unsigned long now;
unsigned int counter;

# define RATE 10000

void setup() {
  Serial.begin(115200);
  Serial.println("hi Mom!");

  Serial.println("advance  kAdvance");

}

unsigned int zit = 0x8011;
unsigned int it = 0xcd55;

void loop() {
  static unsigned long lastTime;
  now = millis();
// loop rate

it = reverseK16(it);
Serial.print(it, HEX);
Serial.println("");

//zit = reverseK(zit);

  static int fork;
  if (++fork > 50) for (; ; );

// once per
  if (now - lastTime < RATE) return;
  lastTime = now;

//  Serial.println(counter); counter++;
}

// the original Moberly advance
unsigned int advance(unsigned int it)
{
  it <<= 1;
  if (it & (1ul << 15))  // 0x8000ul, gack! chain reaction interesting affect
    if (it & (1 << 14)); else it |= 1;  // <--

  else if (it & (1 << 14)) it |= 1;

  if (0) {
    static int counter;
    Serial.print(counter); Serial.print(" ");
    counter++;
    unsigned int the = it & 0xffff;
    Serial.println(the, HEX);
  }
  return it;
}

unsigned int advanceK(unsigned int it)
{
  unsigned int bits = it & 0x6000;
  bool parity = false;

  while (bits) {
    bits &= bits - 1;
    parity = !parity;
  }

  it <<= 1;
  if (parity) it |= 0x1;

  return it;
}

unsigned int reverseK(unsigned int it)
{
  unsigned int bits = it & 0x8002;
  bool parity = false;

  while (bits) {
    bits &= bits - 1;
    parity = !parity;
  }

  it >>= 1;
  if (parity) it |= 0x8000;

  return it;
}

void mobe16()
{
  if (digitalRead(3) == HIGH) it = advanceK16(it);
  else it = reverseK16(it);
}

unsigned int advanceK16(unsigned int it)
{
  unsigned int bits = it & 0xb400;
  bool parity = false;

  while (bits) {
    bits &= bits - 1;
    parity = !parity;
  }

  it <<= 1;
  if (parity) it |= 0x1;

  return it;
}

unsigned int reverseK16(unsigned int it)
{
  unsigned int bits = it & 0x6801;
  bool parity = false;

  while (bits) {
    bits &= bits - 1;
    parity = !parity;
  }

  it >>= 1;
  if (parity) it |= 0x8000;

  return it;
}



void advance16()
{
  unsigned char a = it & (1ul << 15) ? 1 : 0;  // 15 (16/1)
  unsigned char b = it & (1 << 13) ? 1 : 0;  // 13 (14/1)
  unsigned char c = it & (1 << 12) ? 1 : 0;  // 12 (13/1)
  unsigned char d = it & (1 << 10) ? 1 : 0;  // 10 (11/1)

//  unsigned char e = a ^ b ^ c ^ d;
  unsigned char e = a + b + c + d;

  it <<= 1;
  if (e & 1) it |= 0x1;
}



/*
original advance looks correct
hi Mom!
400
800
1000
2000
4001
8003
6
C
18
30
60
C0
180
300
600
C00
1800
3000
6001
C002
8005
A
14
28
50
A0

advanceK looks good
hi Mom!
advance  kAdvance
800   800
1000   1000
2000   2000
4001   4001
8003   8003
6   6
C   C
18   18
30   30
60   60
C0   C0
180   180
300   300
600   600
C00   C00
1800   1800
3000   3000
6001   6001
C002   C002
8005   8005
A   A
14   14
28   28
50   50
A0   A0
140   140

*/