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lumbda/quantum/mod-inv-by-dialog-gcd.lsp
russell@unturf.com 1665893321
factory + quantum + sweep-doctrine: AGPLv3 share-back from foxhop ecdsa 
29 new files publish factory infra (V2 autoscaler with live VRAM
sampling + EWMA peak tracking, HUGE solo-dispatch, two-tier DLQ/rDLQ
classifier + retry), general quantum circuit primitives (Cuccaro
ripple-carry adder, Clifford gate library, Clifford tableau simulator,
mod-arith family, dialog GCD reversible inverse, Karatsuba multiplier,
Solinas fast reduction), and a TCRAUDT reducer harness. Originally
developed in ~/git/www.foxhop.net/ecdsa/ for secp256k1 attack-surface
research; published upstream as obligated by AGPLv3.

Parametrization contract at factory/CONTRACT.md. Consumers export
LUMBDA_REPO_DIR + LUMBDA_QUEUE_DIR + LUMBDA_BACKEND_CMD + LUMBDA_EMITTER_CMD
then exec factory scripts. No fork-and-modify; single source of truth
upstream.

Integration tests gate 7 V2 defect classes that wedged a live factory
on 2026-06-12 (skewed-demand starve, zero-floor reservation,
multi-tier greedy, +-25%% damping, cold-start ramp, DLQ surge halve,
post-damp CPU ceiling) + 28 DLQ classifier cases (auto-retry vs
escalate partition) + bash -n syntax lint across every script.

GPU backend stays in consumer trees; rationale in
factory/GPU-BACKEND-NOTE.md. Bend wire protocol + gpu-worker.lsp
already upstream at examples/cuda-fanout/.

make factory-lint                bash -n on every factory/*.sh
make test-integration            V2 reducer + DLQ classifier + syntax gate
make sweep-doctrine              TCRAUDT reducer gate (serial)
make sweep-doctrine-parallel     xargs -P fan-out

Verified on neoblanka: factory-lint 12 scripts PASS; test-integration
14 V2 cases + 28 DLQ classifier cases + 12 syntax cases all PASS.
2026-06-14 10:37:35 -04:00

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;;; mod-inv-by-dialog-gcd.lsp — Phase B sweep-005: DIALOG_GCD lever.
;;;
;;; Ports HEAD's DIALOG_GCD production wiring
;;; (`configure_ecdsafail_submission_route` at
;;; `~/git/ecdsafail-challenge/src/point_add/mod.rs:31052-31257`) onto
;;; our Bernstein-Yang / Kaliski substrate. See dialog-gcd-design.md
;;; for which HEAD knobs map vs which are HEAD-substrate-specific.
;;;
;;; Three actionable HEAD levers ship here:
;;;
;;; (D1) Smooth linear width envelope per step. HEAD's
;;; `dialog_gcd_tobitvector_active_width`
;;; (mod.rs:24452-24459) replaces our coarse step-function
;;; `mib-uv-width` with a monotone-decreasing formula:
;;;
;;; ideal = N - step * SLOPE + MARGIN
;;; rounded = 2 * ceiling(max(ideal, 1) / 2)
;;; width = clamp(rounded, 1, N)
;;;
;;; At every iter (not only the late half) u/v ops run at the
;;; truncated width. HEAD's production tuning at n=256:
;;; SLOPE = 0.711, MARGIN = 26.
;;;
;;; (D2) Truncated comparator window. HEAD's
;;; `dialog_gcd_cmp_gt_truncated_into_width` (mod.rs:24319)
;;; compares only the top COMPARE_BITS slice of u/v. Sound
;;; because by D1 the high bits above active_width are |0>;
;;; comparing only the top comparator-bits of the active
;;; window is value-exact on the verifier support. HEAD's
;;; production: COMPARE_BITS = 56 at n=256.
;;;
;;; (D3) ACTIVE_ITERATIONS truncation. HEAD's
;;; `dialog_gcd_active_iterations` (mod.rs:24243-24248) caps
;;; the forward sweep at fewer than 2n iters. The verifier-
;;; reachable support converges before 2n; rare overflow is
;;; caught by the Fiat-Shamir reroll machinery. HEAD's
;;; production: 395 at n=256. We do NOT have a reroll
;;; machinery — we VERIFY correctness on every tested input;
;;; cap is set conservatively per-width.
;;;
;;; HEAD knobs that DO NOT map onto our substrate (no-op here):
;;;
;;; DIALOG_GCD_HOST_GATED — needs HEAD's `dialog_log`
;;; register (we have no equivalent)
;;; DIALOG_GCD_APPLY_WINDOW_BLOCKS — applies to HEAD's apply-phase
;;; only (we have no apply-phase)
;;; DIALOG_GCD_BODY_HOST_CIN — phase tracking primitive needed
;;; (pattern 4, not yet shipped)
;;; DIALOG_GCD_FUSED_BRANCH_BITS — HEAD's control-flow shape
;;; diverges from ours
;;;
;;; HEAD knobs landed in v2 (this file, sweep-006):
;;;
;;; DIALOG_GCD_LATE_BORROW_UV_HIGH — borrow u[active..active+uv-w] as
;;; the masking ancilla for ctrl-cuccaro-sub!/add!. Premise:
;;; bits u[uv-w..n+1] are |0> by our width-truncation envelope. We
;;; alias them as the mask scratch via offset-aware ccx-mask +
;;; cuccaro-sub-offset! / cuccaro-add-offset!, computing the mask
;;; in-place on u's high zero slice and uncomputing after. Peak
;;; qubits drop by uv-w on every iteration where the borrow
;;; engages (uv-w + uv-w <= n+1). Engagement gate:
;;; 2 * uv-w <= n+1
;;; HEAD ref: dialog_gcd_pick_borrow_slice (mod.rs:24699-24712),
;;; dialog_gcd_pick_runway_safe_borrow_slice (mod.rs:26328-26354),
;;; production wire at mod.rs:31227.
;;;
;;; DIALOG_GCD_ODD_U_LOWBIT_FASTPATH — skip lane 0 of the cswap +
;;; ctrl-cuccaro-sub!/add! body. Premise: u stays odd across
;;; every Kaliski iter (binary-GCD invariant; p is prime so
;;; initial u=p is odd; v_w-=u when both odd produces even v_w
;;; which gets shifted right; the swap controlled by a_f preserves
;;; u-odd because a_f = (f AND NOT u[0]) is zero whenever u is
;;; odd, so the cswap on lane 0 never fires). Under that
;;; invariant, the lane-0 mask compute collapses to cx(ctrl,
;;; v_w[0]) (a_f's branch never engages on lane 0 because cswap
;;; never swapped it) and the body adder can start at bit 1. HEAD
;;; ref: dialog_gcd_controlled_sub_selected lane-0 skip at
;;; mod.rs:24747-24758, ditto add at mod.rs:24831-24841, cswap
;;; skip at mod.rs:24944, production wire at mod.rs:31256.
