Michael Zucchi

 B.E. (Comp. Sys. Eng.)

  also known as zed
  & handle of notzed


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Thursday, 04 September 2014, 14:31

"Sentinel Saves Single Cycle Shocker!"

Whilst writing the last post I was playing with a tiny fragment to see how just testing the edge equations separate to the zbuffer loop would fare. It's a bit poor actually as even the simplest of loops will still require 9 cycles and so doesn't save anything - although one wouldn't be testing every location like this so it's pretty much irrelevant.

Irrelevant or not I did see an opportunity to save a single cycle ...

If one looks at this loop, it is performing 3 edge equations positive tests and if that fails it then has to perform a loop-bounds test.

0000015e:       orr.l     r3,r18,r19      /|                  1                                             |
00000162:       fadd.l    r18,r18,r24     \|                  1234                                          |
00000166:       add.s     r0,r0,#0x0001   /|                   1                                            |
00000168:       fadd.l    r19,r19,r25     \|                   1234                                         |
0000016c:       orr.l     r3,r3,r20       /|                    1                                           |
00000170:       fadd.l    r20,r20,r26     \|                    1234                                        |
00000174:       bgte.s    0x0000017a       |                     1                                          |
00000176:       sub.s     r2,r0,r2         |                      1                                         |
00000178:       bne.s     0x0000015e       |                       1                                        |

On in C.

  for (int x=x0; x < x1; x++) {
     if ((v0 >= 0) & (v1 >= 0) & (v2 >= 0))
       return x;
     v0 += v0x;
     v1 += v1x;
     v2 += v2x;

Problem is it needs two branches and a specific comparison check.

Can a cycle be saved somehow?

No doubt, don't need Captain Obvious and the Rhetorical Brigadettes to work that one out.

Just as with the edge tests the sign bit of the loop counter can be used too: it can be combined with these so only one test-and-branch is needed in the inner loop. After the loop is finished the actual cause of loop termination can be tested separately and the required x value recovered.

It's not a sentinel it's just combining logic that needs to be uncombined and tested post-loop in a similar way to a sentinel.

000001ba:       orr.l     r3,r18,r19      /|                  1                                             |
000001be:       fadd.l    r18,r18,r24     \|                  1234                                          |
000001c2:       sub.s     r0,r0,#0x0001   /|                   1                                            |
000001c4:       fadd.l    r19,r19,r25     \|                   1234                                         |
000001c8:       orr.l     r3,r3,r20       /|                    1                                           |
000001cc:       fadd.l    r20,r20,r26     \|                    1234                                        |
000001d0:       orr.s     r1,r0,r3         |                     1                                          |
000001d2:       blt.s     0x000001ba       |                      1                                         |

Or something more or less the same in C with the pro/epilogues and probably broken edge cases:

  int ix = x1 - x0 - 1;
  while ((v0 >= 0) & (v1 >= 0) & (v2 >= 0) & (ix >= 0)) {
    ix -= 1;
    v0 += v0x;
    v1 += v1x;
    v2 += v2x;
  if (ix >= 0) {
    return x0 + ix;

I suppose it's more a case of "Pretty Perverse Post Pontificates Pointlessly!"

Or perhaps it's just another pointless end to a another pointless day.

Might go read till I fall asleep, hopefully it doesn't take long.

Tagged hacking.
Thursday, 04 September 2014, 13:42

ezegpu stuff

Did a bit more playing around on the ezegpu. I think i've hit another dead-end in performance although I guess I got somewhere reasonable with it.

Although there are some other things I haven't gotten to yet i've pretty much convinced myself this design is a dead-end now mostly due to the overhead of fragment transfer and poor system utilisation.

First I will put the rasterisers and fragment shaders back together again: splitting them didn't save nearly as much memory as I'd hoped and made it too difficult to fully utilise the flops due to the work imbalance and the transfer overheads. I'm not sure yet on the controller. I could keep the single controller and gang-schedule groups of 2/3/4 cores from the primitive input - i think some sort of multiplier is necessary here for bandwidth. Or I could use 3 or 4 of the first column of cores for this purpose since they all have fair access to the external ram.

