Thermometer on an I2C LCD, on an Arduino Uno

// I2C thermometer: a 10 k NTC bead on A0, the reading on a 16x2 LCD that
// only needs four wires.
//
//   A0      the junction of the bead and a fixed 10 k
//           bead from 5 V down to A0, 10 k from A0 down to GND
//   LCD     SDA -> A4    SCL -> A5    VCC -> 5 V    GND -> GND
//
// Two things are worth the trip here, and they are both about wires.
//
// # Four wires instead of sixteen
//
// The display is the same HD44780 panel as the six-wire one (see the
// `thermometer` example), with a PCF8574 port expander soldered to the back of
// it. Every byte written to the expander lands on its eight pins, and those
// pins are the LCD's RS, RW, E, backlight and D4..D7. So the driver
// (firmware/lib/mokxi_lcd1602_i2c.h) sends a character as six port writes and
// the controller sees exactly what it would have seen from six board pins.
//
// The backlight is bit 3 of that port and nothing else. Forget it and the
// display works perfectly and shows you nothing, which is the one fault this
// module has that the six-wire one does not. begin() turns it on.
//
// # A logarithm without a logarithm
//
// The bead is 10 k at 25 C and falls steeply as it warms; it follows
//
//   R(T) = 10000 x exp(3950 x (1/T - 1/298.15))
//
// with T in kelvin. Turning a reading back into degrees means a logarithm, and
// this board has no floating point at all, let alone a log. So the sketch does
// what a real one does: a table of what the ADC reads at each ten degrees,
// worked out once on a desk, and a straight line between the two entries the
// reading falls between. Ten-degree steps are close enough that the error from
// the interpolation is under half a degree over the whole range, which is
// smaller than the bead's own tolerance.
//
// Drag the slider on the bead to change the temperature. The second line keeps
// the lowest and highest it has seen.

#include "mokxi_lcd1602_i2c.h"

const int SENSOR = A0;
const int SDA_PIN = A4;
const int SCL_PIN = A5;

Lcd1602I2c lcd(SCL_PIN, SDA_PIN);

// What the ADC reads at -20, -10, 0 ... 100 C, for a 10 k bead above a fixed
// 10 k against the 5 V reference. Rising, because a warm bead is a small
// resistance and pulls A0 up.
const int TABLE_LOW_C = -20;
const int TABLE_STEP_C = 10;
const int TABLE_N = 13;
const int READINGS[TABLE_N] = {89, 150, 235, 339, 454, 568, 669, 754, 820, 871, 909, 937, 957};

int lowest = 32767;
int highest = -32768;

// Tenths of a degree for an ADC reading, by walking the table and drawing a
// straight line between the two entries it falls between.
int tenthsFor(int reading) {
  if (reading <= READINGS[0]) {
    return TABLE_LOW_C * 10;
  }
  for (int i = 1; i < TABLE_N; i++) {
    if (reading <= READINGS[i]) {
      long span = READINGS[i] - READINGS[i - 1];
      long into = reading - READINGS[i - 1];
      long base = (long)(TABLE_LOW_C + (i - 1) * TABLE_STEP_C) * 10;
      return (int)(base + (into * TABLE_STEP_C * 10) / span);
    }
  }
  return (TABLE_LOW_C + (TABLE_N - 1) * TABLE_STEP_C) * 10;
}

// Sixteen samples added up and shifted right by four: a divide-free mean, and
// the ADC's last bit is noise so an unfiltered display never stops flickering.
int readAveraged() {
  long total = 0;
  for (int i = 0; i < 16; i++) {
    total += analogRead(SENSOR);
  }
  return (int)(total >> 4);
}

void setup() {
  lcd.begin();
  Serial.begin(115200);
  Serial.println("Mokxi Uno: NTC thermometer on an I2C LCD at 0x27");
  lcd.print("NTC on I2C");
  delay(600);
  lcd.clear();
}

void loop() {
  int tenths = tenthsFor(readAveraged());
  if (tenths < lowest) {
    lowest = tenths;
  }
  if (tenths > highest) {
    highest = tenths;
  }

  lcd.setCursor(0, 0);
  lcd.print("Temp ");
  lcd.printFixed(tenths, 1);
  lcd.write('C');
  lcd.padLine();

  lcd.setCursor(0, 1);
  lcd.print("L");
  lcd.printFixed(lowest, 1);
  lcd.print(" H");
  lcd.printFixed(highest, 1);
  lcd.padLine();

  Serial.print("temp ");
  Serial.print(tenths / 10);
  Serial.println(" C");
  delay(400);
}