We will now cover three tricks—checking whether the signs of integers are different, checking whether a number is a power of 2, and calculating the modulus of a number that is a power of 2. We will show an operators-only notation and one using the corresponding NumPy functions:
The first trick depends on the
XORor^operator. TheXORoperator is also called the inequality operator; so, if the sign bit of the two operands is different, theXORoperation will lead to a negative number (see https://www.khanacademy.org/computing/computer-science/cryptography/ciphers/a/xor-bitwise-operation).The following truth table illustrates the
XORoperator:Input 1
Input 2
XOR
True
True
False
False
True
True
True
False
True
False
False
False
The
^operator corresponds to thebitwise_xor()function, and the<operator corresponds to theless()function:x = np.arange(-9, 9) y = -x print("Sign different?", (x ^ y) < 0) print("Sign different?", np.less(np...