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2020-12-18

Long time no see… I'll try to get back in a habit of writing stuff down here. However, I am also aware that we're going into the holiday season, so… Let's just try our best, shall we?

Reordering statements

In trying to tackle the double-buffer problems I've previously described, I've been trying to write a pass that reorders statements in scopes/bodies to improve code locality. In essence, I want to be able to rewrite this:

1: let main () =
2:   -- compute xs
3:   let xs = ...
4:   -- other stuff, not using xs
5:   let ys = ...
6:   -- copying xs and returning it
7:   let xs' = copy xs
8:   in (xs', ys)

Into this:

1: let main () =
2:   -- compute xs
3:   let xs = ...
4:   let xs' = copy xs
5:   -- other stuff, not using xs
6:   let ys = ...
7:   in (xs', ys)

The theory is that this will enable some further optimizations by my ReuseAllocations pass, because the memory block for xs might be reused in the computation of ys. So, I've been working on that, here and here. The first one is the cleanest, but it doesn't handle memory blocks or statements that consume.

However, as Troels had pointed out, my current approach does not handle aliased memory well. I found out when I inspected the reordered code for OptionPricing1:

--- original.kernel     2020-12-18 22:21:45.587014837 +0100
+++ reordered.kernel    2020-12-18 20:55:34.183619560 +0100
@@ -481,6 +481,15 @@
                 mapout_25496 with [i_25497] <- defunc_1_f_res_24862
               in {lw_dest_25498}
             }
+          -- double_buffer_array_25818 : [sobvctsz_24759]i32@@double_buffer_mem_25816->
+          -- {base: [sobvctsz_24759]; contiguous: True; LMADs: [{offset: 0i64;
+          --                                                     strides: [1i64];
+          --                                                     rotates: [0i64];
+          --                                                     shape: [sobvctsz_24759];
+          --                                                     permutation: [0];
+          --                                                     monotonicity: [Inc]}]}
+          let {[sobvctsz_24759]i32 double_buffer_array_25818} =
+            copy(defunc_1_map_res_24859)
           -- result_25499 : [num_und_24695][num_dates_24697]f32@@mem_25623->
           -- {base: [num_und_24695, num_dates_24697]; contiguous: True;
           --  LMADs: [{offset: 0i64; strides: [num_dates_24697, 1i64]; rotates: [0i64, 0i64];
@@ -1443,15 +1452,6 @@
                 mapout_25520 with [i_25521] <- defunc_1_f_res_25325
               in {lw_dest_25522}
             }
-          -- double_buffer_array_25818 : [sobvctsz_24759]i32@@double_buffer_mem_25816->
-          -- {base: [sobvctsz_24759]; contiguous: True; LMADs: [{offset: 0i64;
-          --                                                     strides: [1i64];
-          --                                                     rotates: [0i64];
-          --                                                     shape: [sobvctsz_24759];
-          --                                                     permutation: [0];
-          --                                                     monotonicity: [Inc]}]}
-          let {[sobvctsz_24759]i32 double_buffer_array_25818} =
-            copy(defunc_1_map_res_24859)
           -- double_buffer_array_25819 : [num_models_24693]f32@@double_buffer_mem_25817->
           -- {base: [num_models_24693]; contiguous: True; LMADs: [{offset: 0i64;
           --                                                       strides: [1i64];

What we're seeing here is that the copy of defunc_1_map_res_24859 into double_buffer_array25818 is all the way up to where defunc_1_map_res_24859 is computed. This should allow us to reuse the memory block defunc_1_map_res_24859 resides in for something else, and it is exactly what I set out to do. Unfortunately, I had missed the fact that double_buffer_array_25818 resides in double_buffer_mem_25816, which is also used for inpacc_24824, one of the loop variables that is used further down in the code.

The problem is that both inpacc_24824 and double_buffer_mem_25816 resides in the same memory, but my current algorithm only looks at "consumes" and direct data dependencies (the computation of x uses y, therefore y must be computed first).

