In convergent rounding, the final result is rounded to the nearest even number (or odd number). In conventional implementations, if the midpoint is detected, then the units-placed bit before the round needs to be examined to determine whether the number is going to be rounded up or down.
In convergent rounding towards even, the final result is rounded
toward the closest even number, for example:
- 2.5 rounds to 2 and –2.5 rounds to –2, but 1.5 rounds to 2 and –1.5 rounds to –2.
In convergent rounding towards odd, the final result is rounded
toward the closest odd number, for example:
- 2.5 rounds to 3 and –2.5 rounds to –3, but 1.5 rounds to 1 and –1.5 rounds to –1.
The convergent rounding techniques require the use of programmable logic (PL) in addition to the DSP58. The different methods of implementing a convergent rounding scheme will be covered in a future revision of this document.