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ADC Sampling Breakthrough - Page 34 — Parallax Forums

ADC Sampling Breakthrough

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  • cgracey wrote: »
    Saucy, I experimented with a lot of filters and some were just noisy. I picked three that I could prove in my program and test on the FPGA with the ADC:
    dim t(70)
    
    for x = 0 to 70
      t(x) = 0
    next x
    
    'a=2 : b=3 : c=8 : d=33 : m=1     '70-tap Tukey window
    'a=2 : b=3 : c=6 : d=14 : m=2     '47-tap Tukey window
    a=1 : b=2 : c=8 : d=01 : m=4     '30-tap Hann window
    
    ...
    

    It would save some logic if the Hann window had identical ramps to the second Tukey window. I've always assumed that's how a Hann would be done. In fact, I think it should be possible to have one set of taps, for the long Tukey window, with shift register shortcuts for the other two. The following shows how similar the two Tukeys are:
    0, 1, 2, 4, 6, 8,11,14,17,20,23,26,29,32,34,36,38,39,40,...
    0, 1, 2, 4, 6, 8,11,14,17,20,23,26,28,30,32,33,34,...
    
  • Three windows need two filter select bits, which means there could be a fourth type of window.
  • cgraceycgracey Posts: 13,610
    TonyB_ wrote: »
    Three windows need two filter select bits, which means there could be a fourth type of window.

    That's right.

    16 bits are dedicated to the trigger mechanism. There could be a mode without trigger that is highest resolution. What we have now with the 70 bit filter is pretty amazing. I will post pictures shortly.
  • Is all of the 71-bit tap register needed? There are only 68 non-zero values (17+34+17) for the long Tukey and adding one for the ADC input makes 69.
  • cgraceycgracey Posts: 13,610
    TonyB_ wrote: »
    Is all of the 71-bit tap register needed? There are only 68 non-zero values (17+34+17) for the long Tukey and adding one for the ADC input makes 69.

    We need extra bits to detect edges now. That's why it's longer.
  • cgraceycgracey Posts: 13,610
    edited 2018-12-13 00:45
    Here are the various filters in the smart pin scope mode.

    In these pictures, you are looking at the apex of a sine wave being digitized and played back on a DAC at 8x amplitude, so that the individual steps can be clearly seen. The longer the filter is, the lower its passband is, making it quieter, but not good for higher frequencies.

    Here is the 70-tap Tukey filter:
    smart_pin_scope_70_tap_Tukey.jpg

    Here is the 47-tap Tukey filter:
    smart_pin_scope_47_tap_Tukey.jpg

    Here is the 30-tap Hann filter:
    smart_pin_scope_30_tap_Hann.jpg
  • What does "higher frequencies" mean?

    Hz, Khz, Mhz?
  • cgraceycgracey Posts: 13,610
    edited 2018-12-13 01:12
    potatohead wrote: »
    What does "higher frequencies" mean?

    Hz, Khz, Mhz?

    These filters slow down edges. In the 70-tap filter (which is actually more like a 68-tap filter, but needs extra bits for edge detection), 68 contiguous 1's must go into the filter before it reaches its max output of 255. Then, 68 contiguous 0's must go in before it reaches its internal 0, though it output 0 three clocks earlier. Rounding could lift things a little bit, but is maybe of no real value.
  • Enough for baseband video?
  • cgraceycgracey Posts: 13,610
    edited 2018-12-13 01:21
    rogloh wrote: »
    Enough for baseband video?

    With a 7/8th reduction in the ADC's integrator capacitance, it will pass higher frequencies much better.

    I was reading that to digitize baseband video, you need to sample at 13.5MHz. So, if you were to run at 216MHz you could have 16 clocks per sample in which an 8-bit-quality Sinc3 conversion could be performed.

    With the ADC change, that should be viable. This will all be in the next silicon.
  • cgracey wrote: »
    rogloh wrote: »
    Enough for baseband video?

    With a 7/8th reduction in the ADC's integrator capacitance, it will pass higher frequencies much better.

    I was reading that to digitize baseband video, you need to sample at 13.5MHz. So, if you were to run at 216MHz you could have 16 clocks per sample in which an 8-bit-quality Sinc3 conversion could be performed.

    With the ADC change, that should be viable. This will all be in the next silicon.

