We are currently solving the following issue within our repository. Here is the issue text:
--- BEGIN ISSUE ---
maths/number_of_digits.py is naive!
<code>[maths/number_of_digits.py](https://github.com/TheAlgorithms/Python/blob/master/maths/number_of_digits.py)</code> has a naive method. The suggested method has a time complexity of O(n). We can count number of digits of a number in O(1).

--- END ISSUE ---

Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
--- BEGIN FILES ---
Path: `maths/number_of_digits.py`
Content:
```
1 def num_digits(n: int) -> int:
2     """
3     Find the number of digits in a number.
4 
5     >>> num_digits(12345)
6     5
7     >>> num_digits(123)
8     3
9     """
10     digits = 0
11     while n > 0:
12         n = n // 10
13         digits += 1
14     return digits
15 
16 
17 if __name__ == "__main__":
18     print(num_digits(12345))  # ===> 5
19
```
--- END FILES ---

Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.

Here is an example:

```diff
diff --git a/examples/server_async.py b/examples/server_async.py
--- a/examples/server_async.py
+++ b/examples/server_async.py
@@ -313,4 +313,4 @@
 
 
 if __name__ == "__main__":
-    asyncio.run(run_async_server("."), debug=True)
+    asyncio.run(run_async_server(), debug=True)
diff --git a/examples/server_sync.py b/examples/server_sync.py
--- a/examples/server_sync.py
+++ b/examples/server_sync.py
@@ -313,5 +313,5 @@
 
 
 if __name__ == "__main__":
-    server = run_sync_server(".")
+    server = run_sync_server()
     server.shutdown()

```

diff --git a/maths/number_of_digits.py b/maths/number_of_digits.py
--- a/maths/number_of_digits.py
+++ b/maths/number_of_digits.py
@@ -1,3 +1,7 @@
+import math
+from timeit import timeit
+
+
 def num_digits(n: int) -> int:
     """
     Find the number of digits in a number.
@@ -14,5 +18,82 @@
     return digits
 
 
+def num_digits_fast(n: int) -> int:
+    """
+    Find the number of digits in a number.
+    abs() is used as logarithm for negative numbers is not defined.
+
+    >>> num_digits_fast(12345)
+    5
+    >>> num_digits_fast(123)
+    3
+    """
+    return (math.floor(math.log(abs(n), 10) + 1))
+
+
+def num_digits_faster(n: int) -> int:
+    """
+    Find the number of digits in a number.
+    abs() is used for negative numbers
+
+    >>> num_digits_faster(12345)
+    5
+    >>> num_digits_faster(123)
+    3
+    """
+    return (len(str(abs(n))))
+
+
+def benchmark() -> None:
+    """
+    Benchmark code for comparing 3 functions,
+    with 3 different length int values.
+    """
+    print('\nFor small_num = ', small_num, ':')
+    print("> num_digits()",
+          '\t\tans =', num_digits(small_num),
+          '\ttime =', timeit("z.num_digits(z.small_num)",
+                             setup="import __main__ as z"), "seconds")
+    print("> num_digits_fast()",
+          '\tans =', num_digits_fast(small_num),
+          '\ttime =', timeit("z.num_digits_fast(z.small_num)",
+                             setup="import __main__ as z"), "seconds")
+    print("> num_digits_faster()",
+          '\tans =', num_digits_faster(small_num),
+          '\ttime =', timeit("z.num_digits_faster(z.small_num)",
+                             setup="import __main__ as z"), "seconds")
+
+    print('\nFor medium_num = ', medium_num, ':')
+    print("> num_digits()",
+          '\t\tans =', num_digits(medium_num),
+          '\ttime =', timeit("z.num_digits(z.medium_num)",
+                             setup="import __main__ as z"), "seconds")
+    print("> num_digits_fast()",
+          '\tans =', num_digits_fast(medium_num),
+          '\ttime =', timeit("z.num_digits_fast(z.medium_num)",
+                             setup="import __main__ as z"), "seconds")
+    print("> num_digits_faster()",
+          '\tans =', num_digits_faster(medium_num),
+          '\ttime =', timeit("z.num_digits_faster(z.medium_num)",
+                             setup="import __main__ as z"), "seconds")
+
+    print('\nFor large_num = ', large_num, ':')
+    print("> num_digits()",
+          '\t\tans =', num_digits(large_num),
+          '\ttime =', timeit("z.num_digits(z.large_num)",
+                             setup="import __main__ as z"), "seconds")
+    print("> num_digits_fast()",
+          '\tans =', num_digits_fast(large_num),
+          '\ttime =', timeit("z.num_digits_fast(z.large_num)",
+                             setup="import __main__ as z"), "seconds")
+    print("> num_digits_faster()",
+          '\tans =', num_digits_faster(large_num),
+          '\ttime =', timeit("z.num_digits_faster(z.large_num)",
+                             setup="import __main__ as z"), "seconds")
+
+
 if __name__ == "__main__":
-    print(num_digits(12345))  # ===> 5
+    small_num = 262144
+    medium_num = 1125899906842624
+    large_num = 1267650600228229401496703205376
+    benchmark()