For completeness, I'll paste the log from our IRC chat here:


<munksgaard> Athas: Jeg tror der er noget galt med min reordering
<munksgaard> Eller
<munksgaard> Jeg skal lige grave lidt mere.
<munksgaard> concieggs: programmeringssprog
<munksgaard> Athas: Jo, minsandten. Hvis jeg tager OptionPricing.fut, og det eneste jeg gør er at rykke double-buffer kopieringen af det første resultat op, så får jeg NaN i stedet for det rigtige resultat.
<Athas>      munksgaard: Jeg sagde det jo!
<munksgaard> Hvad går der galt?
<Athas>      Når du flytter kopieringen op, så overskriver du en memory block der stadigvæk er i brug (men måske under et andet navn, hvis den blev returneret som resultat af løkkekroppen).
<munksgaard> https://munksgaard.me/junk/reordered-just-double-buffer.sexp vs https://munksgaard.me/junk/original.sexp
<munksgaard> (oversæt med `futhark dev --expand-allocations --compile-opencl original.sexp`)
<munksgaard> Athas: Det forstår jeg ikke.
<munksgaard> Eller... måske
<Athas>      munksgaard: Du overskriver den hukommelse inpacc_24824 ligger i før du er færdig med at bruge inpacc_24824.
<Athas>      Så der er ikke engang noget funky aliasing her.  Problemet er at du overser at når du bruger inpacc_24824, så bruger du også implicit double_buffer_mem_25816.
<munksgaard> Ah ja, det kan jeg godt se.
<munksgaard> Men det er jo noget rod... Jeg kan godt finde frem til at double_buffer_mem_25816 også referes til ved kopieringen, men det bliver bøvlet at finde ud af om den refereres andre steder...
<munksgaard> Det er ikke en consume
<Athas>      Når du bruger freeIn på stm Stm, så skal du bagefter løbe igennem alle de navne du finder, og for dem der henviser til et array, også tage hukommelsesblokken med.
<munksgaard> Ja det giver mening. Men hvad hvis en af de stms også overskriver hukommelsen? Så er rækkefølgen ikke ligegyldig, eller hvad?
<munksgaard> foo = xs@mem_1[...]; ys@mem_1 = copy ...; bar = ys@mem_1[...]; zs@mem_1 = copy ...;
<Athas>      Hvad sker der her?
<Athas>      Jeg tror du skal adskille kill- og gen-uses, ligesom med registerallokering.
<munksgaard> Først læses der fra et array i mem_1, så kopieres der nyt data ind i samme hukommelses blok, dernæst læses igen, og til sidst kopieres der ind i samme hukommelsesblok igen. Hvis jeg er i gang med at kigge på sidste stm kan jeg godt afgøre at de andre stms bruger samme hukommelsesblok, og derfor skal ind først, men hvordan enforcer jeg rækkefølgen?
<Athas>      At læse fra et array er ikke en destruktiv anvendelse af dens hukommelsesblok.
<munksgaard> Nej, klart.
<munksgaard> Men altså, så bliver det lige pludselig en del mere kompliceret, ikke?
<munksgaard> Spørgsmålet er om det bedre kan betale sig at lade det ligge og så rykke videre til noget nogle af Cosmins andre idéer
<Athas>      Jeg tror du skal skrive nogle ordningsregler for at det ikke bliver helt hat og briller.  F.eks: Hvis en Stm X bruger et array i en hukommelsesblok M, og Stm Y er senere end X i det oprindelige program og binder et array i hukommelsesblok M, så skal Y være efter X.
<munksgaard> Så vidt jeg kunne se kan jeg, hvis den her reordering-teknik kommer til at virke, spare 1 allokering i OptionPricing.
<munksgaard> Athas: Men det betyder vel at min nuværende metode til reordering ikke rigtig er gangbar?
<Athas>      munksgaard: Du må selv afgøre hvad du tænker er bedst.  Jeg har svært ved at sige det.
<Athas>      Jeg kan ikke huske hvad din nuværende metode er.
