Projective rational arithmetic with floating point

Numerical computation is used nearly in all software packages. Today, computation is based on the floating point representation IEEE754 which offers single and double precision while quadruple or extended precision are supported very rarely in current programming languages. In this paper an alternative representation is presented which offers a higher range of digits of a fraction and a higher range of exponents. It is based on the projective extension of the Euclidean space. Due to this representation the division operation can be nearly eliminated, that leads to faster and more robust computation. The presented projective rational arithmetic is especially convenient for vector-vector architectures like GPU.