Abstract: Generating data structures for computer memory. Provisional data structures are generated that respectively have (i) a significand with an initial value of zero and (ii) an exponent that is included in a range of exponents. A test data structure from a provisional data structure by modifying a significand of the first provisional data structure using a significand of a floating-point number such that the significand of the first provisional data structure has a non-zero value. Modifying at least one provisional data structure based on a content of the test data structure. Generating a new data structure that represents the contents of a plurality of provisional-data structures. The plurality of provisional data structures includes at least one provisional data structure that was modified to include the significands of at least two floating-point numbers. The new data structure represents a value that is expressible by a limited number of memory bits.

Abstract: Generating data structures for computer memory. Provisional data structures are generated that respectively have (i) a significand with an initial value of zero and (ii) an exponent that is included in a range of exponents. A test data structure from a provisional data structure by modifying a significand of the first provisional data structure using a significand of a floating-point number such that the significand of the first provisional data structure has a non-zero value. Modifying at least one provisional data structure based on a content of the test data structure. Generating a new data structure that represents the contents of a plurality of provisional-data structures. The plurality of provisional data structures includes at least one provisional data structure that was modified to include the significands of at least two floating-point numbers. The new data structure represents a value that is expressible by a limited number of memory bits.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.