In http://mattmahoney.net/dc/dce.html#Section_32 Matt Mahoney states:

The simplest of these is the order 0 coder fpaq0.

in http://mattmahoney.net/dc/dce.html#Section_41 he states:

An order 0 model uses no context.

but in http://mattmahoney.net/dc/fpaq0.cpp the Predictor (model) is defined with a context:

class Predictor {
  int cxt;  // Context: last 0-8 bits with a leading 1
  int ct[512][2];  // 0 and 1 counts in context cxt
  Predictor(): cxt(1) {
    memset(ct, 0, sizeof(ct));

  // Assume a stationary order 0 stream of 9-bit symbols
  int p() const {
    return 4096*(ct[cxt][1]+1)/(ct[cxt][0]+ct[cxt][1]+2);

  void update(int y) {
    if (++ct[cxt][y] > 65534) {
      ct[cxt][0] >>= 1;
      ct[cxt][1] >>= 1;
    if ((cxt+=cxt+y) >= 512)

Why is that?


1 Answer 1


From Matt Mahoney himself in an email:

"It is bytewise order 0, not bitwise. It models byte probabilities independently one bit at a time. The bit probabilities depend on previous bits."

  • $\begingroup$ Bravo for going straight to the source! $\endgroup$
    – John L.
    Commented Apr 15, 2022 at 2:16

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