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

[HankMcSpank]

I'd like to resolve 'Comparator interrupt counts' (frequency) to a Musical note & therefore have a table to base a LUT on as follows....

(btw: I've not got the low & high columns mixed up....they are with respect to frequency - as the incoming frequency increases the amount of interrupt counts get less)

Count	low	High	Note
68104	67000	66193	D
64282	66194	62478	D#
60674	62479	58971	E
57269	58972	55662	F
54054	55663	52538	F#
51021	52539	49589	G
48157	49590	46806	G#
45454	46807	44179	A
42903	44180	41699	A#
40495	41700	39359	B
38222	39360	37150	C
36077	37151	35065	C#
34052	35066	33097	D
32141	33098	31239	D#
30337	31240	29486	E
28634	29487	27831	F
27027	27832	26269	F#
25510	26270	24794	G
24078	24795	23403	G#
22727	23404	22089	A
21451	22090	20849	A#
20247	20850	19679	B
19111	19680	18575	C
18038	18576	17532	C#
17026	17533	16548	D
16070	16549	15619	D#
15168	15620	14743	E
14317	14744	13915	F
13513	13916	13134	F#
12755	13135	12397	G
12039	12398	11701	G#
11363	11702	11044	A
10725	11045	10424	A#
10123	10425	9839	B
9555	9840	9287	C5
9019	9288	8766	C#
8513	8767	8274	D
8035	8275	7810	D#
7584	7811	7371	E
7158	7372	6957	F
6756	6958	6567	F#
6377	6568	6198	G
6019	6199	5850	G#
5681	5851	5522	A
5362	5523	5212	A#
5061	5213	4919	B
4777	4920	4643	C
4509	4644	4383	C#
4256	4384	4137	D
4017	4138	3905	D#
3792	3906	3800	E

Therefore if the comparator interrupt count comes in a somewhere between 19680 & 18575.....then I need to establish (look up) what the associated musical note is - in this case a 'C'

If it then changes again to between 4138 & 3905 then it's high 'D#' ....and so on.

Now as a beginner, the simple way I'd approach this is take my comparator 'interrupt count' & go through the list one entry at a time until I get a match.....but if the notes are changing rapidly (&/or are at different ends of the table), then that's quite an overhead - is there a slick way to get to the actual note fast (eg way back, I was taught something in military wrt finding a fault in an electronic cct - the 'split half technique' ...basically to first check if the 'fault' is present at the halfway point in a circuit - if not, split the mid point again and check if it's present there....etc - this quickly gets you to the general area where the fault lies)....I'm sure something similar could be applied like that here?

[rmteo]

Binary Search Algorithm

[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.

[HankMcSpank]

Hi Bert,

I wil digest your code a bit later (seriously, to my untrained eye, everything takes a while decipher & get my head around!). As it goes it seems pretty whippy already (ie just running through the whole 50 deep LUT, top to bottom)...

Here's a quick video I've just made....

(to be able to see what's going on in it, you really need to watch in full screen mode *and* 720p, which I don't know how to embed - these options can be chosen looking at the video directly on you tube via this URL ).....



Green trace is audio 'input' signal (a sine wave sent into my circuit from a synth), the yellow trace is the same signal but squared up (feeding into the PIC's comparator1), the data to the left of the scope is the midi info as transmitted out of the PIC.

the full signal path is as follows...

Synth audio sine wave signal-> squaring cct-> pic comparator->interrupt counter -> PIC LUT ->PIC then outputs midi data using HSEROUT-> into a PC MIDi In port->into an app callec MID- OX (A midi interpreter/viewer - which is what that window/data to the left in the video is)

So the sine wave jumping about is actually me playing different notes on a synth (& thereby changing the sine wave frequency into the PIC - to test the PIC frequency detection & conversion to MIDI)


PS btw I had the data the wrong way round when I posted earlier - the LUT condition was not being met, here it is corrected...

if (comp1time>= 52538 AND comp1time <= 55663) then note = $2A
if (comp1time>= 49589 AND comp1time <= 52539) then note = $2B
etc etc

So maybe I don't need a binary search algorithm, but every little helps wrt to speed, so may still explore that avenue.

[cncmachineguy]

Hank, if it works dont fix it. or if it isn't broke, fix it till it is. lol

Seriously, the only thing i would do is make sure and run your test from the bottom up. By this I mean, check for the low count first on up th to highest count. then you can be sure to have enough time. . Something else about your linear search, Y only need to test for 1 condition in each next IF after the first. heres why:

First check establishes a range, say 3800-3900, if this fails, number must be > 3900. next check just needs to look for <4000 cuz you know its >3900. next check if <4200,again because it must be >3900. and so on. Of course my numbers are fictious, but you should get the point. Only checking 1 condition should almost double the execution speed (half the processing).

the code I posted is not complete, it shows how to go through the levels of searching.

[HankMcSpank]

Well the acid test is when I play a guitar into it & the pic 'triggers' a sound in midi synth module.

A bass E string 'period' is about 12ms (82.4Hz) ....add in the overhead that detecting the frequency will entail, then it's going to be higher.

They reckon the average musician can detect about 10ms of latency (ie from hitting a key, banging a drum,plucking a string .... to actually hearing the sound) so I'm already behind the curve so to speak. The commercial 'guitar to midi' converters pull this frequency 'detection time' in by detecting half a period....so for 82.4Hz, that'd be about 6ms - safely under the 10ms level - but I reckon that'd need a 40Mz oscillator to have the necessary granularity.

So perhaps it's better to go top down (the bass frequencies are at the top of the list), just to rescue back a little bit of 'processing time' for those lower frequencies (for example a 1Khz 'period' is 1ms, so I've far more time to play with vs lower frequencies.)