IC Design 23Fall HW4

author : B10901176 蔡弘祥

Goal

• Using basic logic gates and flip-flops to realize a "Sigmoid Approximator"
• For more Info, please checkout documents in doc/HW4_2023.pdf

Before Running

source ./tool.sh

How To Run

./run.sh
./debug.sh

How To Check Waveform

nWave &

1. Open sigmoid.vcd
2. Get signals : tb/DUT
3. Choose the signals wanna check

Input and Output Signals Explanation

• Input : a 8-bit signed binary number (2's complement), divided by 32 to get decimal value
  • for example :
    • 1000_0000 represent -128, divided by 32 will be -4
    • 0111_1111 represent 127, divided by 32 will be 3.96875
• Output : a 16-bit unsigned binary number, divided by 2^15 to get decimal value
  • for example :
    • 1000_0000_0000_0000 represent 2^15, divided by 2^15 will be 1
    • 0010_0000_0000_0000 represent 2^13, divided by 2^15 will be 0.25

Solution

1. Get the absolute value of the input (2's complement)
   • add a sign bit x[8] ( =x[7]), invert x[7,0] and add 1
2. Find out the range of the absolute value and determine a and b
   • 8-1 Mux
3. Calculate y = ax + b
4. If the input is negative, then invert every bit of y
   • y[15:0]^x[7]

• For more Info, please checkout documents in doc/report.pdf

JS Files Explanation

• JS files are used to precalculate the error

JS File	Result File	Performance	Explanation
js/sigmoidApproximate.js	jsResults/OutApproximate.dat	0.000546	directly use secant lines to approximate on [-4,4]
js/sigmoidPractice.js	jsResults/OutPractice.dat	0.004392	1. use the absolute value (if negative, invert bits) 2. use secant lines to approximate on [0,4] 3. if input is negative, invert output bits
js/sigmoidPractice2.js	jsResults/OutPractice2.dat	0.000537	1. use the absolute value (if negative, invert bits and add 1) 2. use secant lines to approximate on [0,4] 3. if input is negative, invert output bits
js/sigmoidPractice3.js	jsResults/OutPractice3.dat	0.000302	1. use the absolute value (if negative, invert bits and add 1) 2. use self-defined constants to approximate on [0,4] 3. if input is negative, invert output bits
js/sigmoidPractice4.js	jsResults/OutPractice4.dat	0.000300	1. use the absolute value (if negative, invert bits and add 1) 2. use self-defined constants to approximate on [0,4] 3. if input is negative, invert output bits
js/sigmoidPractice5.js	jsResults/OutPractice5.dat	0.000280	1. use the absolute value (if negative, invert bits and add 1) 2. use self-defined constants to approximate on [0,4] 3. if input is negative, invert output bits 4. if negative, y[3:0] = 1011, if positive, y[3:0] = 0011

Different Pipeline Stages Result

Pipeline Stage Number	Clock Cycle	Number of Transistors	Total Excution Cycle	Approximation Error Score	Performance Score
1	9.5 ns	3696	256	1527.0	8988672.0
3	5.4 ns	5100	258	1527.0	7205320.0
5	4.3 ns	4707	260	1508.0	5262426.0
6	3.1 ns	3916	261	1500.0	3168435.6