diff --git a/python/tvm/topi/cuda/scan.py b/python/tvm/topi/cuda/scan.py
index 5d3798e3d27b..6dbaf02191c8 100644
--- a/python/tvm/topi/cuda/scan.py
+++ b/python/tvm/topi/cuda/scan.py
@@ -23,7 +23,7 @@
 from tvm.contrib.thrust import can_use_rocthrust, can_use_thrust
 
 from .. import tag
-from ..math import cast
+from ..math import cast, ceil_log2
 from ..transform import expand_dims, reshape, squeeze, transpose
 from ..utils import ceil_div, get_const_int, prod, swap
 from .injective import schedule_injective_from_existing
@@ -103,9 +103,8 @@ def exclusive_scan_ir(data, output, reduction=None, binop=tvm.tir.generic.add, i
 
         # The following algorithm performs parallel exclusive scan
         # Up Sweep of exclusive scan
-        lim = tvm.tir.generic.cast(
-            tvm.tir.ceil(tvm.tir.log2(tvm.tir.generic.cast(scan_axis_size, "float64"))), "int64"
-        )
+        lim = ceil_log2(scan_axis_size)
+
         with ib.for_range(0, lim, dtype="int64") as l2_width:
             width = 2 << l2_width
 
diff --git a/python/tvm/topi/cuda/sort.py b/python/tvm/topi/cuda/sort.py
index 93e4d3feccc7..25cc7a4e2cfb 100644
--- a/python/tvm/topi/cuda/sort.py
+++ b/python/tvm/topi/cuda/sort.py
@@ -23,7 +23,7 @@
 from ..transform import strided_slice, transpose
 from .. import tag
 from ..utils import ceil_div, swap
-from ..math import cast
+from ..math import cast, ceil_log2
 
 
 def _schedule_sort(outs):
@@ -238,9 +238,7 @@ def compare(a, b):
         return out
 
     # Sort the lower levels of the merge using odd-even sort, it's fast for small inputs
-    lower_lim = tvm.tir.generic.cast(
-        tvm.tir.ceil(tvm.tir.log2(tvm.tir.generic.cast(block_size, "float64"))), "int64"
-    )
+    lower_lim = ceil_log2(block_size)
 
     _odd_even_sort(
         ib,
@@ -254,9 +252,7 @@ def compare(a, b):
         values_swap,
     )
 
-    upper_lim = tvm.tir.generic.cast(
-        tvm.tir.ceil(tvm.tir.log2(tvm.tir.generic.cast(size, "float64"))), "int64"
-    )
+    upper_lim = ceil_log2(size)
 
     def get_merge_begin(source, base_idx, aCount, bCount, aStart, bStart, diag, step_count):
         first = ib.allocate("int64", (1,), name="first", scope="local")
diff --git a/python/tvm/topi/math.py b/python/tvm/topi/math.py
index cf6fcbb88c7e..d3ef3daf10dc 100644
--- a/python/tvm/topi/math.py
+++ b/python/tvm/topi/math.py
@@ -742,3 +742,37 @@ def fast_erf(x):
         The result.
     """
     return cpp.fast_erf(x, x.dtype, tag.ELEMWISE)
+
+
+def ceil_log2(x):
+    """Compute integer ceil log2 with a special code path for vulkan
+    SPIR-V does not support log2 on fp64. Instead, we compute integer ceil_log2 via clz
+    intrinsic when the target is vulkan.
+
+    Parameters
+    ----------
+    x : tvm.te.Tensor
+        Input argument.
+
+    Returns
+    -------
+    y : tvm.te.Tensor
+        The result.
+    """
+    if not isinstance(x, tvm.tir.PrimExpr):
+        x = tvm.tir.const(x)
+
+    if "float" in x.dtype:
+        return tvm.tir.ceil(tvm.tir.log2(x))
+
+    if "vulkan" in tvm.target.Target.current().kind.name:
+        clz = tvm.tir.clz(x)
+        bits = int(x.dtype[-2:])
+        res = tvm.tir.if_then_else(x & (x - 1) == 0, bits - clz - 1, bits - clz)
+
+        if res.dtype != x.dtype:
+            return cast(res, x.dtype)
+
+        return res
+
+    return cast(tvm.tir.ceil(tvm.tir.log2(cast(x, "float64"))), x.dtype)
diff --git a/tests/python/unittest/test_target_codegen_spirv.py b/tests/python/unittest/test_target_codegen_spirv.py
index df42eeb721ab..b9f07cf426fe 100644
--- a/tests/python/unittest/test_target_codegen_spirv.py
+++ b/tests/python/unittest/test_target_codegen_spirv.py
@@ -104,6 +104,16 @@ def test_pushconstants():
 
     check_mod(mod, x_np, res_np)
 
+    # One 64 bit and one 32 bit constants
+    dtype = "int32"
+    x = relay.var("x", shape=(relay.Any(),), dtype=dtype)
+    mod = tvm.IRModule()
+    mod["main"] = relay.Function([x], relay.cumsum(x))
+    x_np = np.random.randint(0, high=10, size=(10,)).astype(dtype)
+    res_np = np.cumsum(x_np)
+
+    check_mod(mod, x_np, res_np)
+
 
 def test_unique():
     if not tvm.testing.device_enabled("vulkan"):