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xor, a left shift as a times 2^b failing as overflow past the range, a right shift as floor(a / 2^b), a count outside 0-63 failing as limit: integers in two's complement without end), BYTE_AT (the byte of any bytes value at a whole position, a number or an i64, else limit), BYTES_OF (a list of one i64 field as bytes, a value outside 0-255 failing as limit) and INDEX_AT (a list's item at a position, not_found where there is none); the fold-shape and batch analyses count their arity and the lists they read; unit tests of the ends (27 bit cases, 11 reads of a constant's and a text state's bytes, 7 refused)
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typed value built of bool, i64, number, bytes (text the UTF-8 ones), records, variants and lists of anything (an unkeyed list keyed by position), anchors for cursors and indexes; functions that may recur and while, ending by the budget as EVM's gas (the module the unit of determinism); bit operations on integers as infinite two's complement within i64; folds left folds in meaning, reordered by the implementation only for the same answer; meaning apart from representation; answers to 026's suspects; five stages (bytes, bits and lists of numbers for SHA-256; nesting, variants, recursion and characters for JSON; nested state stored; patterns gathered; the number model) with bars
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inflate, JSON, UTF-8 and line breaking, relational queries and graphs, text editing, box layout, HTTP/1.1 by packets, retries and timeouts, constant-time crypto) with five criteria (written in aup and Pure alone, no workaround, lines against a Python reference, time against C, the spec's own vectors passing in Pure's checks on three machines); ten probes (044) show today's aup stops at a byte by position, bit operations, nesting, recursion, variants and reading a character; the core's minimal candidates and the rule against piling up (only what two specs need); SHA-256 and JSON first
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1.0: an event a total, atomic, deterministic function step(S, E) -> (S, Out*) or a fault (budgets in instructions and bytes), time an input, views pure functions of the committed snapshot, the history seen a prefix of commits, delivery in order and once with the transport's state in the store, values the same on every path, replacement joined by names; the layers it removes; its own suspects (input and view kinds, cursors and indexes, keyed documents, the number model, the budget's unit, fixed limits); the computation language rebuilt before 1.0, no compatibility kept before it (the user's word)
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spare_count they moved its large arrays and knapsack ran 7% slower at the same instructions (8.79 against 8.29 ms), at its end about 2% (8.45); research 139's afterword: 026 not taken heavily (the user's word), the one light cut made (a nested count loop's rounds sweeping only when few lanes are left: matmul 25.85 to 24.3 ms), the walk loops kept sweeping each round (held, BFS's batches ran out), and the stop; 041 runs of b21
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back only when fewer are left than the most a round has taken and one (fresh and new_mask keep the fewest left; nested rounds' marks given back to the rounds around), else once after the loop as the last round did; matmul 3.6% fewer instructions, 4.5% fewer cycles (a sweep a k-round); a walk's rounds and a spread walk's chunks still sweep each: so held, BFS's batches ran out of lanes and went back to the executor (36.9 ms, the answers the same), what their filters and selections take not told by a round's fewest left; seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources (also sanitized), the unit tests and ASan's pass
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deciding prototype 043): the executor's extra over 041 is interpretation, not semantics (matmul 11.1 ms of it, checks 0.2); the program interpreted a step at a time, with the executor's checks, ran matmul's loop in 10.36 ms and knapsack's in 4.16 (straight kernels 7.17 and 3.76; the executor about 22.2 and 7.3), about 14 and 5.4 ms with the making (bars 15 and 6.5; the compiled code 14.2 and 7.9); the buffer rule it found (registers at load, two buffers each so a result never lands on its operand, 24 lanes apart); the suite's five bodies sorted (matmul, knapsack, join's order loop straight-line; roots and BFS not); 026's scope as straight-line programs with the pass for the rest, and its risk
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a load would make, interpreted a step at a time (scalar steps by the executor's rules, kernel steps over four-byte lane registers fixed at load with two buffers each, a list's cells once a batch, a deferred set after its distance check), against the same kernels called straight and natural.h's C: matmul 10.36 ms (straight 7.17; the executor's 25.8 with 3.6 of making), knapsack 4.16 (straight 3.76; the executor's 8.19); 139's question, bars and b20's split (matmul's 11.1 ms of interpretation, knapsack's 1.9)
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at once in integers (join 116.0 to 110.5 ms, short of 108: what is left is the same cells' memory, read, add and write again), decide's bit found once (BFS 23.2, short of 21.5: the tail's time was its loads more than its instructions), and the batch executor's loops aligned to 64-byte lines (the hot loops' placement had swung knapsack 6% at the same instructions; the lists' loops aligned too cost the bank's queries 1-2% more instructions, so not they); against b9 matmul -36%, knapsack -28%, roots -7.6%, join -6.2%, BFS -3.9%, the executor alone, the bank queries and TPC-C (+0.7%) as they were; 025's bars and what each stage measured; 024 and CHECKPOINT say so
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lists' loops so aligned cost the bank's queries 0.8-2.0% more instructions (the padding) with their cycles mixed
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line (-falign-loops=64 in LIST_OPTIMIZE): a change anywhere in module-batch.c moved knapsack's hot loops and it ran 8.26, 8.74 and 8.20 ms with the same instructions; aligned, every batched work's cycles fell (knapsack 6%, matmul 1.8%, BFS 1.1%) and the executor alone stayed within its noise, at 0.7-2.3% more instructions (the padding)
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(an add of the key it asked, as a filter's is, takes the place found) and clears only the words of the bits it set (their places kept as it sets them): BFS 0.4% fewer instructions; seeds 1 2 3 5 23 (default and PURE_SELECT=all), the fixed sources (GRAPH's exists, memory and work faults where they were) and the unit tests pass
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round 0 (sums_in_words): the rows and e's in four bytes first (vector code) up to the first round whose e is not a whole number below 2^32, then each round's sums in turn in integers for a one- or four-byte cell while it stays in its bytes, as a number for an eight-byte cell while finite; where one is not so the executor's way goes on from that round and sum (nothing faulted or widened before it); join 4.9% fewer cycles; SUMS_SOURCE in check.py (sixteen rows met again and again, a one-byte column widened mid-batch, a four-byte one past 2^32, a masked fraction), 7,912 rounds at once and 3,228 the other way, the same three ways; 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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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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