Decimal and binary floating point rounding

A computer implemented method for performing a floating point arithmetic add/subtract operation on a first floating point number and a second floating point number, wherein the first floating point number has a first magnitude and the second floating point number has a second magnitude, and wherein the first and second floating point numbers are in binary floating point format, the method comprising:

• mapping the binary floating point numbers to decimal floating point format, the mapping comprising padding bits to form digits that share the same fields of the floating point numbers in the decimal floating point format;
• generating a guard digit of zero of at least one of the first or the second floating point numbers by transforming the first and the second floating point numbers by a compressing function;
• determining as a result depending on the arithmetic operation, a sum of the transformed floating point numbers, and a first difference or a second difference of the transformed floating point numbers, wherein for the first difference the second floating point number is subtracted from the first floating point number and for the second difference the first floating point number is subtracted from the second floating point number, and
• determining a corresponding result plus one by additionally adding a value of one to the result;
• generating injection values for rounding a final result in dependence of a rounding mode and of the arithmetic operation;
• generating injection carry values based on the transformed first and second floating point numbers and the injection values;
• and
• selecting the final result from the result, the result plus one and a least significant digit based on the injection carry values and end around carry signals.

A computer program product comprising a non-transitory computer readable medium including a computer readable program, wherein the computer readable program when executed on a computer causes the computer to perform a method for performing a floating point arithmetic add/subtract operation on a first floating point number and a second floating point number, wherein the first floating point number has a first magnitude and the second floating point number has a second magnitude, and wherein the first and second floating point numbers are in binary floating point format, the method comprising:

• mapping the binary floating point numbers to decimal floating point format, the mapping comprising padding bits to form digits that share the same fields of the floating point numbers in the decimal floating point format;
• generating a guard digit of zero of at least one of the first or the second floating point numbers by transforming the first and the second floating point numbers by a compressing function;
• determining as a result depending on the arithmetic operation, a sum of the transformed floating point numbers, and a first difference or a second difference of the transformed floating point numbers, wherein for the first difference the second floating point number is subtracted from the first floating point number and for the second difference the first floating point number is subtracted from the second floating point number, and determining a corresponding result plus one by additionally adding a value of one to the result;
• generating injection values for rounding a final result in dependence of a rounding mode and of the arithmetic operation;
• generating injection carry values based on the transformed first and second floating point numbers and the injection values;
• and
• selecting the final result from the result, the result plus one and a least significant digit based on the injection carry values and end around carry signals.