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forms (geometric mean 1.58 and 1.24, the tier 1.92), the prototypes as a ceiling (124's floor 0.90x became 1.2-2.5x), division a third of the interpreted recurrence, the distance rule for equal strides only, why not copy-and-patch, matmul's miss without a fused multiply-add; CHECKPOINT says so
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operations apart, interpreted, 57.8 ms (C 32.6; fused by hand 48.4, the tier 2.46x); bfs: a node with more edges than the lanes runs its round alone (tested with lanes of 16, LANES_TEST); runs again
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the C compiler makes at build time (no code made at run time, 32 KB of lanes), checks as a batch's flag and a failed batch run again round by round; which loops batch (sums, affine keys at a nonnegative distance, filters that only grow, a count that only grows), sections run round by round interpreted, fused operations from a table, the JIT retired if it is not slower; 041's prototypes against C: roots 0.99, knapsack 0.71, matmul 0.94, BFS 1.03, join 1.59 (the tier 1.20-2.46); CHECKPOINT says so
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four-byte lanes ascending in memory, 4.54 ms (C 6.38, the tier 7.5; fused 2.70): narrow lanes in memory's order are most of the gain, fusing the rest; runs again
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made at build time (no code made at run time), on Pure's forms and checks, against C natural and C given the same restructuring: roots 6.79 ms (C 6.86), knapsack fused four-byte 2.70 (C 6.47, C in the batch's blocks 1.94), matmul lanes over j 6.67 (C 7.10, C swapped and vector 4.88), join 37 / 46 with its recurrence interpreted (C 30), BFS 10.3 (C 10.0, C read ahead 7.0); unfused interpreted operations 11.2 and 17.7-22.1
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generic code's (steps 0.1%), what the tier needs for it (a list's count as a changing value); 023 cites words at e2e56dd
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knapsack 1.19, sort 1.37, join 2.54, words 5.58, matmul 1.85, BFS 1.61; geometric mean 1.92, from 3-300x at 6b45806), what each change did, the forms measured in assembly, the apps unchanged, what is left (text in the executor, BFS's appends, spills); CHECKPOINT says so
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off the number pipes the divisions and sums wait on: roots 10.9 to 9.6 ms (1.39x C). 040 newton.c: roots' loop in the forms the tier may make it (the check as numbers 9.7 ms, in integers 8.7, none 7.7; next in r's register as gcc keeps it 7.0)
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round, in range for every round (its opening found it) and in a full list, reads its cell through a pointer, a phi at the loop's head: the column (read from the list) plus the key at round 0 times four where the loop opens, its key's step a round times four added at its latch. The key's nodes, in range, give up nowhere (no snapshot kept), so a key read by such accesses alone is not made; a list found by key alone with such an access is full where the tier begins (else the generic code runs the nest). matmul 23.0 to 14.2 ms (3.1x to 1.9x C)
module_tier's programs sweep lists by keys stepping with a round (in range or not, a list full or not)
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20.7 ms, pointer with multiply-add 13.1, apart 10.0, with checks 10.2, a bit tested before each load 13.4): the position's multiply and the pre-load branch cost, the checks hardly; 023 section 5 says so and what comes first (pointer induction, then a full list's copy)
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knapsack 1.18, sort 1.37, join 2.62, words 5.46, matmul 3.07, BFS without reading ahead 1.58 (geometric mean 2.09; 3-300x at 6b45806)
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apps there are): six pairs in turns, TPC-C's median -1.2% (the pairs -5.2 to +1.4%), the queries' medians within 1% but in_credit's (0.84 to 0.815 ms); the queries' instructions +0.3 to +1.5% on 49b6196 (2026-10-05-counts-49b6196.jsonl), -0.1 to +0.5% after the list's tree paths left HASHED's checks (2026-10-05-counts.jsonl). runs.sh serve, pairs and counts
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bits): one that an index state then asks where an item went is inserted FLAT, whose key set an item's layout key (-1) would read past; the FLAT and tree key sets kept only for number keys. A list read by position checks for HASHED where it is not a tree alone (stored lists: none of it): the bank queries' instructions within 0.5% of 6b45806 (0.3-0.8% before)
text_keys_equivalence asks where an item went in some events
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(constants between), checks only the last is finite, giving up at the run's first snapshot (the executor makes the run again and fails where it does); a snapshot's constants written as the constants they are, not kept in registers; the generic code's append in a loop keeping its books puts into a HASHED list as append does (its headroom kept). roots 12.2 to 10.9 ms (1.59x C), join 84 to 74 (2.5x)
module_assumptions: a run of products and sums past the largest number (CHAIN_SOURCE)
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slots, as C's table: in the L3), the generic code's APPEND into a HASHED list at its key's slot while its table need not grow, a whole number over a whole one above 0 never -0 (so MINSTD's floor(x * 48271 / p) is whole and x an integer in the tier). join 108 to 84 ms (2.8x C), sort 58 to 37 (1.4x)
