diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index 9132d7a0b0..325c6e4e79 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -696,6 +696,7 @@ static FloatParts sf_canonicalize(FloatParts part, const FloatFmt *parm,
 static FloatParts round_canonical(FloatParts p, float_status *s,
                                   const FloatFmt *parm)
 {
+    const uint64_t frac_lsb = parm->frac_lsb;
     const uint64_t frac_lsbm1 = parm->frac_lsbm1;
     const uint64_t round_mask = parm->round_mask;
     const uint64_t roundeven_mask = parm->roundeven_mask;
@@ -731,6 +732,10 @@ static FloatParts round_canonical(FloatParts p, float_status *s,
             inc = p.sign ? round_mask : 0;
             overflow_norm = !p.sign;
             break;
+        case float_round_to_odd:
+            overflow_norm = true;
+            inc = frac & frac_lsb ? 0 : frac_lsbm1;
+            break;
         default:
             g_assert_not_reached();
         }
@@ -778,9 +783,14 @@ static FloatParts round_canonical(FloatParts p, float_status *s,
             shift64RightJamming(frac, 1 - exp, &frac);
             if (frac & round_mask) {
                 /* Need to recompute round-to-even.  */
-                if (s->float_rounding_mode == float_round_nearest_even) {
+                switch (s->float_rounding_mode) {
+                case float_round_nearest_even:
                     inc = ((frac & roundeven_mask) != frac_lsbm1
                            ? frac_lsbm1 : 0);
+                    break;
+                case float_round_to_odd:
+                    inc = frac & frac_lsb ? 0 : frac_lsbm1;
+                    break;
                 }
                 flags |= float_flag_inexact;
                 frac += inc;
@@ -1988,6 +1998,9 @@ static FloatParts round_to_int(FloatParts a, int rmode,
             case float_round_down:
                 one = a.sign;
                 break;
+            case float_round_to_odd:
+                one = true;
+                break;
             default:
                 g_assert_not_reached();
             }
@@ -2021,6 +2034,9 @@ static FloatParts round_to_int(FloatParts a, int rmode,
             case float_round_down:
                 inc = a.sign ? rnd_mask : 0;
                 break;
+            case float_round_to_odd:
+                inc = a.frac & frac_lsb ? 0 : frac_lsbm1;
+                break;
             default:
                 g_assert_not_reached();
             }
@@ -3314,6 +3330,9 @@ static int32_t roundAndPackInt32(flag zSign, uint64_t absZ, float_status *status
     case float_round_down:
         roundIncrement = zSign ? 0x7f : 0;
         break;
+    case float_round_to_odd:
+        roundIncrement = absZ & 0x80 ? 0 : 0x7f;
+        break;
     default:
         abort();
     }
@@ -3368,6 +3387,9 @@ static int64_t roundAndPackInt64(flag zSign, uint64_t absZ0, uint64_t absZ1,
     case float_round_down:
         increment = zSign && absZ1;
         break;
+    case float_round_to_odd:
+        increment = !(absZ0 & 1) && absZ1;
+        break;
     default:
         abort();
     }
@@ -3424,6 +3446,9 @@ static int64_t roundAndPackUint64(flag zSign, uint64_t absZ0,
     case float_round_down:
         increment = zSign && absZ1;
         break;
+    case float_round_to_odd:
+        increment = !(absZ0 & 1) && absZ1;
+        break;
     default:
         abort();
     }
@@ -3526,6 +3551,8 @@ static float32 roundAndPackFloat32(flag zSign, int zExp, uint32_t zSig,
     case float_round_down:
         roundIncrement = zSign ? 0x7f : 0;
         break;
+    case float_round_to_odd:
+        roundIncrement = zSig & 0x80 ? 0 : 0x7f;
     default:
         abort();
         break;
@@ -3536,8 +3563,10 @@ static float32 roundAndPackFloat32(flag zSign, int zExp, uint32_t zSig,
              || (    ( zExp == 0xFD )
                   && ( (int32_t) ( zSig + roundIncrement ) < 0 ) )
            ) {
+            bool overflow_to_inf = roundingMode != float_round_to_odd &&
+                                   roundIncrement != 0;
             float_raise(float_flag_overflow | float_flag_inexact, status);
-            return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 ));
+            return packFloat32(zSign, 0xFF, -!overflow_to_inf);
         }
         if ( zExp < 0 ) {
             if (status->flush_to_zero) {
@@ -3555,6 +3584,13 @@ static float32 roundAndPackFloat32(flag zSign, int zExp, uint32_t zSig,
             if (isTiny && roundBits) {
                 float_raise(float_flag_underflow, status);
             }
+            if (roundingMode == float_round_to_odd) {
+                /*
+                 * For round-to-odd case, the roundIncrement depends on
+                 * zSig which just changed.
+                 */
+                roundIncrement = zSig & 0x80 ? 0 : 0x7f;
+            }
         }
     }
     if (roundBits) {
