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5.7 ms of 24.1 (decide, keep_filtered, apply_filters and the list side), halved 21.5 ms; join's sums into cells about 17 ns a round, a chain through the same cells, in four-byte integers with the width once a batch about 5 ns, 108 ms; neither moves BFS from about 2.7x the compiled code, and join's recurrence (about 40 ms) stays outside
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comparisons counting their lanes): knapsack 10.07 to 8.25 ms (bar 8.6; b9 11.46, the compiled code 7.9), its instructions 12.2% below b9's; what is left of knapsack's gap is the per-batch interpretation (about 3 ms), not the kernels (ADD 1.7, GT 1.7, the masked set 0.55 ms); the others the same by instructions; make check's server_view_workers timed out once (the known flake), passed 3/3 alone and in a full rerun; bank queries' instructions within 0.1% of b9's, TPC-C -0.3%; the two large gaps left (matmul's nested rounds, BFS's candidate tail) the user's to choose
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in its own loop (TEST, a vector add in the same loop) and its value carries the count (ones), so the branch after it in every running lane needs not count them; seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources and the unit tests pass
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and the branch's counting pass a batch, about 0.35 us), and the general way's floor at 1024 lanes (about 8.3 ms, ADD and GT apart) against the compiled code's 7.9
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memory's order in four or eight bytes is a view of the column itself (cells_at), no copy, read only while the pass runs; what outlives the pass (a local, a set's rows and value, an append's cells, a sum's rows and e, a filter's key, a read's rows) copies it (own); knapsack 4.0% fewer instructions, 6.6% fewer cycles; VIEW_SOURCE in check.py (a local holding a field the batch sets, a set from the same column in the order that overwrites what it reads, a set widening the column under a view), which differs and trips ASan's memcpy overlap when the copies are left out; seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources (also sanitized) and the unit tests pass
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no lanes while every lane's e is the same, a list's cells once a batch): against b9, interleaved, matmul 40.01 to 25.97 ms, knapsack 11.47 to 10.07, roots 8.97 to 8.29, join 117.2 to 115.8, BFS and sort the same; sum0 8.69 to 1.01 (bar 1.5); matmul short of its bar (21): the nested rounds' interpretation (about 14 ms) and the matrices' making (4-5) were left out of the arithmetic; the executor alone and the bank queries' instructions as b9 (0.08%), TPC-C +0.7%; stage 4 next (knapsack's six passes to three)
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its pass reads): no list changes while the pass runs (sets, appends and filters wait for its end, which reads its own); find and item_get read them there; matmul 2.3% fewer instructions (two finds a nested round), knapsack and BFS 0.4%; seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources and the unit tests pass
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uniform max and min, a fraction, a sum past 2^53, a count in a nested loop, the same e then a masked or a lane's own and the other way), against the rounds one by one and the compiled code; it makes lanes from the one number 56 times and folds the one number 77 times
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no lanes while every lane's e is the same), interleaved with b11 and b12, and their counts: matmul 36.10 to 26.56 ms (instructions -20%), roots 8.82 to 8.31 (-6.1%), the executor alone as b9 on all five
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while every step adds (or takes the least or most of) the same e in every lane, every lane's partial is one number and its count one count, made as each lane would make them; the first step that differs makes the lanes from them; fold takes n times the one number (whole numbers below 2^53, as the lanes' sums) or folds it in the rounds' order; sum0 6.09 to 1.01 ms; seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources and the unit tests pass
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ms against 21): the arithmetic left out the nested rounds' interpretation (about 15 ms) and the matrices' making (4-5 ms)
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(POSIX's select in a build without -std=c17 refused the file)
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below 2^32 of whole numbers below it in four-byte lanes, past it the product's high half sends the lanes back to numbers as ADD's sum does (umull and umull2 over four lanes); matmul's products and sums stay in four bytes; seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources and the unit tests pass
