diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index c295f3183f..5ccba76481 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -623,6 +623,9 @@ static float64 roundAndPackFloat64(flag zSign, int zExp, uint64_t zSig,
     case float_round_down:
         roundIncrement = zSign ? 0x3ff : 0;
         break;
+    case float_round_to_odd:
+        roundIncrement = (zSig & 0x400) ? 0 : 0x3ff;
+        break;
     default:
         abort();
     }
@@ -632,8 +635,10 @@ static float64 roundAndPackFloat64(flag zSign, int zExp, uint64_t zSig,
              || (    ( zExp == 0x7FD )
                   && ( (int64_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 packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 ));
+            return packFloat64(zSign, 0x7FF, -(!overflow_to_inf));
         }
         if ( zExp < 0 ) {
             if (status->flush_to_zero) {
@@ -651,6 +656,13 @@ static float64 roundAndPackFloat64(flag zSign, int zExp, uint64_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 & 0x400) ? 0 : 0x3ff;
+            }
         }
     }
     if (roundBits) {
@@ -1149,6 +1161,9 @@ static float128 roundAndPackFloat128(flag zSign, int32_t zExp,
     case float_round_down:
         increment = zSign && zSig2;
         break;
+    case float_round_to_odd:
+        increment = !(zSig1 & 0x1) && zSig2;
+        break;
     default:
         abort();
     }
@@ -1168,6 +1183,7 @@ static float128 roundAndPackFloat128(flag zSign, int32_t zExp,
             if (    ( roundingMode == float_round_to_zero )
                  || ( zSign && ( roundingMode == float_round_up ) )
                  || ( ! zSign && ( roundingMode == float_round_down ) )
+                 || (roundingMode == float_round_to_odd)
                ) {
                 return
                     packFloat128(
@@ -1215,6 +1231,9 @@ static float128 roundAndPackFloat128(flag zSign, int32_t zExp,
             case float_round_down:
                 increment = zSign && zSig2;
                 break;
+            case float_round_to_odd:
+                increment = !(zSig1 & 0x1) && zSig2;
+                break;
             default:
                 abort();
             }
diff --git a/include/fpu/softfloat.h b/include/fpu/softfloat.h
index 842ec6b22a..8a39028664 100644
--- a/include/fpu/softfloat.h
+++ b/include/fpu/softfloat.h
@@ -180,6 +180,8 @@ enum {
     float_round_up           = 2,
     float_round_to_zero      = 3,
     float_round_ties_away    = 4,
+    /* Not an IEEE rounding mode: round to the closest odd mantissa value */
+    float_round_to_odd       = 5,
 };
 
 /*----------------------------------------------------------------------------