   // calCount *= 10e6
   calCount = ((int64_t)(cal2Result - cal1Result) * (int64_t)(1000000 - TIME_DILATION)) / (int64_t)(CAL_PERIODS - 1); 
 
-  // maybe time2Result doesn't add value, so we substitute a fixed value
+  // if FIXED_TIME2 is set, override time2Result with that value
   if (FIXED_TIME2) {
     time2Result = FIXED_TIME2;
   }
   
-  // normLSB *= 10e6 -- remember that we've already multiplied the divisor so we use twice that here
+  // normLSB *= 10e6 -- remember that we've already multiplied the divisor so we need to add six 0s here
   normLSB = ((int64_t)CLOCK_PERIOD *(int64_t)1000000000000) / calCount;
   ring_ticks = (int64_t)time1Result - (int64_t)time2Result;
  
-   // ring_ps *= 10e-6 to get rid of earlier scaling
+  // ring_ps *= 10e-6 to get rid of earlier scaling
   ring_ps = (normLSB * ring_ticks) / (int64_t)1000000;
   
   tof += (uint64_t)ring_ps;
 
   
-//  Serial.print("cal1Result: ");Serial.print(cal1Result);Serial.print(" ");
-//  Serial.print("cal2Result: ");Serial.print(cal2Result);Serial.print(" ");
-//  Serial.print("calCount: ");print_picos_as_seconds(calCount);Serial.print(" ");
-//  Serial.print("normLSB: ");print_picos_as_seconds(normLSB);Serial.print(" ");
+//  Serial.print("normLSB: ");print_unsigned_picos_as_seconds(normLSB);Serial.print(" ");
 //  Serial.print("ring_ticks: ");print_signed_picos_as_seconds(ring_ticks);Serial.print(" ");
 //  print_signed_picos_as_seconds(ring_ps);Serial.print(" ");
 //  Serial.print("ring_ps: ");print_signed_picos_as_seconds(ring_ps);Serial.print(" ");
 //  Serial.print("clock1Result: ");Serial.print(clock1Result);Serial.print(" ");  
-//  Serial.print("time1Result: ");Serial.print(time1Result);Serial.print(" ");  
-//  Serial.print("time2Result: ");Serial.print(time2Result);Serial.print(" ");
-//  Serial.print(time2Result);
-//  Serial.print("time3Result: ");Serial.print(time3Result);Serial.print(" ");
-
-//  Serial.print("tof: ");print_picos_as_seconds(tof);Serial.print(" ");
-  
+//  Serial.print("tof: ");print_unsigned_picos_as_seconds(tof);Serial.print(" ");
   
   return (uint64_t)tof;
 }

  SPI.endTransaction();
}



void print_picos_as_seconds (uint64_t x) {
  uint64_t sec, secx, frac, frach, fracx, fracl;    
  sec = x / 1000000000000;
  secx = sec * 1000000000000;


  sprintf(str,"%ld.",sec), Serial.print(str);
  sprintf(str, "%06ld", frach), Serial.print(str);
  sprintf(str, "%06ld", fracl), Serial.print(str);  
} 