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interleaved): matmul 38.18 to 36.10 ms with 4.5% fewer instructions (segments in its nested rounds), knapsack's per-batch cost 0.68 to 0.63 us but knapsack 10.35 to 10.51 ms with 1% fewer instructions (its per-element loops placed elsewhere), sum0 1,743 instructions a batch: short of 025's stage-2 bars (9.2 ms, 0.45 us, 33 ms): 025 priced a segment's instruction at 50 cycles, the counts show about 25 instructions, and a batch's cost sits in finds, bounds, read records, lane setup, masks and the deferred store's check; a list's cells once a batch measured at 3% and not made; next, per element: stage 3's four-byte MUL (matmul 21 ms)
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unit tests in three modes and under ASan (executor mode too), the sanitized pure-run's fixed sources and seed 23 (both modes), make check and aup's checks in both modes pass
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instructions that make one uniform or affine value (constants, fields, LOADs, a walk's item, locals the block does not set, the loop's value, a nested count loop's, a local a segment set once before; a field at a uniform row; arithmetic and comparisons) and their LOCAL_STORE, planned at load and run at once in scalars by the pass's rules when the batch runs plainly, the pass's own way when a value is not as planned; the check (PURE_BATCH_CHECK) runs each dry and compares with the pass's own: seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources and the unit tests pass, seed 23's programs checking 312,249 segments in 213 of 650 runs
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load, run by the same rules with the per-instruction pass as fallback, and a list's cells once a batch; bars by arithmetic: knapsack's inner block has 10-12 of 24 instructions in segments, so 0.45 us a batch and 9.2 ms (the compiled code's 7.9 needs stage 4's passes), matmul 33 ms, sum0 1,300 instructions a batch
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interleaved): knapsack's per-batch cost 0.90 to 0.68 us and knapsack 11.48 to 10.34 ms, short of 025's bars (0.60 us, 10.3 ms): 025 counted the pass's per-instruction head as lookups; sum0 2,330 to 1,822 instructions a batch (bar 1,550); matmul 40.0 to 38.2 ms with the same instructions and BFS 24.04 to 24.31 with 0.2% fewer (placement); sum0's 8.69 to 6.13 ms mostly the compiler now vectorizing the reductions' first loop; the executor alone the same instructions; what is left a batch is the pass's Val handling (stage 2); 041 runs.sh pairs, pairs and counts data
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the unit tests in three modes and under ASan (executor mode too), the sanitized pure-run's fixed sources and seed 23 (both modes), make check and aup's checks in both modes pass
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their locals, updates and steps, records and a round's actions in the plan, a number that stays planned by its source (a constant, field, LOAD or local the block does not set: the same source one number, two sources of the same value two) and filled in as a batch opens, the pass finding an update or a record by its instruction's role; the check compares updates, records and whether the batch holds them with the block read again each batch: seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources and the unit tests pass
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load (pure_batch_plans, after its instructions' plans are final): the locals it sets and whether it sets items, its sums into cells, and at each instruction a role (a sum's again, add or set) and how far on a LOCAL_LOAD's x = x op e is; batch_run, pass and local_load read the plan instead of scanning the block each batch; PURE_BATCH_LANES to build other lane counts; PURE_BATCH_CHECK (a build flag, while the stage is made) reads the block again each batch and stops if the plan differs; seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources and the unit tests pass with it
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over one round's batches, 3x too high; about 2,300 instructions (0.33 us) in a small block, 0.90 us in knapsack's (38% of its time, not 20%)
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only values each batch: knapsack's per-batch cost measured at 0.90 us, 38% of its 11.5 ms (BATCH 1024 against 256 under a sampled profile: re-reading the block about 39%, value kinds 26%, list facts and dependence 22%, dispatch 14%), sum0's 0.33 us, matmul's inner-round dispatch about 13 ms and float-checked arithmetic about 22; five stages (facts at load, static kinds and list facts once a batch, typed kernels, fewer passes, the tails) with bars from those shares; 041 batch-costs data