    Any chance it could be extended to 20 clocks per sample, or it would mess with the filterings?

    With sysclk@ 270 MHz and 20 clocks per sample, it would enable almost direct coupling of resulting data to HDMI.

    Only a thought...
  • cgracey wrote: »
    rogloh wrote: »
    Enough for baseband video?

    With a 7/8th reduction in the ADC's integrator capacitance, it will pass higher frequencies much better.

    I was reading that to digitize baseband video, you need to sample at 13.5MHz. So, if you were to run at 216MHz you could have 16 clocks per sample in which an 8-bit-quality Sinc3 conversion could be performed.

    With the ADC change, that should be viable. This will all be in the next silicon.

    It sounds pretty good Chip. I hope it all fits in the next rev. Cheers!
    Roger.


  • cgraceycgracey Posts: 13,610
    Yanomani wrote: »
    cgracey wrote: »
    rogloh wrote: »
    Enough for baseband video?

    With a 7/8th reduction in the ADC's integrator capacitance, it will pass higher frequencies much better.

    I was reading that to digitize baseband video, you need to sample at 13.5MHz. So, if you were to run at 216MHz you could have 16 clocks per sample in which an 8-bit-quality Sinc3 conversion could be performed.

    With the ADC change, that should be viable. This will all be in the next silicon.

    Any chance it could be extended to 20 clocks per sample, or it would mess with the filterings?

    With sysclk@ 270 MHz and 20 clocks per sample, it would enable almost direct coupling of resulting data to HDMI.

    Only a thought...

    Sure. 20 clocks per sample would be better. You can use whatever decimation rate you want. Then, there's the need to use some Goertzel analysis on the chroma signal and then do some colorspace conversion to RGB.
  • cgracey wrote: »
    rogloh wrote: »
    Enough for baseband video?

    With a 7/8th reduction in the ADC's integrator capacitance, it will pass higher frequencies much better.

    I was reading that to digitize baseband video, you need to sample at 13.5MHz. So, if you were to run at 216MHz you could have 16 clocks per sample in which an 8-bit-quality Sinc3 conversion could be performed.

    With the ADC change, that should be viable. This will all be in the next silicon.


    7/8 reduction? The figures I think I've seen you post were 3.5 ~ 6.5 MHz current bandwidth. But that'd imply you only needed to halve or quarter the capacitor
  • potatoheadpotatohead Posts: 10,188
    edited 2018-12-13 02:40
    Thanks Chip. I get it, the more taps, longer filter, the more clocks needed per effective sample. That and sysclock tells us where the roll off is, and a bit about what it will look like.

    Boy, that 70 tap looks perty

  • So is all this recent stuff for the current chip or some future one?
    Some of Chip's comments seem to involve changing the pad stuff and not just verilog? Or an I misunderstanding?
  • evanhevanh Posts: 11,044
    He's going ahead with tweaking some component values only, no layout changes, in the custom pad ring.

  • cgraceycgracey Posts: 13,610
    Reducing the ADC integrator cap is a pad-ring change, but only involves the routing metal. All this will be in the next silicon.
  • cgracey wrote: »
    Saucy, I experimented with a lot of filters and some were just noisy. I picked three that I could prove in my program and test on the FPGA with the ADC:
    dim t(70)
    
    for x = 0 to 70
      t(x) = 0
    next x
    
    
    'a=2 : b=3 : c=8 : d=33 : m=1     '70-tap Tukey window
    'a=2 : b=3 : c=6 : d=14 : m=2     '47-tap Tukey window
    a=1 : b=2 : c=8 : d=01 : m=4     '30-tap Hann window
    
    t0  = 0
    t1  = t0  + a
    t2  = t1  + b
    t3  = t2  + c
    t4  = t3  + b
    t5  = t4  + a
    t6  = t5  + d
    t7  = t6  + a
    t8  = t7  + b
    t9  = t8  + c
    t10 = t9  + b
    t11 = t10 + a
    
    print "taps",,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11
    print
    
    inta = 0
    intb = 0
    intc = 0
    
    print "iter","inta","intb","intc","sample"
    
    for y = 0 to 70*2-1
    
    for x = 70 to 1 step -1
      t(x) = t(x-1)
    next x
    
    t(0) = 1
    if y >= 70 then t(0) = 0
    
    delta = 0
    
    if (t(t0) = 1 and t(t0+1) = 0) then delta = delta + 1
    if (t(t0) = 0 and t(t0+1) = 1) then delta = delta - 1
    
    if (t(t1) = 1 and t(t1+1) = 0) then delta = delta + 1
    if (t(t1) = 0 and t(t1+1) = 1) then delta = delta - 1
    
    if (t(t2) = 1 and t(t2+1) = 0) then delta = delta + 1
    if (t(t2) = 0 and t(t2+1) = 1) then delta = delta - 1
    
    if (t(t3) = 1 and t(t3+1) = 0) then delta = delta - 1
    if (t(t3) = 0 and t(t3+1) = 1) then delta = delta + 1
    
    if (t(t4) = 1 and t(t4+1) = 0) then delta = delta - 1
    if (t(t4) = 0 and t(t4+1) = 1) then delta = delta + 1
    
    if (t(t5) = 1 and t(t5+1) = 0) then delta = delta - 1
    if (t(t5) = 0 and t(t5+1) = 1) then delta = delta + 1
    
    if (t(t6) = 1 and t(t6+1) = 0) then delta = delta - 1
    if (t(t6) = 0 and t(t6+1) = 1) then delta = delta + 1
    
    if (t(t7) = 1 and t(t7+1) = 0) then delta = delta - 1
    if (t(t7) = 0 and t(t7+1) = 1) then delta = delta + 1
    
    if (t(t8) = 1 and t(t8+1) = 0) then delta = delta - 1
    if (t(t8) = 0 and t(t8+1) = 1) then delta = delta + 1
    
    if (t(t9) = 1 and t(t9+1) = 0) then delta = delta + 1
    if (t(t9) = 0 and t(t9+1) = 1) then delta = delta - 1
    
    if (t(t10) = 1 and t(t10+1) = 0) then delta = delta + 1
    if (t(t10) = 0 and t(t10+1) = 1) then delta = delta - 1
    
    if (t(t11) = 1 and t(t11+1) = 0) then delta = delta + 1
    if (t(t11) = 0 and t(t11+1) = 1) then delta = delta - 1
    
    inta = inta + delta
    intb = intb + inta
    intc = intc + intb * m
    
    sample = int(intc/8)
    print y,inta,intb,intc,sample
    
    next y
    

    You still did not fix the issue of differentiating the input data. While the BASIC program shows 12 taps, it actually uses 24 taps since it uses tn and (tn)+1. It's not actually a bad idea to integrate 3 times if the filter was designed for cubic curves. As it is now, one of the integrators is just undoing the differentiation that was inadvertently added. Surely the code below would be much cheaper to implement.
    dim t(70)
    
    for x = 0 to 70
      t(x) = 0
    next x
    
    
    '=2 : b=3 : c=8 : d=33 : m=1     '70-tap Tukey window
    '=2 : b=3 : c=6 : d=14 : m=2     '47-tap Tukey window
    a=1 : b=2 : c=8 : d=01 : m=4     '30-tap Hann window
    
    t0  = 0
    t1  = t0  + a
    t2  = t1  + b
    t3  = t2  + c
    t4  = t3  + b
    t5  = t4  + a
    t6  = t5  + d
    t7  = t6  + a
    t8  = t7  + b
    t9  = t8  + c
    t10 = t9  + b
    t11 = t10 + a
    
    print "taps",,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11
    print
    
    inta = 0
    intb = 0
    intc = 0
    
    print "iter","inta","intb","sample"
    
    for y = 0 to 70*2-1
    
    for x = 70 to 1 step -1
      t(x) = t(x-1)
    next x
    
    t(0) = 1
    if y >=70 then t(0) = 0
    
    delta = 0
    
    
    delta = delta + t(t0) 
    delta = delta + t(t1) 
    delta = delta + t(t2) 
    delta = delta - t(t3) 
    delta = delta - t(t4) 
    delta = delta - t(t5) 
    delta = delta - t(t6) 
    delta = delta - t(t7) 
    delta = delta - t(t8) 
    delta = delta + t(t9) 
    delta = delta + t(t10) 
    delta = delta + t(t11)  
    
    
    inta = inta + delta * m
    intb = intb + inta
    
    sample = int(intb/8)
    print y," ",inta," ",intb," ",sample
    
    next y
    

  • cgracey wrote: »
    TonyB_ wrote: »
    Is all of the 71-bit tap register needed? There are only 68 non-zero values (17+34+17) for the long Tukey and adding one for the ADC input makes 69.