<munksgaard> Det er vist nogenlunde ækvivalent med en dybde-først søgning af et afhængighedstræ. Jeg tror det bliver svært at modellere afhængigheder mellem gen/kill statements, men det kan være jeg lige skal prøve at tænke lidt over det inden jeg opgiver helt.
<Athas>      Du kan også tilføje "falsk" consumption.  Det er måske den nemmeste måde at implementere det på.  Lad som om en Stm der laver et array i blok M også consumer alle eksisterende arrays i blok M.
<munksgaard> Tja, det har du måske ret i.
<Athas>      Det er i virkeligheden det der sker, men det er ikke udtrykt i vores typesystem.  Det kunne være vi skulle tilføje det med aliasing...
<munksgaard> Så `let xs@mem_1 = copy(...)` consumer mem_1
<Athas>      Nej, så får du problemer.
<Athas>      Det consumer ethvert eksisterende array der bruger mem_1.
<munksgaard> Åh
<Athas>      Kun arrays kan consumes, ikke hukommelsesblokke.
<munksgaard> Hvorfor ikke?
<Athas>      Jeg er faktisk ret sikker på det er den rigtige måde at modellere det på.  På sigt burde vi også udtrykke det direkte i alias-repræsentationen, men det er ikke teknisk muligt lige nu.
<Athas>      Det er bare sådan typesystemet er.
<munksgaard> Okay
<Athas>      Men tænk over det: Resultatet af en Update har samme hukommelsesblok som dets input, så hvis du consumede blokken ville du ikke kunne bruge resultatet.
<munksgaard> Så hvis man har et array `xs@mem_1`, og der så senere er et statemet `let ys@mem_1 = ...` så bliver xs consumed.
<Athas>      Ja.
<Athas>      Hm.  Der er nok brug for lidt mere special-casing, for 'let ys@mem_1 = transpose xs' skal ikke consume 'xs'.
<Athas>      Du bliver nok nødt til at lave en funktion der afgør hvilke Exps der er "destruktive".
<Athas>      Men idéen er den samme.
<Athas>      Måske skal reglen være at 'let ys@mem_1 = ...' consumer alle arrays i mem_1, *bortset* fra dem som 'ys' aliaser.
<munksgaard> Så er man nok nødt til at lave analysen fra start mod slut, så man ikke løber ind i samme problem som jeg prøvede at beskrive før (givet `xs@mem_1`, så kommer der en `let ys@mem_1 = ...` og xs bliver consumet, så kommer der senere en `let zs@mem_1 = ...`, så er det vel kun ys og ikke xs der skal consumes)
<Athas>      Går det galt hvis 'xs' consumes flere gange?
<munksgaard> Med min nuværende algoritme kunne det godt, ja. For så ville `xs` indsættes i listen af værdier der skal beregnes, og det er ikke garanteret at det sker før beregningen af `ys`.
<Athas>      Okay, det ville du så være nødt til at tage højde for.
<Athas>      Men jeg tror idéen er den rigtige.
<Athas>      Det er også bedre end at have to separate mekanismer til hukommelsesblokke og consumption.  Det er jo samme princip.
<munksgaard> grunden til at `transpose` skal ikke consume xs, er vel at den kun rører ved index-funktionen, ikke?
<munksgaard> Kan man generalisere ud fra det?
<Athas>      Ja, jeg tror den aliasing-baserede regel jeg skrev ovenfor ville være nok.
<munksgaard> Hvad er reglen for hvornår `ys` aliaser et andet array?
<munksgaard> Hvordan beregnes det?
<Athas>      Det beregnes af alias-analyse-passet.
<munksgaard> Okay, den må jeg kigge på.
<Athas>      Bruger du det ikke allerede?
<Athas>      https://github.com/diku-dk/futhark/blob/67827ae2534d67f5cdfbb51f509a8656f0d76709/src/Futhark/Optimise/ReorderStatements.hs#L141
<munksgaard> Athas: Jo jo, ville bare gerne forstå præcis hvornår noget aliaser noget andet. Lige nu bruger jeg den mest som en black-box
<munksgaard> Athas: Okay, tak.
<Athas>      Se Futhark.IR.Prop.Aliases.

