1. In an electronic computer operating in a floating point system and wherein data is defined as a function of (b, l, e.sub.1, e.sub.2) where b is the base, 1 is the number of digits of the mantissa, e.sub.1 is the least exponent and e.sub.2 is the highest exponent, the improvement comprising means receiving two floating point vectors each having a finite number of vector components for performing a scalar product operation thereon with maximum accuracy wherein the scalar product is produced from a sum of a plurality of partial scalar products of the vector components, including first means for performing fixed point arithmetic operations on the mantissas and exponents of each of the vector components to produce the plurality of partial scalar products, second means receiving the partial scalar products from the first means for storing each partial scalar product in fixed point format in a store having a length L which is 21+2e.sub.2 +2 times greater than the absolute value of e.sub.1 ; third means receiving the partial scalar products from the second means for summing the stored fixed point partial scalar products; fourth means receiving the summed partial scalar products from the third means for rounding the resulting sum of partial scalar products to the floating point number closest thereto to obtain maximum accuracy; and fifth means receiving the rounded sum from the fourth means for converting the rounded sum into floating point format.