Cycle Time Analysis II : Natural Ratio vs. Enhanced Natural Ratio

Basic Assumption

(1) Technology : 0.35um CMOS process
(2) Operating Voltage : 2.5 V
(3) Operating Temperature : 25 C
(4) Circuit : Dual-Rail Domino Logic
(5) 6 subcycles : 1 main cycle is divided by 6 subcycles
(6) 16 bit Multiplier : Wallace Tree + 32bit CLA Adder
(7) Architectural Change but No Change for Circuit and Process Technology


Cycle Time Estimation Method

(1) The Cycle Time calculation is based on the paper, Carl Lemonds, "A High Throughput 16 by 16 Bit Multiplier for DSP Cores", IEEE International Symposium on Circuits and Systems, 1996. p479.
(2) Transformation of Cycle Time Calculation of Enhanced Ratio in Table III of the paper, Carl Lemonds

Cycle Time

@1200 MHz

Sail Boat Allocation

1 subcycle

32bit Wallace Tree Compression

2 subcycles

32bit Addition

3 subcycles

Pipelined 16bit Multiplication Latency

3 subcycles

48bit Wallace Tree Compression

2 subcycle

64bit Addition

4 subcycles

32bit FP Conversion

4 subcycles

96bit Wallace Tree Compression

2 subcycle

128 bit Addition

5 subcycles

96 bit FP Conversion

5 subcycles

[ TABLE 9 ]


(3) Cycle Time Table 8 : Enhanced Natural Ratio

Cycle Time

mult16 FIX/INT

mult32 FIX/INT

mult32 FP

mult64 FIX/INT

mult64 FP

Sail Boat Allocation

1 subcycle

1 subcycle

1 subcycle

1 subcycle

1 subcycle

32bit Wallace Tree Compression

2 subcycles

2 subcycles

2 subcycles

2 subcycles

2 subcycles

32bit Addition

3 subcycles

N/A

N/A

N/A

N/A

Pipelined 32bit Addition Latency

3 subcycles

N/A

N/A

N/A

N/A

48bit Wallace Tree Compression

N/A

2 subcycles

2 subcycles

2 subcycles

2 subcycles

64bit Addition

N/A

4 subcycles

4 subcycles

N/A

N/A

32bit FP Conversion

N/A

N/A

4 subcycles

N/A

N/A

96bit Wallace Tree Compression

N/A

N/A

N/A

2 subcycles

2 subcycles

128bit Addition

N/A

N/A

N/A

5 subcycles

5 subcycles

64 bit FP Conversion

N/A

N/A

N/A

N/A

5 subcycle

Total Subcycles

9 subcycles

9 subcycles

13 subcycles

12 subcycles

17 subcycles

Total Main Cycles

2 cycles

2 cycles

3 cycles

2 cycles

3 cycles

[ TABLE 10 ]


(4) Cycle Time Comparison between Natural Ratio and Enhanced Natural Ratio

Cycle Time

mult16 FIX/INT

mult32 FIX/INT

mult32 FP

mult64 FIX/INT

mult64 FP

Natural Ratio

3 cycles

3 cycles

4 cycles

4 cycles

5 cycles

Enhanced Natural Ratio

2 cycles

2 cycles

3 cycles

2 cycles

3 cycles

[ TABLE 11 ]