Given a statement let x@mem = ..., Troels' suggestion is to first determine if the statement writes to x, and therefore mem by inspection. look through all the statements that haven't yet been inserted and find out if there are any free arrays that reside in the same memory block. Any such arrays should then be pushed to the stack before we can insert the current statement. We can do that by saying that any array that resides in the same memory is consumed by the statement in question. However, that is too simplistic: Some statements, like a transpose, do not actually change the underlying memory, and can therefore peacefully coexist. Luckily, that is already encoded in the aliasing information. We can say that, given let ys@mem_1 = ... that statement consumes all arrays in mem_1, except those that ys aliases.

There's another problem though: There may be several statements that are overwriting the same memory block, so we need to make sure that their ordering is preserved. For instance:

let xs@mem_1 = ...
let x = xs[0]
let ys@mem_1 = ...
let y = ys[0]
let zs@mem_1 = ...

Assume that we're processing the last statement: We find that both xs and ys are consumed by this statement, because they both reside in the same memory block. Therefore they are both added to the list of values to insert. If ys is then processed first, we find that xs and zs are consumed by it and now they have to be processed first… That's not going to fly. I'm going to need to sleep on it.

Manually moving stuff around to prove a point

Aha! If we manually move the copy down below the loop that's a bit further down, it seems to work!

--- original.kernel	2020-12-18 22:21:45.587014837 +0100
+++ manual.kernel	2020-12-18 22:36:45.994915413 +0100
@@ -868,6 +868,15 @@
                 }
               in {lw_dest_25502}
             }
+          -- double_buffer_array_25818 : [sobvctsz_24759]i32@@double_buffer_mem_25816->
+          -- {base: [sobvctsz_24759]; contiguous: True; LMADs: [{offset: 0i64;
+          --                                                     strides: [1i64];
+          --                                                     rotates: [0i64];
+          --                                                     shape: [sobvctsz_24759];
+          --                                                     permutation: [0];
+          --                                                     monotonicity: [Inc]}]}
+          let {[sobvctsz_24759]i32 double_buffer_array_25818} =
+            copy(defunc_1_map_res_24859)
           -- result_25507 : [num_models_24693]f32@@mem_25700->
           -- {base: [num_models_24693]; contiguous: True; LMADs: [{offset: 0i64;
           --                                                       strides: [1i64];
@@ -1443,15 +1452,6 @@
                 mapout_25520 with [i_25521] <- defunc_1_f_res_25325
               in {lw_dest_25522}
             }
-          -- double_buffer_array_25818 : [sobvctsz_24759]i32@@double_buffer_mem_25816->
-          -- {base: [sobvctsz_24759]; contiguous: True; LMADs: [{offset: 0i64;
-          --                                                     strides: [1i64];
-          --                                                     rotates: [0i64];
-          --                                                     shape: [sobvctsz_24759];
-          --                                                     permutation: [0];
-          --                                                     monotonicity: [Inc]}]}
-          let {[sobvctsz_24759]i32 double_buffer_array_25818} =
-            copy(defunc_1_map_res_24859)
           -- double_buffer_array_25819 : [num_models_24693]f32@@double_buffer_mem_25817->
           -- {base: [num_models_24693]; contiguous: True; LMADs: [{offset: 0i64;
           --                                                       strides: [1i64];

Running out of registers(?) on NVIDIA OpenCL

I was playing around with tridag, a function from the LocVolCalib benchmark and ran into some weird issues when I converted it to f64 and applied my reuse-allocations pass.

