SpiceWare's Blog

I did some tests using ENT, which showed a significant improvement in serial correlation if you rotate Rand8 and Rand16 in opposite directions (like you do). Which is no surprise because the return value XORs both values
(though, the higher the value for the XOR value, the less relevant this becomes; especially $eb and $fc are even slightly better without reversing the direction; I guess the number of high bits set plays a role here).

I also tested all possible values for XOR ($9c, $b4, $bd, $ca, $eb, $fc) and especially $9c gave good results for all tests (especially chi square).

There's been some questions regarding the ifconst and endif in the Random subroutine. Basically they're instructions that dasm uses to determine whether or not dasm "sees" the code appears between the two instructions.

 

Basically ifconst is asking "does the value listed next exist in the program?". If the answer is yes, then anything text between the ifconst and endif will be included in your program. If the answer is no, then dasm will ignore any text between the ifconst and endif.

 

In the case of the Random subroutine dasm checks to see if Rand16 exists in the program. As written our program has this in it:

 

   ; optionally define space for Rand16 for 16 bit random number
Rand16:         ds 1    ; stored in $AC    

---

So the answer to ifconst Rand16 is "yes, the value exists" and dasm will "see" the code like this:

Random:
        lda Rand8
        lsr
        rol Rand16      ; this command is only used if Rand16 has been defined
        bcc noeor
        eor #$B4 
noeor 
        sta Rand8
        eor Rand16      ; this command is only used if Rand16 has been defined
        rts    

---

If we deleted the following from our program:

; optionally define space for Rand16 for 16 bit random number

Rand16: ds 1 ; stored in $AC

 

 

the answer to ifconst Rand16 is "no, the value does not exist" so dasm will "see" the code like this:

Random:
        lda Rand8
        lsr
        bcc noeor
        eor #$B4 
noeor 
        sta Rand8
        rts   

Hi!

 

Two things.. I'm amazed that the LSFR will always go through 255 or 65,535 cycles without repeating. I would think that at least some seed values would cause that to change...

 

Secondly a question. What is the reason the CollectBox routine switches to decimal mode? Does it have to do with displaying the score? I could see masking the left or right nibble to get the offset for 10s or 1s digit graphics. Is that it?

Howdy!

1 - the EOR value (also known as the tap) is what dictates the number of cycles without repeating. At Maximal Length LFSR Feedback Terms, you can find a list of values that give the maximum cycles before repeating. For 8 bit values there are 16 different taps. For 16 bit values there are 2048 (one of which is $B400, which is why this routine works for both 8 bit and 16 bit LFSR).

2 - Normally when you add $02 to $09 you'd get $0B. Decimal Mode changes it so that each nybble of the byte is treated like a decimal value of 0-9. That makes it so the same addition of $02 and $09 results in $11 instead. We use it because displaying $0B as a human readable value of "11" is computationally expensive, while displaying $11 as "11" is not.

Ahh.. I think I only had (have, really) a grasp of the two bit tap (The Wikipedia example). So it looks like from the description you gave, once the LSFR is seeded, any seed will produce all sorts of cycle lengths all chained together one after another. Correct?

For any given tap, the sequence of numbers is always the same. Slide 81 of the last presentation I gave shows the sequence returned if tap $B4 is used with a seed value of $84. If you seed it with $7C (last value on first line), the values returned would begin with $3E (first value on second line).

 

If you change the code to use a different tap value, but still one from that list I linked to yesterday, you'll get a different sequence of 255 values.

 

If you use a tap with a value other than those 16 you'll end up using one of multiple shorter sequences, which sequence you're in will depend upon the seed value.

One note - a maxlen LFSR will have one "dead" value (typically 0, but might be another value) where the output value is the same as the input value. It's therefore a good idea to either initialize the LFSR with a good seed or detect the "dead" value and handle it.

Yep, covered that in paragraph 4, not counting the air quotes comment. I didn't realize the dead value could be something other than 0, so that's good to know

Hmm, I doubt that there is any other dead value, especially for a maxlen LFSR.

 

I am sure that 0 is always the one and only dead value (at least for the code above), because there is no bit to trigger the EOR. And by definition a maxlen LFSR has 2^n-1 values. So there cannot be any other dead value.