Calculator on an Arduino Uno

// Calculator: a 5x4 keypad, a 16x2 LCD, and four functions on an Uno.
//
//   pins 13, 12, 11, 10, 9   keypad rows R1 to R5
//   pins 8, 7, 6, 5          keypad columns C1 to C4
//   A0  LCD RS               A1  LCD E
//   A2, A3, A4, A5           LCD D4 to D7   (RW and V0 to GND)
//
// Fifteen pins, and an Uno has fourteen digital ones, so the display's six
// go on the analog header, which is what A0 to A5 are when nothing is
// reading a voltage on them: ordinary digital pins. This is the pin budget
// that sends most people to a shift register or an I2C backpack.
//
// The pad is printed the way a desk calculator is:
//
//     C  <  %  /
//     7  8  9  x
//     4  5  6  -
//     1  2  3  +
//     0  .  +/- =
//
// Type a number, press an operator, type another, press =. `C` clears
// everything, `<` rubs out the last digit, `%` divides what you are typing by a
// hundred and `+/-` changes its sign. Divide by zero says `Err` and waits for
// `C`, because that is the honest answer and a calculator that quietly printed
// something would be worse.
//
// # There is no chip in the keypad
//
// Twenty keys on nine pins, and nothing else inside: each key shorts its row to
// its column. mokxi_keypad.h scans it (one row driven low at a time, the four
// columns read with their pull-ups on) and debounces, so `pressed()` gives one
// character per press. Rows are never driven high: two keys held in the same
// column would put one driven output straight across another.
//
// # Why the arithmetic is whole numbers
//
// There is no floating point here, and there does not need to be. Every value
// is a `long` counting hundredths, so 12.34 is 1234, and two decimal places are
// exactly what a two-line display can show. That keeps addition exact, and it
// puts the interesting work in two places:
//
//   * multiply is a*b/100, and a*b overflows a 32-bit long long before the
//     divide does any good. So it is done in halves, (a/100)*b plus
//     (a%100)*b/100, with the overflow checked *before* the multiply that
//     would cause it, against MAX_VALUE.
//   * divide is a*100/b, and a*100 is why MAX_VALUE is 99999.99 rather than
//     something longer: 9999999 * 100 still fits in a long, and one more digit
//     would not.
//
// Anything that would go past MAX_VALUE is `Err` as well. A calculator that
// wraps round to a negative number is lying.

#include "mokxi_keypad.h"
#include "mokxi_lcd1602.h"

const uint8_t ROWS[5] = {13, 12, 11, 10, 9};
const uint8_t COLS[4] = {8, 7, 6, 5};

Keypad5x4 pad(ROWS, COLS);
Lcd1602 lcd(A0, A1, A2, A3, A4, A5);

/** The largest number this calculator will hold, in hundredths: 99999.99. */
const long MAX_VALUE = 9999999L;

long acc = 0;         // what has been worked out so far, in hundredths
long entry = 0;       // the number being typed, in hundredths, never negative
char op = 0;          // the operator waiting for its second operand
uint8_t places = 0;   // 0 no point yet, 1 just after it, 2 tenths in, 3 full
bool typing = false;  // whether `entry` is what the display should show
bool negative = false;
bool error = false;

/** The number being typed, with its sign. */
static long current()
{
  return negative ? -entry : entry;
}

static void resetEntry()
{
  entry = 0;
  places = 0;
  negative = false;
  typing = false;
}

static void clearAll()
{
  acc = 0;
  op = 0;
  error = false;
  resetEntry();
}

/** a + b, or false when the answer is too big to hold. */
static bool addTo(long a, long b, long *out)
{
  long r = a + b;
  if (r > MAX_VALUE || r < -MAX_VALUE) {
    return false;
  }
  *out = r;
  return true;
}

/**
 * a * b, both in hundredths, answer in hundredths.
 *
 * Split so nothing overflows: the whole part of `a` multiplied by `b` is
 * checked against MAX_VALUE before it is worked out, and the hundredths left
 * over are at most 99, so 99 * b fits with room to spare.
 */
static bool mulTo(long a, long b, long *out)
{
  bool minus = (a < 0) != (b < 0);
  unsigned long ua = (unsigned long)(a < 0 ? -a : a);
  unsigned long ub = (unsigned long)(b < 0 ? -b : b);
  unsigned long whole = ua / 100u;
  unsigned long rest = ua % 100u;
  if (ub != 0u && whole > (unsigned long)MAX_VALUE / ub) {
    return false;
  }
  unsigned long r = whole * ub + (rest * ub) / 100u;
  if (r > (unsigned long)MAX_VALUE) {
    return false;
  }
  *out = minus ? -(long)r : (long)r;
  return true;
}

