diff --git a/research/complex-coefficient-rescaling/CLAIM.md b/research/complex-coefficient-rescaling/CLAIM.md new file mode 100644 index 0000000000..5cfad9f85f --- /dev/null +++ b/research/complex-coefficient-rescaling/CLAIM.md @@ -0,0 +1,53 @@ +# Sprint claim + +- Track: complex supplier; OS assignment seed **39**, drawn with `secrets.randbelow(100)` on 2026-10-13. Odd parity selects JP8. +- Exact base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`. +- Scope: selected #626 JP8 full-frame cleanup; consecutive same-source additions with **distinct coefficient magnitudes related by powers of two**. Keep target-update order and use the existing private coefficient work stream. Price source access, initialization, rescaling, accumulation and final clearing before implementing a witness. +- Method: exhaustive scan of this fixed finite word in both orientations; choose disjoint profitable blocks, exact rational arbitrary-input replay and prefix bounds. No randomized search, time-limited search, or kappa claim. +- Expected deliverable: executable finite circuit witness and scoped proof, or a complete negative census if the optimistic budget gives no gain. +- Expected finish: 2026-10-13 05:37 UTC. Reserve 05:27 onward for verification and handoff. +- Coordination: GitHub reported no pinned issues and only open issue #650 (Discussions request). Local claim recorded instead of a reservation issue. Open PR snapshot: 551 PRs through #732. + +## Candidates considered + +1. Joint target-basis rewrite of the selected cleanup; related bit work #710 and CK pair obstruction #719 mean a broader resynthesis obligation. +2. Source-basis rewrite of the selected factory; substantial overlap with #645/#681, so not selected. +3. Distinct-coefficient private-work rescaling in JP8 cleanup, selected. #722 shares equal coefficients and #723 changes individual numerator encodings. This instead connects differing magnitudes across macros, with a complete incremental cost comparison against equal-coefficient sharing. + +## Related pending work inspected + +- #696, `5a3f983715027c4fd83f50bc9001d4b18463bed1`: copy/unit scalar lowerings. +- #722, `a0766ab0fab379e1997fadc3ca157578d57986c1`: equal-coefficient JP8 cleanup sharing. +- #723, `d3bc41b87fc7d23f50d064a0f06f1a89e3ab02a7`: signed-digit numerator lowering. +- #719, `a3d9c0aa0a16b68b1f4dd064671ad018013e6dd4`: CK repeated-pair rank obstruction. +- #698, `ab78f797cffcbeddbb17a7eb069741085ffe3351`: fixed-boundary CK B-frame optimization. +- #681, `fdc2e4f3c6825530b02143b30deab5de10209479`: raw factory resynthesis. + +No pending implementation is imported. The selected construction and review were followed through #626's retained supplier, local event stream, emitter and source manifest. The review ledger marks #626 and #622 incorporated, while the newer PRs above remain pending. + +## Completed result — 2026-10-13 + +Submitted [PR #739](https://github.com/CrocSwap/integer-mult-bounds/pull/739), +**research construction / finite complex-supplier circuit improvement; no new +κ**. Initial contribution commit: `db5271d831d506ecf446609dc431e02bc3da8e0e`. + +The complete fixed-word scan found 1,211 profitable distinct-magnitude edges. +Combined with the explicitly credited equal-magnitude method, 1,015 blocks +reduce forward real-component primitives from 257,232 to 227,206. The new +increment beyond #722's 237,544 is **10,338**. Backward is unchanged. Both +716-column scalar projections, all 6,279 independent block basis cases, exact +prefix envelopes, negative controls and nine focused tests pass. The selected +κ and paid recursive profiles are unchanged. Production block-interface +admission and invoice integration remain open. + +The final pre-submission snapshot covered 556 open PRs through #737, including +new #734 at `21606831df4b08f79d87fd420c558a520dca571e`, whose per-macro +signed-Horner work is credited separately. #738 arrived during submission; +its Gaussian copy-floor theorem is unrelated to coefficient-work rescaling. +There was still no pinned coordination issue. The one delegated reviewer +stayed within this package, supplied the independent checker and found no +correctness blocker. One wording correction from that review distinguishes +endpoint-neutral extra instructions from equal-cost instructions. + +Reproduce: `python3 -I -B research/complex-coefficient-rescaling/verify.py`. +Expected: `PASS_JP8_COEFFICIENT_RESCALING incremental_real_saved=10338 blocks=1015 columns=716 orientations=2 controls=11`. diff --git a/research/complex-coefficient-rescaling/EXPECTED.json b/research/complex-coefficient-rescaling/EXPECTED.json new file mode 100644 index 0000000000..5958c0bd68 --- /dev/null +++ b/research/complex-coefficient-rescaling/EXPECTED.json @@ -0,0 +1,1207 @@ +{ + "schema": "complex-coefficient-rescaling/1", + "assignment_seed": 39, + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "macro_library_cases": 591, + "negative_controls": [ + "omitted_initial_clear", + "omitted_final_clear", + "wrong_accumulation_sign", + "inverted_rescale", + "endpoint_neutral_prefix_excursion", + "source_alias", + "changed_source", + "changed_odd_numerator", + 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"to_magnitude": "2", + "shift": 4, + "extra_real_primitives_if_merged": 0, + "count": 1 + }, + { + "from_magnitude": "16", + "to_magnitude": "1/2", + "shift": -5, + "extra_real_primitives_if_merged": 2, + "count": 12 + }, + { + "from_magnitude": "16384", + "to_magnitude": "16", + "shift": -10, + "extra_real_primitives_if_merged": 6, + "count": 1 + }, + { + "from_magnitude": "16777216", + "to_magnitude": "4", + "shift": -22, + "extra_real_primitives_if_merged": 34, + "count": 1 + }, + { + "from_magnitude": "32", + "to_magnitude": "2", + "shift": -4, + "extra_real_primitives_if_merged": 0, + "count": 10 + }, + { + "from_magnitude": "32768", + "to_magnitude": "32", + "shift": -10, + "extra_real_primitives_if_merged": 4, + "count": 1 + }, + { + "from_magnitude": "64", + "to_magnitude": "2", + "shift": -5, + "extra_real_primitives_if_merged": 2, + "count": 4 + }, + { + "from_magnitude": "8", + "to_magnitude": "1/2", + "shift": -4, + "extra_real_primitives_if_merged": 0, + "count": 16 + }, + { + "from_magnitude": "8", + "to_magnitude": "1/4", + "shift": -5, + "extra_real_primitives_if_merged": 0, + "count": 1 + }, + { + "from_magnitude": "8192", + "to_magnitude": "2", + "shift": -12, + "extra_real_primitives_if_merged": 16, + "count": 1 + }, + { + "from_magnitude": "8388608", + "to_magnitude": "2", + "shift": -22, + "extra_real_primitives_if_merged": 36, + "count": 1 + } + ], + "semantic_negative_controls_rejected": [ + "missing_entry_clear", + "missing_exit_clear", + "wrong_accumulation_sign", + "wrong_rescale_direction" + ], + "scope": "Finite primitive maps on arbitrary live/work input; exact DP optimum only within fixed-source, ordered power-of-two rescaling blocks." + } + }, + "backward": { + "original_real_primitives": 257280, + "equal_magnitude_real_primitives": 257280, + "rescaled_real_primitives": 257280, + "incremental_real_saving": 0, + "equal_magnitude_blocks": 0, + "rescaled_blocks": 0, + "all_live_columns": 