;;;
;;; On HEAD this fastpath co-tunes with the Fiat-Shamir reroll;
;;; our substrate verifies every input, so we GATE-test soundness
;;; at circuit build by classically tracing u[0] across every
;;; iteration and erroring if u ever lands on even.
;;;
;;; ── Sign / correction handling ──────────────────────────────────
;;;
;;; classical-kaliski-trace runs the SAME classical Kaliski loop body
;;; as the quantum circuit, parameterized by the iteration count. When
;;; we cap iters at *dgcd-active-iters* we MUST recompute K-correct and
;;; the trace at the SAME capped count, else the forward & backward
;;; sweeps disagree and free! trips on dirty registers.
;;;
;;; Soundness gate: for each input a we verify
;;;
;;; classical-kaliski-r-final(a, p, iters-cap, n+1) * K = a^{-1} mod p
;;;
;;; at circuit-build time. If the cap is too aggressive for some a, K
;;; would have to differ per-a, which our 1-K-fits-all wiring can't
;;; support. We detect this and ERROR, NOT silently drop.
;;;
;;; All ancillae return to |0> by classical-replay backward sweep on
;;; the capped trace (mirrors mod-inv-by-refined!'s R1).
;;; ── *field-prime* convention ─────────────────────────────────────
;;;
;;; Dialog-GCD primitives are field-prime agnostic: classical Kaliski
;;; trace consumes p as integer arg, never reads *field-prime* directly.
;;; Consumers binding *field-prime* upstream-style still need to pass p
;;; through Kaliski entry points (mod-inv-by-dialog-gcd! &c). Width
;;; derives from caller's n+1 arg or (bit-length p). See quantum/README.md.
(load "quantum/gates.lsp")
(load "quantum/adder.lsp")
(load "quantum/mod-arith.lsp")
(load "quantum/mod-inv-by.lsp")
;;; ── knob flags ────────────────────────────────────────────────────
;;; *mod-inv-by-dialog-gcd* — main dispatcher.
;;;
;;; When non-#f, mod-inv-by! routes through mod-inv-by-dialog-gcd!.
;;; Default #f so existing sweeps reproduce byte-for-byte.
(define *mod-inv-by-dialog-gcd* #f)
;;; *dgcd-width-margin* — HEAD's DIALOG_GCD_WIDTH_MARGIN.
;;;
;;; Added to the ideal width per step. Default 37 = HEAD's pre-tuning
;;; baseline (mod.rs:24438). HEAD's production tightens to 26.
(define *dgcd-width-margin* 37)
;;; *dgcd-width-slope-x1000* — HEAD's DIALOG_GCD_WIDTH_SLOPE_X1000.
;;;
;;; Per-step shrink rate × 1000 (so an integer knob). Default 708 ~=
;;; 0.5 * 1.415 (HEAD's baseline at mod.rs:24449). HEAD's production:
;;; 711.
(define *dgcd-width-slope-x1000* 708)
;;; *dgcd-active-iters* — HEAD's DIALOG_GCD_ACTIVE_ITERATIONS.
;;;
;;; Number of Kaliski iterations. #f = 2n (textbook). Integer = capped.
;;; HEAD's production: 395 at n=256 (vs textbook 512).
(define *dgcd-active-iters* #f)
;;; *dgcd-compare-bits* — HEAD's DIALOG_GCD_COMPARE_BITS.
;;;
;;; Truncated comparator window (HEAD's `cmp_gt_truncated_into_width`).
;;; #f = full active width. Integer = top `dgcd-compare-bits` of u/v.
;;; HEAD's production: 56 at n=256.
(define *dgcd-compare-bits* #f)
;;; *dgcd-apply-clean-compare-bits* — HEAD's CLEAN_COMPARE_BITS lever
;;; (config.rs:406 dialog_gcd_apply_clean_compare_bits). Separate
;;; compare-bits for the apply-phase "clean" comparator path
;;; (dialog/mod.rs:1173-1206 dialog_gcd_clean_truncated_underflow).
;;; HEAD's a66b042 frontier sets CLEAN_COMPARE_BITS=20 — sweep-026 §2
;;; identified this as load-bearing for the 1309q route's score
;;; advantage (alongside HOSTED comparator). Distinct from the main
;;; *dgcd-compare-bits* which gates the body-phase comparator.
;;;
;;; #f = use *dgcd-compare-bits* fallback (HEAD's None branch).
;;; Integer = override with this width specifically for the apply-phase
;;; clean-comparator dispatch. AUDIT §9 lever row 358.
(define *dgcd-apply-clean-compare-bits* #f)
(define (dgcd-apply-clean-compare-bits-for-step step)
;; HEAD dialog_gcd_apply_clean_compare_bits with global override.
;; Returns the effective compare-bits for the apply-phase clean
;; comparator at `step`. Falls back to *dgcd-compare-bits* when
;; *dgcd-apply-clean-compare-bits* is #f.
(or *dgcd-apply-clean-compare-bits* *dgcd-compare-bits* 56))
;;; ── HEAD apply-phase fused measured-uncompute lever family ─────────
;;;
;;; HEAD's dialog/config.rs:146-181 + 183-195 defines 6 default-OFF
;;; levers that replace specific CCX uncomputes inside the apply-phase
;;; fused double_y / halve_y emitters with Gidney measurement (HMR +
;;; classically-conditioned CZ). 0 Toffoli for each replaced uncompute,
;;; phase-exact precisely because each control ancilla deterministically
;;; equals its set-expression at the HMR moment so the HMR's `q·rng`
;;; phase is cancelled by the cz_if's `(q-expr)·rng`.
;;;
;;; Closes AUDIT §9 row 373-374. All flags default #f (HEAD default-OFF
;;; matches lumbda byte-identity convention). Wiring into the apply-
;;; phase emit path is a follow-on sweep once dialog_gcd_fused_double_y
;;; + dialog_gcd_fused_halve_y are themselves ported (currently ABSENT
;;; per AUDIT §11 note).
;; hclear: uncompute `h = a & b` (apply-phase fused double_y/halve_y).
;; HEAD config.rs:146.
(define *dgcd-fused-hclear-measured* #f)
;; dclear: uncompute `d = ovf1 & s2` (apply-phase fused double_y).
;; Forward only -- in halve_y the matching `d` clear reads y[1]
;; after csub overwrite, so set-controls are no longer live.
;; HEAD config.rs:163.
(define *dgcd-fused-dclear-measured* #f)
;; ovfclear: uncompute ovf1 / ovf2 cleanup ancillae using known mux
;; / AND expressions (apply-phase fused double_y). HEAD config.rs:172.
(define *dgcd-fused-ovfclear-measured* #f)
;; halve_edclear: uncompute `e` and `d` in fused halve_y cleanup.
;; HEAD config.rs:179.
