2144	 On Accurate Floating-Point Summation	 The accumulation of floating-point sums is considered on a computer which performs t-digit base B floating-point addition with exponents in the range -m to M. An algorithm is given for accurately summing N t-digit floating-point numbers. Each of these N numbers is split into q parts forming qN t-digit floating-point numbers. Each of these is then added to the appropriate one of n auxiliary t-digit accumulators. Finally the accumulators are added together to yield the computed sum. In all qN n- t-digit floating-point additions are performed. Under usual conditions the relative error in the computed sum is at most t v B -t for some v. Further with an additional q n- t-digit additions the computed sum can be corrected to full t-digit accuracy. For example for the IBM B t M m typical values for q and n are q and n . In this case becomes N and we have t v B -t x - . floating-point summation error analysis
