Artificial intelligence in mathematical computations

The basic concepts of heuristic decisions making during the computational process related to mathematical computations on floating point data are discussed. New arithmetic architecture of the next generation computer systems with hardware-software support of a system for tracing the computational process including the relative accuracy of the input, intermediary and output data is proposed. This system will make heuristic decisions during the computer execution of mathematical computations for receiving the set relative accuracy of the final results on the basis of relative accuracy of the input data, the received relative accuracy of the intermediate results and the chosen computational algorithm. It is assumed that the mathematical computations will be performed by widely using the interval arithmetic and the achievements of the interval analysis. The proposed hardware support of the mathematical computations consists of a new format of the numbers with floating point, the lengths of the exponent and mantissa which will not be bounded from the top; "pulsed" arithmetic of such numbers (from here comes the PULSAR system); a series of adders with equal length by avoiding at the same time overflow, underflow and normalization with shift; the PULSAR hardware-software system for tracing the computational process and making heuristic decisions for data accuracy control.