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keyed by a text is HASHED from its first item, its table's slots holding the texts' hashes (FNV-1a), a match the key cell's bytes too; HAS and a field by key read the table; its order made by a merge sort (the first eight bytes as a number, then all). A FIND whose index only an ITEM_SET of its list takes, the code between in a line finding by key alone, sets the item where it was found (PLAN_ROW: a HASHED list's slot, no position made). words 453 to 217 ms (5.8x C)
text_keys_equivalence: adds, has, fields by key, sets where found, positions, runs, removes and clears against a tree keyed by the text
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each item's cells at its key's slot in its members' table, found by key there (the key and its cells read at one slot, as C's table); its order made by a radix sort of the slots' keys when something asks for a position (twice an event, then FLAT or a tree). The tier finds by key alone in a HASHED list (its bits' bit 1, its limit all ones: the bounds checked at a loop's opening still hold) out of the line; a list keyed by each count in order is DENSE from its first item. join 531 to 108 ms (3.5x C), sort 98 to 58 (2.1x)
arrays_equivalence counts the HASHED form against a tree; module_tier's programs read a HASHED list by key
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one (the round's register the next's: no move on the way back), a way's moves only for phis something needs, a number over a power of two times its reciprocal (the same number), a constant only numbers' arithmetic reads a number made where the tier begins, the 2^53 check in three instructions. roots 14.1 to 12.2 ms (1.78x C), knapsack 8.5 to 7.8 (1.26x)
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rounds it does not run given back where it breaks or gives up), a comparison only a branch reads its flags, a full list's keys read without its bits (a key's position found: its key's register), an add's or sub's register its operand's where that is read last. knapsack 16.5 to 8.5 ms (1.37x C), matmul 25.7 to 22.9
Two bugs the work checks found, there since 6cd7f5a: the outermost loop's round past the work budget gave up at the loop's instruction, with nothing on the stack (the executor opened it again: LIMIT where WORK), now at its iteration; and a phi where an if's ways meet took its merge's loop (-1), so a value made of it was taken as made outside its loop and made once for all rounds. pure-run's budget and work commands; module_tier compares the work and runs four small budgets; module_assumptions keeps both programs
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their loop opens (each affine in its round: both ends below the limit), the checks in the round gone; constants in the instructions (add, sub, cmp); one-byte columns widened to four where the tier begins, its loads and stores of four bytes only. roots 14.0 to 14.0 ms, knapsack 38.8 to 16.5, matmul 48.6 to 25.7
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values in registers (x20-x28 too, the frame's read again where it ends), whole numbers integers by their facts, the message's fields and lists' columns read once, invariants made before inner loops; where anything does not hold it gives up to the executor at the instruction (pure_run_rest) and the generic code goes on. roots 22.9 to 14.0 ms, knapsack 1,030 to 38.8, matmul 908 to 48.6; module_tier checks random handlers against the executor
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often (the bank queries' instructions as before, within 0.4%)
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DENSE list answers by position without becoming FLAT: its keys counted once per change of them (full: a key is its position; else ranks by word). knapsack 1,880 to 1,029 ms, matmul 2,284 to 908 (023 stage 1)
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not past it; representation first, since a keyed list given keys in order stays FLAT and is searched by halves (knapsack's and matmul's 300x)
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without), the suite of seven kinds of work at 3-300x C, floors at 0.90x C with the meaning's checks hoisted to 0-3%; CHECKPOINT says so
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place fault where they are; now is the host's per-event value); value numbering of pure operations, which words' floor assumes
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types and ranges, hoists the meaning's checks out of loops, counts work per loop, allocates registers; criteria on research 124's suite of seven kinds of work against C (each within 1.25x, the geometric mean below 1.0, the meaning's checks within 5%), from floors at 0.90x C
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lists' representation, its meaning) bare, with the checks a compiler could hoist, and with every check where the meaning puts it: hoisted 0.64-1.02x C (0.90 by the geometric mean), naive up to 12x
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(knapsack), 4.8x (sort), 22x (join), 12x (words), 304x (matmul), BFS 1.57x without reading ahead; only roots and BFS run as code
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knapsack, sort, join, words, matmul, BFS), each against the C one would write, in one process with the same inputs and answers; PURE_AHEAD=0 to measure the code without reading ahead
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reading ahead to the bucket's last cell, the edge loop's checks; that past C is the reading ahead (16.1 ms without it, C 9.8), and that the criteria move to 023's suite
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executor), so their list's columns are there; the keys a list's bits reach none without bits, so one compare asks both; has's rare ways out of the line: a seen edge 14 to 11 instructions, BFS core 8.6 to 7.4 ms (022)