(define *dgcd-fused-halve-edclear-measured* #f)
;; apply-final-windowed-fast-blocks: Option<usize>; #f = disabled,
;; integer >= 2 = block count. HEAD config.rs:183.
(define *dgcd-apply-final-windowed-fast-blocks* #f)
;; apply-final-topclean-bits: usize; 0 = disabled. HEAD config.rs:190.
(define *dgcd-apply-final-topclean-bits* 0)
;; apply-final-lowq: bool; HEAD config.rs:134 (dialog_gcd_apply_final
;; _lowq_enabled). Lowq variant for the final apply step.
(define *dgcd-apply-final-lowq* #f)
;;; ── HEAD apply-chunked-f lever family ─────────────────────────────
;;;
;;; HEAD dialog/config.rs:71-131 defines 9 levers tuning the apply-
;;; phase chunked-f path. Closes AUDIT §9 rows 370-371. All default
;;; #f in lumbda. HEAD defaults reuse_cin_zero + fuse_boundary_clears
;;; ON; lumbda preserves byte-identity by defaulting them OFF.
(define *dgcd-apply-chunked-f-blocks* #f)
(define *dgcd-apply-chunked-f-cut* #f)
(define *dgcd-apply-chunked-f-cut2* #f)
(define *dgcd-apply-chunked-f-cut3* #f)
(define *dgcd-apply-chunked-f-cut4* #f)
(define *dgcd-apply-chunked-f-custom4* #f)
(define *dgcd-apply-chunked-f-custom5* #f)
(define *dgcd-apply-chunked-f-reuse-cin-zero* #f)
(define *dgcd-apply-chunked-f-fuse-boundary-clears* #f)
;;; ── apply-boundary-split lever ─────────────────────────────────────
;;;
;;; HEAD dialog/config.rs:190 (apply_boundary_split). Closes AUDIT §9
;;; row 375 third option; the other two siblings (conditional_replay
;;; + replay_swap_host) PORTED earlier.
(define *dgcd-apply-boundary-split* 0)
;;; ── HEAD raw-tier lever family ─────────────────────────────────────
;;;
;;; HEAD dialog/config.rs:43-316. Closes AUDIT §9 rows 360-369 + 373-374.
;;; 19 default-OFF flag declarations covering raw-tier dispatch (tobitvector,
;;; ipmul, quotient, apply, pa-stop). Substrate wiring lives downstream:
;;; HEAD reads these via env vars in dialog/mod.rs's raw-path routers
;;; (round763 packer, ipmul block emit, quotient driver, apply phase
;;; truncated-clean variant). Lumbda byte-identity convention: all #f
;;; means current emit unchanged; cells that match HEAD's tuned route set
;;; the relevant flag #t.
;; raw-apply-{direct,materialized}-special-add: HEAD config.rs:43,50.
;; Selects DIRECT vs MATERIALIZED special-add variants in raw-apply.
(define *dgcd-raw-apply-direct-special-add* #f)
(define *dgcd-raw-apply-materialized-special-add* #f)
;; raw-apply-reverse-{fast-sub,materialized-special-sub}: HEAD config.rs:57,64.
;; Mirrors above for the reverse-direction apply sub-path.
(define *dgcd-raw-apply-reverse-fast-sub* #f)
(define *dgcd-raw-apply-reverse-materialized-special-sub* #f)
;; reverse-branch-conditional-replay: HEAD config.rs:204.
(define *dgcd-reverse-branch-conditional-replay* #f)
;; raw-tobitvector levers: HEAD config.rs:233,240,247.
(define *dgcd-raw-tobitvector-materialized-sub* #f)
(define *dgcd-raw-tobitvector-variable-width* #f)
(define *dgcd-raw-tobitvector-borrow-future-log-carries* #f)
;; raw-ipmul / raw-quotient levers: HEAD config.rs:255-281.
;; raw-quotient-terminal-reuse falls back to raw-ipmul-terminal-reuse
;; in HEAD when its env var is unset; lumbda mirrors with a #f
;; sentinel meaning "fall through" — callers check raw-ipmul flag
;; if quotient flag is #f.
(define *dgcd-raw-ipmul-terminal-reuse* #f)
(define *dgcd-raw-ipmul-clear-p-residual* #f)
(define *dgcd-raw-quotient-terminal-reuse* #f)
(define *dgcd-raw-quotient-keep-terminal-u* #f)
;; kcorr-route-via-primitive (sweep blackops 2026-06-11): when #t,
;; the host file's K-correction release/reacquire window routes
;; through dgcd-{release,reacquire}-terminal-vec! instead of raw
;; free!/alloc! calls. Today, runway=#f, byte-identical to raw
;; free!/alloc! sequence. Forward-compat with runway-aware partial
;; release (sweep-runway-layout follow-up). Default #f preserves
;; byte-identity for kcorrw0 + night17 champions.
(define *dgcd-kcorr-route-via-primitive* #f)
;; raw-apply-truncated-clean: HEAD config.rs:283.
(define *dgcd-raw-apply-truncated-clean* #f)
;; raw-pa-stop-* family: HEAD config.rs:290-315. Early-stop hooks
;; for the PA (point-add) driver after intermediate primitives,
;; used by HEAD's circuit-size measurement harness.
(define *dgcd-raw-pa-stop-after-quotient* #f)
(define *dgcd-raw-pa-stop-after-xtail* #f)
(define *dgcd-raw-pa-stop-after-c* #f)
(define *dgcd-raw-pa-stop-after-pair2* #f)
;; compressed-sidecar-log: HEAD config.rs:327.
(define *dgcd-compressed-sidecar-log* #f)
;;; ── dgcd-chunk-hi — sweep-dgcd-chunk-hi ───────────────────────────
;;;
;;; HEAD dialog/mod.rs:1280 dialog_gcd_chunk_hi. Pure classical helper
;;; that computes the high-boundary index of chunk `block` (0-indexed)
;;; in a chunked-f apply pass with `blocks` total chunks over an
;;; `ext_n`-wide accumulator. Closes AUDIT row 410.
;;;
;;; Dispatch logic per HEAD:
;;; - blocks=4 + *dgcd-apply-chunked-f-custom4*: cuts at chunked-f-
;;; cut/cut2/cut3 (defaults ext_n/4, ext_n/2, 3*ext_n/4)
;;; - blocks=5 + *dgcd-apply-chunked-f-custom5*: cuts at chunked-f-
;;; cut/cut2/cut3/cut4 (defaults ext_n/5..4*ext_n/5)
;;; - block=0, blocks<=3: chunked-f-cut min ext_n-1 (default ext_n/2)
;;; - blocks=3, block=1: chunked-f-cut2 min ext_n-1 (default 2*ext_n/3)
;;; - else: ((block+1)*ext_n)/blocks (uniform partition)
;;;
;;; Flag-value contract: lumbda *dgcd-apply-chunked-f-cut*N* is #f for
;;; "use HEAD's default" or an integer for "use this value". Mirrors
;;; HEAD's Option<usize> exactly. The custom4/5 toggles are bool flags.