    We need extra bits to detect edges now. That's why it's longer.
    The length grows each time the taps are differentiated. Here's a demo with a small triangular window:
    impulse    1   2   1  
    d1       1   1  -1  -1 
    d2      1  0  -2   0   1
    d3     1 -1 -2   2   1  -1
    d4    1 -2 -1  4  -1  -2   1  
    
    We have to assume that there are zeros before and after the values shown. So using a derivative of the filter requires a few more bits in the shift register, but if done properly we come out way ahead because there will only be a handful of terms to sum.

    It's rather inconvenient for me that the Matlab "diff" function does not assume that anything exists beyond the array boundaries, so the output gets shorter with each differentiation.
  • Cluso99Cluso99 Posts: 17,761
    Roy Eltham wrote: »
    So is all this recent stuff for the current chip or some future one?
    Some of Chip's comments seem to involve changing the pad stuff and not just verilog? Or an I misunderstanding?
    It's only a tiny tweek. Only adding 6-10% extra silicon/logic - nothing major.

    And it's all theory and a little testing on the FPGA with external ADC which is not like the real P2-ES. No testing on the real P2-ES as far as I can tell.
  • evanhevanh Posts: 11,044
    That is what the FPGA is for. :P

    I think Christmas is tying people up. I'll be offline soon enough. Testing with P2D2 and ES boards will have to wait till January.

  • evanhevanh Posts: 11,044
    edited 2018-12-13 12:39
    jmg wrote: »
    Good progress. Did you check continual RX did not drop any bits?
    Maybe a second pin counting edges can do that ?

    AD7400 clock generator is not particularly stable. With Prop2 recording it varies about 150 ppm wrt the FPGA crystal. The scope is showing worse over shorter intervals.

    EDIT: Prop2 is, agreeing with scope, up to 240 ppm wobble on repeated 0.1 second recordings. Compared to earlier 0.4 s recordings.

  • cgraceycgracey Posts: 13,610
    cgracey wrote: »
    Saucy, I experimented with a lot of filters and some were just noisy. I picked three that I could prove in my program and test on the FPGA with the ADC:
    dim t(70)
    
    for x = 0 to 70
      t(x) = 0
    next x
    
    
    'a=2 : b=3 : c=8 : d=33 : m=1     '70-tap Tukey window
    'a=2 : b=3 : c=6 : d=14 : m=2     '47-tap Tukey window
    a=1 : b=2 : c=8 : d=01 : m=4     '30-tap Hann window
    
    t0  = 0
    t1  = t0  + a
    t2  = t1  + b
    t3  = t2  + c
    t4  = t3  + b
    t5  = t4  + a
    t6  = t5  + d
    t7  = t6  + a
    t8  = t7  + b
    t9  = t8  + c
    t10 = t9  + b
    t11 = t10 + a
    
    print "taps",,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11
    print
    
    inta = 0
    intb = 0
    intc = 0
    
    print "iter","inta","intb","intc","sample"
    
    for y = 0 to 70*2-1
    
    for x = 70 to 1 step -1
      t(x) = t(x-1)
    next x
    
    t(0) = 1
    if y >= 70 then t(0) = 0
    
    delta = 0
    
    if (t(t0) = 1 and t(t0+1) = 0) then delta = delta + 1
    if (t(t0) = 0 and t(t0+1) = 1) then delta = delta - 1
    
    if (t(t1) = 1 and t(t1+1) = 0) then delta = delta + 1
    if (t(t1) = 0 and t(t1+1) = 1) then delta = delta - 1
    
    if (t(t2) = 1 and t(t2+1) = 0) then delta = delta + 1
    if (t(t2) = 0 and t(t2+1) = 1) then delta = delta - 1
    
    if (t(t3) = 1 and t(t3+1) = 0) then delta = delta - 1
    if (t(t3) = 0 and t(t3+1) = 1) then delta = delta + 1
    
