Serial, Numbers sent as Floating Point and Characters are different at 1e-8 level

Question

I have some code that generates random numbers on the Arduino, it then sends these random numbers firstly, using Serial.print(float data,int lenght) and as a floating point number using the following function

void send_float (float arg)
{
 // get access to the float as a byte-array:
 byte * data = (byte *) &arg; 
 // write the data to the serial
 Serial.write (data, sizeof (arg));
 Serial.println();
}

I then receive this data using python, take the absolute difference of the two values, discard any differences less than the length with which I send the string and output the rest to the screen.

I observe two things, a) Fluctuations of the order with which I send the data (ie. if I send to 6 decimal places then I see fluctuations of ~1e-6), this is reasonable and b) I see fluctuations of absolute value 1e-8 or lower independent of what accuracy I send the string.

Even if I send the string to 11 decimal places, when I compare against the float I see fluctuations up to but not above 1e-8.

Why? This doesn't make any sense. My full code is actually the answer to an old unanswered stack exchange question

• BrettFolkins: The precision of a float is around 7.2 decimal digits. en.wikipedia.org/wiki/Single-precision_floating-point_format

Answer 1

This is a somewhat dumb question but, in case anyone else searches it as pointed out:

The precision of a float is around 7.2 decimal digits. en.wikipedia.org/wiki/Single-precision_floating-point_format – BrettAM

So in python the number goes float -> double -> decmial, whereas on the arduino the number goes float -> decimal. The additional step of the double in the case of python causes the discrepancies. But anything after the 7th decimal place is nonesense anyway.