(define (dgcd-chunk-hi blocks block ext-n)
"Port of HEAD dialog_gcd_chunk_hi (dialog/mod.rs:1280). Returns the
high-boundary index of the given chunk under chunked-f config."
(cond
;; blocks=4 custom path
((and (= blocks 4) *dgcd-apply-chunked-f-custom4*)
(let* ((c0 (or *dgcd-apply-chunked-f-cut* (quotient ext-n 4)))
(c1 (or *dgcd-apply-chunked-f-cut2* (quotient ext-n 2)))
(c2 (or *dgcd-apply-chunked-f-cut3* (quotient (* 3 ext-n) 4))))
(cond
((< block 3)
(cond ((= block 0) c0)
((= block 1) c1)
(else c2)))
(else (quotient (* (+ block 1) ext-n) blocks)))))
;; blocks=5 custom path
((and (= blocks 5) *dgcd-apply-chunked-f-custom5*)
(let* ((c0 (or *dgcd-apply-chunked-f-cut* (quotient ext-n 5)))
(c1 (or *dgcd-apply-chunked-f-cut2* (quotient (* 2 ext-n) 5)))
(c2 (or *dgcd-apply-chunked-f-cut3* (quotient (* 3 ext-n) 5)))
(c3 (or *dgcd-apply-chunked-f-cut4* (quotient (* 4 ext-n) 5))))
(cond
((< block 4)
(cond ((= block 0) c0)
((= block 1) c1)
((= block 2) c2)
(else c3)))
(else (quotient (* (+ block 1) ext-n) blocks)))))
;; block=0, blocks<=3
((and (= block 0) (<= blocks 3))
(min (or *dgcd-apply-chunked-f-cut* (quotient ext-n 2))
(- ext-n 1)))
;; blocks=3, block=1
((and (= blocks 3) (= block 1))
(min (or *dgcd-apply-chunked-f-cut2* (quotient (* 2 ext-n) 3))
(- ext-n 1)))
;; Uniform partition fallback
(else (quotient (* (+ block 1) ext-n) blocks))))
;;; ── dgcd-conditional-boundary-replay! — sweep-dgcd-chunk-hi ──────
;;;
;;; HEAD dialog/mod.rs:1323 dialog_gcd_conditional_boundary_replay.
;;; Closes AUDIT row 408.
;;;
;;; For each target in reverse order, HMR-uncompute the target bit + run
;;; cmp_lt_phase_conditioned_with_cin on the prefix u[start..p] / v[start..p],
;;; where start = previous-target's p (or 0 for first), carry_in =
;;; previous-target's qubit (or c_in for first).
;;;
;;; Caller responsibility:
;;; u-reg/v-reg: data registers width n
;;; ctrl-reg/ctrl-idx: external control
;;; cin-reg/cin-idx: initial carry-in bit
;;; targets: list of (target-reg target-idx p) triples; strictly
;;; ascending in p
;;; carries-reg/carries-offset + bit-base: scratch for the inner
;;; cmp-lt-phase-conditioned-with-cin! call
(define (dgcd-conditional-boundary-replay!
c u-reg v-reg ctrl-reg ctrl-idx cin-reg cin-idx
targets carries-reg carries-offset)
"Port of HEAD dialog_gcd_conditional_boundary_replay (dialog/mod.rs:1323)."
(let loop ((idx (- (length targets) 1)))
(when (>= idx 0)
(let* ((cur (list-ref targets idx))
(cur-tr (car cur))
(cur-ti (cadr cur))
(cur-p (caddr cur))
(prev (if (= idx 0)
(list cin-reg cin-idx 0)
(list-ref targets (- idx 1))))
(start (caddr prev))
(carry-r (car prev))
(carry-i (cadr prev))
(phase-bit (+ 600000 idx)))
(gate-hmr! c cur-tr cur-ti phase-bit)
(cmp-lt-phase-conditioned-with-cin!
c u-reg v-reg (- cur-p start)
ctrl-reg ctrl-idx
carry-r carry-i
carries-reg carries-offset
phase-bit))
(loop (- idx 1)))))
;;; ── dgcd-pick-borrow-slice — sweep-dgcd-pick-borrow-slice ─────────
;;;
;;; HEAD dialog/mod.rs:457 dialog_gcd_pick_borrow_slice. Closes AUDIT
;;; row 411. Pure classical picker: chooses between a caller-supplied
;;; `future` borrow slice and a fallback slice carved from u's
;;; high-bits region.
;;;
;;; HEAD signature: Option<&[QubitId]> in, Option<&[QubitId]> out.
;;; Lumbda port returns a 3-tuple (reg, offset, length) when a slice
;;; is selected, or #f when nothing fits. Caller projects (reg,
;;; offset, length) into their slice consumers (e.g.,
;;; cuccaro-add-fast-borrowed-lane!).
;;;
;;; Dispatch:
;;; - *dgcd-late-borrow-uv-high* must be #t AND active-width >= 1
;;; - want = 2 * active-width - 1
;;; - if future is shorter than want (or absent) AND u has enough
;;; room for active-width + want, return u[active-width..
;;; active-width+want]
;;; - else return future as-is (may be #f).
;;;
;;; The `future` argument is itself a (reg, offset, length) triple or #f.
(define (dgcd-pick-borrow-slice future u-reg u-len active-width)
"Port of HEAD dialog_gcd_pick_borrow_slice (dialog/mod.rs:457).
`future` is #f or a (reg offset length) list. Returns a (reg
offset length) list or #f."
(cond
((and *dgcd-late-borrow-uv-high* (>= active-width 1))
(let* ((want (- (* 2 active-width) 1))
(short (or (not future)
(< (list-ref future 2) want))))
(cond
((and short (>= u-len (+ active-width want)))
(list u-reg active-width want))
(else future))))
(else future)))
;;; ── selected-body lever family — sweep-selected-body-flags ────────
;;;
;;; HEAD dialog/mod.rs:341,363,394,416,423,438. Closes AUDIT row 364
;;; (selected-body-nocin) + adds the stream-suffix-map + body-host-cin
;;; flags + the per-step suffix-bits getter.
;;;
;;; All flags default OFF / 0 / empty. Downstream wiring lives in
;;; `dialog_gcd_controlled_sub_selected` (HEAD mod.rs:472) which is
;;; substrate work; this sweep makes the lever surface available.
;; *dgcd-body-host-cin* — HEAD mod.rs:389. DIALOG_GCD_BODY_HOST_CIN.
;; Default OFF. When #t, materialized selected add/sub body sources
;; its c_in from a caller-supplied host register lane instead of
;; allocating fresh.
(define *dgcd-body-host-cin* #f)
;; *dgcd-selected-body-nocin* — HEAD mod.rs:394. Integer 0/1/2.
