Associative summing for high performance computing

A system, comprising:

• a plurality of networked computers;
• and
• at least one network switch, configured to:
• receive, from the computers, a plurality of numbers, and
• calculate a sum of the numbers that is independent of an order in which the numbers are received, by:
• converting any of the numbers that are received in a floating-point representation to a derived floating-point representation that includes a plurality of signed integer multiplicands corresponding to different respective orders of magnitude, and
• summing the numbers in the derived floating-point representation, by separately summing integer multiplicands that correspond to the same order of magnitude.

A method, comprising, using a network switch:

• receiving a plurality of numbers;
• and
• calculating a sum of the numbers that is independent of an order in which the numbers are received, by:
• converting any of the numbers that are received in a floating-point representation to a derived floating-point representation that includes a plurality of signed integer multiplicands corresponding to different respective orders of magnitude, and
• summing the numbers in the derived floating-point representation, by separately summing integer multiplicands that correspond to the same order of magnitude.

A computer software product comprising a tangible non-transitory computer-readable medium in which program instructions are stored, which instructions, when read by a processor, cause the processor to:

• receive a plurality of numbers, and
• calculate a sum of the numbers that is independent of an order in which the numbers are received, by:
• converting any of the numbers that are received in a floating-point representation to a derived floating-point representation that includes a plurality of signed integer multiplicands corresponding to different respective orders of magnitude, and
• summing the numbers in the derived floating-point representation, by separately summing integer multiplicands that correspond to the same order of magnitude.