Tagged code, hacking, parallella.
Tuesday, 02 September 2014, 17:17

simplex noise, less memory

I thought i'd look at something a bit different today: noise. Something to get the fragment shaders doing some more work.

I've looked at some of this before but it's been a while and never had much use for it.

I started with "wavelet noise" but when I realised it needed big lookup tables I went back to looking at the simplex noise algorithm. It seems wavelets are being used to create bandwidth limited versions of existing noise so that it scales better; but this isn't something I need to worry about.

A paper and implementation by Stefan Gustavson and others pretty much had me covered but I wanted to try and remove the 512+256 element lookup tables used to hash the integer coordinates to save some memory on the epiphany.

I came up with two working solutions in the end.

The first one uses a 32-element lookup table of prime numbers to implement a 2D hash function. I just grabbed the first 32 primes (20 apart) for the table and fiddled with eor/mul and shift until I had something that seemed to work. I arbitrarily chose 32 because it was a nice round number.

// there's nothing particularly good or useful here

    static final int[] hasha = {
        71, 173, 281, 409, 541, 659, 809, 941,
        1069, 1223, 1373, 1511, 1657, 1811, 1987, 2129,
        2287, 2423, 2617, 2741, 2903, 3079, 3257, 3413,
        3571, 3772, 3907, 4057, 4231, 4409, 4583, 4751

    private static int hash16(int a, int b) {
        return ((((b ^ hasha[a & 31]) * (a ^ hasha[b & 31])) >> 5) & 15);

Because I was only interested in the 2D case I changed the gradient normal array to 16 elements so I didn't have to modulo the result as well. TBH it's kind of surprising it works as well as it does since hashing numbers is pretty tricky to get right and I really didn't know what I was doing.

When I started I didn't realise exactly what it was for so once I had a better understanding of why it was there I thought i'd try an existing integer hash function. In general they failed miserably but I found one that came from the h2 database which worked sufficiently well.

    private static int hash(int x) {
        x = ((x >> 16) ^ x) * 0x45d9f3b;
        x = ((x >> 16) ^ x) * 0x45d9f3b;
        x = ((x >> 16) ^ x);
        return x;

    private static int hash16(int a, int b) {
        return (hash(a * b + a + b)) & 15;

I used the (a*b+a+b) calculation to turn it into a 2D hash function.

So this final version requires no lookup table for the gradient table permute at all - nice. But it requires 3 integer multiplies - not so nice for epiphany. And even the other version needs an integer multiply and thus the same costly fpu mode changes on epiphany.

Since I only need a limited number of output bits it might (should?) be possible to change this to using float multiplies to avoid the costly mode change; but this is something for further study. The first version might make this easier.

Screenshots ... this first is a simple 4-octave fractal noise generated using the 2D Simplex Noise code from Stefan. I think the 2D noise function has a small bug because it's using the 12-point 3D gradient bases which don't always evaluate to vectors of the same length in 2D but it isn't apparent once fractal noise is generated as here.

The next one is an example using the naive hash function (it may be a different scale to the others since I ran it separately). Covering 4 octaves hides some problems it might have but I've done some very basic testing to larger scales and it seems about as stable and nicely random as the others.

And the final shot is using the M2 hash function and 16 gradients evenly spaced around the unit circle rather than 12 evenly spaced around the unit sphere as in the traditional version.

Look about the same to me?

I don't know if it's useful for anything I might do or if it is even fast enough to run in a shader on the epiphany but I learnt a couple of interesting things along the way.


I've been doing some little bits and pieces on the ezegpu code as well.

Together the NEON changes amount to a 6% improvement to the total runtime of the all-ARM code for my current testing case (8x8x8 stars). Nothing major, although it goes up on simpler scenes mostly due to the faster RGBA float to byte conversion.