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well as its first: a node's edges cross a line more often than not. BFS core 12.2 to 8.6 ms, 29.4M to 20.7M cycles, past C's 9.4 ms (022)
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small constants and powers of two's products in the instruction; where a check may give up, make the result in x16, the operands as they were for the executor (aup's check caught a register shared with its operand): BFS core 12.5 to 12.2 ms, 46.2M to 43.0M instructions (022)
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items added as its appends make them, the event's headroom, written back before a call, at a fault and as the nest ends: BFS core 14.6 to 12.5 ms, 57.8M to 46.2M instructions (022)
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(narrow columns, counts, their arithmetic within 2^53), giving up to the executor for the rest of a round when that fails: BFS core 14.9 to 13.4 ms (022)
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(TPC-C's) runs in the executor, 2.7% faster there (022); PURE_JIT=all compiles every loop for the checks
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integers assumed, the rest of a round in the executor when they break, the books in registers
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opens it, read an item and find it in key bits as one, branch back once a round: BFS core 19.6 to 14.9 ms (022)
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list's keys as its slots), open a packed list's slice in code with an integer index, keep a nest of loops' values in registers of their own: BFS core 27.5 to 19.6 ms (022)
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on, each loop's columns, key bits and place kept in registers, and appends to an event's list as code: BFS core 55 to 27.5 ms (022)
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fitted to the keys searched, between events, and build trees from the leaves up: BFS core 89 to 55 ms (022)
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searched, narrow columns, a JIT with registers and loop guards, read ahead; criteria first
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forms by hand beat C only packed, narrow and read ahead (123)
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a frame's fields one by one, and inline group_of (021)
- Compiled code paid only where blocks repeat; a block run once (a view's
cell, a fold's item, most handlers) ran slower through the code's entry
and its calls of step: the bank's table queries took 16-24% more
instructions. Now only a block with an EACH or a LOOP is compiled, and
a module with none keeps no compiled code.
- run() set its whole frame each time (the compiled code's run among it);
now its fields one by one.
- group_of is inlined into its pass: after the executor's refactor it
was a call per row (per_branch +4-5% instructions; now +1.1-1.3%).
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tree's seek, still seven times C's (021)
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find a slice against C's 21 (021)
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at the finger's leaf, and move indices only for a list an index refers to (021)
- The frame keeps the run compiled code read a tree's item from last (the
list as it was: its version); an item it holds is read from its column,
else pure_run_item takes the item's run and steps.
- pure_list_run starts at the leaf the finger keeps when it holds the
position (a slice found by key just before): no second descent; the
run after it is found from the root (PureRun.pathless).
- LIST_APPEND and LIST_REMOVE move index states only for a list one
refers to.
- A search (core only): 89 ms compiled (answers the executor's).
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arithmetic, has by bits, a DENSE field by key, a FLAT item, and loop iterations (021)
- module-jit.c writes CONST, LOAD, STORE, the local and row loads,
INDEX_FIRST, LIST_COUNT, INDEX_MOVE, NOT, NEG, FLOOR, the number
arithmetic and comparisons (DIVIDE and NON_FINITE faults where the
executor gives them), LIST_HAS by a key set's bits, a joined FIND's
field of a DENSE list, a FLAT list's ITEM_GET, and a walk's and a
count's iteration (work charged as the executor charges it). Anything
else, or a list in another form, still calls step.
- module-list.c says where a list keeps what the code reads
(pure_list_layout); list_of and item_field are shared.
- PURE_JIT_DUMP=file writes the code made, to read with objdump.
- A search (core only): 103 ms compiled, 122 ms executed; the answers
(hops, reached, work) are the executor's.
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call the same steps (021)
- run() keeps a block's operand stack and open loops in a Frame; step()
runs one instruction (branches and loops too, one dispatch), and
enter_each, enter_loop, leave_loop and iterate are their own functions.
The executor is the same machine code, 7% fewer instructions.
- The verifier records each instruction's stack height (from its block's
start), so compiled code knows each slot's place.
- module-jit.c (AArch64 Linux; elsewhere, or PURE_JIT=0, none): a
module's handlers', views' and folds' blocks compiled when it loads.
Branches and loops are branches; every other instruction calls the
executor's own step, so both run the same meaning. A loop that is not
opened lands where its iteration would have ended; an empty loop
iterates in place.
- test-module recompiles a module whose code a test changes after load.
- A search (100,000 nodes, 1,000,000 edges, core only) is 150 ms
compiled, against 122 ms executed: a call of step for every instruction
costs more than the executor's switch; the hot instructions are written
as code next.
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