diff --git a/python/test/unit/language/test_random.py b/python/test/unit/language/test_random.py
index 042065403..39ae59e35 100644
--- a/python/test/unit/language/test_random.py
+++ b/python/test/unit/language/test_random.py
@@ -175,3 +175,24 @@ def test_randn(size, seed, device='cuda'):
     kernel[grid](x, N, seed)
     assert abs(x.mean()) < 1e-2
     assert abs(x.std() - 1) < 1e-2
+
+
+# tl.rand() should never produce >=1.0
+
+def test_rand_limits():
+    @triton.jit
+    def kernel(input, output, n: tl.constexpr):
+        idx = tl.arange(0, n)
+        x = tl.load(input + idx)
+        y = tl.random.uint32_to_uniform_float(x)
+        tl.store(output + idx, y)
+
+    min_max_int32 = torch.tensor([
+        torch.iinfo(torch.int32).min,
+        torch.iinfo(torch.int32).max,
+    ], dtype=torch.int32, device='cuda')
+    output = torch.empty(2, dtype=torch.float32, device='cuda')
+    kernel[(1,)](min_max_int32, output, 2)
+
+    assert output[0] == output[1]
+    assert 1.0 - torch.finfo(torch.float32).eps <= output[0].item() < 1.0
diff --git a/python/triton/language/random.py b/python/triton/language/random.py
index c95eac9fc..67de92c43 100644
--- a/python/triton/language/random.py
+++ b/python/triton/language/random.py
@@ -91,9 +91,10 @@ def uint32_to_uniform_float(x):
     Numerically stable function to convert a random uint32 into a random float uniformly sampled in [0, 1).
     """
     x = x.to(tl.int32, bitcast=True)
-    max = 4.656613e-10  # = 1/MAX_INT = 1/2147483647.
+    # maximum value such that `MAX_INT * scale < 1.0` (with float rounding)
+    scale = 4.6566127342e-10
     x = tl.where(x < 0, -x - 1, x)
-    return x * max
+    return x * scale
 
 
 @triton.jit