Polynomial Counter
The polynomial counter is the less significant 7 bits of the CIC's program counter. Unlike most program counters which increment by the size of an instruction, the polynomial counter is stepped according to a special formula:
void CIC::poly_step()
{
bool bit0 = pc & 0x01;
bool bit1 = pc & 0x02;
bool bits01_xnor = !(bit0 ^ bit1);
pc = (pc & 0x380) + (bits01_xnor * 0x40) + (pc & 0x7E) / 2;
}
Presumably, it takes fewer transistors to step this way than a standard ripple carry incrementor.
If the polynomial counter begins at 00h and runs a straightforward control flow graph (e.g. no jumps/branches/calls/returns), this is the sequence it will count through:
00 40 60 70 78 7c 7e 3f 5f 6f 77 7b 7d 3e 1f 4f 67 73 79 3c 5e 2f 57 6b 75 3a 1d 0e 07 43 61 30 58 6c 76 3b 5d 2e 17 4b 65 32 19 0c 46 23 51 28 54 6a 35 1a 0d 06 03 41 20 50 68 74 7a 3d 1e 0f 47 63 71 38 5c 6e 37 5b 6d 36 1b 4d 26 13 49 24 52 29 14 4a 25 12 09 04 42 21 10 48 64 72 39 1c 4e 27 53 69 34 5a 2d 16 0b 45 22 11 08 44 62 31 18 4c 66 33 59 2c 56 2b 55 2a 15 0a 05 02 01
before cycling back to 00h.
Note that 7Fh is unique in that it is the only 7-bit value that does not appear in this sequence. That is because 7Fh is idempotent - if the counter ever reaches 7Fh somehow (like through a JMP) then trying to step it will only result in it staying at 7F, so the CIC hangs at that address.
Source: