public static class QuaternionExtensions
    {
        public static Quaternion Pow(this Quaternion input, float power)
        {
            float inputMagnitude = input.Magnitude();
            Vector3 nHat = new Vector3(input.x, input.y, input.z).normalized;
            Quaternion vectorBit = new Quaternion(nHat.x, nHat.y, nHat.z, 0)
                .ScalarMultiply(power * Mathf.Acos(input.w / inputMagnitude))
                .Exp();
            return vectorBit.ScalarMultiply(Mathf.Pow(inputMagnitude, power));
        }

        public static Quaternion Exp(this Quaternion input)
        {
            float inputA = input.w;
            Vector3 inputV = new Vector3(input.x, input.y, input.z);
            float outputA = Mathf.Exp(inputA) * Mathf.Cos(inputV.magnitude);
            Vector3 outputV = Mathf.Exp(inputA) * (inputV.normalized * Mathf.Sin(inputV.magnitude));
            return new Quaternion(outputV.x, outputV.y, outputV.z, outputA);
        }

        public static float Magnitude(this Quaternion input)
        {
            return Mathf.Sqrt(input.x * input.x + input.y * input.y + input.z * input.z + input.w * input.w);
        }

        public static Quaternion ScalarMultiply(this Quaternion input, float scalar)
        {
            return new Quaternion(input.x * scalar, input.y * scalar, input.z * scalar, input.w * scalar);
        }

        public static Quaternion Normalize(this Quaternion input)
        {
            input = input.ScalarMultiply(2f);
            float magnitude = input.Magnitude() - float.Epsilon;
            return new Quaternion(input.x / magnitude, input.y / magnitude, input.z / magnitude, input.w / magnitude);
        }
    }