716, + "arbitrary_work_input": true, + "original_prefix_l1": "16753412757380464429924108070201913461/8388608", + "equal_prefix_l1": "16753412757380464429924108070201913461/8388608", + "rescaled_prefix_l1": "16753412757380464429924108070201913461/8388608", + "paid_profile": { + "1": 2512, + "2": 400, + "3": 448, + "4": 160, + "5": 70, + "6": 8, + "8": 8 + }, + "blocks": [], + "independent": { + "status": "PASS_INDEPENDENT_DP_AND_SCALAR_BASIS", + "eligible_additions": 5909, + "maximal_fixed_source_runs": 5909, + "largest_run": 1, + "dp_candidate_blocks_checked": 5909, + "selected_blocks": 0, + "scalar_basis_inputs_checked": 0, + "selected_block_component_primitives": 0, + "eligible_singleton_component_primitives": 45969, + "eligible_optimal_component_primitives": 45969, + "saved_real_component_primitives": 0, + "profitable_edges": {}, + "incompatible_odd_numerator_edges": 0, + "nonpositive_transition_count": 0, + "nonpositive_transition_census": [], + "semantic_negative_controls_rejected": [], + "scope": "Finite primitive maps on arbitrary live/work input; exact DP optimum only within fixed-source, ordered power-of-two rescaling blocks." + } + } + } +} diff --git a/research/complex-coefficient-rescaling/README.md b/research/complex-coefficient-rescaling/README.md new file mode 100644 index 0000000000..d79979424a --- /dev/null +++ b/research/complex-coefficient-rescaling/README.md @@ -0,0 +1,211 @@ +# JP8 cleanup: reuse coefficient work across different magnitudes + +**Status: finite complex-supplier circuit improvement / research note; no new +κ.** Rescaling a prepared coefficient between consecutive additions saves +**10,338 real-component primitives beyond equal-magnitude sharing** in the +selected #626 JP8 forward program. The backward program has no eligible joins. + +| Complete scalar program | Original #626 lowering | Equal-magnitude sharing (#722 method) | This rescaling lowering | +|---|---:|---:|---:| +| JP8 forward | 257,232 | 237,544 | **227,206** | +| JP8 inverse-transpose | 257,280 | 257,280 | 257,280 | + +The 30,026 total saving includes 19,688 already obtained by @ellipsi2 in +[#722](https://github.com/CrocSwap/integer-mult-bounds/pull/722). Only the +additional **10,338** is new here. The comparison implements that PR's +equal-**magnitude** rule, including opposite signs, with the original binary +Horner preparation. Its pinned implementation was inspected; no pending code +is imported. This is an arithmetic operation count, not a runtime benchmark. + +## Reproduce + +From the repository root, Python 3.11+ and its standard library suffice: + +```sh +python3 -I -B research/complex-coefficient-rescaling/verify.py +``` + +Expected: + +```text +PASS_JP8_COEFFICIENT_RESCALING incremental_real_saved=10338 blocks=1015 columns=716 orientations=2 controls=11 +``` + +The command is offline and read-only. It checks all source pins, the binding +to #626's SPEC, every block's primitive count and arbitrary-input map, both +complete scalar projections, the exact positive prefix envelopes and the +committed [certificate](EXPECTED.json). It retains the selected program's +paid-child census. It does not re-prove the unchanged Clifford operations. + +Additional adversarial and finite-domain checks: + +```sh +python3 -I -B research/complex-coefficient-rescaling/test_verify.py +make selected-record-check +``` + +## A concrete new block + +Forward event indices `[18840, 18843)` contain, in order, at the full frame: + +```text +L655 -= 2 * L470 +L97 -= (1/4) * L470 +L656 -= (1/2) * L470 +``` + +All three magnitudes differ, so equal-magnitude sharing does not change this +block. Prepare `W = 2 * L470`, perform the first subtraction, halve W three +times, perform the second subtraction, double W, perform the last subtraction, +and clear W. Including the entry clear and first source read, this costs 11 +primitives per real component instead of 16: **22 instead of 32** for the +complex value. L470 is never written. Arbitrary incoming target values are +preserved with the stated updates, and arbitrary incoming W is erased. + +## Circuit and complete price + +The domain is consecutive, full-frame cleanup additions +`t_i += q_i * s`, with one unchanged live source s, no `t_i = s`, and nonzero +dyadic coefficients satisfying `|q_i| != 1`. Target updates keep their original +order, including repeated targets. A block may join magnitudes only when their +ratio is an integral power of two. No operation crosses a phase, scalar-kind, +source, or frame boundary. Unit coefficients are excluded to keep this +comparison separate from the unit lowering in #696. + +Write `|q_i| = m * 2**e_i`, where m is a positive odd integer, and set +`d(m) = floor(log2(m)) + popcount(m)`. The inherited Horner preparation costs +`1 + d(m) + |e_i|`: entry clear, every source addition, binary doubling and +denominator halving. Accumulation and final clear add two. Thus r separate +macros cost, per real component, + +```text +C_separate = r * (d(m) + 3) + sum_i |e_i|. +``` + +[lowering.py](lowering.py) emits the same preparation for the first magnitude, +one signed target accumulation per macro, `|e_i-e_(i-1)|` doubles or halves +between magnitudes, and one final clear: + +```text +C_block = d(m) + |e_1| + 2 + r + sum_(i=2..r) |e_i-e_(i-1)|. +``` + +There are no extra helper registers, source copies, frame changes, recursive +children or restoration operations. The existing private coefficient stream +is the only scratch. Both real components are counted, so every table entry +is twice its component cost. Unchanged scalar macros are also fully priced; +adapters, wrappers, compiler overhead and recursive calls lie outside this +scalar subcount and retain their inherited costs. + +Joining an edge saves +`d(m) + 2 + |e_i| - |e_i-e_(i-1)|` per component. These savings are additive +and do not depend on the other cuts. The planner takes strictly profitable +edges and cuts ties. Therefore it minimizes this explicit prepare/rescale/ +clear cost among segmentations in the stated class. This is not an optimum +over other arithmetic circuits, register allocations or supplier designs. + +## Exact map, prefix and interface argument + +At block entry, clear W. The first Horner preparation gives `W=|q_1|s`. +Rescaling by `2**(e_i-e_(i-1))` gives `W=|q_i|s`; the signed accumulation +therefore gives the original target update. Induction works for arbitrary +source/target values, not only for reachable clean inputs. The final clear +erases W. The independent checker tests all touched-register basis vectors +and a separate incoming W basis vector for every block. + +The source's positive envelope is constant throughout a block. The first +preparation is unchanged. Later W rescalings are monotone between their two +endpoint magnitudes, so their envelope is at most +`max(|q_(i-1)|, |q_i|) * envelope(s)`. Each endpoint magnitude is bounded by +the corresponding old Horner numerator. Live-register envelopes agree after +each target accumulation. Thus the maximum over a complete block is dominated +by the old maximum; an aligned-microstep domination claim is unnecessary. +The complete forward and inverse-transpose upper envelopes reproduce exactly +as 64 and 101 bits respectively, below the inherited 192-bit allowance. + +**Changed local interface:** W is cleared at block boundaries, rather than +after every macro