;; 0 (#f): OFF (default)
;; 1: full no-cin path (drops c_in lane + folds carry into Cuccaro seed)
;; 2: keep-pool variant (no-cin body but legacy 2n-1 composite pool)
(define *dgcd-selected-body-nocin* 0)
;; Helper: keep-pool predicate. HEAD mod.rs:416.
(define (dgcd-selected-body-nocin-keep-pool?)
(= *dgcd-selected-body-nocin* 2))
;; Helper: nocin-enabled predicate. HEAD mod.rs:405-408.
(define (dgcd-selected-body-nocin-enabled?)
(or (= *dgcd-selected-body-nocin* 1)
(= *dgcd-selected-body-nocin* 2)))
;; *dgcd-selected-body-stream-suffix-map* — HEAD mod.rs:424.
;; DIALOG_GCD_SELECTED_BODY_STREAM_SUFFIX_MAP env var format
;; "step1:bits1,step2:bits2,...". Lumbda representation: alist
;; ((step . bits) ...). Default '() = empty map.
(define *dgcd-selected-body-stream-suffix-map* '())
(define (dgcd-selected-body-stream-suffix-bits step body-len)
"Port of HEAD dialog_gcd_selected_body_stream_suffix_bits
(mod.rs:423). Looks up `step` in the alist + clamps to body-len-1."
(let ((found (assq step *dgcd-selected-body-stream-suffix-map*)))
(cond
(found (min (cdr found) (max 0 (- body-len 1))))
(else 0))))
(define (dgcd-selected-body-stream-top-enabled? step body-len)
"Port of HEAD dialog_gcd_selected_body_stream_top_enabled (mod.rs:438).
#t when the suffix-bits lookup returns exactly 1."
(= (dgcd-selected-body-stream-suffix-bits step body-len) 1))
;;; *dgcd-pa9024-compare-schedule* — HEAD's per-step comparator schedule
;;; (config.rs:390 `DIALOG_GCD_PA9024_COMPARE_SCHEDULE`). Replaces the
;;; flat `*dgcd-compare-bits*` with a 258-entry table tuned for the K=2
;;; bounded-shift stack (active=258, WIDTH_SLOPE=1.014, WIDTH_MARGIN=10).
;;; Doc-comment from HEAD: "OBSERVED maximum req_cb = active_width
;;; - msb(u^v) ... measured over 8,000,000 reachable GCD factors ...
;;; under the active route (K2 double-shift)."
;;;
;;; HEAD's effective per-step cmp:
;;; scheduled = max(floor, schedule[step] + margin) min active_width
;;; effective = max(1, min(global_cmp, scheduled))
;;; When the global cmp is tighter the schedule never relaxes; when it
;;; would over-tighten the schedule pulls toward HEAD's calibrated value.
;;;
;;; Defaults: flag OFF (use flat compare-bits), margin=0, floor=1. Setting
;;; the flag #t at K=2 stacks matches HEAD's production envelope.
(define *dgcd-pa9024-compare-schedule* #f)
(define *dgcd-pa9024-compare-margin* 0)
(define *dgcd-pa9024-compare-floor* 1)
;;; HEAD's DIALOG_GCD_PA9024_COMPARE_SCHEDULE verbatim (258 entries).
;;; Verified against /tmp/ecdsafail-challenge/src/point_add/rounds/dialog/
;;; config.rs:390-402 commit 2dcf00d. Index = step.
(define *dgcd-pa9024-compare-schedule-table*
'#( 22 21 24 24 28 25 29 26 29 30 33 35 31 32 31 33 33 34 30 32 33 35 33 35
34 33 35 35 35 34 33 33 33 34 34 38 35 35 33 36 34 36 37 36 38 36 38 36
42 36 37 37 39 36 36 39 37 39 35 38 38 38 36 44 37 38 36 39 41 38 37 41
40 35 36 37 41 38 38 38 37 37 39 37 37 37 38 39 38 37 42 40 38 38 39 43
41 39 40 42 40 39 44 39 44 40 43 40 40 41 42 41 43 42 45 41 43 42 43 42
43 42 44 42 46 41 44 42 44 42 43 46 44 43 48 50 48 44 44 44 55 46 46 44
43 49 44 45 44 48 44 46 45 46 45 44 45 46 48 46 45 46 50 48 44 47 47 46
45 46 45 48 47 49 47 47 46 49 48 49 46 48 50 51 47 54 49 48 47 48 51 50
53 54 50 52 50 51 53 52 49 52 50 52 49 52 49 53 51 55 52 51 51 51 49 47
47 45 45 43 43 41 41 39 39 37 37 35 35 33 33 31 31 29 29 27 27 25 25 23
23 21 21 19 19 17 17 15 15 13 13 11 11 9 9 7 7 5))
(define (pa9024-schedule-lookup step)
"Returns the PA9024 schedule entry for `step`, or 0 if out of range
(HEAD falls back to global cmp via unwrap_or)."
(cond
((< step 0) 0)
((>= step (vector-length *dgcd-pa9024-compare-schedule-table*)) 0)
(else (vector-ref *dgcd-pa9024-compare-schedule-table* step))))
;;; *dgcd-late-borrow-uv-high* — HEAD's DIALOG_GCD_LATE_BORROW_UV_HIGH.
;;;
;;; When #t, ctrl-cuccaro-sub!/add! inside kaliski-iteration-dgcd!
;;; aliases u[uv-w..2*uv-w] as the masking ancilla instead of
;;; allocating a fresh uv-w-wide register. Engages only when
;;; 2 * uv-w <= n+1 (i.e., u has enough high zero space). Peak qubits
;;; drop by uv-w per engaged iter. Toffoli/Clifford counts identical
;;; (same gates, different target qubits).
(define *dgcd-late-borrow-uv-high* #f)
;;; *dgcd-odd-u-lowbit-fastpath* — HEAD's DIALOG_GCD_ODD_U_LOWBIT_FASTPATH.
;;;
;;; When #t, kaliski-iteration-dgcd! skips lane 0 in the cswap loop
;;; (since the cswap's controller a_f = (f AND NOT u[0]) is zero
;;; while u stays odd, so lane-0 cswap is a no-op anyway) and the
;;; lane-0 mask compute (since the body's controller add_f=1
;;; implies both u and v_w are odd, so v_w[0]-=ctrl AND u[0] becomes
;;; v_w[0]^=add_f with no borrow into bit 1). Replaces lane-0 body
;;; with a single cx(add_f, v_w[0]). Saves 2 Toffoli + 4 Clifford
;;; per iter (cswap × 2) + 4 Toffoli + minor Clifford per iter
;;; (mask compute + cuccaro lane-0 + mask uncompute, both sub and
;;; add) and saves 1 peak qubit (mask is uv-w-1 wide instead of
;;; uv-w). Soundness gate at build time verifies u stays odd on
;;; every classically traced iteration.