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executor's way (memory's order, ascending): clang -O2 1.87 ms, gcc -O3 2.11, gcc -O2 9.02 (C 6.2, the compiled code 7.9)
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clang -Wpedantic refuses
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bar on roots (0.71x the compiled code's cycles a step), not on knapsack (4x) or BFS (2.4x), as NEON has no gather and a tile's lanes go out and in one by one; tight passes of the batch executor's own shape in the same run at 1.2x (BFS) and 0.4x (knapsack, clang): the shape is right and the 3x is implementation, so 132's A (a batch program made once at load, loops tight by type, width and stride, fewer passes) is the way; tiles kept aside for chains of arithmetic; 132, 024 and CHECKPOINT say so
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goto in one function (make.py: GCC spills every slot across the indirect branch) and threaded tail calls with the slots as vector arguments (make2.py: an operation its vector instructions, a load and a branch; clang's musttail, GCC's sibling calls); knapsack's inner loop, BFS's frontier and roots' Newton steps against tight passes and C: roots 5.8 ms (C 6.9, the compiled code 9.57), knapsack 29.4 (passes 2.9 with clang, 9.6 gcc; C 6.2; compiled 7.9), BFS 18.1 (passes 9.8; C 8.6; compiled 7.7); NEON gathers lane by lane cost the tiles what they gain in registers
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passes through memory; a batch's fixed cost about 6,500 instructions, 1 us, measured by 1024 against 256 lanes: fewer lanes are slower, so 024's L1 sizing was the wrong lever; a candidate's tail about 250), what the database literature measured of the same shape (X100, Kersten 2018's cycles and instructions a tuple, Sompolski 2011, Gubner 2017's in-register aggregation, Photon, Ertl and Gregg), the ways judged by the philosophy (a batch program made once at load; register tiles with threaded dispatch as the one general way past the floor; a table of fused operations and AOT C out), and the deciding experiment with its bar first (three bodies in tiles of 4, 8, 16: within 1.3x the compiled code's cycles an element, or it is not the answer); 041 lanes data
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general way over a table of fused operations: values computed by the same code taken from the first, if !c one branch, selections (an arm's few lanes alone), keys as bits asked in one loop, L.first + i affine, a slice's bounds at once: the suite's BFS 211 to 112 instructions an edge, 41 to 24 ms (the compiled code 38.5, 7.7); where the rest goes and the floor of the general way (about twice the compiled code); knapsack and matmul 10% slower, cause not fully told; 024 and CHECKPOINT say so
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batches BFS 24.0 ms, the compiled code 7.7, alone 92.7; knapsack 11.45 and matmul 40.0, up from b7's 10.3 and 36.5; the executor alone as before) and the search counts on b9 (BFS 112 instructions an edge, 57 cycles; the frontier sum 56 and 20; the compiled code 38.5 and 19, 35 and 15)
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are (a loop's value gathered: the end's checks know them, where lanes of rows gave the batch back: knapsack 48 to 11.5 ms); a module with no value planned for reuse spares the batch the looks (reuses); local_load inlined again
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as an earlier one in a line of the block (nothing between setting what it reads: planned at load, reuse_from and reuse_length) is taken from the earlier, kept for it; if !c { ... } one branch the other way, no NOT; an arm whose lanes are a quarter or fewer runs in those lanes alone (a selection: outer values gathered by sel, reductions into their lanes around, locals set given back masked at its end, stores and sums expanded, appends and a filter's kept rounds by sel; PURE_SELECT=all every straight arm, 0 none); a list whose keys are bits asked by them in one loop of lanes, a filter decided by its bits and bits of our own (no hash set; a key with no bit is not there); L.first + i affine while within the list; a slice's two bounds in one call (pure_list_slice); a filter's kept rounds copied from numbers made once. The suite's BFS 211 to 112 instructions an edge (the compiled code 38.5), 41.0 to 23.5 ms; the frontier sum 70 to 56 (35). Seeds 1, 2, 3, 5, 23 alike by default and with every arm selected
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batch's rounds together or spread into lanes, filters asked as a batch opens and again at its end): the suite's BFS batched, 93 to 41 ms (the compiled code 7.7, C 10); where it goes (211 instructions an edge against 38.5: a filter's code over every lane the most); the floor of operations each a pass over the lanes (about 50 an edge, 1.3x the compiled code) and what would pass it (fused operations from a table, 024's); the choice left: a table of them, or the compiled code kept for such work; 024 and CHECKPOINT say so
