SoftwareSerial magic numbers

submitted as proposal - -

@Marc G

A serial protocol is like a train with wagons and on each wagon there is one bit, 10 bits in total (including start/stop bits). The baud rate represents the speed of the train.

The software serial receiving code is triggered by the edge of the start bit (train). To read a bit properly one wants to read the value of the signal (HIGH/LOW) in the middle of the bit, not at the edges.

rxCenter is the time to the (approx) middle of the first (start) bit, rxIntra, rxStop are used as timings from the middle of one bit to the middle of the next. The higher the baud rate the lower these numbers.

tx is used for the timing for the transmit.

You can see this in the code of the library - C:\Program Files (x86)\arduino-1.0\libraries\SoftwareSerial - (windows) and search for this function - void SoftwareSerial::recv() -

Did a more extensive test with the SoftwareSerial using the formula approach. I connected two Arduino's - UNO, 16Mhz (resonator) + 2009, 16Mhz (crystal) + IDE 1.0 - both using SoftwareSerial, one Master and the other Slave (essentially an echo).

The master sent byte 0x55 at baudrate 100 and waits until the slave echos it back. If the answer is not 0x55, the test fails and master prints a message. Otherwise it just increases the baud rate with 100 and starts over.

The results are pretty good as it only gets constantly distorted above 190K baud. Between 90K and 190K it only failed 10 times.

I took 0x55 as test pattern 0x55 == 01010101 ; it helps to see what happened. (see comments after output

Typical output (multiple runs had comparable output) Note: started with baud rate 100 in steps of 100...

97600   F5   FAIL  // = 11110101    ??
111200  AA   FAIL  // = 10101010   1 bit shifted
114400  D5   FAIL  // = 11010101   1 bit failed (interference with start bit ?
124600  AA   FAIL
140600  D5   FAIL
145500  AA   FAIL
149000  D5   FAIL
163200  AF   FAIL  // = 10101111  ??
190500  FF   FAIL  // = 11111111  expect sync lost 
190600  FF   FAIL
190700  FF   FAIL
190800  FF   FAIL
190900  FF   FAIL
191000  FF   FAIL

The master and the slave were kept in sync by starting at the same baud rate an wait for each other.

To repeat the test start the master, then start the slave, and press a char in the serial monitor of the master.

Slave program (essentially echo)

//    FILE: serialSlave (echo)
//  AUTHOR: Rob Tillaart
//    DATE: 2013-01-02
// PUPROSE: test SW serial with formulas


SoftwareSerial mySerial(2, 3);

void setup()
  Serial.println("start slave...");

unsigned long baud=0;

void loop()
  baud += 100;
  while (mySerial.available() == 0);
  int b =;

master program

//    FILE: serialMaster
//  AUTHOR: Rob Tillaart
//    DATE: 2013-01-02
// PUPROSE: test SW serial


SoftwareSerial mySerial(2, 3);

void setup()

unsigned long baud=0;

void loop()
  if (Serial.available() > 0)

    baud += 100;
    while (mySerial.available() == 0);
    int b =;
    if (b != 0x55)
      Serial.print(b, HEX);
      Serial.println(" FAIL");

As always comments/remarks are welcome

same test with stepsize 10 gave some more errors (typical run started with baud rate 10, step 10)

70660   D5   FAIL
81950   AD   FAIL
88870   AF   FAIL
89570   BD   FAIL
94410   D5   FAIL
95340   AA   FAIL
96590   D5   FAIL
98980   AA   FAIL
100750  AB   FAIL
103590  BD   FAIL
105740  D5   FAIL
110600  AA   FAIL
113260  AF   FAIL
120200  AA   FAIL


Up till 70K no failures ( that are 7000 different baudrates tested !) between 70K and 115K "only" 13 failures (13 fail on 4500 baudrates tested ~~ 1/300 above 120K the failures increased, not shown

Conclusion from the tests, SoftwareSerial "by formula" works very good up to 70.000 and reasonable well up to 115.200 Tweaking the formulas further may improve the test results but for now I'm quite satisfied.

This SoftwareSerial "by formula" allows one to build a communication channel in which the baud rate is constantly altered, making it very difficult to eavesdrop - and yes to get in sync :)


I applaud this effort. Thanks for investigating so thoroughly. I always thought it might be fun to develop some equations that allow the synthesis of the "table" values on the fly, and now it looks like you are pretty close to doing just that.

It's good that you are getting error-free transmission up to 70K. Make sure you test not just the single byte round trip, but also lots of bursts. The values should vary Example:

  1. Arduino sends 0x55 as fast as possible to host for one minute.
  2. Arduino sends 0xFE as fast as possible to host for one minute.
  3. Arduino sends 0x01 as fast as possible to host for one minute.
  4. Host sends 0x55 as fast as possible to Arduino for one minute.
  5. Host sends 0xFE as fast as possible to Arduino for one minute.
  6. Host sends 0x01 as fast as possible to Arduino for one minute.

