Overcoming double-rounding errors under IEEE 754-2008 using software

The IEEE 754-2008 floating-point standard requires rounding to all available formats (e.g., single and double precision) from any combination of operand formats. Under the original standard, operands and results had the same format, and current hardware is likely to provide only this much. When trying to fulfil the new requirement on such hardware, there are potential double rounding problems. The problems include both incorrect incrementation and incorrect truncation. We present a software solution to both problems that requires no additional hardware, and yet still has acceptable performance.