{"golden_diff": "diff --git a/maths/number_of_digits.py b/maths/number_of_digits.py\n--- a/maths/number_of_digits.py\n+++ b/maths/number_of_digits.py\n@@ -1,3 +1,7 @@\n+import math\n+from timeit import timeit\n+\n+\n def num_digits(n: int) -> int:\n     \"\"\"\n     Find the number of digits in a number.\n@@ -14,5 +18,82 @@\n     return digits\n \n \n+def num_digits_fast(n: int) -> int:\n+    \"\"\"\n+    Find the number of digits in a number.\n+    abs() is used as logarithm for negative numbers is not defined.\n+\n+    >>> num_digits_fast(12345)\n+    5\n+    >>> num_digits_fast(123)\n+    3\n+    \"\"\"\n+    return (math.floor(math.log(abs(n), 10) + 1))\n+\n+\n+def num_digits_faster(n: int) -> int:\n+    \"\"\"\n+    Find the number of digits in a number.\n+    abs() is used for negative numbers\n+\n+    >>> num_digits_faster(12345)\n+    5\n+    >>> num_digits_faster(123)\n+    3\n+    \"\"\"\n+    return (len(str(abs(n))))\n+\n+\n+def benchmark() -> None:\n+    \"\"\"\n+    Benchmark code for comparing 3 functions,\n+    with 3 different length int values.\n+    \"\"\"\n+    print('\\nFor small_num = ', small_num, ':')\n+    print(\"> num_digits()\",\n+          '\\t\\tans =', num_digits(small_num),\n+          '\\ttime =', timeit(\"z.num_digits(z.small_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_fast()\",\n+          '\\tans =', num_digits_fast(small_num),\n+          '\\ttime =', timeit(\"z.num_digits_fast(z.small_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_faster()\",\n+          '\\tans =', num_digits_faster(small_num),\n+          '\\ttime =', timeit(\"z.num_digits_faster(z.small_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+\n+    print('\\nFor medium_num = ', medium_num, ':')\n+    print(\"> num_digits()\",\n+          '\\t\\tans =', num_digits(medium_num),\n+          '\\ttime =', timeit(\"z.num_digits(z.medium_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_fast()\",\n+          '\\tans =', num_digits_fast(medium_num),\n+          '\\ttime =', timeit(\"z.num_digits_fast(z.medium_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_faster()\",\n+          '\\tans =', num_digits_faster(medium_num),\n+          '\\ttime =', timeit(\"z.num_digits_faster(z.medium_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+\n+    print('\\nFor large_num = ', large_num, ':')\n+    print(\"> num_digits()\",\n+          '\\t\\tans =', num_digits(large_num),\n+          '\\ttime =', timeit(\"z.num_digits(z.large_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_fast()\",\n+          '\\tans =', num_digits_fast(large_num),\n+          '\\ttime =', timeit(\"z.num_digits_fast(z.large_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_faster()\",\n+          '\\tans =', num_digits_faster(large_num),\n+          '\\ttime =', timeit(\"z.num_digits_faster(z.large_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+\n+\n if __name__ == \"__main__\":\n-    print(num_digits(12345))  # ===> 5\n+    small_num = 262144\n+    medium_num = 1125899906842624\n+    large_num = 1267650600228229401496703205376\n+    benchmark()\n", "issue": "maths/number_of_digits.py is naive!\n<code>[maths/number_of_digits.py](https://github.com/TheAlgorithms/Python/blob/master/maths/number_of_digits.py)</code> has a naive method. The suggested method has a time complexity of O(n). We can count number of digits of a number in O(1).