    if (t(t4) = 1 and t(t4+1) = 0) then delta = delta - 1
    if (t(t4) = 0 and t(t4+1) = 1) then delta = delta + 1
    
    if (t(t5) = 1 and t(t5+1) = 0) then delta = delta - 1
    if (t(t5) = 0 and t(t5+1) = 1) then delta = delta + 1
    
    if (t(t6) = 1 and t(t6+1) = 0) then delta = delta - 1
    if (t(t6) = 0 and t(t6+1) = 1) then delta = delta + 1
    
    if (t(t7) = 1 and t(t7+1) = 0) then delta = delta - 1
    if (t(t7) = 0 and t(t7+1) = 1) then delta = delta + 1
    
    if (t(t8) = 1 and t(t8+1) = 0) then delta = delta - 1
    if (t(t8) = 0 and t(t8+1) = 1) then delta = delta + 1
    
    if (t(t9) = 1 and t(t9+1) = 0) then delta = delta + 1
    if (t(t9) = 0 and t(t9+1) = 1) then delta = delta - 1
    
    if (t(t10) = 1 and t(t10+1) = 0) then delta = delta + 1
    if (t(t10) = 0 and t(t10+1) = 1) then delta = delta - 1
    
    if (t(t11) = 1 and t(t11+1) = 0) then delta = delta + 1
    if (t(t11) = 0 and t(t11+1) = 1) then delta = delta - 1
    
    inta = inta + delta
    intb = intb + inta
    intc = intc + intb * m
    
    sample = int(intc/8)
    print y,inta,intb,intc,sample
    
    next y
    

    You still did not fix the issue of differentiating the input data. While the BASIC program shows 12 taps, it actually uses 24 taps since it uses tn and (tn)+1. It's not actually a bad idea to integrate 3 times if the filter was designed for cubic curves. As it is now, one of the integrators is just undoing the differentiation that was inadvertently added. Surely the code below would be much cheaper to implement.
    dim t(70)
    
    for x = 0 to 70
      t(x) = 0
    next x
    
    
    '=2 : b=3 : c=8 : d=33 : m=1     '70-tap Tukey window
    '=2 : b=3 : c=6 : d=14 : m=2     '47-tap Tukey window
    a=1 : b=2 : c=8 : d=01 : m=4     '30-tap Hann window
    
    t0  = 0
    t1  = t0  + a
    t2  = t1  + b
    t3  = t2  + c
    t4  = t3  + b
    t5  = t4  + a
    t6  = t5  + d
    t7  = t6  + a
    t8  = t7  + b
    t9  = t8  + c
    t10 = t9  + b
    t11 = t10 + a
    
    print "taps",,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11
    print
    
    inta = 0
    intb = 0
    intc = 0
    
    print "iter","inta","intb","sample"
    
    for y = 0 to 70*2-1
    
    for x = 70 to 1 step -1
      t(x) = t(x-1)
    next x
    
    t(0) = 1
    if y >=70 then t(0) = 0
    
    delta = 0
    
    
    delta = delta + t(t0) 
    delta = delta + t(t1) 
    delta = delta + t(t2) 
    delta = delta - t(t3) 
    delta = delta - t(t4) 
    delta = delta - t(t5) 
    delta = delta - t(t6) 
    delta = delta - t(t7) 
    delta = delta - t(t8) 
    delta = delta + t(t9) 
    delta = delta + t(t10) 
    delta = delta + t(t11)  
    
    
    inta = inta + delta * m
    intb = intb + inta
    
    sample = int(intb/8)
    print y," ",inta," ",intb," ",sample
    
    next y
    

    Wow! This is way better!!!

    I wish I knew how to think about math more easily, because this should have occurred to me, too. I remember thinking it was weird that I needed to run that first integrator. There are so many neat things to learn about.

    Anyway, this is going to save a lot of logic! Thanks for pointing this out.
  • TonyB_TonyB_ Posts: 1,728
    edited 2018-12-13 12:29
    cgracey wrote: »
    You still did not fix the issue of differentiating the input data. While the BASIC program shows 12 taps, it actually uses 24 taps since it uses tn and (tn)+1. It's not actually a bad idea to integrate 3 times if the filter was designed for cubic curves. As it is now, one of the integrators is just undoing the differentiation that was inadvertently added.