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ms, the compiled code 7.66, alone 93.4; the others and the executor alone as b6's) and search/: the suite's graph loaded and one handler run again and again (frontier-run: each node's edges' to summed, 70 instructions an edge batched, 35 compiled; search-run: the BFS, 211 and 38.5), counted with icount (2026-10-08-search-counts.jsonl)
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walk's spread items (PLAN_FILTER; L only grown there, one filter a list, none in a nested LOOP): each round asked as the batch opens, its code run in the rounds it said no to, those rounds kept (k and the appends' cells) and asked again at the end in the rounds' order (L as it is and what the kept rounds before add), the rest added at once (pure_list_add_many) once the lists take them and the memory budget all of them (else, or a key added there already, the batch gives its rounds back); a list such a filter grows read in the block only as no earlier round's item would change (its count in the guard, its first, a place when it has no key, a field by key). Keys kept as bits (pure_list_bits) asked by a loop of lanes, fields of a DENSE list found at their keys (pure_list_dense); an outer lane's affine value in four bytes. The suite's BFS batched: PURE_JIT=0 93 to 39.6 ms (the compiled code 7.7, C 10). module_tier's walks filter d (seeds 1, 2, 3, 5, 23 alike: 5,806 filters decided in seed 23's); GRAPH_SOURCE: a graph built by a filter, searched twice, marks whose filter adds another key (EXISTS), under work and memory budgets
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only grown in it) batches to L's count as each batch opens (PLAN_GUARD; fewer than LEAST rounds left there: the executor's, then batches again); a walk in a batch's block (its slice per lane, no where's range) runs each lane's items, its work counted as each opens: together round by round (BREAK as a nested loop's), or spread into lanes in the rounds' order a chunk of up to 1024 at a time when its items' rounds may run apart (PLAN_SPREAD: no break, the locals it sets reductions or its items' own: an outer lane's value read by each item's outer lane, a reduction added into its outer lane's in the items' order, an own local left as the last item that set it); rows in four bytes read and checked by loops of their own. A frontier walk of the suite's graph (each node's edges' to summed) PURE_JIT=0 55.2 to 10.4 ms (the compiled code 6.24). module_tier makes guarded loops with a walk in each (seeds 1, 2, 3, 5, 23 alike: 8,819 spread and 7,651 together in seed 23's); FRONT_SOURCE
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ms, a recurrence's steps as numbered values and one loop of actions 44.4 to 21.8, reductions' ends in any order where it cannot tell 9.80 to 4.00): knapsack 10.8, matmul 36.4, join 118, sort 55.5 ms without machine code; where each work's time goes now; BFS's arithmetic (a tail of about a tenth of the edges, done batch-side; edges spread into lanes, not walked together) and the three pieces it needs; the view-workers check's flake; 024 and CHECKPOINT say so
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compiled code 7.93), matmul 36.41 (14.20), join 118.3 (78.7), sort 55.5 (35.6), roots 8.87 (9.57); the executor alone as many instructions as b4's; costs three ways on b5 and b6 (tagged by version, b4's too: adds 0.65, ops 4.00, recur 21.8, recur4 36.0); frontier.c: the suite's BFS as frontier batches (105,232 of 999,913 edges asked again in order, 99,997 added; walking a batch's edges together 2.17x the edges)
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(steps, x set by an update's last step itself, records), the numbers through a restrict pointer; a record of x where x was not set since an earlier one shares its lanes (join's four reads of x: one store a round). 1,000,000 rounds of MINSTD 25.7 to 21.9 ms, with four reads of x into a sum 50.4 to 36.0 (the compiled code 18.5 and 19.9); PURE_JIT=0 join 131 to 118
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and the most; a sum of whole numbers whose magnitudes together stay below 2^53, four sums at a time), the rounds' order kept for the rest; each lane's least and most step and their fold over the numbers as integers in their order (-0 below +0), loops of vector code; a reduction's lanes cleared by a loop that keeps its count: 1,024,000 rounds of a max 9.80 to 4.00 ms (the compiled code 4.27), of a count 4.51 to 1.61