Tagged code, hacking, parallella.
Sunday, 31 August 2014, 09:43

egpu mk ii part 2

After a couple of days relaxing break including a nice ride down to the coast yesterday I had another look and the ezegpu today.

First task was just to create a common 'demo' frontend which can be linked to different backends so I can easily test different cases. I then created a backend based on the current mk ii state.

Well, I guess I jumped the gun a bit the other day by testing it with a poor example of large and mostly coincident triangles. Using the star-grid test the implementation is considerably faster than the line based renderer. The test code uses slightly different parameters but a 4x4x4 star test is now hitting 57fps vs 35fps for the line-based version, versus 31fps for single-core arm.

Then I upped the test to 8x8x8 stars (total of 4096 triangles) and zoomed out a bit and now the improved primitive input stage and 2d grouping really starts to show it's paces: 22fps vs 7fps. The single-core ARM code is coping a bit better at 11fps.

Well that was nice to see I guess.

I guess i'll have a look through the points of the last few posts to decide what to look at next.

Tagged hacking, parallella.
Thursday, 28 August 2014, 03:14

some notes

Some waking up thoughts to jot down for later. It's too nice to be inside today. I have stuff I should be doing but i'm a little immobile due to hurting my foot again so I might just sit in the sun drinking. I thought it was better and over-tested it last weekend - and I wasn't even drinking :(. I can get around ok - it just doesn't heal at all if i don't rest it enough.

I had some further thoughts on the results of yesterday; even though it's half the speed of the line renderer considering the complexity of the interactions and the forced requirement of an additional read/write cycle across another core for each fragment - it's probably actually fairly good. The main bottleneck seems to be the mismatch of rasterisation to fragment rendering time which has nothing to do with the architecture - but the fragment shaders are only trivial 3-term colour interpolations and if they were more complex then shifting the rasterisation to another core would leave more time for them to execute. So I will still hook it up to the gl frontend to test it and other backends which can use the same or similar controller setup.

Although I think due to the possibility of other highly optimised special cases a combined implementation will still be the ultimate target.

Tagged hacking, parallella.
Wednesday, 27 August 2014, 08:50

egpu mk ii.5

Well that took a bit longer than I wanted; and all i've done is rejigged all the comms around but that's enough for today.

I made a bunch of changes to address some of the problems; i'm still not sure it will fix the performance but it's some stuff I wanted to look at anyway. The big performance issue remaining is the rasteriser to fragment processor stream; I have a new communication protocol that addresses it as much as possible and have changed the fragment processor to use it but I haven't written the rasteriser to feed it yet. I was going to do a quick-and-dirty but that would just be wasted work and working toward the current target goal ended up ballooning out into a big pile of changes.

Hmm, so what was again going to be a short little poke turned into a whole afternoon and now the sun is rapidly leaving this hemisphere to a crisp but cold evening. This stuff is just too interesting to put down and i've just spent another hour and a half writing this and tweaking a few things I found while writing it. Might keep going now ...

Update: Hacked into the later evening ... did some profiling. It's about half the speed of the combined by-line processor at this point. Whilst this is a very large improvement as to where it was, it's obviously not enough.

From some numbers I think the bottleneck is the rasteriser. The rasteriser routine is very simple and compiles quite well and the dma interface is about as minimal as possible so there is little possibility of improvement. It's probably just the 1:4 fan-out being too much.

Tagged hacking, parallella.
Sunday, 24 August 2014, 08:14

then again ...

After the post yesterday I had a bit of a play around with the ideas. There are a couple of details I missed.

Firstly the current rasteriser implicitly maintains a per-primitive index of live pixels for the fragment processor. If I group them all together indexed (implicitly) by the column location then I have to somehow re-group the fragments afterwards so they can all be processed by the same inner loop to amortise the setup costs. After a couple of ideas I think this needs to be implemented by sorting the fragments by shader, then primitive, then X location. Because I want to leave as much processing time as possible for complex fragment shaders I was thinking of putting this onto the REZ cores; as they currently don't have a lot of work to do. This may be tunable depending on the shader vs geometry complexity.