inside the block. The selected emitter currently advertises +macro-boundary clearing. Integration must explicitly admit this block contract +and refresh its scalar invoices. This package supplies the replacement +primitive circuits and their evidence; it does not silently change that emitter. + +All changed reads and writes are at the full frame, on registers whose native +final frame is full. No wrapped helper is used beyond its existing lifetime; +the pinned event stream's wrappers and children remain in their original +positions. The full scalar replay checks all 716 live input columns, including +492 arbitrary helper inputs, in **both separately emitted orientations**. +The inverse-transpose program is not obtained by reversing a forward block. + +## Completed finite coverage + +The OS assignment seed **39** selected the complex track and JP8 by parity. +There is no random search after that choice, time-based stop or incomplete +solver run. Both fixed 27,909-event programs are scanned completely. + +- Each orientation contains 5,909 eligible nonunit cleanup additions. +- Forward: 1,611 maximal fixed-source runs; the separate DP evaluates 18,925 + permitted candidate blocks and reproduces all 1,015 selected blocks covering + 4,249 additions. Of these blocks, 556 contain a magnitude change. +- The accepted edges comprise 2,023 equal-magnitude edges and **1,211 distinct + magnitude edges**. There are 1,015 incompatible odd-numerator edges. +- All 49 nonprofitable power-of-two edges are cut: 28 tie and 21 cost more. + For example, `16 -> 1/2` costs two extra real primitives if merged. The + certificate records every rejected transition class, not just successes. +- Backward: all 5,909 fixed-source runs are singletons; no join is possible in + this class. This does not exclude other backward-circuit improvements. + +[crosscheck.py](crosscheck.py) uses dynamic programming instead of greedy edge +selection and scalar basis propagation instead of sparse row propagation. Its +6,279 basis cases check every emitted block. Eleven primary controls cover +initial/final erasure, signs, rescaling, source aliasing, changed source/odd +numerator/frame, an endpoint-neutral prefix excursion, nonprofitable joining, +and phase boundaries. Four further independent semantic mutations reject. +The tests also cover all 343 triples over a stated seven-value signed domain, +early-ended helpers, endpoint-neutral extra instructions, input corruption and +receipt corruption. These are finite checks, not a formal proof of the full +multiplication theorem. + +## Pins, attribution and remaining scope + +Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`. Selected #626 source: +`660de893d27bb7abd1d5b01b1640207528a5c851`; #622 construction: +`f69477f4f6d3c7eb1f740b166881bffed4ffa9f6`; retained #543 bit supplier: +`2065fe4f72a914d907f1046603f5a36f17018535`. +[SOURCE-PINS.json](SOURCE-PINS.json) records every consumed source with exact +Git blob identities and full-payload SHA-256 hashes. Gzip container headers are +not mathematical inputs. The canonical word and event hashes are additionally +checked against the preserved #626 SPEC. The checker does not depend on a +future mutable selected-frontier pointer. + +Credit to Jeremy Kothe and the #622 Claude Code contributors; Chafik Boukhalfa's +#626 packaging; icekylinx's direct-delivery, scalar architecture and emitter +lineage; DreamingOfClouds' cold-helper and verifier work; Dugongue's preceding +circuits; eumemic's retained bit supplier; and the earlier contributors in +the [source notice](../complex-k492-owner-repair/NOTICE.md) and +[maintainer review](../../docs/research/community-k492-review.md). +Eumemic's #411 is also credited for its earlier explicit paid dyadic +microcircuits; the present result changes reuse between macros. + +@ellipsi2's #722 at `a0766ab0fab379e1997fadc3ca157578d57986c1` is the direct +methodological predecessor and comparison. Sagar Thakrar's #696 and #723 alter +single-macro preparation; the latter recodes numerators with signed digits. +No composition with those lowerings is asserted. #681 changes a raw factory, +#698 changes the frame search class and #719 studies a CK rank obstruction; +none is an implementation dependency. See [the claim](CLAIM.md) for their pins. +The final overlap check also found Chris Pagolu's #734 at +`21606831df4b08f79d87fd420c558a520dca571e`, which bounds signed-Horner prefixes +inside each macro. Its separate contribution is credited; this experiment +retains ordinary Horner preparation and instead changes work sharing between +macros. No combined savings with #734 are claimed. + +Prepared for **Jeffrey Cox (@namredips)** with substantial **OpenAI Codex +assistance** in research, implementation, proof analysis, testing and writing, +including one scoped AI reviewer who supplied the independent checker. This +does not claim independent human review. New work is Apache-2.0. + +The selected κ remains **0.001635527380375392** at the base commit. Native +geometry, paid profiles and global ownership are not redesigned; no new +assembly is submitted. Uniform compilation, common-label/mutable-basis +realization, hosting, precision/tape/recovery, analytic transfer and the bit +supplier assumptions remain inherited. This contribution neither proves a +stronger exponent nor closes those obligations. `upstream/` is untouched. diff --git a/research/complex-coefficient-rescaling/SOURCE-PINS.json b/research/complex-coefficient-rescaling/SOURCE-PINS.json new file mode 100644 index 0000000000..1dd9a8834a --- /dev/null +++ b/research/complex-coefficient-rescaling/SOURCE-PINS.json @@ -0,0 +1,29 @@ +{ + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "selected_source_head": "660de893d27bb7abd1d5b01b1640207528a5c851", + "construction_pr622_head": "f69477f4f6d3c7eb1f740b166881bffed4ffa9f6", + "retained_bit_pr543_head": "2065fe4f72a914d907f1046603f5a36f17018535", + "hash_policy": "SHA-256 of complete uncompressed payload for gzip; exact bytes otherwise. Git blob ids identify committed input containers but are not regeneration checks.", + "files": { + "research/complex-k492-owner-repair/data/SPEC.json": { + "payload_sha256": "2a2577ac526535826fed9d5f7f83f6e2e0ec058a146c64f7286720b995fa2323", + "git_blob": "cdc4f6ce03e96fd1ffc5a19926e1d0d4bce4e9de" + }, + "research/community-k492-audit/pr626/replay/mixed-global/base/providers/jp8/CANONICAL-WORD.json.gz": { + "payload_sha256": "fb4a8d14ed2a8048698bea6ae16f86163a1aa6c80f2eb622222eee5cdbce9b3b", + "git_blob": "7fd7cd1fefbb8b0e12397b355d9f6e227813bd58" + }, + "research/community-k492-audit/pr626/replay/mixed-global/base/providers/jp8/LOCAL-PROGRAMS.json.gz": { + "payload_sha256": "efe45ce7fb025a6f53cc9eb54e951ac2211a5ed927e689a049e4f68ca680654b", + "git_blob": "e22169a1633638213a5c63425a1919c7185f4c43" + }, + "research/complex-k492-owner-repair/code/hpe_emit_local.py": { + "payload_sha256": "7e4a6fbc38c8228157b6311457d1496bf460291393043932d2c365f004f77805", + "git_blob": "534fdc71f7641c704575efc038363d7eb206b2df" + }, + "research/complex-k492-owner-repair/code/hpe_audit_local.py": { + "payload_sha256": "6bd9a1e279c9c9e4f3767d9f82e537b559292906feb2ddab02f380fb6523a810", + "git_blob": "17bccb64fdca54f329a3ce16e369449cb76c2802" + } + } +} diff --git a/research/complex-coefficient-rescaling/VALIDATION.md b/research/complex-coefficient-rescaling/VALIDATION.md new file mode 100644 index 0000000000..33d3356240 --- /dev/null +++ b/research/complex-coefficient-rescaling/VALIDATION.md @@ -0,0 +1,63 @@ +# Validation and handoff + +Base commit: `66849e1475c930fd7732b1a0067ffee7e1e95f60`. +Platform: macOS arm64. Python versions: CPython 3.14.7 and 3.11.14. +No third-party Python dependencies. Assignment seed: 39. + +## Executed checks + +| Check | Result | +|---|---| +| `python3 -I -B research/complex-coefficient-rescaling/verify.py` | PASS; 10,338 incremental real primitives saved; 1,015 blocks; both 716-column projections | +| `python3 -I -O -B research/complex-coefficient-rescaling/verify.py` | Same receipt; validation does not depend on assertions | +| `python3.11 -I -B research/complex-coefficient-rescaling/verify.py` | Same receipt | +| `python3.11 -I -O -B research/complex-coefficient-rescaling/verify.py` | Same receipt | +| `python3 -I -B research/complex-coefficient-rescaling/test_verify.py` | Nine tests pass, including all 343 signed triples | +| `python3.11 -I -O -B research/complex-coefficient-rescaling/test_verify.py` | Same nine tests pass | +| `ruff check research/complex-coefficient-rescaling` | PASS after import/style corrections | +| `make selected-record-check` | PASS; selected κ remains `51110230636731/31250000000000000` | +| Local Markdown links and `git diff --cached --check` | PASS | + +The primary verifier checks 591 distinct add/scale cases used by the actual +JP8 programs. Unchanged macros then use their checked rational semantics in +the complete scalar projection; changed blocks execute their literal primitive +instructions. A separately implemented checker verifies every block using +scalar basis propagation, including arbitrary incoming W. Both exact positive +prefix maxima match the original selected contract. + +The independent segmentation DP evaluates 18,925 forward and 5,909 backward +candidate blocks. It matches the chosen spans and costs, and records the 49 +nonprofitable transitions. The full census and block hashes are in +`EXPECTED.json`; each block is reproduced from its source event interval. + +The tests reject an omitted profitable block, a correct-endpoint extra clear, +an early-ended helper, a changed source payload and an altered receipt. A +minimal source tree relocated into a path with spaces accepts gzip files +recompressed at another level/time and then rejects a changed decompressed +event. Eleven primary mathematical/interface controls and four further +independent semantic controls are recorded in the main receipt. + +One scoped AI reviewer checked the mathematics and implementation and authored +`crosscheck.py`. The reviewer independently corroborated the 10,338 incremental +saving and found no mathematical blocker. This is not independent human review. + +## Coordination and limits + +The initial full open-PR snapshot contained 551 PRs through #732. The final +intermediate snapshot contained 553 through #734, and the immediate +pre-submission snapshot contained 556 through #737; #696, #722 and #723 retained +their pinned heads. #734's body, head and changed-file inventory were inspected and its +distinct per-macro signed-Horner contribution was credited in the README. +GitHub reported no pinned coordination issue at either check, so the claim is +local. No separate reservation issue was opened. #738 arrived during submission; +its distinct Gaussian copy-floor result was checked for overlap. The single +submission is [PR #739](https://github.com/CrocSwap/integer-mult-bounds/pull/739). + +Only this research package is changed. No selected supplier, production +emitter, global invoice, frontier pointer or `upstream/` file is modified. +The full `make verify` target regenerates many unrelated historical and current +packages, so it was not run for this isolated research addition. The cold +supplier rebuild, global physical admission, Linux CI and Lean were not run or +claimed. Integrating the block-level private-work contract into the production +emitter remains future work. All inherited uniform/physical/analytic assumptions +remain as stated in the README and the selected construction's maintainer review. diff --git a/research/complex-coefficient-rescaling/crosscheck.py b/research/complex-coefficient-rescaling/crosscheck.py new file mode 100644 index 0000000000..1604c6130b --- /dev/null +++ b/research/complex-coefficient-rescaling/crosscheck.py @@ -0,0 +1,236 @@ +"""Independent segmentation and scalar-basis check of the local rescaling witness. + +Prepared for Jeff Cox (@namredips) with substantial OpenAI Codex assistance. +Apache-2.0. This checker does not import the planner or its cost functions. +""" + +from collections import Counter +from fractions import Fraction +from itertools import pairwise + +WORK = ("W", 0) + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def _log2_power(value): + """Integer division recognizes exact powers independently of bit lengths.""" + numerator, denominator = value.numerator, value.denominator + if numerator <= 0: + return None + exponent = 0 + while numerator % 2 == 0: + numerator //= 2 + exponent += 1 + while denominator % 2 == 0: + denominator //= 2 + exponent -= 1 + return exponent if numerator == denominator == 1 else None + + +def _horner_work(coefficient): + digits = bin(abs(coefficient.numerator))[2:] + denominator_power = _log2_power(Fraction(coefficient.denominator)) + require(coefficient != 0 and denominator_power is not None, + "crosscheck requires nonzero dyadic coefficients") + return len(digits) - 1 + digits.count("1") + denominator_power + + +def _runs(events): + """Maximal consecutive nonunit, full-frame, fixed-source cleanup runs.""" + phase, source, current, runs = None, None, [], [] + for index, event in enumerate(events): + if event[0] == "phase": + phase = event[1] + candidate = None + if (phase == "full_frame_cleanup" and event[0] == "scalar" + and event[2] == 1 and event[1][0] == "add"): + op = event[1] + target, source_register = tuple(op[1]), tuple(op[2]) + coefficient = Fraction(op[3], op[4]) + if (target[0] == source_register[0] == "L" + and target != source_register and abs(coefficient) != 1): + _horner_work(coefficient) + candidate = (index, coefficient, source_register) + if candidate is None or candidate[2] != source: + if current: + runs.append(current) + current = [] + if candidate is not None: + current.append(candidate) + source = candidate[2] + else: + source = None + if current: + runs.append(current) + return runs + + +def _optimal_partition(run): + """Dynamic programming over every permitted final block of each prefix. + + Minimize primitive cost, then prefer more blocks at equal cost. The latter + canonically cuts all zero-saving edges, avoiding needless work lifetimes. + """ + costs, partitions, candidate_blocks = [0], [[]], 0 + for stop in range(1, len(run) + 1): + best, best_partition, shift_cost = None, None, 0 + for start in range(stop - 1, -1, -1): + if start < stop - 1: + step = _log2_power(abs(run[start + 1][1] / run[start][1])) + if step is None: + break + shift_cost += abs(step) + block_cost = _horner_work(run[start][1]) + 2 + stop - start + shift_cost + partition = partitions[start] + [(run[start][0], run[stop - 1][0] + 1)] + key = (costs[start] + block_cost, -len(partition)) + candidate_blocks += 1 + if best is None or key < best: + best, best_partition = key, partition + costs.append(best[0]) + partitions.append(best_partition) + return costs[-1], partitions[-1], candidate_blocks + + +def _execute(values, circuit): + for instruction in circuit: + op, target = instruction[:2] + require(target in values, "circuit writes an undeclared register") + if op == "clear": + values[target] = Fraction(0) + elif op == "double": + values[target] *= 2 + elif op == "halve": + values[target] /= 2 + elif op == "neg": + values[target] = -values[target] + elif op in ("copy", "inc"): + source = instruction[2] + require(source in values, "circuit reads an undeclared register") + if op == "copy": + values[target] = values[source] + else: + require(instruction[3] in (-1, 1), "nonprimitive signed addition") + values[target] += instruction[3] * values[source] + else: + raise ValueError("unknown primitive: " + str(op)) + + +def _check_map(events, circuit): + """One scalar replay per basis vector, including the incoming work vector.""" + live = {tuple(event[1][i]) for event in events for i in (1, 2)} + registers = sorted(live | {WORK}) + for basis in registers: + actual = {register: Fraction(register == basis) for register in registers} + expected = actual.copy() + for event in events: + op = event[1] + expected[tuple(op[1])] += Fraction(op[3], op[4]) * expected[tuple(op[2])] + expected[WORK] = Fraction(0) + _execute(actual, circuit) + require(actual == expected, "block boundary differs on basis " + str(basis)) + return len(registers) + + +def _semantic_controls(events, circuit): + """The first selected block witnesses dirty work, erasure, sign and shift.""" + require(circuit[0] == circuit[-1] == ("clear", WORK), + "selected circuit must clear work at entry and exit") + mutations = [("missing_entry_clear", circuit[1:]), + ("missing_exit_clear", circuit[:-1])] + accumulate = next(i for i, op in enumerate(circuit) + if op[0] == "inc" and op[1] != WORK) + changed = list(circuit) + op = changed[accumulate] + changed[accumulate] = (*op[:3], -op[3]) + mutations.append(("wrong_accumulation_sign", changed)) + for index in range(accumulate + 1, len(circuit)): + if circuit[index][0] in ("double", "halve"): + changed = list(circuit) + op = changed[index] + changed[index] = ("halve" if op[0] == "double" else "double", op[1]) + mutations.append(("wrong_rescale_direction", changed)) + break + rejected = [] + for name, changed in mutations: + try: + _check_map(events, changed) + except ValueError as error: + require(str(error).startswith("block boundary differs"), + "negative control failed for an unrelated reason: " + name) + rejected.append(name) + else: + raise ValueError("semantic negative control accepted: " + name) + return rejected + + +def crosscheck(events, spans, lower_block): + """Check the complete restricted optimum and every supplied primitive map.""" + runs = _runs(events) + expected_spans, baseline, optimum, candidate_blocks = [], 0, 0, 0 + rejected_edges, profitable_edges = Counter(), Counter() + incompatible_edges = 0 + for run in runs: + baseline += sum(_horner_work(entry[1]) + 3 for entry in run) + cost, partition, checked = _optimal_partition(run) + optimum += cost + candidate_blocks += checked + expected_spans.extend(span for span in partition if span[1] - span[0] > 1) + for previous, following in pairwise(run): + left, right = abs(previous[1]), abs(following[1]) + step = _log2_power(right / left) + if step is None: + incompatible_edges += 1 + continue + gain = _horner_work(right) + 2 - abs(step) + if gain > 0: + profitable_edges["equal_magnitude" if left == right else "distinct_magnitude"] += 1 + else: + rejected_edges[(str(left), str(right), step, -2 * gain)] += 1 + supplied_spans = [tuple(span) for span in spans] + require(supplied_spans == expected_spans, + "provided spans differ from canonical dynamic-programming optimum") + basis_cases, actual_saved, primitive_count, controls = 0, 0, 0, [] + for start, stop in supplied_spans: + block = events[start:stop] + circuit = lower_block(block) + coefficients = [Fraction(*event[1][3:]) for event in block] + standalone = sum(_horner_work(q) + 3 for q in coefficients) + block_cost = _horner_work(coefficients[0]) + 2 + len(block) + block_cost += sum(abs(_log2_power(abs(right / left))) + for left, right in pairwise(coefficients)) + require(len(circuit) == block_cost, + "emitted block length differs from independent cost") + basis_cases += _check_map(block, circuit) + actual_saved += standalone - len(circuit) + primitive_count += len(circuit) + if not controls: + controls = _semantic_controls(block, circuit) + require(actual_saved == baseline - optimum, + "emitted primitive length differs from independent optimum") + return { + "status": "PASS_INDEPENDENT_DP_AND_SCALAR_BASIS", + "eligible_additions": sum(map(len, runs)), + "maximal_fixed_source_runs": len(runs), + "largest_run": max(map(len, runs), default=0), + "dp_candidate_blocks_checked": candidate_blocks, + "selected_blocks": len(supplied_spans), + "scalar_basis_inputs_checked": basis_cases, + "selected_block_component_primitives": primitive_count, + "eligible_singleton_component_primitives": baseline, + "eligible_optimal_component_primitives": optimum, + "saved_real_component_primitives": 2 * actual_saved, + "profitable_edges": dict(sorted(profitable_edges.items())), + "incompatible_odd_numerator_edges": incompatible_edges, + "nonpositive_transition_count": sum(rejected_edges.values()), + "nonpositive_transition_census": [ + {"from_magnitude": left, "to_magnitude": right, "shift": step, + "extra_real_primitives_if_merged": extra, "count": count} + for (left, right, step, extra), count in sorted(rejected_edges.items()) + ], + "semantic_negative_controls_rejected": controls, + "scope": "Finite primitive maps on arbitrary live/work input; exact DP optimum only within fixed-source, ordered power-of-two rescaling blocks.", + } diff --git a/research/complex-coefficient-rescaling/lowering.py b/research/complex-coefficient-rescaling/lowering.py new file mode 100644 index 0000000000..481dd16c42 --- /dev/null +++ b/research/complex-coefficient-rescaling/lowering.py @@ -0,0 +1,143 @@ +"""Exact private-work circuits for fixed-source dyadic cleanup blocks. + +Prepared for Jeff Cox (@namredips) with substantial OpenAI Codex assistance. +Apache-2.0. The equal-magnitude comparison follows @ellipsi2's PR #722; +the original Horner circuit follows the attributed PR #626 emitter. +""" + +from fractions import Fraction + +WORK = ("W", 0) + + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def power_exponent(value): + """Return k for value = 2**k, or None for other positive rationals.""" + a, b = value.numerator, value.denominator + if a <= 0 or a & (a - 1) or b & (b - 1): + return None + return a.bit_length() - b.bit_length() + + +def coefficient(op): + q = Fraction(op[3], op[4]) + require(q != 0 and power_exponent(Fraction(1, q.denominator)) is not None, + "addition coefficient must be nonzero and dyadic") + return q + + +def prepare_cost(q): + a, b = abs(q.numerator), q.denominator + return 1 + a.bit_length() - 1 + a.bit_count() + b.bit_length() - 1 + + +def shift(register, exponent): + return [("double" if exponent > 0 else "halve", register)] * abs(exponent) + + +def prepare(source, q): + """Original clear, binary Horner, then halve circuit (one real component).""" + a, b = abs(q.numerator), q.denominator + require(a > 0 and b & (b - 1) == 0, "non-dyadic preparation") + ops = [("clear", WORK), ("inc", WORK, source, 1)] + for bit in bin(a)[3:]: + ops.append(("double", WORK)) + if bit == "1": + ops.append(("inc", WORK, source, 1)) + ops.extend(shift(WORK, -(b.bit_length() - 1))) + return ops + + +def lower_macro(op): + tag, target = op[0], tuple(op[1]) + require(target != WORK, "work register aliases macro target") + if tag == "clear": + return [("clear", target)] + if tag == "copy": + source = tuple(op[2]) + require(source != WORK, "work register aliases macro source") + return [("copy", target, source)] + if tag == "scale": + q = Fraction(op[2], op[3]) + exponent = power_exponent(abs(q)) + require(exponent is not None, "scale must be a signed power of two") + return shift(target, exponent) + ([("neg", target)] if q < 0 else []) + require(tag == "add", "unknown scalar macro") + source, q = tuple(op[2]), coefficient(op) + require(source != target and source != WORK, "addition register alias") + return prepare(source, q) + [("inc", target, WORK, 1 if q > 0 else -1), + ("clear", WORK)] + + +def block_data(events): + require(len(events) >= 2, "block must contain at least two additions") + source, magnitudes = None, [] + for event in events: + require(event[0] == "scalar" and event[2] == 1 and event[1][0] == "add", + "block must contain consecutive full-frame additions") + op = event[1] + target, current_source, q = tuple(op[1]), tuple(op[2]), coefficient(op) + require(target[0] == current_source[0] == "L", "block uses non-live register") + require(target != current_source, "block mutates its source") + require(abs(q) != 1, "unit coefficients are outside this experiment") + if source is None: + source = current_source + require(current_source == source, "block changes source") + if magnitudes: + require(power_exponent(abs(q) / magnitudes[-1]) is not None, + "block changes odd numerator") + magnitudes.append(abs(q)) + return source, magnitudes + + +def lower_block(events): + source, magnitudes = block_data(events) + ops = prepare(source, magnitudes[0]) + for i, event in enumerate(events): + if i: + ops.extend(shift(WORK, power_exponent(magnitudes[i] / magnitudes[i - 1]))) + q = coefficient(event[1]) + ops.append(("inc", tuple(event[1][1]), WORK, 1 if q > 0 else -1)) + ops.append(("clear", WORK)) + return ops + + +def plans(events, mode): + """All profitable adjacent merges in a fixed word; no gate reordering. + + The end-clear + next preparation saved by each edge is independent of + other edges. Equal/negative savings are cut to keep shorter lifetimes. + """ + require(mode in ("equal", "rescale"), "unknown planning mode") + phase, run, result, previous = None, [], [], None + for index, event in enumerate(events): + if event[0] == "phase": + phase = event[1] + eligible = (phase == "full_frame_cleanup" and event[0] == "scalar" + and event[2] == 1 and event[1][0] == "add") + current = None + if eligible: + op, q = event[1], coefficient(event[1]) + eligible = (abs(q) != 1 and op[1][0] == op[2][0] == "L" + and op[1] != op[2]) + if eligible: + current = (tuple(op[2]), abs(q)) + merge = False + if previous is not None and current is not None and previous[0] == current[0]: + k = power_exponent(current[1] / previous[1]) + merge = (k is not None and (mode == "rescale" or k == 0) + and abs(k) < 1 + prepare_cost(current[1])) + if not merge: + if len(run) > 1: + result.append((run[0], run[-1] + 1)) + run = [] + if eligible: + run.append(index) + previous = current + if len(run) > 1: + result.append((run[0], run[-1] + 1)) + return result diff --git a/research/complex-coefficient-rescaling/test_verify.py b/research/complex-coefficient-rescaling/test_verify.py new file mode 100644 index 0000000000..55a36cc36a --- /dev/null +++ b/research/complex-coefficient-rescaling/test_verify.py @@ -0,0 +1,112 @@ +"""Focused adversarial tests; run with Python's standard-library unittest.""" + +import copy +import gzip +import itertools +import json +import subprocess +import sys +import tempfile +import unittest +from fractions import Fraction +from pathlib import Path +from unittest.mock import patch + +HERE = Path(__file__).resolve().parent +sys.path.insert(0, str(HERE)) + +import verify +from crosscheck import crosscheck +from lowering import WORK, lower_block, plans + + +def stream(coefficients): + events = [["phase", "full_frame_cleanup"]] + for target, q in enumerate(coefficients, 1): + q = Fraction(q) + events.append(["scalar", ["add", ["L", target], ["L", 0], q.numerator, q.denominator], 1]) + return events + [["phase", "done"]] + + +class RescalingTests(unittest.TestCase): + def test_exhaustive_small_signed_domain(self): + # Includes different odd families and both profitable and losing shifts. + domain = [Fraction(1, 8), Fraction(-1, 2), Fraction(3, 2), + Fraction(-3), Fraction(2), Fraction(-8), Fraction(16)] + for coefficients in itertools.product(domain, repeat=3): + events = stream(coefficients) + crosscheck(events, plans(events, "rescale"), lower_block) + + def test_exact_but_unprofitable_shift(self): + events = stream([16, Fraction(1, 2)]) + self.assertEqual(plans(events, "rescale"), []) + result = crosscheck(events, [], lower_block) + self.assertEqual(result["nonpositive_transition_census"][0]["extra_real_primitives_if_merged"], 2) + + def test_equal_cost_tie_keeps_work_lifetime_short(self): + events = stream([8, Fraction(1, 2)]) + self.assertEqual(plans(events, "rescale"), []) + crosscheck(events, [], lower_block) + + def test_missing_profitable_block_is_rejected(self): + with self.assertRaisesRegex(ValueError, "dynamic-programming optimum"): + crosscheck(stream([Fraction(3, 2), 3]), [], lower_block) + + def test_endpoint_neutral_extra_work_is_rejected(self): + events = stream([Fraction(3, 2), 3]) + def redundant(block): + return lower_block(block) + [("clear", WORK)] + with self.assertRaisesRegex(ValueError, "independent cost"): + crosscheck(events, plans(events, "rescale"), redundant) + + def test_early_ended_register_is_rejected(self): + native, programs, _ = verify.load_inputs() + events = programs["forward"] + spans = plans(events, "rescale") + native = copy.deepcopy(native) + native["final"][events[spans[0][0]][1][2][1]] = 0 + with self.assertRaisesRegex(ValueError, "early-ended"): + verify.replay(events, native, spans, "forward") + + def test_all_mathematical_controls(self): + self.assertEqual(len(verify.negative_controls()), 11) + + def test_relocated_inputs_recompression_and_corruption(self): + pins = json.loads((HERE / "SOURCE-PINS.json").read_text()) + with tempfile.TemporaryDirectory(prefix="rescaling space ") as directory: + root = Path(directory) + for name in pins["files"]: + source, destination = verify.ROOT / name, root / name + destination.parent.mkdir(parents=True, exist_ok=True) + payload = source.read_bytes() + if name.endswith(".gz"): + payload = gzip.compress(gzip.decompress(payload), compresslevel=1, mtime=123) + destination.write_bytes(payload) + with