diff --git a/stage0/sema.c b/stage0/sema.c
index 30c93fcfed..68dcbea8e0 100644
--- a/stage0/sema.c
+++ b/stage0/sema.c
@@ -526,10 +526,12 @@ static TypeIndex semaTypeOf(Sema* sema, AirInstRef ref) {
     case AIR_INST_MUL_WRAP:
     case AIR_INST_ADD_SAT:
     case AIR_INST_SUB_SAT:
+    case AIR_INST_MUL_SAT:
     case AIR_INST_BIT_AND:
     case AIR_INST_BIT_OR:
     case AIR_INST_XOR:
     case AIR_INST_SHL:
+    case AIR_INST_SHL_SAT:
     case AIR_INST_SHR:
         return semaTypeOf(sema, sema->air_inst_datas[inst_idx].bin_op.lhs);
     // cmp bin_op: result type is bool.
@@ -3214,6 +3216,16 @@ static bool analyzeBodyInner(
                 zirArithmetic(sema, block, inst, AIR_INST_SUB_SAT));
             i++;
             continue;
+        case ZIR_INST_MUL_SAT:
+            instMapPut(&sema->inst_map, inst,
+                zirArithmetic(sema, block, inst, AIR_INST_MUL_SAT));
+            i++;
+            continue;
+        case ZIR_INST_SHL_SAT:
+            instMapPut(&sema->inst_map, inst,
+                zirArithmetic(sema, block, inst, AIR_INST_SHL_SAT));
+            i++;
+            continue;
 
         // Comparisons: same binary pattern as arithmetic.
         case ZIR_INST_CMP_LT:
diff --git a/stage0/sema_test.zig b/stage0/sema_test.zig
index 5578bd66d5..0cafde6616 100644
--- a/stage0/sema_test.zig
+++ b/stage0/sema_test.zig
@@ -1032,6 +1032,14 @@ test "sema air: sub_sat" {
     try semaAirRawCheck("export fn f(x: u32, y: u32) u32 { return x -| y; }");
 }
 
+test "sema air: mul_sat" {
+    try semaAirRawCheck("export fn f(x: u32, y: u32) u32 { return x *| y; }");
+}
+
+test "sema air: shl_sat" {
+    try semaAirRawCheck("export fn f(x: u32) u32 { return x <<| 1; }");
+}
+
 test "sema air: bit_or" {
     try semaAirRawCheck("export fn f(x: u32, y: u32) u32 { return x | y; }");
 }