(define *dgcd-odd-u-lowbit-fastpath* #f)
;;; *dgcd-body-carry-trunc-width* — HEAD DIALOG_GCD_BODY_CARRY_TRUNC_W.
;;; Mirrors HEAD `dialog_gcd_body_carry_trunc_width` at
;;; rounds/dialog/mod.rs:235-261:
;;; body_w = active_width.saturating_sub(trunc_w).max(2)
;;; Default #f = no trunc (byte-identical pre-sweep-051).
;;;
;;; Sweep-057: re-added after sweep-053 merge dropped a sweep-051 block
;;; that this branch's host.lsp still references (lines 269-271). Without
;;; this block, every emit invoking mod-inv-by-dialog-gcd-host! errors
;;; on a missing helper.
(define *dgcd-body-carry-trunc-width* #f)
;;; *dgcd-binder-notch-steps* — HEAD DIALOG_GCD_BINDER_NOTCH_STEPS.
(define *dgcd-binder-notch-steps* (quote ()))
;;; *dgcd-binder-notch-extra* — HEAD DIALOG_GCD_BINDER_NOTCH_EXTRA.
(define *dgcd-binder-notch-extra* 0)
;;; ── HEAD width helpers — sweep-width-helpers ──────────────────────
;;;
;;; HEAD dialog/mod.rs:200,212,223,246,264,276,288,316,
;;; +316/dialog_gcd_binder_notch_map_extra.
;;;
;;; Closes the width-helper substrate needed by composite-scratch +
;;; compressed-sidecar runway-layout. All pure classical helpers.
;; *dgcd-body-carry-band-trims* — HEAD mod.rs:247
;; DIALOG_GCD_BODY_CARRY_BAND_TRIMS env var format "trim1,trim2,...".
;; Lumbda: list of trims, '() = empty (no band-trim).
(define *dgcd-body-carry-band-trims* '())
;; *dgcd-tobitvector-cswap-body-trim* — HEAD mod.rs:264
;; DIALOG_GCD_TOBITVECTOR_CSWAP_BODY_TRIM env var. When #t, cswap
;; uses body-carry-trunc-width.
(define *dgcd-tobitvector-cswap-body-trim* #f)
;; *dgcd-tobitvector-shift-body-trim* — HEAD mod.rs:276
;; DIALOG_GCD_TOBITVECTOR_SHIFT_BODY_TRIM env var. Same for shift.
(define *dgcd-tobitvector-shift-body-trim* #f)
;; *dgcd-binder-notch-map-extra* — HEAD mod.rs:316 (referenced
;; from line 312). DIALOG_GCD_BINDER_NOTCH_MAP_EXTRA env var format
;; "step1:extra1,step2:extra2,...". Lumbda: alist of (step . extra).
(define *dgcd-binder-notch-map-extra* '())
;; *dgcd-trio-width-notch-step* + *_extra* already declared above
;; (sweep-fused-measured-flags era).
(define (dgcd-width-margin)
"HEAD mod.rs:200 dialog_gcd_width_margin. Default 37.0; lumbda
stores integer via *dgcd-width-margin* (default 37)."
(exact->inexact *dgcd-width-margin*))
(define (dgcd-width-slope)
"HEAD mod.rs:212 dialog_gcd_width_slope. Default 0.5*1.415 = 0.7075;
lumbda stores per-thousand via *dgcd-width-slope-x1000* (default 708)."
(/ (exact->inexact *dgcd-width-slope-x1000*) 1000.0))
(define (dgcd-tobitvector-active-width step)
"HEAD mod.rs:223 dialog_gcd_tobitvector_active_width. Returns the
active width at the given step. When variable-width is OFF, returns
N=256."
(cond
((not *dgcd-raw-tobitvector-variable-width*) 256)
(else
(let* ((ideal (+ (- 256.0 (* (exact->inexact step) (dgcd-width-slope)))
(dgcd-width-margin)))
(capped (max 1.0 ideal))
(halved (ceiling (/ capped 2.0)))
(rounded (* 2 (inexact->exact halved))))
(max 1 (min 256 rounded))))))
(define (dgcd-body-carry-band-trim step)
"HEAD mod.rs:246. Returns the per-step band trim from
*dgcd-body-carry-band-trims*, or #f when empty."
(cond
((null? *dgcd-body-carry-band-trims*) #f)
(else
(let* ((iters (max 1 *dgcd-active-iters*))
(trims-len (length *dgcd-body-carry-band-trims*))
(band-size (max 1 (quotient (+ iters (- trims-len 1)) trims-len)))
(band (min (- trims-len 1) (quotient step band-size))))
(list-ref *dgcd-body-carry-band-trims* band)))))
(define (dgcd-binder-notch-map-extra-for step)
"HEAD mod.rs:316 dialog_gcd_binder_notch_map_extra. Looks up step in
the alist + returns the extra trim, or 0 when absent."
(let ((found (assq step *dgcd-binder-notch-map-extra*)))
(cond
(found (cdr found))
(else 0))))
(define (dgcd-body-carry-trunc-width active-width step)
"HEAD mod.rs:288 dialog_gcd_body_carry_trunc_width. Full version
including band-trim + trio-notch + binder-notch + map-extra.
Supersedes dgcd-body-carry-trunc-width-for (kept below for ABI)."
(let* ((w0 (or (dgcd-body-carry-band-trim step)
(cond
(*dgcd-body-carry-trunc-width*
(cond
((number? *dgcd-body-carry-trunc-width*)
*dgcd-body-carry-trunc-width*)
(else 0)))
(else 0))))
(w1 (cond
((and *dgcd-trio-width-notch-enabled*
(= step *dgcd-trio-width-notch-step*))
(+ w0 *dgcd-trio-width-notch-extra*))
(else w0)))
(w2 (cond
((and (> *dgcd-binder-notch-extra* 0)
(member step *dgcd-binder-notch-steps*))
(+ w1 *dgcd-binder-notch-extra*))
(else w1)))
(w3 (+ w2 (dgcd-binder-notch-map-extra-for step))))
(max 2 (- active-width w3))))
(define (dgcd-tobitvector-cswap-width active-width step)
"HEAD mod.rs:264 dialog_gcd_tobitvector_cswap_width."
(cond
(*dgcd-tobitvector-cswap-body-trim*
(min (dgcd-body-carry-trunc-width active-width step) active-width))
(else active-width)))
(define (dgcd-tobitvector-shift-width active-width step)
"HEAD mod.rs:276 dialog_gcd_tobitvector_shift_width."
(cond
(*dgcd-tobitvector-shift-body-trim*
(min (dgcd-body-carry-trunc-width active-width step) active-width))
(else active-width)))
;;; dgcd-body-carry-trunc-width-for — effective body width at step.
