diff --git a/src/lj_opt_fold.c b/src/lj_opt_fold.c
index e2171e1b48..2702f79f12 100644
--- a/src/lj_opt_fold.c
+++ b/src/lj_opt_fold.c
@@ -382,10 +382,10 @@ static uint64_t kfold_int64arith(jit_State *J, uint64_t k1, uint64_t k2,
   case IR_BOR: k1 |= k2; break;
   case IR_BXOR: k1 ^= k2; break;
   case IR_BSHL: k1 <<= (k2 & 63); break;
-  case IR_BSHR: k1 = (int32_t)((uint32_t)k1 >> (k2 & 63)); break;
-  case IR_BSAR: k1 >>= (k2 & 63); break;
-  case IR_BROL: k1 = (int32_t)lj_rol((uint32_t)k1, (k2 & 63)); break;
-  case IR_BROR: k1 = (int32_t)lj_ror((uint32_t)k1, (k2 & 63)); break;
+  case IR_BSHR: k1 >>= (k2 & 63); break;
+  case IR_BSAR: k1 = (uint64_t)((int64_t)k1 >> (k2 & 63)); break;
+  case IR_BROL: k1 = lj_rol(k1, (k2 & 63)); break;
+  case IR_BROR: k1 = lj_ror(k1, (k2 & 63)); break;
   default: lj_assertJ(0, "bad IR op %d", op); break;
   }
 #else
diff --git a/test/tarantool-tests/lj-1079-fix-64-bitshift-folds.test.lua b/test/tarantool-tests/lj-1079-fix-64-bitshift-folds.test.lua
new file mode 100644
index 0000000000..6cc0b319b9
--- /dev/null
+++ b/test/tarantool-tests/lj-1079-fix-64-bitshift-folds.test.lua
@@ -0,0 +1,74 @@
+local tap = require('tap')
+
+-- Test file to demonstrate LuaJIT misbehaviour on folding
+-- for bitshift operations.
+-- See also, https://github.com/LuaJIT/LuaJIT/issues/1079.
+
+local test = tap.test('lj-1079-fix-64-bitshift-folds'):skipcond({
+  ['Test requires JIT enabled'] = not jit.status(),
+})
+
+local bit = require('bit')
+
+test:plan(4)
+
+-- Generic function for `bit.ror()`, `bit.rol()`.
+local function bitop_rotation(bitop)
+  local r = {}
+  for i = 1, 4 do
+    -- (i & k1) o k2 ==> (i o k2) & (k1 o k2)
+    local int64 = bit.band(i, 7LL)
+    r[i] = tonumber(bitop(int64, 32))
+  end
+  return r
+end
+
+-- Similar function for `bit.rshift()`.
+local function bitop_rshift_signed()
+  local r = {}
+  for i = 1, 4 do
+    -- (i & k1) o k2 ==> (i o k2) & (k1 o k2)
+    -- XXX: Use `-i` instead of `i` to prevent other folding due
+    -- to IR difference so the IRs don't match fold rule mask.
+    -- (-i & 7LL) < 1 << 32 => result == 0.
+    local int64 = bit.band(-i, 7LL)
+    r[i] = tonumber(bit.rshift(int64, 32))
+  end
+  return r
+end
+
+-- A little bit different example, which leads to the assertion
+-- failure due to the incorrect recording.
+local function bitop_rshift_huge()
+  local r = {}
+  for i = 1, 4 do
+    -- (i & k1) o k2 ==> (i o k2) & (k1 o k2)
+    -- XXX: Need to use cast to the int64_t via `+ 0LL`, see the
+    -- documentation [1] for the details.
+    -- [1]: https://bitop.luajit.org/semantics.html
+    local int64 = bit.band(2 ^ 33 + i, 2 ^ 33 + 0LL)
+    r[i] = tonumber(bit.rshift(int64, 32))
+  end
+  return r
+end
+
+local function test_64bitness(subtest, payload_func, bitop)
+  subtest:plan(1)
+
+  jit.off()
+  jit.flush()
+  local results_joff = payload_func(bitop)
+  jit.on()
+  -- Reset hotcounters.
+  jit.opt.start('hotloop=1')
+  local results_jon = payload_func(bitop)
+  subtest:is_deeply(results_jon, results_joff,
+                    'same results for VM and JIT for ' .. subtest.name)
+end
+
+test:test('rol', test_64bitness, bitop_rotation, bit.rol)
+test:test('ror', test_64bitness, bitop_rotation, bit.ror)
+test:test('rshift signed', test_64bitness, bitop_rshift_signed)
+test:test('rshift huge',   test_64bitness, bitop_rshift_huge)
+
+test:done(true)