Secondly if blending is not enabled/required then the primitives can be sorted by Z before they are sent to the epiphany; and this implicitly reduces most of the fragment processing to single pixels as well (depending on geometry) due to culling via the zbuffer test. i.e. all the work to split the fragment shaders from the rasterisers might not be much of a pay-off, particularly if it means losing 'free' alpha blending.

I did some testing using more stars (24x24x24) and found that proper z-order (front to back) makes a difference, but it's only something like 50%; but this is with a trivial fragment shader which isn't terribly representative.

Since time is not money here I'll give it a go anyway and see how it ends up. Now I write it down, restoring the primitive index by sorting would mean the same fragment processor could also support blending by just changing how and when the rasteriser outputs fragments; so I might be able to get the best of both.

I might also try changing the way the primitives are loaded in the mk i design: using (and/or dedicating) core 0,0 to load and distribute each band of primitives to the rendering engines to achieve (up to) a 16x bandwidth reduction of external reads should more than outweigh any wasted flops. I will also experiment with splitting the output into tiles instead of whole rows - the pathalogical case of a primitive taking up the whole row should be rare and if core 0,0 is handling the primitive index anyway i can add extra fidelity to the index without needing more memory to store it. I originally did rows because of the better/easier dma output and to reduce redundant setup costs and address calculations for the rasteriser, but its pretty much a wash on that front between the two approaches and 2D tiles might be a better fit.

Update: Had more of a poke today working on the setup and communications. I decided to go with tiles for the rendering off the bat because it allows more flexibility with memory: if i have a whole row in each core it forces a potentially excessively large fixed minimum size for various buffers throughout the pipeline - or an unreasonably narrow rendering resolution. But if I split it into tiles then the height can be adjusted if I need more memory. My first attempt is with tiles of 64x8 pixels which allows for a rendering width of 768 pixels if 12 cores are used for fragment shaders and only requires the same modest 8K for a 4-channel floating point colour buffer as the 512-pixel-width whole-row implementation.

I also decided to drop the fully deferred rendering idea for now - the cost of the sorting required in the rasteriser is putting me off. But It's something I can add later with most work required isolated in the rasteriser code.i

I'm still using the same topology as in the previous post with 3x rasterisers each feeding 4x fragment processors; the main driving factor for that split is the memory requirements of each stage and trying to have as many fragment processors in a round-number of cores as possible. The fact that it should route well though the mesh was mostly just a nice bonus. I'm just hoping at this point that this is also a reasonable work-balance fit as well. Because the rasteriser is going to be a fixed-function unit i'm trying to use as much of it's resources as possible, i'm sitting on around 27K of the RAM used total but I might be able to get that "a lot" higher with a bit of effort+luck.

So as of now I have a simple streaming protocol for the fragment shaders using an ezeport to arbitrate each individual fragment; this has a high(ish) overhead but it could be batched up by rows per processor. The primitive is fully rasterised across the 4 target tiles into a list of active fragments (x, y, w) - 8 bytes each. The w value of all are inverted together and then the fragments are streamed to the fragment processors with a bit of protocol compaction to reduce the transfer size and buffers required ('update y & prim id' message, 'render @ x' message). The work is streamed by row so interleaves across the 4x fragment processors - with enough buffer space (i.e. at least 64 fragments) should allow for some pipelining to hide latency across each 5-core rasteriser+fragment processor sub-system so long as the fragment shaders have enough work to perform.

Well that's where i'm at for the day. I haven't implemented the fragment shaders in the fragment processor or some of the global state broadcast from the controller. But having single messages to core 0,0 being exploded into a whole cascade of work across the mesh which is a pretty big step.

(It didn't quite go as smoothly as that suggests as I hit a bug in libezehost when dealing with heterogeneous workgroups which was a little frustrating till I worked out what was going on).

Update: Another day another bit of progress. Today I hooked up a fragment shader to the rasteriser and got it to render the single triangle test. At this point it's probably a bit slower than the previous code but there is more optimisation to be done.

