diff --git a/tcg/s390/tcg-target.c b/tcg/s390/tcg-target.c
index 826a2c8..795ddcd 100644
--- a/tcg/s390/tcg-target.c
+++ b/tcg/s390/tcg-target.c
@@ -33,8 +33,9 @@
     do { } while (0)
 #endif
 
-#define TCG_CT_CONST_S16                0x100
-#define TCG_CT_CONST_U12                0x200
+#define TCG_CT_CONST_32    0x100
+#define TCG_CT_CONST_NEG   0x200
+#define TCG_CT_CONST_ADDI  0x400
 
 /* Several places within the instruction set 0 means "no register"
    rather than TCG_REG_R0.  */
@@ -49,6 +50,9 @@
    halves of the 16-bit quantity may appear 32 bits apart in the insn.
    This makes it easy to copy the values from the tables in Appendix B.  */
 typedef enum S390Opcode {
+    RIL_AFI     = 0xc209,
+    RIL_AGFI    = 0xc208,
+    RIL_ALGFI   = 0xc20a,
     RIL_BRASL   = 0xc005,
     RIL_BRCL    = 0xc004,
     RIL_LARL    = 0xc000,
@@ -303,9 +307,17 @@ static int target_parse_constraint(TCGArgConstraint *ct, const char **pct_str)
         tcg_regset_clear(ct->u.regs);
         tcg_regset_set_reg(ct->u.regs, TCG_REG_R3);
         break;
+    case 'N':                  /* force immediate negate */
+        ct->ct &= ~TCG_CT_REG;
+        ct->ct |= TCG_CT_CONST_NEG;
+        break;
+    case 'W':                  /* force 32-bit ("word") immediate */
+        ct->ct &= ~TCG_CT_REG;
+        ct->ct |= TCG_CT_CONST_32;
+        break;
     case 'I':
         ct->ct &= ~TCG_CT_REG;
-        ct->ct |= TCG_CT_CONST_S16;
+        ct->ct |= TCG_CT_CONST_ADDI;
         break;
     default:
         break;
@@ -322,12 +334,31 @@ static inline int tcg_target_const_match(tcg_target_long val,
 {
     int ct = arg_ct->ct;
 
-    if ((ct & TCG_CT_CONST) ||
-       ((ct & TCG_CT_CONST_S16) && val == (int16_t)val) ||
-       ((ct & TCG_CT_CONST_U12) && val == (val & 0xfff))) {
+    if (ct & TCG_CT_CONST) {
         return 1;
     }
 
+    /* Handle the modifiers.  */
+    if (ct & TCG_CT_CONST_NEG) {
+        val = -val;
+    }
+    if (ct & TCG_CT_CONST_32) {
+        val = (int32_t)val;
+    }
+
+    /* The following are mutually exclusive.  */
+    if (ct & TCG_CT_CONST_ADDI) {
+        /* Immediates that may be used with add.  If we have the
+           extended-immediates facility then we have ADD IMMEDIATE
+           with signed and unsigned 32-bit, otherwise we have only
+           ADD HALFWORD IMMEDIATE with a signed 16-bit.  */
+        if (facilities & FACILITY_EXT_IMM) {
+            return val == (int32_t)val || val == (uint32_t)val;
+        } else {
+            return val == (int16_t)val;
+        }
+    }
+
     return 0;
 }
 
@@ -649,6 +680,29 @@ static inline void tgen_ext32u(TCGContext *s, TCGReg dest, TCGReg src)
     tcg_out_insn(s, RRE, LLGFR, dest, src);
 }
 
+static void tgen32_addi(TCGContext *s, TCGReg dest, int32_t val)
+{
+    if (val == (int16_t)val) {
+        tcg_out_insn(s, RI, AHI, dest, val);
+    } else {
+        tcg_out_insn(s, RIL, AFI, dest, val);
+    }
+}
+
+static void tgen64_addi(TCGContext *s, TCGReg dest, int64_t val)
+{
+    if (val == (int16_t)val) {
+        tcg_out_insn(s, RI, AGHI, dest, val);
+    } else if (val == (int32_t)val) {
+        tcg_out_insn(s, RIL, AGFI, dest, val);
+    } else if (val == (uint32_t)val) {
+        tcg_out_insn(s, RIL, ALGFI, dest, val);
+    } else {
+        tcg_abort();
+    }
+
+}
+
 static void tgen32_cmp(TCGContext *s, TCGCond c, TCGReg r1, TCGReg r2)
 {
     if (c > TCG_COND_GT) {
@@ -1095,22 +1149,32 @@ static inline void tcg_out_op(TCGContext *s, TCGOpcode opc,
 
     case INDEX_op_add_i32:
         if (const_args[2]) {
-            tcg_out_insn(s, RI, AHI, args[0], args[2]);
+            tgen32_addi(s, args[0], args[2]);
         } else {
             tcg_out_insn(s, RR, AR, args[0], args[2]);
         }
         break;
-
     case INDEX_op_add_i64:
-        tcg_out_insn(s, RRE, AGR, args[0], args[2]);
+        if (const_args[2]) {
+            tgen64_addi(s, args[0], args[2]);
+        } else {
+            tcg_out_insn(s, RRE, AGR, args[0], args[2]);
+        }
         break;
 
     case INDEX_op_sub_i32:
-        tcg_out_insn(s, RR, SR, args[0], args[2]);
+        if (const_args[2]) {
+            tgen32_addi(s, args[0], -args[2]);
+        } else {
+            tcg_out_insn(s, RR, SR, args[0], args[2]);
+        }
         break;
-
     case INDEX_op_sub_i64:
-        tcg_out_insn(s, RRE, SGR, args[0], args[2]);
+        if (const_args[2]) {
+            tgen64_addi(s, args[0], -args[2]);
+        } else {
+            tcg_out_insn(s, RRE, SGR, args[0], args[2]);
+        }
         break;
 
     case INDEX_op_and_i32:
@@ -1383,8 +1447,8 @@ static const TCGTargetOpDef s390_op_defs[] = {
     { INDEX_op_st16_i32, { "r", "r" } },
     { INDEX_op_st_i32, { "r", "r" } },
 
-    { INDEX_op_add_i32, { "r", "0", "rI" } },
-    { INDEX_op_sub_i32, { "r", "0", "r" } },
+    { INDEX_op_add_i32, { "r", "0", "rWI" } },
+    { INDEX_op_sub_i32, { "r", "0", "rWNI" } },
     { INDEX_op_mul_i32, { "r", "0", "r" } },
 
     { INDEX_op_div2_i32, { "b", "a", "0", "1", "r" } },
@@ -1444,8 +1508,8 @@ static const TCGTargetOpDef s390_op_defs[] = {
     { INDEX_op_st32_i64, { "r", "r" } },
     { INDEX_op_st_i64, { "r", "r" } },
 
-    { INDEX_op_add_i64, { "r", "0", "r" } },
-    { INDEX_op_sub_i64, { "r", "0", "r" } },
+    { INDEX_op_add_i64, { "r", "0", "rI" } },
+    { INDEX_op_sub_i64, { "r", "0", "rNI" } },
     { INDEX_op_mul_i64, { "r", "0", "r" } },
 
     { INDEX_op_div2_i64, { "b", "a", "0", "1", "r" } },
