Rounding
if the absolute value of a’ is not lower than b, then decrement n (multiply the increment m by b), increment the scaling exponent c’, divide the signed mantissa a by b, and restart the rounding of the new signed mantissa a into a’ with the same formula; this step may be avoided only if the abtract "round()" function is always rounding a towards 0 (i.e. when it is a simple truncation), but is necessary if it may be rounding a towards infinity, because the rounded mantissa may have a higher scaling exponent in this case, leaving an extra digit of precision.