I had to engineer a bit more of a streaming protocol between the rasteriser and the fragment shader; so I took the opportunity to batch up rows so they can be more efficiently written and read. I added some control codes in there as well for communicating other state and parameterising some of the processing.

I'm still not that happy with the way the rasteriser is forming the fragments: the actual rasterisation process is clean/simple but it has to output the fragments to a combined staging buffer across all tiles which must then be post-processed and broken into chunks for the 4x fragment processors. Having 4x tiles across makes the queue addressing calculation overly complex (in a loop of about 15 instructions almost anything is overly complex). As I am no longer doing deferred rendering without changing the current stream protocol it is possible to remove all the staging buffers from the rasteriser and just write directly to the stream buffers on the target cores; but I don't have a good solution yet (close though). Although i'm not sure what i'm going to do with the massive 16K x 3 this would free up!

Update: Oh damn. I tried rendering more than one triangle ... yeah its not good. Very slow proportional to the number of rendered (non-z-binned) fragments and at least for this workload the load balancing is also very bad - some cores render a ton of pixels and others render none due to the static scheduling. It looks like i miscalculated the rasteriser to fragment processor balance too; that 4x factor adds up very fast.

I went to my timing tester and did some off-core write tests: It seems i misunderstood the overhead of direct off-core writes from the EPUs - they seem to take a fixed (and unaccounted?) 9 cycles even if they "don't block". Yeah that's not going to cut it for this task. DMA seems to be able to get this down to about 1.7 cycles per float but the real benefit is that the epu runs independently and that easily outstrips the data generation rate. But it's going to need some bulky and hairy code to manage across multiple cores which is going to eat into any benefits. This definitely rules out a couple of ideas I had.

Hmm, maybe mk iii is closer than i thought. Perhaps just start with tiles so the output size is flexible and add some dynamic load balancing and a 2D primitive index. Perhaps group 2-4 cores together in terms of the front-end to try to deal with the primitive bandwidth issue; unless that upsets the balancing too much.

Tagged hacking, parallella.
Saturday, 23 August 2014, 05:48

ezegpu mk i

Yesterday afternoon I started to clean up the current rasterisation code in order to dump to another point release of ezesdk. After hitting some hardware issues I found a good-enough workaround (for now) and this morning came up with a slightly more taxing/useful example for some more realistic profiling.

(imagine each is rotating on its centroid independently and all 64 are rotating around together, playfield is 512x512x32-bit)

Here's it's running on a single ARM core at about 30fps (but don't read too much into this since it isn't arm optimised). The main visible rendering artefact is a screen tear. The epiphany can only manage 43fps on this one - so as i'm adding more geometry to the scene it's performance over the arm is dropping (it's about 3x with a single star).

The loading of the primitives is becoming a bottleneck I always knew it was: I know this because if i zoom in closer the epiphany drops to 33fps but the arm chugs right down to about 15. So at least that is something I guess. OTOH I'm only uising one arm core. I can have two running with little impact on each other. Actually I had 3 outputs running at once with little impact on each other (one epiphany and two arms) which was starting to get a little bit impressive to me - combining them all together with a bit of NEON would provide a meaningful boost if they had nothing better to do.

But the problem is that currently each core runs the same code. Each row is rendered completely which involves scanning all the primitives in that band and rendering them. The sequence is essentially:

clear colour and zwbuffer
for each primitive
  for bounding box
    interpolate edge functions, z/w, 1/w
    if inside triangle and zbuffer test passes
      save new zbuffer value
      save 1/w and x location
  for saved 1/w values
    calculate reciprocal
  for saved fragments
    render fragment to colour buffer
for each pixel

The primitives include the 3 float values for each of the 3 edge functions, the 1/w interpolator, the z/w interpolator, and the 3 colour channels: and all this data is being loaded each time through each row through each core - i.e. at least N cores per primitive (i'm using 12 to work around some stability issues and its enough to saturate the bus handily anyway) and another multiplying factor for the number of bands their bounding box crosses. With a bounding box and control word this is 136 bytes per primitive and it adds up very fast - to multiple megabytes.

