Polynomial Counter

The polynomial counter is a Fibonacci linear-feedback shift register that serves as 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. The sum-of-three-terms formula in the pc assignment statement is equivalent to a bit shift and bitwise or:

	pc = (pc >> 1) | (bits01_comb * 0x40);

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.

Sources:

• https://problemkaputt.de/fullsnes.htm#snescartridgecicnotes
• https://hackmii.com/2010/01/the-weird-and-wonderful-cic/