diff --git a/bitsandbytes/functional.py b/bitsandbytes/functional.py
index 161f58f..5198526 100644
--- a/bitsandbytes/functional.py
+++ b/bitsandbytes/functional.py
@@ -218,7 +218,7 @@ def create_custom_map(seed=0, scale=0.01):
     assert values.numel() == 256
     return values
 
-def create_normal_map(offset=0.966666, use_extra_value=True):
+def create_normal_map(offset=0.9677083, use_extra_value=True):
 
     if use_extra_value:
         # one more positive value, this is an asymmetric type
diff --git a/tests/test_functional.py b/tests/test_functional.py
index 47a30a6..074135e 100644
--- a/tests/test_functional.py
+++ b/tests/test_functional.py
@@ -2318,3 +2318,19 @@ def test_bench_fp4_dequant():
     #    torch.matmul(b, a.t())
     #torch.cuda.synchronize()
     #print((time.time()-t0)/iters*1e6)
+
+
+
+def test_normal_map_tree():
+    code = F.create_normal_map()
+    values =code[:8].tolist() + code[-8:].tolist()
+    num_pivots = 1
+    while num_pivots <16:
+        idx = list(range(16//num_pivots//2, 16, 16//num_pivots))
+        print(idx)
+        num_pivots *= 2
+        pivots = []
+        for i in idx:
+            pivots.append((values[i-1]+values[i])/2)
+        print(pivots)
+