I knew this was a bottleneck but I didn't (and still don't) have a feel yet for how much work a real fragment shader is going to be. But i'm pretty sure you'll be doing interesting stuff and still not hiding this.

Despite everything being on the core there is still plenty of space left, although 512 pixels is a little on the narrow side.

ezegpu mk ii

While waking up this morning I had a few ideas that might be able to address this and hope to implement in the coming days and weeks depending on motivation (i'll have some time due to another fortunate break in work). This is still just the first shot and I haven't tested any of them with real code; so as I discover problems I may need to alter the plans - although i do seem to be approaching the original ideas I had. This whole thing is a journey for me as the last time I did any "serious" 3D was using assembly language on an Amiga and it was pretty shit really. I don't have any expectations or baggage from the last 20 years of gpu progress and have no end-goal in mind (so if you're reading this and shaking your head with all the mistakes i'm making; well yes, i just don't know what i'm doing).

So these are a grab bag of ideas just off the top of my head right now and not all of them are compatible with each other.

So putting most of that together this the current image forming in my head:

  +------+   +------+    +------+    +------+
  | CTRL |   | FR00 |    | FR10 |    | FR20 |
  +------+   +------+    +------+    +------+
    |||      |           |           |
  +------+   +------+    +------+    +------+
  | REZ0 |--o| FR01 |    | FR11 |    | FR21 |
  +------+   +------+    +------+    +------+
     ||      |           |           |
  +------+   +------+    +------+    +------+
  | REZ1 |-  | FR02 | --o| FR12 |    | FR22 |
  +------+   +------+    +------+    +------+
      |      |           |           |
  +------+   +------+    +------+    +------+
  | REZ2 |-  | FR03 | -- | FR13 | --o| FR23 |
  +------+   +------+    +------+    +------+

This is arranged assuming the mesh goes across rows first (i think it does) so all writes between cores should never block. REZ0 only writes to FR0x, REZ1 only writes to FR1x, etc.

Main controller/primitive reader. This isn't actually much work and it leaves room/time for other functional blocks such as caches. It reads the primitives for each band and then copies them to the rasterisers. The bands will be indexed (or populated) in rows of 12. It could also be in charge of writing rendered pixels from the memory of the fragment shader cores to the framebuffer as an easy way to serialise (optimise) the writes.

Rasteriser - edges and zwbuffer. These rasterise and perform zbuffering on 12 rows at once (4 rows each). It can send the (primid, x,1/w) tuple to the fragment processors using a single 8-byte, non-blocking, non-arbitrated(!) write. This is just splitting the first inner loop into a separate processor.

Fragment processors. Whilst the rasteriser is populating the next row of input the fragment processor is rendering the deferred pixels. This doesn't need a floating point framebuffer since each pixel is only rendered once. Also means it doesn't need to clear it (ok; alpha blending would affect both of these but it affects the whole pipeline). The reciprocal pass will probably go here and the fact that it only needs to run once per visible pixel is another bonus from deferred rendering (although some reverse painters algorithm would also help the number of times a pixel makes it to the fragment processor in the mk i design).

The controller and fragment processors can be further pipelined internally to employ scatter-gather DMA to reduce latency effects.

This all looks pretty complicated but it should be a fairly modest amount of code - it has to be otherwise it wont fit! Actually by using deferred rendering and splitting the stuff up I will have big chunks of memory to spare; I could probably up the maximum rasterisation width to 1024 pixels although now i think about it that's too big for the memory speed. Something in the middle is more likely to be useful.

Because there are now different parts doing different things the differences in runtime of each component will start to dictate the total system performance (and hopefully not the read memory bandwidth). I don't know yet what that will be and it will depend on the rendering task and fragment shaders. If for example the fragment shaders are complicated and dominating execution time then scaling/clamping of the output, and/or reciprocal of the input could be moved elsewhere memory permitting.

Tagged hacking, parallella.
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