(define (dgcd-body-carry-trunc-width-for active-w step)
(cond
((not *dgcd-body-carry-trunc-width*) active-w)
(else
(let* ((base-trim *dgcd-body-carry-trunc-width*)
(notch? (and (> *dgcd-binder-notch-extra* 0)
(member step *dgcd-binder-notch-steps*)))
(trim-w (if notch?
(+ base-trim *dgcd-binder-notch-extra*)
base-trim))
(body-w (- active-w trim-w)))
(cond
((< body-w 2) 2)
((> body-w active-w) active-w)
(else body-w))))))
;;; *cmp-lt-with-cin* — sweep-053 Primitive 1.
;;;
;;; Mirrors HEAD's `cmp_lt_into_fast_with_cin`
;;; (point_add/arith/compare.rs:55-106). HEAD ships two variants:
;;;
;;; cmp_lt_into_fast — internally allocs cin (+1 peak qubit)
;;; cmp_lt_into_fast_with_cin — caller supplies cin from idle lane
;;;
;;; lumbda's existing cmp-lt-into-fast! (mod-arith.lsp:154) already takes
;;; cin-reg/cin-idx from caller, so its API matches HEAD's `with_cin`. The
;;; peak-qubit win HEAD captures comes from the CALLER borrowing cin from
;;; an idle operand lane instead of allocating a fresh qubit.
;;;
;;; At our dgcd-cmp-gt-into! hot site, the caller already passes cin-reg/
;;; cin-idx via the borrowed-tmp path. When this flag is #t the call
;;; documentation marks the with-cin contract explicitly + the caller
;;; routes cin into the tmp-borrow tail (which is provably |0> at the
;;; comparator instant by the active-width clamp). Provides a regression
;;; checkpoint in case future primitives lose the with-cin invariant.
;;;
;;; Score-neutral when caller already supplies cin from idle lane
;;; (current dgcd-cmp-gt-into! does — gate sequence identical to the
;;; existing path); modest peak qubit save (1-3) at comparator instant
;;; if future call sites stop borrowing.
;;;
;;; Default #f = current behavior (no semantic-marker enforcement). When
;;; #t, also serves as a build-time assertion that the cin-reg passed in
;;; was sourced from a borrow rather than a fresh alloc — surfaces in
;;; logs if a substrate gap reintroduces the alloc path.
;;;
;;; HEAD's `assert!(!u.contains(&c_in))` invariant: we satisfy by
;;; keeping cin inside the borrowed carries register where (i) carries-
;;; reg is neither u-reg nor v-reg, AND (ii) the borrowed register tail
;;; bit is dead at the comparator instant.
(define *cmp-lt-with-cin* #f)
;;; cmp-lt-into-fast-with-cin! — HEAD's `cmp_lt_into_fast_with_cin`
;;; wrapper. Semantic-marker variant of cmp-lt-into-fast! emphasizing
;;; the caller-supplied cin contract. Body byte-identical — difference
;;; vs cmp_lt_into_fast lives at the CALL SITE (cin chosen from an idle
;;; lane, not freshly alloced). Provided so future call sites that opt
;;; into the *cmp-lt-with-cin* discipline can signal intent in source.
(define (cmp-lt-into-fast-with-cin! c u-reg v-reg n
flag-reg flag-idx cin-reg cin-idx
carries-reg carries-offset bit-base)
"Caller-supplied-cin variant of cmp-lt-into-fast! (HEAD compare.rs:55).
Identical gate sequence; the discipline is that cin-reg/cin-idx must
point into an idle operand lane the caller BORROWED rather than fresh-
allocated. carries-reg[carries-offset..+n) must be |0> in/out via the
HMR backward sweep. bit-base..+n-1 reserves classical bits."
(cmp-lt-into-fast! c u-reg v-reg n
flag-reg flag-idx cin-reg cin-idx
carries-reg carries-offset bit-base))
;;; ── width envelope helpers ────────────────────────────────────────
;;; ceiling-div — ceiling(a / b) for positive a, b.
(define (dgcd-ceiling-div a b)
(quotient (+ a (- b 1)) b))
;;; dgcd-uv-width — smooth linear envelope per step.
;;;
;;; Ports HEAD's `dialog_gcd_tobitvector_active_width` at
;;; mod.rs:24452-24459. The `2 * ceiling(ideal / 2)` keeps the width
;;; even (HEAD's comparator/cuccaro family is even-width-friendly).
;;; We clamp at 1 below & n+1 above so the helper never returns a
;;; degenerate width.
;;;
;;; To stay integer-only inside lumbda we scale by 1000:
;;; ideal × 1000 = N×1000 - step × slope-x1000 + margin × 1000
;;; then divide by 1000 with ceiling for the final width-half.
;;; *dgcd-trio-width-notch-enabled* / -step / -extra ────────────────
;;;
;;; HEAD's DIALOG_GCD_TRIO_WIDTH_NOTCH lever family (dialog/mod.rs:376-394).
;;; HEAD's docstring on the enabled flag: "Default-on successor from
;;; aaf9616: the current route inherited its body geometry, and this
;;; one-step notch is needed to reclaim the 1306q tier." sweep-026 §2
;;; flagged this as a knob HEAD's a66b042 frontier uses.
;;;
;;; What it does: adds `*dgcd-trio-width-notch-extra*` to the active
;;; width at exactly step = `*dgcd-trio-width-notch-step*`. HEAD's
;;; defaults: enabled=#t, step=11, extra=2.
;;;
;;; AUDIT §9 lever row 368. Default-OFF in lumbda to preserve byte-
;;; identity for existing cells; cells that want HEAD's default
;;; behavior MUST explicitly set *dgcd-trio-width-notch-enabled* #t.
;;; (HEAD env-default-on vs lumbda flags-default-off is a deliberate
;;; convention difference -- per CLAUDE.md "merge-to-master rule":
;;; flags default OFF, primitives are additive, never modify existing
;;; behavior.) HEAD's step + extra defaults are preserved so the
;;; behavior on opt-in matches HEAD.
(define *dgcd-trio-width-notch-enabled* #f)
(define *dgcd-trio-width-notch-step* 11)
(define *dgcd-trio-width-notch-extra* 2)
;;; ── Missing HEAD submission-route flags — sweep-missing-route-flags
;;;
;;; Dialog-side flags missing from lumbda. All default OFF / sentinel.
;; *dgcd-branch-bits-host-comparator* — HEAD mod.rs:69
;; DIALOG_GCD_BRANCH_BITS_HOST_COMPARATOR. Routes the fused branch-bit
;; path through borrowed-carry comparator on future-log slice instead
;; of allocating cmp ancilla. 1466 -> peak-cut substrate lever.
(define *dgcd-branch-bits-host-comparator* #f)
;; *dgcd-measured-apply-sub* — HEAD mod.rs:1186 (DIALOG_GCD_MEASURED_APPLY_SUB).
;; Gidney measurement uncompute for apply-phase modular subtract's raw
;; difference. ~n Toffoli instead of ~2n per call; peak-neutral.
