feat: add utils.py for helper functions

Author: gy001

utils.py

@@ -0,0 +1,59 @@
+#!/usr/bin/env python3
+
+def bits_le_with_width(i, width):
+    if i >= 2**width:
+        return "Failed"
+    bits = []
+    while width:
+        bits.append(i % 2)
+        i //= 2
+        width -= 1
+    return bits
+    
+
+def pow_2(n):
+    return 1 << n
+
+def is_power_of_two(n):
+    d = n
+    k = 0
+    while d > 0:
+        d >>= 1
+        k += 1
+    if n == 2**(k-1):
+        return True
+    else:
+        return False
+
+def next_power_of_two(n):
+    assert n >= 0, "No negative integer"
+    if is_power_of_two(n):
+        return n
+    d = n
+    k = 1
+    while d > 0:
+        d >>= 1
+        k <<= 1
+    return k
+
+def log_2(x):
+    """
+    Compute the integer part of the logarithm base 2 of x.
+
+    Args:
+        x (int): The number to compute the logarithm of. Must be a positive integer.
+
+    Returns:
+        int: The floor of the logarithm base 2 of x.
+
+    Raises:
+        ValueError: If x is not a positive integer.
+    """
+    if not isinstance(x, int) or x <= 0:
+        raise ValueError("x must be a positive integer")
+    
+    result = 0
+    while x > 1:
+        x >>= 1  # Bit shift right (equivalent to integer division by 2)
+        result += 1
+    return result