diff --git a/target-arm/neon_helper.c b/target-arm/neon_helper.c
index bf29bbe..5971275 100644
--- a/target-arm/neon_helper.c
+++ b/target-arm/neon_helper.c
@@ -540,6 +540,9 @@ uint64_t HELPER(neon_shl_s64)(uint64_t valop, uint64_t shiftop)
     return val;
 }
 
+/* The addition of the rounding constant may overflow, so we use an
+ * intermediate 64 bits accumulator, which is really needed only when
+ * dealing with 32 bits input values.  */
 #define NEON_FN(dest, src1, src2) do { \
     int8_t tmp; \
     tmp = (int8_t)src2; \
@@ -548,11 +551,12 @@ uint64_t HELPER(neon_shl_s64)(uint64_t valop, uint64_t shiftop)
     } else if (tmp < -(ssize_t)sizeof(src1) * 8) { \
         dest = src1 >> (sizeof(src1) * 8 - 1); \
     } else if (tmp == -(ssize_t)sizeof(src1) * 8) { \
-        dest = src1 >> (tmp - 1); \
+        dest = src1 >> (-tmp - 1); \
         dest++; \
         dest >>= 1; \
     } else if (tmp < 0) { \
-        dest = (src1 + (1 << (-1 - tmp))) >> -tmp; \
+        int64_t big_dest = ((int64_t)src1 + (1 << (-1 - tmp))); \
+        dest = big_dest >> -tmp; \
     } else { \
         dest = src1 << tmp; \
     }} while (0)
@@ -561,6 +565,8 @@ NEON_VOP(rshl_s16, neon_s16, 2)
 NEON_VOP(rshl_s32, neon_s32, 1)
 #undef NEON_FN
 
+/* Handling addition overflow with 64 bits inputs values is more
+ * tricky than with 32 bits values.  */
 uint64_t HELPER(neon_rshl_s64)(uint64_t valop, uint64_t shiftop)
 {
     int8_t shift = (int8_t)shiftop;
@@ -569,18 +575,37 @@ uint64_t HELPER(neon_rshl_s64)(uint64_t valop, uint64_t shiftop)
         val = 0;
     } else if (shift < -64) {
         val >>= 63;
-    } else if (shift == -63) {
+    } else if (shift == -64) {
         val >>= 63;
         val++;
         val >>= 1;
     } else if (shift < 0) {
-        val = (val + ((int64_t)1 << (-1 - shift))) >> -shift;
+        int64_t round = (int64_t)1 << (-1 - shift);
+        /* Reduce the range as long as the addition overflows.  It's
+         * sufficient to check if (val+round) is < 0 and val > 0
+         * because round is > 0.  */
+        while ((val > 0) && ((val + round) < 0) && round > 1) {
+            shift++;
+            round >>= 1;
+            val >>= 1;
+        }
+        if ((val > 0) && (val + round) < 0) {
+            /* If addition still overflows at this point, it means
+             * that round==1, thus shift==-1, and also that
+             * val==0x7FFFFFFFFFFFFFFF.  */
+            val = 0x4000000000000000LL;
+        } else {
+            val = (val + round) >> -shift;
+        }
     } else {
         val <<= shift;
     }
     return val;
 }
 
+/* The addition of the rounding constant may overflow, so we use an
+ * intermediate 64 bits accumulator, which is really needed only when
+ * dealing with 32 bits input values.  */
 #define NEON_FN(dest, src1, src2) do { \
     int8_t tmp; \
     tmp = (int8_t)src2; \
@@ -588,9 +613,10 @@ uint64_t HELPER(neon_rshl_s64)(uint64_t valop, uint64_t shiftop)
         tmp < -(ssize_t)sizeof(src1) * 8) { \
         dest = 0; \
     } else if (tmp == -(ssize_t)sizeof(src1) * 8) { \
-        dest = src1 >> (tmp - 1); \
+        dest = src1 >> (-tmp - 1); \
     } else if (tmp < 0) { \
-        dest = (src1 + (1 << (-1 - tmp))) >> -tmp; \
+        uint64_t big_dest = ((uint64_t)src1 + (1 << (-1 - tmp))); \
+        dest = big_dest >> -tmp; \
     } else { \
         dest = src1 << tmp; \
     }} while (0)
@@ -602,14 +628,29 @@ NEON_VOP(rshl_u32, neon_u32, 1)
 uint64_t HELPER(neon_rshl_u64)(uint64_t val, uint64_t shiftop)
 {
     int8_t shift = (uint8_t)shiftop;
-    if (shift >= 64 || shift < 64) {
+    if (shift >= 64 || shift < -64) {
         val = 0;
     } else if (shift == -64) {
         /* Rounding a 1-bit result just preserves that bit.  */
         val >>= 63;
-    } if (shift < 0) {
-        val = (val + ((uint64_t)1 << (-1 - shift))) >> -shift;
-        val >>= -shift;
+    } else if (shift < 0) {
+        uint64_t round = (uint64_t)1 << (-1 - shift);
+        /* Reduce the range as long as the addition overflows.  It's
+         * sufficient to check if (val+round) is < val
+         * because val and round are > 0.  */
+        while (((val + round) < val) && round > 1) {
+            shift++;
+            round >>= 1;
+            val >>= 1;
+        }
+        if ((val + round) < val) {
+            /* If addition still overflows at this point, it means
+             * that round==1, thus shift==-1, and also that
+             * val==0x&FFFFFFFFFFFFFFF.  */
+            val = 0x8000000000000000LL;
+        } else {
+            val = (val + round) >> -shift;
+        }
     } else {
         val <<= shift;
     }
diff --git a/target-arm/translate.c b/target-arm/translate.c
index 4cf2ecd..b14fa4b 100644
--- a/target-arm/translate.c
+++ b/target-arm/translate.c
@@ -4885,13 +4885,24 @@ static int disas_neon_data_insn(CPUState * env, DisasContext *s, uint32_t insn)
                         tcg_gen_shli_i64(cpu_V0, cpu_V0, shift);
                         if (size < 2 || !u) {
                             uint64_t imm64;
-                            if (size == 0) {
+                            switch(size) {
+                            case 0:
                                 imm = (0xffu >> (8 - shift));
                                 imm |= imm << 16;
-                            } else {
+                                break;
+                            case 1:
                                 imm = 0xffff >> (16 - shift);
+                                break;
+                            case 2:
+                                imm = 0xffffffff >> (32 - shift);
+                                break;
+                            }
+                            if (size < 2) {
+                                imm64 = imm | (((uint64_t)imm) << 32);
+                            } else {
+                                imm64 = imm;
                             }
-                            imm64 = imm | (((uint64_t)imm) << 32);
+                            imm64 = ~imm64;
                             tcg_gen_andi_i64(cpu_V0, cpu_V0, imm64);
                         }
                     }
