diff --git a/fpu/softfloat-parts.c.inc b/fpu/softfloat-parts.c.inc
index bbeadaa189..a9f268fcab 100644
--- a/fpu/softfloat-parts.c.inc
+++ b/fpu/softfloat-parts.c.inc
@@ -214,18 +214,35 @@ static void partsN(uncanon_normal)(FloatPartsN *p, float_status *s,
                 p->frac_lo &= ~round_mask;
             }
         } else if (unlikely(exp >= exp_max)) {
-            flags |= float_flag_overflow | float_flag_inexact;
-            if (overflow_norm) {
+            flags |= float_flag_overflow;
+            if (s->rebias_overflow) {
+                exp -= fmt->exp_re_bias;
+            } else if (overflow_norm) {
+                flags |= float_flag_inexact;
                 exp = exp_max - 1;
                 frac_allones(p);
                 p->frac_lo &= ~round_mask;
             } else {
+                flags |= float_flag_inexact;
                 p->cls = float_class_inf;
                 exp = exp_max;
                 frac_clear(p);
             }
         }
         frac_shr(p, frac_shift);
+    } else if (unlikely(s->rebias_underflow)) {
+        flags |= float_flag_underflow;
+        exp += fmt->exp_re_bias;
+        if (p->frac_lo & round_mask) {
+            flags |= float_flag_inexact;
+            if (frac_addi(p, p, inc)) {
+                frac_shr(p, 1);
+                p->frac_hi |= DECOMPOSED_IMPLICIT_BIT;
+                exp++;
+            }
+            p->frac_lo &= ~round_mask;
+        }
+        frac_shr(p, frac_shift);
     } else if (s->flush_to_zero) {
         flags |= float_flag_output_denormal;
         p->cls = float_class_zero;
diff --git a/fpu/softfloat.c b/fpu/softfloat.c
index 4a871ef2a1..c7454c3eb1 100644
--- a/fpu/softfloat.c
+++ b/fpu/softfloat.c
@@ -521,6 +521,7 @@ typedef struct {
 typedef struct {
     int exp_size;
     int exp_bias;
+    int exp_re_bias;
     int exp_max;
     int frac_size;
     int frac_shift;
@@ -532,6 +533,7 @@ typedef struct {
 #define FLOAT_PARAMS_(E)                                \
     .exp_size       = E,                                \
     .exp_bias       = ((1 << E) - 1) >> 1,              \
+    .exp_re_bias    = (1 << (E - 1)) + (1 << (E - 2)),  \
     .exp_max        = (1 << E) - 1
 
 #define FLOAT_PARAMS(E, F)                              \
diff --git a/include/fpu/softfloat-types.h b/include/fpu/softfloat-types.h
index 7a6ea881d8..0884ec4ef7 100644
--- a/include/fpu/softfloat-types.h
+++ b/include/fpu/softfloat-types.h
@@ -195,6 +195,10 @@ typedef struct float_status {
     bool snan_bit_is_one;
     bool use_first_nan;
     bool no_signaling_nans;
+    /* should overflowed results subtract re_bias to its exponent? */
+    bool rebias_overflow;
+    /* should underflowed results add re_bias to its exponent? */
+    bool rebias_underflow;
 } float_status;
 
 #endif /* SOFTFLOAT_TYPES_H */