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(a step's result, a recurrence's value, the loop's value, a number that stays) rather than a stack's pushes and pops, an operation computed twice in its statement once (x the same until it is done): 1,000,000 rounds of MINSTD 44.4 to 25.7 ms (the compiled code 18.5, the executor alone 73.0); costs/recur.aup
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128) when every list takes its items so (an event's list, no index into it, one append to it: FLAT not keyed at its end, DENSE by keys it holds at its count, HASHED by number; never past its arrays' limit) and the memory budget takes them all (each item only grows what it counts): columns grown and widened once, the first key there already the executor's EXISTS at its round; else round by round as before, tried at once again after a round that changed a list's form. 50,000 DENSE adds 5.18 to 0.65 ms (the compiled code 0.28). APPEND_SOURCE: keys there already at rounds q and p, keys past a DENSE list's from round p, two appends to one list, widened columns, under memory budgets (seeds 1, 2, 3, 5, 23 alike: 31,402 batches at once in seed 23's, 292 by the budget round by round)
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walks (join 423 to 161 ms without machine code, the tier 74) and what a batch pays for, measured apart: an instruction about 20 ns a batch (0.02 ns a round at 1024 lanes), a reduction's end 4-9 ns a round, an append about 100 ns (the executor's), join's recurrence about 60 ns a round; BFS not batched (a count that grows, a filter that only grows, nested walks), so the JIT stays for now; the next in that order: appends at once, the recurrence's steps in registers, reductions' ends; 022 and 024 and CHECKPOINT say so
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c67f988): batches join 161.2 ms (the compiled code 74.4, alone 423.4), matmul 46.1, knapsack 15.1, roots 9.22; costs/: small modules timed three ways (an instruction about 20 ns a batch, a sum's end about 4 ns a round, an append about 100 ns as the executor's, the nested rounds 10.2 ms against the compiled code's 23.1)
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at a time: each lane an item's place (ROW of the walked list affine), its work counted as it opened, its place moved past the batch; no append to the walked list. module_tier makes walks of rounds apart (f, g, h, slices of g; seeds 1, 2, 3, 5, 23 alike: 1,891 walk batches in seed 1); BATCH_SOURCE walks a slice
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e, neither reading L; the set at k's row as found), keeps its rows and e from the pass (the second k, its find and the cell's read skipped) and adds them at the batch's end round by round as the executor adds and sets (a sum not finite: the executor's fault at its round; a column too narrow widened); a batch reading or setting those cells otherwise gives its rounds back. Recurrence steps one dispatch each. PURE_JIT=0 join 428 to 165 ms (the compiled code 78). module_tier makes sums into cells (seeds 1, 23 alike: 278 batches with them in seed 1); BATCH_SOURCE sums into three cells in turn
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sets it, every set of it x = e of x, numbers, fields, states, the loop's value and locals the block does not set, in no branch's way; its sets planned PLAN_RECUR) runs ahead of the batch round by round as steps decoded once a batch, as the executor computes them (a round's fault gives the batch back), leaving its value at each other read in each lane; the batch's pass skips its sets. matmul's, knapsack's and join's table loops batch: matmul 50 to 46 ms. module_tier makes loops with a recurrence (x1) ahead of appends, sets and sums (seeds 1, 2, 3, 5, 23 alike); RECUR_SOURCE: two updates a round, a division by 0 and a product past the numbers at some round, under work and memory budgets
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with no room left for a list's headroom kept its live count anyway (in x30, the 13th register) and wrote that stale count over the list's own after its appends went the unbooked way (a loop of appends after a doubly nested loop reading t.has, PURE_JIT=all: e.count 1 for 36)
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appended in a batch's block (to a list the block reads nowhere else, no index into it, no nested loop) is made at the batch's end round by round through the executor's own step: keys there already, the memory budget, its undo log as the executor's; a fault there is the executor's at that round (the event undone: its kind, its instruction and the work so far tell), pure_batch_run's third way out. module_tier's handlers append (e, d) in rounds apart and run under a memory budget too (seeds 1, 2, 3, 5, 23 alike); knapsack's table loop batched (13.8 to 13.7 ms: the appends cost as the executor's)
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