diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index 3988bd10990df8fcd1af268c8555500f9d7e6718..e66a5d46c81a6415509ef945b3b5eada2fe80d21 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -5479,8 +5479,14 @@ float32 float32_scalbn( float32 a, int n STATUS_PARAM )
     if ( aExp == 0xFF ) {
         return a;
     }
-    aExp += n;
-    return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
+    if ( aExp != 0 )
+        aSig |= 0x00800000;
+    else if ( aSig == 0 )
+        return a;
+
+    aExp += n - 1;
+    aSig <<= 7;
+    return normalizeRoundAndPackFloat32( aSign, aExp, aSig STATUS_VAR );
 }
 
 float64 float64_scalbn( float64 a, int n STATUS_PARAM )
@@ -5496,8 +5502,14 @@ float64 float64_scalbn( float64 a, int n STATUS_PARAM )
     if ( aExp == 0x7FF ) {
         return a;
     }
-    aExp += n;
-    return roundAndPackFloat64( aSign, aExp, aSig STATUS_VAR );
+    if ( aExp != 0 )
+        aSig |= LIT64( 0x0010000000000000 );
+    else if ( aSig == 0 )
+        return a;
+
+    aExp += n - 1;
+    aSig <<= 10;
+    return normalizeRoundAndPackFloat64( aSign, aExp, aSig STATUS_VAR );
 }
 
 #ifdef FLOATX80
@@ -5514,9 +5526,12 @@ floatx80 floatx80_scalbn( floatx80 a, int n STATUS_PARAM )
     if ( aExp == 0x7FF ) {
         return a;
     }
+    if (aExp == 0 && aSig == 0)
+        return a;
+
     aExp += n;
-    return roundAndPackFloatx80( STATUS(floatx80_rounding_precision),
-                                 aSign, aExp, aSig, 0 STATUS_VAR );
+    return normalizeRoundAndPackFloatx80( STATUS(floatx80_rounding_precision),
+                                          aSign, aExp, aSig, 0 STATUS_VAR );
 }
 #endif
 
@@ -5534,8 +5549,14 @@ float128 float128_scalbn( float128 a, int n STATUS_PARAM )
     if ( aExp == 0x7FFF ) {
         return a;
     }
-    aExp += n;
-    return roundAndPackFloat128( aSign, aExp, aSig0, aSig1, 0 STATUS_VAR );
+    if ( aExp != 0 )
+        aSig0 |= LIT64( 0x0001000000000000 );
+    else if ( aSig0 == 0 && aSig1 == 0 )
+        return a;
+
+    aExp += n - 1;
+    return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1
+                                          STATUS_VAR );
 
 }
 #endif