1. Random Number Generator (RNG) for Microcontrollers
Tom Dickens
The Boeing Company

2. Introduction RNG Wisdom Motivation for an RNG Other RNG Methods
Requirements for a “Good” RNG
Approaches Taken
Testing
Implementation
Summary
Tom Dickens

3. RNG Wisdom…
“Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.” John von Neumann ( ).
“The generation of random numbers is too important to be left to chance.” Robert R. Coveyou, Oak Ridge National Laboratory in Tennessee.
Tom Dickens

4. Motivation For An RNG For Microcontrollers
More Interesting Robotic Behavior
Avoid Stuck-In-A-Corner Logic
Used In AI Techniques
Genetic Algorithms
Neural Networks
Fuzzy Logic
Tom Dickens

5. Other RNG Methods Hardware-Based (true) RNGs
White-Noise Source
Transistor Circuits
Our desire is to have a pseudo random number generator, as defined by…
Tom Dickens

6. Requirements - a “Good” RNG
Key Requirements (detailed list in paper).
N = F(), where…
N is in the range 0 to 255
Large cycle of N’s before pattern repeats.
All values of N are generated the same number of times in the cycle.
Windows of consecutive N’s in cycle meet…
Constraints for Average, Min, and Max values.
Small Code Size
Tom Dickens

7. Approaches Taken Table-Based Method Define a table of 128 values.
Use EXOR to generate 128 other values.
Cycle through these 256 values 64 different ways.
Cycle length of 16,384.
Met the goodness criteria.
62 bytes of code bytes for table = 190 total bytes. 4 bytes of RAM.
Tom Dickens

8. Approaches Taken Equation-Based Method 2-byte seed value in RAM
seed = 181 * seed + 359
Return top 8 bits of seed.
Cycle length of 65,536.
Met the goodness criteria.
25 bytes of code, 4 bytes of RAM.
Tom Dickens

9. Approaches Taken Notes:
181 and 359 determined by a program searching for values to meet the goodness criteria.
Table method also used a program to find right 128 table values.
Tom Dickens

10. Generated Numbers First 240 numbers:
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11. Testing The Numbers Met The Defined Goodness Criteria Inspection
Graphical Plots
Plot number pairs on 256x256 grid.
Tom Dickens

12. Testing
1024 pairs plotted
Tom Dickens

13. Testing
Half the pairs plotted
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14. Testing
All pairs plotted
Tom Dickens

15. Testing
All pairs with another set of constants
Tom Dickens

16. Implementation – 25 Bytes of 68HC11 Code
Random:
PSHB ; (1,3) Remember the current value of B
* scratch = seed * multiplier
LDAA #MULTIPLIER ; (2,2) A = #181
LDAB SEED_LOW ; (2,3) B = the low byte of the seed
MUL ; (1,10) D = A x B
STD RandomScratch ; (1,4) scratch = D
LDAB SEED_HIGH ; (2,3) B = the high byte of the seed
* low byte of MUL result is added to the high byte of scratch
ADDB RandomScratch ; (2,3) B = B + scratch_high
STAB RandomScratch ; (2,3) scratch = seed * 181 *
LDD RandomScratch ; (2,4) D = scratch
ADDD #ADDER ; (3,4) D = D + 359
STD RandomSeed ; (2,4) remember new seed value
* (A = SEED_HIGH from ADDD instruction)
PULB ; (1,4) Restore the value of B
RTS ; (1,5) A holds the new 8-bit random number
Tom Dickens

17. Summary RNG Studied RNG Goodness Criteria Developed
Two RNG Methods Developed
Both Methods Were Critiqued
Equation-Based RNG Chosen For Number Coverage and Code Size
68HC11 Code Implemented and Tested
Tom Dickens