ACCURACY-CONSERVING FLOATING-POINT VALUE AGGREGATION

摘要

A method for enhancing an accuracy of a sum of a plurality of floating-point numbers. The method receives a floating-point number and generates a plurality of provisional numbers with a value of zero. The method further generates a surjective map from the values of an exponent and a sign of a mantissa to the provisional numbers in the plurality of provisional numbers. The method further maps a value of the exponent and the sign of the mantissa to a first provisional number with the surjective map. The method further generates a test number from the first provisional number and if the test number exceeds a limit, modifies a second provisional number by using at least part of the test number. The method further equates the first provisional number to the test number if the test number does not exceed the limit. The method further sums the plurality of provisional numbers.

主权项

1. A method for enhancing an accuracy of a sum of a plurality of floating-point numbers, the method comprising:
receiving a floating-point number; generating a plurality of provisional numbers each with a value of zero; generating a surjective map from one or more possible values of an exponent and a sign of a mantissa in the floating-point number to one or more provisional numbers in the plurality of provisional numbers; mapping a value of the exponent and the sign of the mantissa in the floating-point number to a first provisional number with the surjective map; generating a test number from the first provisional number by modifying the first provisional number using the mantissa; responsive to the test number exceeding a limit, modifying a second provisional number by using at least part of the test number; responsive to the test number not exceeding the limit, making the first provisional number equal to the test number; and summing the plurality of provisional numbers.