    Wow! This is way better!!!

    I wish I knew how to think about math more easily, because this should have occurred to me, too. I remember thinking it was weird that I needed to run that first integrator. There are so many neat things to learn about.

    Anyway, this is going to save a lot of logic! Thanks for pointing this out.

    Hann/Tukey is a cosine-squared function. Just rename new 12-tap delta to inta and all the program outputs will be the same. There is still shift register skipping for smaller windows to try.

  • cgraceycgracey Posts: 13,610
    edited 2018-12-13 12:51
    Here is the simplified version of the filter tester, per Saucy's recommendation. This is way better now:
    a=2 : b=3 : c=8 : d=33 : m=1     '70-tap Tukey window
    'a=2 : b=3 : c=6 : d=14 : m=2     '47-tap Tukey window
    'a=1 : b=2 : c=8 : d=01 : m=4     '30-tap Hann window
    
    t0  = 0
    t1  = t0  + a
    t2  = t1  + b
    t3  = t2  + c
    t4  = t3  + b
    t5  = t4  + a
    t6  = t5  + d
    t7  = t6  + a
    t8  = t7  + b
    t9  = t8  + c
    t10 = t9  + b
    t11 = t10 + a
    
    print "taps",,t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11
    print
    
    dim t(70)
    for x = 0 to 70 : t(x) = 0 : next x 'clear bits
    
    inta = 0
    intb = 0
    
    print "iter","delt","inta","intb","samp"
    
    for y = 0 to 70*2-1
    
    for x = 70 to 1 step -1 : t(x) = t(x-1) : next x 'shift bits
    t(0) = (y < 70) 'insert new bit
    
    delta = t(t0) + t(t1)  + t(t2)  &
          - t(t3) - t(t4)  - t(t5)  &
          - t(t6) - t(t7)  - t(t8)  &
          + t(t9) + t(t10) + t(t11)
    
    inta = inta + delta
    intb = intb + inta * m
    
    sample = int(intb/8)
    print y,delta,inta,intb,sample
    
    next y
    

    Now we'll see what kind of logic reduction this yields.

    It's just amazing that so little math can compute the area under the filter curve on every clock. I wouldn't have thought this was possible. It's the miracle of calculus. Makes me wonder how many other things could be tackled like this. Seems like some live Goertzel could be done.
  • TonyB_TonyB_ Posts: 1,728
    edited 2018-12-13 13:11
    To make things more clear, if window function is y = ƒ(t) then

    delta = dy
    inta = y
    intb = inty = ∫ydt
  • cgraceycgracey Posts: 13,610
    edited 2018-12-13 14:52
    TonyB_ wrote: »
    To make things more clear, if window function is y = ƒ(t) then

    delta = dy
    inta = y
    intb = inty = ∫ydt

    We could even go a level deeper and define the filter by only six points:

    (1) initially from Y=0, begin upwards acceleration (+1)
    (2) at the inflection point of the filter rise, begin upwards deceleration (-2)
    (3) at the start of the plateau when delta is now zero, cancel deceleration (+1)
    (4) at the end of the plateau, begin downwards acceleration (-1)
    (5) at the inflection point of the filter fall, begin downwards deceleration (+2)
    (6) at the end of the filter when Y and delta are now 0, cancel deceleration (-1)

    It would take only two parameters to define the filter:

    a) the acceleration/deceleration period for filter rise and fall
    b) the plateau period

    With a few more bits of resolution, we could dial it in much better than we have been.
  • cgraceycgracey Posts: 13,610
    edited 2018-12-13 14:12
    I compiled the simplified algorithm per Saucy's recommendation and it works great. It cut 18 ALMs from each smart pin.

    Here is what the code looks like now. It's just amazing how much this has been simplified:

    1295 x 1378 - 43K
  • cgracey wrote: »
    I compiled the simplified algorithm per Saucy's recommendation and it works great. It cut 18 ALMs from each smart pin.

    Here is what the code looks like now. It's just amazing how much this has been simplified:

    I think we've had separate savings of 34, 10 and now 18 ALMs, with a logic increase between the second and third. At one time it was 80+ ALMs per smart pin.

    I'll look at modifying the BASIC program for shift register skipping to allow a single set of 12 taps later this afternoon.
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