The code looks like this:

 1: let tridagPar [n] (a:  [n]f64, b: [n]f64, c: [n]f64, y: [n]f64 ): *[n]f64 =
 2:   #[unsafe]
 3:   ----------------------------------------------------
 4:   -- Recurrence 1: b[i] = b[i] - a[i]*c[i-1]/b[i-1] --
 5:   --   solved by scan with 2x2 matrix mult operator --
 6:   ----------------------------------------------------
 7:   let b0   = b[0]
 8:   let mats = map  (\i ->
 9:                      if 0 < i
10:                      then (b[i], 0.0-a[i]*c[i-1], 1.0, 0.0)
11:                      else (1.0,  0.0,             0.0, 1.0))
12:                   (iota n)
13:   let scmt = scan (\(a0,a1,a2,a3) (b0,b1,b2,b3) ->
14:                      let value = 1.0/(a0*b0)
15:                      in ( (b0*a0 + b1*a2)*value,
16:                           (b0*a1 + b1*a3)*value,
17:                           (b2*a0 + b3*a2)*value,
18:                           (b2*a1 + b3*a3)*value))
19:                   (1.0,  0.0, 0.0, 1.0) mats
20:   let b    = map (\(t0,t1,t2,t3) ->
21:                     (t0*b0 + t1) / (t2*b0 + t3))
22:                  scmt
23:   ------------------------------------------------------
24:   -- Recurrence 2: y[i] = y[i] - (a[i]/b[i-1])*y[i-1] --
25:   --   solved by scan with linear func comp operator  --
26:   ------------------------------------------------------
27:   let y0   = y[0]
28:   let lfuns= map  (\i  ->
29:                      if 0 < i
30:                      then (y[i], 0.0-a[i]/b[i-1])
31:                      else (0.0,  1.0))
32:                   (iota n)
33:   let cfuns= scan (\(a: (f64,f64)) (b: (f64,f64)): (f64,f64)  ->
34:                      let (a0,a1) = a
35:                      let (b0,b1) = b
36:                      in ( b0 + b1*a0, a1*b1 ))
37:                   (0.0, 1.0) lfuns
38:   let y    = map (\(tup: (f64,f64)): f64  ->
39:                     let (a,b) = tup
40:                     in a + b*y0)
41:                  cfuns
42:   ------------------------------------------------------
43:   -- Recurrence 3: backward recurrence solved via     --
44:   --             scan with linear func comp operator  --
45:   ------------------------------------------------------
46:   let yn   = y[n-1]/b[n-1]
47:   let lfuns= map (\k  ->
48:                     let i = n-k-1
49:                     in  if   0 < k
50:                         then (y[i]/b[i], 0.0-c[i]/b[i])
51:                         else (0.0,       1.0))
52:                  (iota n)
53:   let cfuns= scan (\(a: (f64,f64)) (b: (f64,f64)): (f64,f64)  ->
54:                      let (a0,a1) = a
55:                      let (b0,b1) = b
56:                      in (b0 + b1*a0, a1*b1))
57:                   (0.0, 1.0) lfuns
58:   let y    = map (\(tup: (f64,f64)): f64  ->
59:                     let (a,b) = tup
60:                     in a + b*yn)
61:                  cfuns
62:   let y    = map (\i -> y[n-i-1]) (iota n)
63:   in y
64: 
65: let main [m] [n] (as:  [m][n]f64) (bs: [m][n]f64) (cs: [m][n]f64) (ys: [m][n]f64): *[m][n]f64 =
66:   map4 (\a b c y -> tridagPar (a, b, c, y)) as bs cs ys

And after compiling with my reuse-allocations branch2, I get the following error when I run it:

