Fix num_digits_fast for powers of ten

maths/number_of_digits.py

@@ -44,13 +44,17 @@ def num_digits_fast(n: int) -> int:
     5
     >>> num_digits_fast(123)
     3
+    >>> num_digits_fast(1000)
+    4
+    >>> num_digits_fast(10**15)
+    16
     >>> num_digits_fast(0)
     1
     >>> num_digits_fast(-1)
     1
     >>> num_digits_fast(-123456)
     6
-    >>> num_digits('123')  # Raises a TypeError for non-integer input
+    >>> num_digits_fast('123')  # Raises a TypeError for non-integer input
     Traceback (most recent call last):
         ...
     TypeError: Input must be an integer
@@ -59,7 +63,12 @@ def num_digits_fast(n: int) -> int:
     if not isinstance(n, int):
         raise TypeError("Input must be an integer")
 
-    return 1 if n == 0 else math.floor(math.log(abs(n), 10) + 1)
+    if n == 0:
+        return 1
+
+    abs_n = abs(n)
+    digits = math.floor(math.log10(abs_n)) + 1
+    return digits + 1 if 10**digits <= abs_n else digits
 
 
 def num_digits_faster(n: int) -> int:
@@ -77,7 +86,7 @@ def num_digits_faster(n: int) -> int:
     1
     >>> num_digits_faster(-123456)
     6
-    >>> num_digits('123')  # Raises a TypeError for non-integer input
+    >>> num_digits_faster('123')  # Raises a TypeError for non-integer input
     Traceback (most recent call last):
         ...
     TypeError: Input must be an integer