diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index 9b1eccf..8459ca6 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -4814,6 +4814,10 @@ int32_t floatx80_to_int32(floatx80 a, float_status *status)
     int32_t aExp, shiftCount;
     uint64_t aSig;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return 1 << 31;
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -4842,6 +4846,10 @@ int32_t floatx80_to_int32_round_to_zero(floatx80 a, float_status *status)
     uint64_t aSig, savedASig;
     int32_t z;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return 1 << 31;
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -4888,6 +4896,10 @@ int64_t floatx80_to_int64(floatx80 a, float_status *status)
     int32_t aExp, shiftCount;
     uint64_t aSig, aSigExtra;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return 1 << 63;
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -4929,6 +4941,10 @@ int64_t floatx80_to_int64_round_to_zero(floatx80 a, float_status *status)
     uint64_t aSig;
     int64_t z;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return 1 << 63;
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -4971,6 +4987,10 @@ float32 floatx80_to_float32(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return float32_default_nan(status);
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -4999,6 +5019,10 @@ float64 floatx80_to_float64(floatx80 a, float_status *status)
     int32_t aExp;
     uint64_t aSig, zSig;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return float64_default_nan(status);
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -5027,6 +5051,10 @@ float128 floatx80_to_float128(floatx80 a, float_status *status)
     int aExp;
     uint64_t aSig, zSig0, zSig1;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return float128_default_nan(status);
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -5052,6 +5080,10 @@ floatx80 floatx80_round_to_int(floatx80 a, float_status *status)
     uint64_t lastBitMask, roundBitsMask;
     floatx80 z;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return floatx80_default_nan(status);
+    }
     aExp = extractFloatx80Exp( a );
     if ( 0x403E <= aExp ) {
         if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) {
@@ -5279,6 +5311,10 @@ floatx80 floatx80_add(floatx80 a, floatx80 b, float_status *status)
 {
     flag aSign, bSign;
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return floatx80_default_nan(status);
+    }
     aSign = extractFloatx80Sign( a );
     bSign = extractFloatx80Sign( b );
     if ( aSign == bSign ) {
@@ -5300,6 +5336,10 @@ floatx80 floatx80_sub(floatx80 a, floatx80 b, float_status *status)
 {
     flag aSign, bSign;
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return floatx80_default_nan(status);
+    }
     aSign = extractFloatx80Sign( a );
     bSign = extractFloatx80Sign( b );
     if ( aSign == bSign ) {
@@ -5323,6 +5363,10 @@ floatx80 floatx80_mul(floatx80 a, floatx80 b, float_status *status)
     int32_t aExp, bExp, zExp;
     uint64_t aSig, bSig, zSig0, zSig1;
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return floatx80_default_nan(status);
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -5380,6 +5424,10 @@ floatx80 floatx80_div(floatx80 a, floatx80 b, float_status *status)
     uint64_t aSig, bSig, zSig0, zSig1;
     uint64_t rem0, rem1, rem2, term0, term1, term2;
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return floatx80_default_nan(status);
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -5461,6 +5509,10 @@ floatx80 floatx80_rem(floatx80 a, floatx80 b, float_status *status)
     uint64_t aSig0, aSig1, bSig;
     uint64_t q, term0, term1, alternateASig0, alternateASig1;
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return floatx80_default_nan(status);
+    }
     aSig0 = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -5556,6 +5608,10 @@ floatx80 floatx80_sqrt(floatx80 a, float_status *status)
     uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0;
     uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return floatx80_default_nan(status);
+    }
     aSig0 = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
@@ -5620,10 +5676,11 @@ floatx80 floatx80_sqrt(floatx80 a, float_status *status)
 int floatx80_eq(floatx80 a, floatx80 b, float_status *status)
 {
 
-    if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
-              && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
-         || (    ( extractFloatx80Exp( b ) == 0x7FFF )
-              && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)
+        || (extractFloatx80Exp(a) == 0x7FFF
+            && (uint64_t) (extractFloatx80Frac(a) << 1))
+        || (extractFloatx80Exp(b) == 0x7FFF
+            && (uint64_t) (extractFloatx80Frac(b) << 1))
        ) {
         float_raise(float_flag_invalid, status);
         return 0;
@@ -5649,10 +5706,11 @@ int floatx80_le(floatx80 a, floatx80 b, float_status *status)
 {
     flag aSign, bSign;
 
-    if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
-              && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
-         || (    ( extractFloatx80Exp( b ) == 0x7FFF )
-              && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)
+        || (extractFloatx80Exp(a) == 0x7FFF
+            && (uint64_t) (extractFloatx80Frac(a) << 1))
+        || (extractFloatx80Exp(b) == 0x7FFF
+            && (uint64_t) (extractFloatx80Frac(b) << 1))
        ) {
         float_raise(float_flag_invalid, status);
         return 0;
@@ -5682,10 +5740,11 @@ int floatx80_lt(floatx80 a, floatx80 b, float_status *status)
 {
     flag aSign, bSign;
 
