A speed-tatstic way to look up a value? (LUTs)

[HankMcSpank]

Binary Search Algorithm

That's exactly what I was thinking of - so now, how to implement in picbasic!

Imagine an array 100 deep (& for simplicity's sake, populated with values 1 thru 100), with an incoming number of 90 to 'look up' against...

So, the methodology....

is new incoming value higher or lower than 50

(result = higher therefore the next stage...)

is new incoming number higher of lower than 75

result = higher again, & so on it continues...

but eventually it all starts getting tricky (because half way between 75 & 100 is 87.5 ....what to do here, etc?)

[cncmachineguy]

something I've been thinking about. since this is music, i assume there is a predictable difference between the low or high numbers? I ask because if you could divide all the numbers to create a case type lookup.

The answer to 87.5 IMHO is to use 87 or 88. Since the half tests are hard coded in(at least for your example) no need to be exact.

[HankMcSpank]

something I've been thinking about. since this is music, i assume there is a predictable difference between the low or high numbers? I ask because if you could divide all the numbers to create a case type lookup.

The answer to 87.5 IMHO is to use 87 or 88. Since the half tests are hard coded in(at least for your example) no need to be exact.

The table I posted earlier was the shortened version, I had diffs formatting the full version, but this screenshot shows what I'm getting at...



(note the first two notes in the table will actually cause a timer 1 overflow and therefore can't be monitored when using a 20Mhz Osc - well not without extra code in the interrupt handler - so I include them only for completeness)


the frequency of the incoming signal is derived from the the number of comparator interrupts rx'ed for the frequency 'peroid' ...& becuase I want to map the frequency to a midi 'note' - and musical 'notes' are set in stone (ie no such thing a middle C.23) - I therefore also need to establish what the midway count is between successive note 'frequencies' (the note boundary if you like)

....but with a LUT 50 deep & with two conditions to check for per LUT entry, eg .....

if (comp1time>= 66194 and comp1time <= 62478) then note = $27

then if the incoming frequency is changing rapidly (becuase the notes are changing rapidly), then I need to have a fast way of resolving the incoming frequency to a note value.

[cncmachineguy]

Well I only count 32 notes, but I'm on my phone so maybe I don't get to see the whole thing.

That said, A is the last note I see, and it seems there is a count of ~11,000 for that note. So to me that's ~11,000 instructions to waste before a new interupt. That's tons of time if I understand your chart correctly. In any event, I like to get things done fast. My suggestion is a hybrid search. Maybe check the middle, decide higher or lower, then do a linear search from there.

Now back to the numbers: If each test took 25 instructions and you have 50 tests: that's 1250 instructions. Approx 10% of the time between interupts. So still no prob.

[cncmachineguy]

Let me just add, 25 instructions is a lot of asm just to check that. See, this is why I want to know how long things take.

[HankMcSpank]

Well I only count 32 notes, but I'm on my phone so maybe I don't get to see the whole thing.

Sorry, should have made it clear...the table I posted above is actually longer, but I shortened it to be easier on the eye! (the jist of the table was just to show the methodology of converting incoming frequency (guitar notes), to counts (comparator1 interrupt counts) & finally the end goal - a midi note value.

the LUT will only have something like this (first two columns are upper and lower comparator 'counts' for each individual musical note boundary)

Lo       Hi       Midi Note 
62479	58971	28
58972	55662	29
55663	52538	2A
52539	49589	2B
49590	46806	2C
46807	44179	2D
44180	41699	2E
41700	39359	2F
39360	37150	30
37151	35065	31
35066	33097	32
33098	31239	33
31240	29486	34
29487	27831	35
27832	26269	36
26270	24794	37
24795	23403	38
23404	22089	39
22090	20849	3A
20850	19679	3B
19680	18575	3C
18576	17532	3D
17533	16548	3E
16549	15619	3F
15620	14743	40
14744	13915	41
13916	13134	42
13135	12397	43
12398	11701	44
11702	11044	45
11045	10424	46
10425	9839	47
9840	9287	48
9288	8766	49
8767	8274	4A
8275	7810	4B
7811	7371	4C
7372	6957	4D
6958	6567	4E
6568	6198	4F
6199	5850	50
5851	5522	51
5523	5212	52
5213	4919	53
4920	4643	54
4644	4383	55
4384	4137	56
4138	3905	57
3906	3800	58

There are about 50 individual notes on a guitar - from lowest open E (82.4Hz) thru the highest E fretted at the 24th fret of the top E string (1318.51Hz)....so an LUT will need an array 50 deep & a check condition along these lines for any change in the count value...

if (comp1time>= 66194 and comp1time <= 62478) then note = $27

but to apply 50 of code like that each & every time guitar note changes is going to get time consuming, hence wanting something like a binary search algorithm for picbasic (a search on the forum yields almost nothing)

[cncmachineguy]

based on your chart, I would look first to see if count < 10000. thats the one to take care of the quickest. then check somewhere between 10000 and 65000.

Of course when you find the range, just use if then like you posted

[cncmachineguy]

How bout something like this?

'Is this the right symbel for comments?
'This is what I'm using it for
'
'Assuming count is the number to be checked
'
'This set of checks breaks it into 3 16 possible chuncks

If count < 3800 then ERROR                            ' count under 3800 must be wrong, but it could mean TMR rolled over
If (count <= 9288) and (count >= 3800) then LowCount ' 
If count <= 23404 then MidCount                       ' no need to check lower limit because that was in last check
if count <= 62479 then HighCount                      ' still no lower check

'now do the same for the each section:

LowCount
if count <= 4920 then LLowCount
if count <= 6568 then MLowCount
' must be High low count
'at this point do another chunck break or code for all possibles
'another chunck break

if count <=8275 then LhLowCount
'choice of 4 now
'at this point count MUST be >8275 and <=9288

LhLowCount ' count between 6569 and 8275
if (count >=6569) and (count <=7372) then note=4D : goto NoteFound
If (count >=7371) and (count <=7372) then note=4C : goto NoteFound
if (count >=7810) and (count <=8275) then note=4B : goto NoteFound

Dose this make any sense? I think there is a problem with your numbers, but it could be me. Seems like high and low of next up note are reversed. For instance note 4D is 7372-6957, and 4C is 7811-7371.