The panchangam calculation requires two important heavenly bodies – the sun and the moon, and will be as accurate as how these heavenly bodies are calculated. In ancient times, there were many methods of calculating them. The most ancient one is Surya Siddhanta, another is the Vakyam Siddhanta and the later one is the Driga Ganita (Thirukanitha).
The Vakiyam is an ancient system where planetary motions are described in simple sentences (hence the vakya).
This mathematical system of the slogans or Simple Sentance, which were organised by the Rishis together thousands of years ago, is an alphabet based on writing. As the rituals are performed in the temples are following vakiyam panchangam people often follow the same. The Vakiyam comes out as an unmodified panchagam of anciant system.