The solar position algorithm (SPA) is a very accurate but slow algorithm for the computation of the Sun position with respect to an observer at ground surface. We compare the results of three fast algorithms to the SPA and establish their performances. We propose a new algorithm SG2 that is faster than the three others and offers the same level of accuracy than the most accurate, i.e., maximum error in solar vector of order of 10″, for a multi-decadal time period, with an example of a 50-year period: 1980-2030. This performance is achieved by devising approximations of the original equations of the SPA to decrease the number of operations. This yields a decrease in accuracy that is controlled and bounded. The mathematical tools permitting to determine these approximations with a selected uncertainty level are described.