By Liang-Kai Wang and Michael J. Schulte Joseph Schneider March 12, 2010

 Goal is to improve latency for DFP Adder  Number of modifications performed to achieve this, such as an implementation of a new internal format  Overall focus is on the design of a decimal LZA

 Detects location of most significant bit  Previous designs have been for binary, not decimal  Design of decimal LZA expected to improve latency

 Exponent field uncompressed  Significand encoded in BCD  New section for Leading Zero Count; Removes leading zero detection from critical path

 Internal Format removes need for Forward and Backward conversion units  Pre-correction moved in front of Swapping unit and duplicated; Keeps it out of critical path  Leading Zero Detection no longer performed in Shift Amount unit; Lead Zero Count is now an input signal, LZA used so later decimal operations do not need to recalculate it

 Needed in addition and subtraction to guarantee leading zero count of output is correct  Only needed when result after addition or subtraction is not rounded; LZC is always zero when result is rounded

 Preliminary LZC is the minimum number of leading zeros between the two significands being added  If there is a carry, final LZC obtained by reducing preliminary LZC by one

 Requires Encoding unit, Correction unit, and a parallel array of decimal digit adders  Encoding unit ◦ Converts BCD digits into strings of zeros and ones ◦ Detects position of most significant non-zero digit in the string  Correction unit ◦ Flag generation modules and correction trees determine if correction needs to be performed on Encoding unit’s result

 IBM decNumber library version 3.56 used to verify correctness of adder  Sign, exponent, and length and value of significand randomly generated  Adder successfully passed numerous random tests and the corner cases of IBM’s test suite  Previous adder version and new adder implemented in Verilog RTL using TSMC 45nm bulk technology

 Both designs use same floorplan so Area Util. Rate reflects how much area used by each design  New adder 14% faster but at the cost of 18% more area

 LZA takes up significant amount of area, though Kogge-Stone adder is still the largest component

 LZA synthesized alone; Critical path has maximum delay of 24 FO4 inverter delays  Subtractor takes up over 60% of LZA area