When constructing the tables, I found several times that I thought the values were good--until I tested the large bursts.

If we want to improve performance at baud rates > 57.6K, I think we're going to have to optimize the timer tick vector. I studied this for some time with the logic analyzer and discovered that the occasional glitch was due to a timer tick interrupt being processed exactly when a pin change was pending.

Lastly, and you probably already know this, but if your formula is off a bit for the lower baud rates, it shouldn't be a big deal. They are very tolerant.




like the idea of a formula, but could be slow to change baud rate could it not.

not certain, and for interest, did you try two boards connected using the standard software serial code, did you try two boards using the standard hardware uart.

@Dr John,
Yep a changing baudrate communication would certainly be slower than a fixed speed, but calculating the values take micro-seconds, no FP math involved.

I did the test with 2 Arduinos - UNO + DUemillanove - so one with a crystal and one with resonator (?) and used for both SW serial (you could have seen this in the code :wink:

I did not try a HW serial against the SW serial yet although I did test it with a (19200) HW serial LCD - see earlier post.

This analysis is not final yet as I expect the formulas can be improved a bit for the higher speeds. This can be done by non-linear polynomes at the cost of extra footprint or maybe by slighty tuning the constants in the formulas. Need some time to test (a lot more)

@Mikal, stuff to think through, thanks

well done

testing this sort of thing is a real pain I know,

Tweaked the numbers in the spreadsheet to minimize the cumulative relative error. There was a large relative error in the higher baud rates, now the relative error is minimized, while keeping the functions linear

(not extensively tested yet)

// 16MHZ
rxstop = 16000000L/(7 * baudrate) - 2;
rxintra = rxstop;  
tx = rxstop - 4; 
rxcenter = rxstop/2 - 7; 

// 8MHZ
rxstop = 8000000L/(7 * baudrate) - 4;
rxintra = rxstop;  
tx = rxstop - 2; 
rxcenter = rxstop/2 - 10; 

// 20MHZ
rxstop = 20000000L/(7 * baudrate) - 3;
rxintra = rxstop;  
tx = rxstop - 3; 
rxcenter = rxstop/2 - 7;

to be continued...

Run with the previous formulas

70660   D5   FAIL
81950   AD   FAIL
88870   AF   FAIL
89570   BD   FAIL
94410   D5   FAIL
95340   AA   FAIL
96590   D5   FAIL
98980   AA   FAIL
100750  AB   FAIL
103590  BD   FAIL
105740  D5   FAIL
110600  AA   FAIL
113260  AF   FAIL
120200  AA   FAIL

Now a run with the new offsets

90440   D5   FAIL
97150   AD   FAIL
101140  AA   FAIL
101210  D5   FAIL
103180  D5   FAIL
105430  AA   FAIL
106130  D5   FAIL
108400  A9   FAIL
108990  AA   FAIL
109440  D5   FAIL
111270  AA   FAIL
111320  D5   FAIL
117300  D5   FAIL
118480  AA   FAIL

The first fail with new parameters lies about 20 K higher, but other runs started to fail at ~79/80K .

Conclusion for now: The new offsets are definitely better than the previous, but still not good enough to get a fail free software serial up to 115200. TODO: test @8Mhz and @20Mhz (don't have such duinos)

A deep dive in the code might be needed. TBC...

Next test - longer string "the quick brown fox jumps over the lazy dog" (42 chars) sent from A-> B at different speeds starting at 100 baud step size 100. B sends back the number of chars correctly received from start of the string. so when receiving "theXquick brown fox jumps over the lazy dog" the answer would be 3.

Again we see baud rates up to 70K perform 100%, above failing starts...

74800   34   FAIL
79900   11   FAIL
81000   3    FAIL
84900   31   FAIL
85200   23   FAIL
85800   21   FAIL
86200   15   FAIL
86300   20   FAIL
86600   38   FAIL
86900   41   FAIL
87100   38   FAIL
87300   15   FAIL
87400   20   FAIL
87700   38   FAIL
88300   20   FAIL
88400   170  FAIL  <<<< a very strange one ???
88500   37   FAIL
88700   18   FAIL
88800   15   FAIL
89000   38   FAIL
89200   38   FAIL
89500   15   FAIL
89600   12   FAIL
89800   18   FAIL
90000   31   FAIL

For the statistics: highest successful transfer rate was 103800 baud,

Conclusion: Up to 70K the formula based SoftSerial does work as expected, that is about 20% faster than 57600 from the fixed tables.