-    if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
-              && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
-         || (    ( extractFloatx80Exp( b ) == 0x7FFF )
-              && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)
+        || (extractFloatx80Exp(a) == 0x7FFF
+            && (uint64_t) (extractFloatx80Frac(a) << 1))
+        || (extractFloatx80Exp(b) == 0x7FFF
+            && (uint64_t) (extractFloatx80Frac(b) << 1))
        ) {
         float_raise(float_flag_invalid, status);
         return 0;
@@ -5712,10 +5771,11 @@ int floatx80_lt(floatx80 a, floatx80 b, float_status *status)
 *----------------------------------------------------------------------------*/
 int floatx80_unordered(floatx80 a, floatx80 b, float_status *status)
 {
-    if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
-              && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
-         || (    ( extractFloatx80Exp( b ) == 0x7FFF )
-              && (uint64_t) ( extractFloatx80Frac( b )<<1 ) )
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)
+        || (extractFloatx80Exp(a) == 0x7FFF
+            && (uint64_t) (extractFloatx80Frac(a) << 1))
+        || (extractFloatx80Exp(b) == 0x7FFF
+            && (uint64_t) (extractFloatx80Frac(b) << 1))
        ) {
         float_raise(float_flag_invalid, status);
         return 1;
@@ -5733,6 +5793,10 @@ int floatx80_unordered(floatx80 a, floatx80 b, float_status *status)
 int floatx80_eq_quiet(floatx80 a, floatx80 b, float_status *status)
 {
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return 0;
+    }
     if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
               && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
          || (    ( extractFloatx80Exp( b ) == 0x7FFF )
@@ -5764,6 +5828,10 @@ int floatx80_le_quiet(floatx80 a, floatx80 b, float_status *status)
 {
     flag aSign, bSign;
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return 0;
+    }
     if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
               && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
          || (    ( extractFloatx80Exp( b ) == 0x7FFF )
@@ -5800,6 +5868,10 @@ int floatx80_lt_quiet(floatx80 a, floatx80 b, float_status *status)
 {
     flag aSign, bSign;
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return 0;
+    }
     if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
               && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
          || (    ( extractFloatx80Exp( b ) == 0x7FFF )
@@ -5833,6 +5905,10 @@ int floatx80_lt_quiet(floatx80 a, floatx80 b, float_status *status)
 *----------------------------------------------------------------------------*/
 int floatx80_unordered_quiet(floatx80 a, floatx80 b, float_status *status)
 {
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return 1;
+    }
     if (    (    ( extractFloatx80Exp( a ) == 0x7FFF )
               && (uint64_t) ( extractFloatx80Frac( a )<<1 ) )
          || (    ( extractFloatx80Exp( b ) == 0x7FFF )
@@ -7374,6 +7450,10 @@ static inline int floatx80_compare_internal(floatx80 a, floatx80 b,
 {
     flag aSign, bSign;
 
+    if (floatx80_invalid_encoding(a) || floatx80_invalid_encoding(b)) {
+        float_raise(float_flag_invalid, status);
+        return float_relation_unordered;
+    }
     if (( ( extractFloatx80Exp( a ) == 0x7fff ) &&
           ( extractFloatx80Frac( a )<<1 ) ) ||
         ( ( extractFloatx80Exp( b ) == 0x7fff ) &&
@@ -7645,6 +7725,10 @@ floatx80 floatx80_scalbn(floatx80 a, int n, float_status *status)
     int32_t aExp;
     uint64_t aSig;
 
+    if (floatx80_invalid_encoding(a)) {
+        float_raise(float_flag_invalid, status);
+        return floatx80_default_nan(status);
+    }
     aSig = extractFloatx80Frac( a );
     aExp = extractFloatx80Exp( a );
     aSign = extractFloatx80Sign( a );
diff --git a/include/fpu/softfloat.h b/include/fpu/softfloat.h
index 0e57ee5..c2ef9f2 100644
--- a/include/fpu/softfloat.h
+++ b/include/fpu/softfloat.h
@@ -658,6 +658,21 @@ static inline int floatx80_is_any_nan(floatx80 a)
     return ((a.high & 0x7fff) == 0x7fff) && (a.low<<1);
 }
 
+/*----------------------------------------------------------------------------
+| Return whether the given value is an invalid floatx80 encoding.
+| Invalid floatx80 encodings arise when the integer bit is not set, but
+| the exponent is not zero. The only times the integer bit is permitted to
+| be zero is in subnormal numbers and the value zero.
+| This includes what the Intel software developer's manual calls pseudo-NaNs,
+| pseudo-infinities and un-normal numbers. It does not include
+| pseudo-denormals, which must still be correctly handled as inputs even
+| if they are never generated as outputs.
+*----------------------------------------------------------------------------*/
+static inline bool floatx80_invalid_encoding(floatx80 a)
+{
+    return (a.low & (1 << 63)) == 0 && (a.high & 0x7FFF) != 0;
+}
+
 #define floatx80_zero make_floatx80(0x0000, 0x0000000000000000LL)
 #define floatx80_one make_floatx80(0x3fff, 0x8000000000000000LL)
 #define floatx80_ln2 make_floatx80(0x3ffe, 0xb17217f7d1cf79acLL)
