *expPtr = 1;
+    }
+
+}
diff --git a/source/s_canonicalizeExtF80MUI.c b/source/s_canonicalizeExtF80MUI.c
new file mode 100644
index 00000000..0de3b7fc
--- /dev/null
+++ b/source/s_canonicalizeExtF80MUI.c
@@ -0,0 +1,62 @@
+
+/*============================================================================
+
+This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
+Package, Release 3e, by John R. Hauser.
+
+Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+ 1. Redistributions of source code must retain the above copyright notice,
+    this list of conditions, and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright notice,
+    this list of conditions, and the following disclaimer in the documentation
+    and/or other materials provided with the distribution.
+
+ 3. Neither the name of the University nor the names of its contributors may
+    be used to endorse or promote products derived from this software without
+    specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
+EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
+DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
+DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+=============================================================================*/
+
+/* This particular file was written by John Byrd. */
+
+#include <stdint.h>
+#include "platform.h"
+#include "internals.h"
+
+/*----------------------------------------------------------------------------
+| Canonicalizes an extFloat80 value whose exponent and sign are stored in the
+| packed 'signExp' layout used by the non-FAST_INT64 comparison functions.
+| The packed 16-bit field '*signExpPtr' holds the sign in bit 15 and the
+| 15-bit biased exponent in bits 14:0.  This function extracts the exponent,
+| passes it along with '*sigPtr' to 'softfloat_canonicalizeExtF80M' (see
+| s_canonicalizeExtF80.c for the full canonicalization rules), and repacks
+| the possibly-modified exponent back into '*signExpPtr' with the original
+| sign bit preserved.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_canonicalizeExtF80MUI(
+     uint_fast16_t *signExpPtr, uint64_t *sigPtr )
+{
+    int32_t exp = expExtF80UI64( *signExpPtr );
+
+    softfloat_canonicalizeExtF80M( &exp, sigPtr );
+    *signExpPtr = packToExtF80UI64( signExtF80UI64( *signExpPtr ), exp );
+
+}
diff --git a/source/s_canonicalizeExtF80UI.c b/source/s_canonicalizeExtF80UI.c
new file mode 100644
index 00000000..dbc1ea34
--- /dev/null
+++ b/source/s_canonicalizeExtF80UI.c
@@ -0,0 +1,62 @@
+
+/*============================================================================
+
+This C source file is part of the SoftFloat IEEE Floating-Point Arithmetic
+Package, Release 3e, by John R. Hauser.
+
+Copyright 2011, 2012, 2013, 2014 The Regents of the University of California.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+ 1. Redistributions of source code must retain the above copyright notice,
+    this list of conditions, and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright notice,
+    this list of conditions, and the following disclaimer in the documentation
+    and/or other materials provided with the distribution.
+
+ 3. Neither the name of the University nor the names of its contributors may
+    be used to endorse or promote products derived from this software without
+    specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY
+EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE
+DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
+DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+=============================================================================*/
+
+/* This particular file was written by John Byrd. */
+
+#include <stdint.h>
+#include "platform.h"
+#include "internals.h"
+
+/*----------------------------------------------------------------------------
+| Canonicalizes an extFloat80 value whose exponent and sign are stored in the
+| packed 'signExp' layout used by the FAST_INT64 comparison functions.  The
+| packed 16-bit field '*signExpPtr' holds the sign in bit 15 and the 15-bit
+| biased exponent in bits 14:0.  This function extracts the exponent, passes
+| it along with '*sigPtr' to 'softfloat_canonicalizeExtF80' (see
+| s_canonicalizeExtF80.c for the full canonicalization rules), and repacks
+| the possibly-modified exponent back into '*signExpPtr' with the original
+| sign bit preserved.
+*----------------------------------------------------------------------------*/
+void
+ softfloat_canonicalizeExtF80UI(
+     uint_fast16_t *signExpPtr, uint_fast64_t *sigPtr )
+{
+    int_fast32_t exp = *signExpPtr & 0x7FFF;
+
+    softfloat_canonicalizeExtF80( &exp, sigPtr );
+    *signExpPtr = (*signExpPtr & 0x8000) | exp;
+
+}
diff --git a/source/s_compareNonnormExtF80M.c b/source/s_compareNonnormExtF80M.c
index 6712e576..4d6b9833 100644
--- a/source/s_compareNonnormExtF80M.c
+++ b/source/s_compareNonnormExtF80M.c
@@ -56,16 +56,16 @@ int
     sigA = aSPtr->signif;
     signB = signExtF80UI64( uiB64 );
     sigB = bSPtr->signif;
+    expA = expExtF80UI64( uiA64 );
+    expB = expExtF80UI64( uiB64 );
+    softfloat_canonicalizeExtF80M( &expA, &sigA );
+    softfloat_canonicalizeExtF80M( &expB, &sigB );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     if ( (uiA64 ^ uiB64) & 0x8000 ) {
         if ( ! (sigA | sigB) ) return 0;
         goto resultFromSignB;
     }
-    /*------------------------------------------------------------------------
-    *------------------------------------------------------------------------*/
-    expA = expExtF80UI64( uiA64 );
-    expB = expExtF80UI64( uiB64 );
     if ( expA == 0x7FFF ) {
         if (expB == 0x7FFF) return 0;
         signB = ! signB;
diff --git a/source/s_subMagsExtF80.c b/source/s_subMagsExtF80.c
index 86ffd9b8..1a2ec530 100644
--- a/source/s_subMagsExtF80.c
+++ b/source/s_subMagsExtF80.c
@@ -68,6 +68,8 @@ extFloat80_t
     sigA = uiA0;
     expB = expExtF80UI64( uiB64 );
     sigB = uiB0;
+    softfloat_canonicalizeExtF80( &expA, &sigA );
+    softfloat_canonicalizeExtF80( &expB, &sigB );
     /*------------------------------------------------------------------------
     *------------------------------------------------------------------------*/
     expDiff = expA - expB;
@@ -112,6 +114,12 @@ extFloat80_t
     sigExtra = sig128.v0;
  newlyAlignedBBigger:
     expZ = expB;
+    if ( sigA < sigB ) goto bBigger;
+    if ( sigB < sigA ) goto aBigger;
+    uiZ64 =
+        packToExtF80UI64( (softfloat_roundingMode == softfloat_round_min), 0 );
+    uiZ0 = 0;
+    goto uiZ;
  bBigger:
     signZ = ! signZ;
     sig128 = softfloat_sub128( sigB, 0, sigA, sigExtra );
@@ -122,7 +130,7 @@ extFloat80_t
     if ( expA == 0x7FFF ) {
         if ( sigA & UINT64_C( 0x7FFFFFFFFFFFFFFF ) ) goto propagateNaN;
         uiZ64 = uiA64;
-        uiZ0  = uiA0;
+        uiZ0  = UINT64_C( 0x8000000000000000 );
         goto uiZ;
     }
     if ( ! expB ) {
@@ -135,6 +143,12 @@ extFloat80_t
     sigExtra = sig128.v0;
  newlyAlignedABigger:
     expZ = expA;
+    if ( sigB < sigA ) goto aBigger;
+    if ( sigA < sigB ) goto bBigger;
+    uiZ64 =
+        packToExtF80UI64( (softfloat_roundingMode == softfloat_round_min), 0 );
+    uiZ0 = 0;
+    goto uiZ;
  aBigger:
     sig128 = softfloat_sub128( sigA, 0, sigB, sigExtra );
     /*------------------------------------------------------------------------