/** a / b, both in hundredths, answer in hundredths, truncated. */
static bool divTo(long a, long b, long *out)
{
  if (b == 0) {
    return false;
  }
  bool minus = (a < 0) != (b < 0);
  unsigned long ua = (unsigned long)(a < 0 ? -a : a);
  unsigned long ub = (unsigned long)(b < 0 ? -b : b);
  unsigned long r = (ua * 100u) / ub;
  if (r > (unsigned long)MAX_VALUE) {
    return false;
  }
  *out = minus ? -(long)r : (long)r;
  return true;
}

/** Fold the number just typed into the accumulator with the waiting operator. */
static void apply()
{
  long v = current();
  if (!typing && op == 0) {
    return;
  }
  if (op == 0) {
    acc = v;
    return;
  }
  bool ok = false;
  switch (op) {
    case '+': ok = addTo(acc, v, &acc); break;
    case '-': ok = addTo(acc, -v, &acc); break;
    case 'x': ok = mulTo(acc, v, &acc); break;
    case '/': ok = divTo(acc, v, &acc); break;
    default: ok = true; break;
  }
  if (!ok) {
    error = true;
  }
}

/** Take one digit off whatever is being typed. */
static void backspace()
{
  if (!typing) {
    return;
  }
  if (places == 3) {
    entry = (entry / 10) * 10;
    places = 2;
  } else if (places == 2) {
    entry = (entry / 100) * 100;
    places = 1;
  } else if (places == 1) {
    places = 0;
  } else {
    entry = (entry / 1000) * 100;
  }
}

static void digit(char c)
{
  if (!typing) {
    resetEntry();
    typing = true;
  }
  long d = (long)(c - '0');
  if (places == 0) {
    if (entry > (MAX_VALUE - d * 100) / 10) {
      return;  // already as long as this display can show
    }
    entry = entry * 10 + d * 100;
  } else if (places == 1) {
    entry += d * 10;
    places = 2;
  } else if (places == 2) {
    entry += d;
    places = 3;
  }
}

/** One line of the display: a number in hundredths, left aligned and padded. */
static void showValue(uint8_t row, long value, char suffix)
{
  lcd.setCursor(0, row);
  lcd.printFixed(value, 2);
  if (suffix != 0) {
    lcd.write(' ');
    lcd.write(suffix);
  }
  lcd.padLine();
}

static void redraw()
{
  lcd.setCursor(0, 0);
  if (error) {
    lcd.print("Err");
    lcd.padLine();
    lcd.setCursor(0, 1);
    lcd.print("C to clear");
    lcd.padLine();
    return;
  }
  showValue(0, acc, op);
  showValue(1, typing ? current() : acc, 0);
}

void setup()
{
  pad.begin();
  lcd.begin();
  lcd.print("Calculator");
  lcd.setCursor(0, 1);
  lcd.print("C clears");
  delay(700);
  clearAll();
  redraw();
}

void loop()
{
  char key = pad.pressed();
  if (key == 0) {
    return;
  }

  if (key == 'C') {
    clearAll();
    redraw();
    return;
  }
  if (error) {
    return;  // nothing but C gets out of an error, the way a real one behaves
  }

  switch (key) {
    case '+':
    case '-':
    case 'x':
    case '/':
      apply();
      op = key;
      resetEntry();
      break;
    case '=':
      apply();
      op = 0;
      resetEntry();
      break;
    case '.':
      if (!typing) {
        resetEntry();
        typing = true;
      }
      if (places == 0) {
        places = 1;
      }
      break;
    case '~':
      if (!typing) {
        resetEntry();
        typing = true;
      }
      negative = !negative;
      break;
    case '<':
      backspace();
      break;
    case '%':
      if (typing) {
        entry /= 100;
        places = 3;
      }
      break;
    default:
      if (key >= '0' && key <= '9') {
        digit(key);
      }
      break;
  }
  redraw();
}