115200: As the values are identical to the table based SS for 115200, I do not expect the (exisiting) table version to work at least for receiving data.

Another test; steps of 1000 start @ 1000 (so not as fine grained but much faster).

The string length is 42, the value returned is now the number of same characters.
So 41 means that of the characters received 41 matched “the quick brown fox …dog”.

Missing chars start now at 83K and we see the quality gradually drop, missing 8 chars at 115K => that is 20%!)

(baudrates without extra info are OK)

83000	41	 FAIL
85000	41	 FAIL
87000	40	 FAIL
88000	41	 FAIL
91000	41	 FAIL
92000	41	 FAIL
93000	41	 FAIL
95000	39	 FAIL
96000	41	 FAIL
97000	41	 FAIL
98000	41	 FAIL
99000	41	 FAIL
100000	40	 FAIL
101000	40	 FAIL
102000	39	 FAIL
103000	41	 FAIL
104000	40	 FAIL
105000	39	 FAIL
106000	39	 FAIL
107000	39	 FAIL
108000	38	 FAIL
109000	39	 FAIL
110000	37	 FAIL
111000	38	 FAIL
112000	39	 FAIL
113000	39	 FAIL
114000	37	 FAIL
115000	34	 FAIL
116000	34	 FAIL
117000	39	 FAIL
118000	36	 FAIL
119000	36	 FAIL
120000	38	 FAIL

No new conclusions from this test.

I like what you are doing robtillaart!

Would it be possible to write a code that auto calibrates the "magic numbers".

I would imagine using two serial communication links. One link could be the hardware serial port that would send to the slave the baud rate to be tested. Next, at the determined baud rate, the master would send a byte or string that is predetermined. The slave would then adjust the timing variables (within an allowed range) until the string is captured successfully "x" number of times. Lastly, the slave would perhaps save the variable results to EPROM or send to the serial monitor.

Would it be possible to write a code that auto calibrates the "magic numbers".

Definitely, but because the tables existed It was easier to let Excel find them.

In fact you can derive the magic numbers from the protocol. You know that the a data bit has 1/baudrate seconds between the edges. As you can see how much time the machine code takes to read and store a bit you can derive the magic numbers even quite exact for a given baud rate.

The real problem is that you need to find a protocol that works for all given baud rates, so an auto calibrating mode needs a number of known patterns to learn. Best to start with the highest baud rate as this is the most critical one. If you have the basic formula rxbit = CLOCKSPEED/(alpha * baudrate) - beta; you can try all possible combinations for alpha and beta between 1..20 so after 400 bytes you get the ranges for alpha and beta that work. You try the next baud rate and the ranges will decrease until all baudrates done. Then take the middle of the ranges and you're done.

A better faster approach is first find the optimal alpha, the search the optimal beta then alpha again then beta again until same values appear. That will bring you to the optimal value within 50 or so bytes (~10x faster).

Instead of linear search through the ranges you can do a binary search,...

For me the strange thing is the value SEVEN where I expected EIGHT in the formula - 16000000L/(7 * baudrate) - 3; but I did not really investigate 16000000L/(8 * baudrate) + BETA ... => todo list ;)

I'm glad to hear it is possible. You have helped my understanding of the process a lot although, it is a bit over my head to try to program an auto-calibration program.

Thanks, Mark

There are 4 levels of acting -> goal -> strategy -> tactics -> operations

You did define your goal, but you were thinking tactics (how to program) and operations (details) . You skipped one level.

You must think of the strategies how such thing can be done and do "thought experiments" to find the tactics that belong to the strategy to make the strategy choice.

strategies can be : - brute force (test all), random search (aka darting;), hill climbing (change any param that improves the result), analytics etc

imho it is not over your head, it's not easy but you can do it, give it a try

Hey Rob, I just wanted to say thank you for your research on this. As it turns out I have a need for SoftwareSerial to do 7800 baud to read from a motorcycle ECU->Dash communication link and it sounds like you've solved my problem. :)


Let me hear the results of your tests, I'm interested. I can imagine that a motorcycle can generate quite some noise which may be disruptive to the signal. Did you think shielding/grounding etc?

I haven’t even begun to think/worry about that yet. Hopefully it just works. Ha!

In all seriousness, I’m literally waiting for FedEx to deliver my 'scope (hopefully Friday) so I’ll have a better idea then for what I’m dealing with. I do know that at 9600 baud it seems to kinda-sorta work, but I do seem to be getting some corruption, but that mostly seems to be due to the timing differences from what I can tell/guess. So it appears the line is pretty clean.

That being said, I haven’t tried it with the bike actually running yet, so things could get a whole lot noisier once those coils start firing.