\n", "before_files": [{"content": "def num_digits(n: int) -> int:\n    \"\"\"\n    Find the number of digits in a number.\n\n    >>> num_digits(12345)\n    5\n    >>> num_digits(123)\n    3\n    \"\"\"\n    digits = 0\n    while n > 0:\n        n = n // 10\n        digits += 1\n    return digits\n\n\nif __name__ == \"__main__\":\n    print(num_digits(12345))  # ===> 5\n", "path": "maths/number_of_digits.py"}], "after_files": [{"content": "import math\nfrom timeit import timeit\n\n\ndef num_digits(n: int) -> int:\n    \"\"\"\n    Find the number of digits in a number.\n\n    >>> num_digits(12345)\n    5\n    >>> num_digits(123)\n    3\n    \"\"\"\n    digits = 0\n    while n > 0:\n        n = n // 10\n        digits += 1\n    return digits\n\n\ndef num_digits_fast(n: int) -> int:\n    \"\"\"\n    Find the number of digits in a number.\n    abs() is used as logarithm for negative numbers is not defined.\n\n    >>> num_digits_fast(12345)\n    5\n    >>> num_digits_fast(123)\n    3\n    \"\"\"\n    return (math.floor(math.log(abs(n), 10) + 1))\n\n\ndef num_digits_faster(n: int) -> int:\n    \"\"\"\n    Find the number of digits in a number.\n    abs() is used for negative numbers\n\n    >>> num_digits_faster(12345)\n    5\n    >>> num_digits_faster(123)\n    3\n    \"\"\"\n    return (len(str(abs(n))))\n\n\ndef benchmark() -> None:\n    \"\"\"\n    Benchmark code for comparing 3 functions,\n    with 3 different length int values.\n    \"\"\"\n    print('\\nFor small_num = ', small_num, ':')\n    print(\"> num_digits()\",\n          '\\t\\tans =', num_digits(small_num),\n          '\\ttime =', timeit(\"z.num_digits(z.small_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_fast()\",\n          '\\tans =', num_digits_fast(small_num),\n          '\\ttime =', timeit(\"z.num_digits_fast(z.small_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_faster()\",\n          '\\tans =', num_digits_faster(small_num),\n          '\\ttime =', timeit(\"z.num_digits_faster(z.small_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n\n    print('\\nFor medium_num = ', medium_num, ':')\n    print(\"> num_digits()\",\n          '\\t\\tans =', num_digits(medium_num),\n          '\\ttime =', timeit(\"z.num_digits(z.medium_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_fast()\",\n          '\\tans =', num_digits_fast(medium_num),\n          '\\ttime =', timeit(\"z.num_digits_fast(z.medium_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_faster()\",\n          '\\tans =', num_digits_faster(medium_num),\n          '\\ttime =', timeit(\"z.num_digits_faster(z.medium_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n\n    print('\\nFor large_num = ', large_num, ':')\n    print(\"> num_digits()\",\n          '\\t\\tans =', num_digits(large_num),\n          '\\ttime =', timeit(\"z.num_digits(z.large_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_fast()\",\n          '\\tans =', num_digits_fast(large_num),\n          '\\ttime =', timeit(\"z.num_digits_fast(z.large_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_faster()\",\n          '\\tans =', num_digits_faster(large_num),\n          '\\ttime =', timeit(\"z.num_digits_faster(z.large_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n\n\nif __name__ == \"__main__\":\n    small_num = 262144\n    medium_num = 1125899906842624\n    large_num = 1267650600228229401496703205376\n    benchmark()\n", "path": "maths/number_of_digits.py"}]}