$ futhark dataset -b -g [1][1024]f64 -g [1][1024]f64 -g [1][1024]f64 -g [1][1024]f64 | ./tridag64-reuse-allocations --build-option='-cl-nv-maxrregcount=128' -D  > /dev/null
Using platform: NVIDIA CUDA
Using device: GeForce RTX 2080 Ti
Lockstep width: 32
Default group size: 256
Default number of groups: 272
Creating OpenCL program...
OpenCL compiler options: -DLOCKSTEP_WIDTH=32 -Dmainzisegmap_group_sizze_9431=256 -Dmainzisegmap_group_sizze_9490=256 -Dmainzisegmap_group_sizze_9570=256 -Dmainzisegmap_group_sizze_9624=256 -Dmainzisegmap_group_sizze_9778=256 -Dmainzisegmap_num_groups_9572=272 -Dmainzisegscan_group_sizze_9537=256 -Dmainzisegscan_group_sizze_9671=256 -Dmainzisegscan_group_sizze_9883=256 -Dmainzisegscan_num_groups_9539=272 -Dmainzisegscan_num_groups_9673=272 -Dmainzisegscan_num_groups_9885=272 -Dmainzisuff_intra_par_1=32 -cl-nv-maxrregcount=128
Building OpenCL program...
Created kernel main.scan_stage1_9543.
Created kernel main.scan_stage1_9677.
Created kernel main.scan_stage1_9889.
Created kernel main.scan_stage2_9543.
Created kernel main.scan_stage2_9677.
Created kernel main.scan_stage2_9889.
Created kernel main.scan_stage3_9543.
Created kernel main.scan_stage3_9677.
Created kernel main.scan_stage3_9889.
Created kernel main.segmap_9428.
Created kernel main.segmap_9487.
Created kernel main.segmap_9568.
Created kernel main.segmap_9621.
Created kernel main.segmap_9775.
Created kernel main.segmap_intragroup_8752.
Allocating 8192 bytes for arr->mem in space 'device' (then allocated: 8192 bytes) (new peak).
Actually allocating the desired block.
Allocating 8192 bytes for arr->mem in space 'device' (then allocated: 16384 bytes) (new peak).
Actually allocating the desired block.
Allocating 8192 bytes for arr->mem in space 'device' (then allocated: 24576 bytes) (new peak).
Actually allocating the desired block.
Allocating 8192 bytes for arr->mem in space 'device' (then allocated: 32768 bytes) (new peak).
Actually allocating the desired block.
n: 1024, max_group_size: 1024
Compared 32 <= 1024.
bytes: 40960, local_memory_capacity: 49136, intra_suff_and_fits: true, private_mem_size: 0, local_mem_size: 1, workgroup_size: 256, dev_local_mem_size: 49152
Allocating 8192 bytes for mem_10354 in space 'device' (then allocated: 40960 bytes) (new peak).
Actually allocating the desired block.
Launching main.segmap_intragroup_8752 with global work size [1024] and local work size [1024]; local memory parameters sum to 40960 bytes.
local   mem: 41000
private mem: 0
./tridag64-reuse-allocations: tridag64-reuse-allocations.c:5793: OpenCL call
  clEnqueueNDRangeKernel(ctx->opencl.queue, ctx->mainzisegmap_intragroup_8752, 1, ((void *)0), global_work_sizze_10807, local_work_sizze_10811, 0, ((void *)0), ctx->profiling_paused || !ctx->profiling ? ((void *)0) : opencl_get_event(&ctx->opencl, &ctx->mainzisegmap_intragroup_8752_runs, &ctx->mainzisegmap_intragroup_8752_total_runtime))
failed with error code -5 (Out of resources)

What we see here is that we only need to allocate five shared arrays of 8192 bytes each, totalling 40960 bytes. Some more bytes are needed for reasons I don't remember, but the total is 41000 bytes, which is well under the reported local memory capacity. However, the kernel crashes with an out of resources error. Troels thinks it might have to do with running out of registers, perhaps the NVIDIA OpenCL compiler does something wrong.

However, his proposed fix of suppling the option --build-option='-cl-nv-maxrregcount=128' to to the binary doesn't seem to work. On the other hand, adding an attribute of __attribute__((reqd_work_group_size(1024, 1, 1))) (remember to update 1024 to the right number) does seem to work.

Correction! -cl-nv-maxregcount=64 and lower works, but not any higher. 64 seems to be fastest.

Footnotes:

1

To produce the reordered kernel, first produce the reordered sexp:

futhark dev --sexp --kernels -a -e --cse -e --double-buffer -e --reorder-statements futhark-benchmarks/finpar/OptionPricing.fut > reordered.sexp

Then manually remove the other changes, which are valid and compile with:

futhark dev --expand-allocations --compile-opencl reordered.sexp

Finally, run it and verify that we get NaN instead of the correct result

cat futhark-benchmarks/finpar/OptionPricing-data/medium.in | ./reordered
2

I also added some extra instrumentation by editing the generated C-file directly.