patch.object(verify, "ROOT", root): + verify.load_inputs() + target = root / verify.PROVIDER / "LOCAL-PROGRAMS.json.gz" + programs = json.loads(gzip.decompress(target.read_bytes())) + programs["forward"].pop() + target.write_bytes(gzip.compress(json.dumps(programs).encode())) + with self.assertRaisesRegex(ValueError, "source payload changed"): + verify.load_inputs() + + def test_corrupt_receipt_is_rejected(self): + with tempfile.TemporaryDirectory() as directory: + here = Path(directory) + for name in ("verify.py", "lowering.py", "crosscheck.py", "SOURCE-PINS.json"): + (here / name).write_bytes((HERE / name).read_bytes()) + receipt = json.loads((HERE / "EXPECTED.json").read_text()) + receipt["orientations"]["forward"]["incremental_real_saving"] -= 1 + (here / "EXPECTED.json").write_text(json.dumps(receipt)) + # The public entry point still runs all checks before the comparison. + code = ("import sys; from pathlib import Path; sys.path.insert(0, sys.argv[1]); " + "import verify; verify.ROOT=Path(sys.argv[2]); sys.argv=[sys.argv[0]]; verify.main()") + run = subprocess.run([sys.executable, "-I", "-B", "-c", code, str(here), str(verify.ROOT)], + capture_output=True, text=True, check=False) + self.assertNotEqual(run.returncode, 0) + self.assertIn("committed receipt mismatch", run.stderr) + + +if __name__ == "__main__": + unittest.main() diff --git a/research/complex-coefficient-rescaling/verify.py b/research/complex-coefficient-rescaling/verify.py new file mode 100644 index 0000000000..7f508bcbaf --- /dev/null +++ b/research/complex-coefficient-rescaling/verify.py @@ -0,0 +1,330 @@ +"""Replay the scoped JP8 coefficient-rescaling witness, offline and read-only.""" + +import gzip +import hashlib +import json +import sys +from collections import Counter +from fractions import Fraction as Q +from itertools import pairwise +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +sys.path.insert(0, str(HERE)) + +from lowering import ( + WORK, + block_data, + coefficient, + lower_block, + lower_macro, + plans, + power_exponent, + prepare_cost, + require, +) + +PROVIDER = "research/community-k492-audit/pr626/replay/mixed-global/base/providers/jp8/" +SPEC = "research/complex-k492-owner-repair/data/SPEC.json" + + +def digest(value): + return hashlib.sha256(json.dumps(value, sort_keys=True, separators=(",", ":")).encode()).hexdigest() + + +def load_inputs(): + pins = json.loads((HERE / "SOURCE-PINS.json").read_text()) + data = {} + for path, expected in pins["files"].items(): + payload = (ROOT / path).read_bytes() + if path.endswith(".gz"): + payload = gzip.decompress(payload) + require(hashlib.sha256(payload).hexdigest() == expected["payload_sha256"], + "source payload changed: " + path) + if path.endswith((".json", ".json.gz")): + data[path] = json.loads(payload) + native = data[PROVIDER + "CANONICAL-WORD.json.gz"] + programs = data[PROVIDER + "LOCAL-PROGRAMS.json.gz"] + spec = data[SPEC]["providers"]["jp8"] + for name in ("CANONICAL-WORD.json.gz", "LOCAL-PROGRAMS.json.gz"): + require(digest(data[PROVIDER + name]) == spec["artifact_semantic_sha256"][name], + "selected SPEC artifact binding failed: " + name) + for orientation, events in programs.items(): + require(digest(events) == spec["program_hashes"][orientation], "selected program binding failed") + require(native["v"] == 112 and native["R"] == 492 and native["h"] == 9, + "unexpected supplier dimensions") + return native, programs, spec + + +class Machine: + """Sparse exact linear forms and a separate positive prefix envelope.""" + + def __init__(self, registers): + self.rows = {r: {i: Q(1)} for i, r in enumerate(registers)} + self.norms = {r: Q(1) for r in registers} + self.prefix = Q(1) + + def update(self, target, source, scalar): + require(target != source, "interpreter received aliased addition") + row = self.rows.setdefault(target, {}) + for col, value in self.rows[source].items(): + new = row.get(col, Q(0)) + scalar * value + if new: + row[col] = new + else: + row.pop(col, None) + self.norms[target] = self.norms.get(target, Q(0)) + abs(scalar) * self.norms[source] + + def primitive(self, op): + tag, target = op[:2] + if tag == "clear": + self.rows[target], self.norms[target] = {}, Q(0) + elif tag == "copy": + self.rows[target], self.norms[target] = dict(self.rows[op[2]]), self.norms[op[2]] + elif tag == "inc": + require(op[3] in (-1, 1), "non-unit primitive addition") + self.update(target, op[2], op[3]) + else: + require(tag in ("double", "halve", "neg"), "unknown primitive") + scalar = {"double": Q(2), "halve": Q(1, 2), "neg": Q(-1)}[tag] + self.rows[target] = {j: scalar * x for j, x in self.rows[target].items()} + self.norms[target] *= abs(scalar) + self.prefix = max(self.prefix, self.norms[target]) + + def macro(self, op): + tag, target = op[0], tuple(op[1]) + if tag == "add": + source, q = tuple(op[2]), coefficient(op) + self.prefix = max(self.prefix, abs(q.numerator) * self.norms[source]) + self.update(target, source, q) + self.rows[WORK], self.norms[WORK] = {}, Q(0) + elif tag == "scale": + q = Q(op[2], op[3]) + require(power_exponent(abs(q)) is not None, "invalid scale") + self.rows[target] = {j: q * x for j, x in self.rows[target].items()} + self.norms[target] *= abs(q) + elif tag in ("clear", "copy"): + self.primitive((tag, target, tuple(op[2])) if tag == "copy" else (tag, target)) + else: + raise ValueError("unknown macro") + self.prefix = max(self.prefix, self.norms[target]) + + +def macro_cost(op): + if op[0] in ("clear", "copy"): + return 1 + if op[0] == "add": + return prepare_cost(coefficient(op)) + 2 + q = Q(op[2], op[3]) + exponent = power_exponent(abs(q)) + require(exponent is not None, "invalid scale cost") + return abs(exponent) + int(q < 0) + + +def check_macro_library(programs): + """Certify every unchanged arithmetic macro type on independent local inputs.""" + cases = set() + for events in programs.values(): + for event in events: + if event[0] != "scalar": + continue + op = event[1] + if op[0] == "add": + cases.add(("add", coefficient(op))) + elif op[0] == "scale": + cases.add(("scale", Q(op[2], op[3]))) + target, source = ("L", 0), ("L", 1) + for tag, q in sorted(cases): + op = ([tag, list(target), list(source), q.numerator, q.denominator] + if tag == "add" else [tag, list(target), q.numerator, q.denominator]) + actual, reference = Machine([target, source, WORK]), Machine([target, source, WORK]) + primitives = lower_macro(op) + for primitive in primitives: + actual.primitive(primitive) + reference.macro(op) + require(actual.rows == reference.rows, "macro library endpoint mismatch") + require(actual.prefix == reference.prefix, "macro library prefix mismatch") + require(len(primitives) == macro_cost(op), "macro library cost mismatch") + return len(cases) + + +def replay(events, native, spans, orientation): + require(orientation in ("forward", "backward"), "unknown orientation") + n = 2 * native["v"] + native["R"] + machine = Machine([("L", r) for r in range(n)] + [WORK]) + selected = dict(spans) + require(len(selected) == len(spans), "duplicate block starts") + paid, cost, index, phase = Counter(), 0, 0, None + blocks = [] + while index < len(events): + event = events[index] + if event[0] == "phase": + phase = event[1] + if index in selected: + stop = selected[index] + block = events[index:stop] + require(phase == "full_frame_cleanup", "block outside cleanup") + source, magnitudes = block_data(block) + registers = {source} | {tuple(e[1][1]) for e in block} + require(all(native["final"][r[1]] == 1 for r in registers), "block touches early-ended register") + require(not machine.rows[WORK], "work not clear on block entry") + reference_rows = {r: dict(machine.rows[r]) for r in registers} + reference = Machine([]) + reference.rows = reference_rows + reference.norms = {r: machine.norms[r] for r in registers} + reference.prefix = machine.prefix + for old_event in block: + reference.macro(old_event[1]) + primitives = lower_block(block) + for primitive in primitives: + machine.primitive(primitive) + require(all(machine.rows[r] == reference.rows[r] for r in registers | {WORK}), + "block changed live-register boundary or left private work") + require(all(machine.norms[r] == reference.norms[r] for r in registers), + "block changed live positive envelope") + require(machine.prefix <= reference.prefix, "block exceeded original prefix envelope") + old_cost = sum(macro_cost(e[1]) for e in block) + require(len(primitives) < old_cost, "unprofitable block") + distinct = sum(a != b for a, b in pairwise(magnitudes)) + blocks.append({"start": index, "stop": stop, "source": source[1], + "distinct_transitions": distinct, + "real_primitives_before": 2 * old_cost, + "real_primitives_after": 2 * len(primitives), + "primitive_sha256": digest(primitives)}) + cost += len(primitives) + index = stop + continue + if event[0] == "scalar": + machine.macro(event[1]) + cost += macro_cost(event[1]) + elif event[0] == "climb": + paid[event[5]] += 1 + elif event[0] == "center": + paid[event[4]] += 1 + index += 1 + v = native["v"] + for r in range(n): + expected = {r: Q(1)} + if orientation == "forward" and v <= r < 2 * v: + expected[r - v] = Q(1) + if orientation == "backward" and r < v: + expected[v + r] = Q(-1) + require(machine.rows[("L", r)] == expected, "full scalar projection endpoint mismatch") + require(all(not row for reg, row in machine.rows.items() if reg[0] != "L"), + "private register not erased") + require(machine.prefix < 2**192, "192-bit local prefix allowance exceeded") + require(dict(paid) == {int(r): k for r, k in native["local_profile"].items()}, + "paid recursive profile changed") + return {"orientation": orientation, "all_live_columns": n, "arbitrary_work_input": True, + "real_component_primitives": 2 * cost, "prefix_l1_upper": str(machine.prefix), + "paid_profile": {str(r): count for r, count in sorted(paid.items())}, "blocks": blocks} + + +def reject(call, name): + try: + call() + except (ValueError, KeyError): + return name + raise ValueError("negative control accepted: " + name) + + +def negative_controls(): + def event(t, s, p, q=1, frame=1): + return ["scalar", ["add", ["L", t], ["L", s], p, q], frame] + + block = [event(1, 0, 3, 2), event(2, 0, -3, 1)] + good = lower_block(block) + registers = [("L", i) for i in range(3)] + [WORK] + baseline = Machine(registers) + for e in block: + baseline.macro(e[1]) + + def endpoint(ops): + machine = Machine(registers) + for op in ops: + machine.primitive(op) + require(machine.rows == baseline.rows, "control endpoint") + require(machine.prefix <= baseline.prefix, "control prefix") + + endpoint(good) + controls = [reject(lambda: endpoint(good[1:]), "omitted_initial_clear"), + reject(lambda: endpoint(good[:-1]), "omitted_final_clear")] + bad = list(good) + i = next(i for i, op in enumerate(bad) if op[0] == "inc" and op[1] == ("L", 2)) + bad[i] = ("inc", ("L", 2), WORK, 1) + controls.append(reject(lambda: endpoint(bad), "wrong_accumulation_sign")) + bad = list(good) + i = len(bad) - 3 + require(bad[i] == ("double", WORK), "bad rescale-control fixture") + bad[i] = ("halve", WORK) + controls.append(reject(lambda: endpoint(bad), "inverted_rescale")) + bad = list(good) + bad[-1:-1] = [("double", WORK)] * 8 + [("halve", WORK)] * 8 + controls.append(reject(lambda: endpoint(bad), "endpoint_neutral_prefix_excursion")) + for name, mutated in ( + ("source_alias", [event(0, 0, 3, 2), block[1]]), + ("changed_source", [block[0], event(2, 1, -3)]), + ("changed_odd_numerator", [block[0], event(2, 0, -5)]), + ("wrong_frame", [block[0], event(2, 0, -3, frame=0)]), + ): + controls.append(reject(lambda m=mutated: lower_block(m), name)) + losing = [["phase", "full_frame_cleanup"], event(1, 0, 16), event(2, 0, 1, 2)] + require(plans(losing, "rescale") == [], "unprofitable rescaling selected") + controls.append("unprofitable_exact_rescaling_cut") + boundary = [["phase", "full_frame_cleanup"], block[0], ["phase", "done"], block[1]] + require(plans(boundary, "rescale") == [], "block crossed phase boundary") + controls.append("phase_boundary_cut") + return controls + + +def build_receipt(): + from crosscheck import crosscheck + + native, programs, spec = load_inputs() + result = {"schema": "complex-coefficient-rescaling/1", "assignment_seed": 39, + "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60", + "macro_library_cases": check_macro_library(programs), + "negative_controls": negative_controls(), "orientations": {}} + for orientation in ("forward", "backward"): + events = programs[orientation] + spans, equal_spans = plans(events, "rescale"), plans(events, "equal") + original = replay(events, native, [], orientation) + equal = replay(events, native, equal_spans, orientation) + rescaled = replay(events, native, spans, orientation) + original_contract = spec["complete_contract"]["local"][orientation] + require(original["orientation"] == orientation, "orientation mismatch") + require(original["real_component_primitives"] == original_contract["real_component_primitives"], + "original count differs from selected contract") + require(original["prefix_l1_upper"] == original_contract["prefix_l1"], + "original prefix differs from selected contract") + independent = crosscheck(events, spans, lower_block) + result["orientations"][orientation] = { + "original_real_primitives": original["real_component_primitives"], + "equal_magnitude_real_primitives": equal["real_component_primitives"], + "rescaled_real_primitives": rescaled["real_component_primitives"], + "incremental_real_saving": equal["real_component_primitives"] - rescaled["real_component_primitives"], + "equal_magnitude_blocks": len(equal_spans), "rescaled_blocks": len(spans), + "all_live_columns": rescaled["all_live_columns"], "arbitrary_work_input": True, + "original_prefix_l1": original["prefix_l1_upper"], + "equal_prefix_l1": equal["prefix_l1_upper"], + "rescaled_prefix_l1": rescaled["prefix_l1_upper"], + "paid_profile": rescaled["paid_profile"], + "blocks": rescaled["blocks"], "independent": independent, + } + return result + + +def main(): + require(len(sys.argv) == 1, "usage: python3 -I -B research/complex-coefficient-rescaling/verify.py") + result = build_receipt() + require(result == json.loads((HERE / "EXPECTED.json").read_text()), "committed receipt mismatch") + forward = result["orientations"]["forward"] + print("PASS_JP8_COEFFICIENT_RESCALING" + f" incremental_real_saved={forward['incremental_real_saving']}" + f" blocks={forward['rescaled_blocks']} columns=716 orientations=2" + f" controls={len(result['negative_controls'])}") + + +if __name__ == "__main__": + main()