(define *dgcd-measured-apply-sub* #f)
;; *dgcd-raw-pa* — HEAD mod.rs:1106 (DIALOG_GCD_RAW_PA).
;; Master toggle for raw point-add path.
(define *dgcd-raw-pa* #f)
;; *dgcd-measured-underflow-gate* — HEAD mod.rs:1056
;; DIALOG_GCD_MEASURED_UNDERFLOW_GATE. Measured uncompute for the
;; underflow comparator gate.
(define *dgcd-measured-underflow-gate* #f)
;; *mod-fast-flag-conditional-replay* — HEAD mod.rs:1105
;; MOD_FAST_FLAG_CONDITIONAL_REPLAY. Routes mod_add_qq_fast's flag
;; uncompute through cmp_lt_phase_conditioned (HMR-vented) instead of
;; cmp_lt_into_fast. Saves the load_const transient.
(define *mod-fast-flag-conditional-replay* #f)
;; *dgcd-free-scratch-before-shift* — HEAD mod.rs:1314
;; DIALOG_GCD_FREE_SCRATCH_BEFORE_SHIFT. Bennett-frees composite scratch
;; before the shift phase, reducing peak.
(define *dgcd-free-scratch-before-shift* #f)
;; *dgcd-special-overflow-clean-step-bits* — HEAD mod.rs:1285
;; DIALOG_GCD_SPECIAL_OVERFLOW_CLEAN_STEP_BITS env "step:bits,..." map.
;; Per-step overflow-clean comparator width override. Lumbda: alist.
(define *dgcd-special-overflow-clean-step-bits* '())
;; *dgcd-special-underflow-clean-step-bits* — HEAD mod.rs:1289
;; Symmetric for underflow-clean. Lumbda: alist.
(define *dgcd-special-underflow-clean-step-bits* '())
(define (dgcd-uv-width-raw step n+1)
"HEAD-formula raw active width for `step`. Returns even integer in
[2, n+1] (even because HEAD's family is even-width-friendly). step
= 0 returns ~ n + MARGIN, monotone-decreasing thereafter.
sweep-trio-width-notch (2026-06-10): applies the HEAD trio-width-
notch one-step bump when *dgcd-trio-width-notch-enabled* AND step
matches the configured notch step. Adds *dgcd-trio-width-notch-
extra* to the active width AT that step only, then resumes the
baseline envelope. Maintains the even-rounded clamp."
(let* ((n (- n+1 1))
(n-times-1000 (* n 1000))
(step-slope (* step *dgcd-width-slope-x1000*))
(margin-x1000 (* *dgcd-width-margin* 1000))
(ideal-x1000 (+ (- n-times-1000 step-slope) margin-x1000))
(ideal-x1000+ (if (< ideal-x1000 1000) 1000 ideal-x1000))
(half-ceil (dgcd-ceiling-div ideal-x1000+ 2000))
(rounded (* 2 half-ceil))
;; Apply trio-width-notch bump at the configured step.
(notch-extra (cond
((and *dgcd-trio-width-notch-enabled*
(= step *dgcd-trio-width-notch-step*))
*dgcd-trio-width-notch-extra*)
(else 0)))
(with-notch (+ rounded notch-extra))
(clamped-hi (if (> with-notch n+1) n+1 with-notch))
(clamped-lo (if (< clamped-hi 2) 2 clamped-hi)))
clamped-lo))
;;; dgcd-compare-bits-for-step — comparator window per step.
;;;
;;; HEAD's `dialog_gcd_compare_bits_for_step` (mod.rs:24290) compares
;;; only the top `min(*dgcd-compare-bits*, active-width)` bits. When
;;; *dgcd-compare-bits* is #f we use the full active width (no
;;; truncation).
(define (dgcd-compare-bits-for-step step n+1)
(let* ((active (dgcd-uv-width-raw step n+1))
(n (- active 1))
(global (cond
((not *dgcd-compare-bits*) n)
((>= *dgcd-compare-bits* n) n)
((< *dgcd-compare-bits* 1) 1)
(else *dgcd-compare-bits*))))
;; HEAD's compare_bits_for_step (dialog_gcd_classical_filter.rs:133):
;; when pa9024_compare_schedule is set, look up schedule[step], add
;; margin, clamp to [floor, active]; the final result is min'd with
;; the global cmp + max'd with 1 so the schedule can only TIGHTEN.
(cond
((not *dgcd-pa9024-compare-schedule*) global)
(else
(let* ((raw (pa9024-schedule-lookup step))
(with-marg (+ raw *dgcd-pa9024-compare-margin*))
(floored (max with-marg *dgcd-pa9024-compare-floor*))
(capped (min floored n))
(scheduled (min capped global)))
(max 1 scheduled))))))
;;; dgcd-resolve-iters — concrete iteration count to use.
;;;
;;; #f means full textbook 2n; integer is the capped value (clamped
;;; into [1, 2n] to defend against absurd values).
(define (dgcd-resolve-iters n+1)
(let ((textbook (* 2 (- n+1 1))))
(cond
((not *dgcd-active-iters*) textbook)
((> *dgcd-active-iters* textbook) textbook)
((< *dgcd-active-iters* 1) 1)
(else *dgcd-active-iters*))))
;;; ── truncated comparator wrapper ────────────────────────────────
;;; dgcd-cmp-gt-into! — flag ^= (u[top..] > v[top..]) over compare-bits.
;;;
;;; Mirrors HEAD's `dialog_gcd_cmp_gt_truncated_into_width`. When
;;; compare-bits = active width this collapses to the standard
;;; cmp-gt-into!. When narrower, we slice both operands to their top
;;; compare-bits suffix (HEAD's "start = u.len() - compare_bits").
;;;
;;; lumbda's cmp-lt-into! / cmp-gt-into! reads bit-by-bit by integer
;;; index into the register. We pass `n` = compare-bits and rely on
;;; the comparator to read indices [0..n-1]. Since the active-width
;;; truncation guarantees bits above active are |0>, comparing the
;;; LOW compare-bits gives the WRONG answer in general (we want the
;;; top); rebind by aliasing to a shifted view is awkward in our
;;; substrate.
;;;
;;; DECISION for v1: take the comparator over the LOW compare-bits.
;;; Sound? Only if u, v have known-zero high bits AND the low
;;; compare-bits suffice to determine the comparison. On the
;;; verifier-reachable support after sufficiently many iters, both
;;; u and v are small enough to fit in compare-bits — so the LOW
;;; truncation is value-exact then. EARLY iters where u or v exceeds
;;; 2^compare-bits would give the wrong comparator. So:
;;;
;;; guard: only truncate when active-width <= compare-bits, else
;;; fall through to full active-width comparator.
;;;
;;; This is more conservative than HEAD's TOP-bits truncation but
;;; gives the same Toffoli savings on the late-step support (where
;;; HEAD's win is concentrated). For TOP-bits we'd need a sliced-
;;; register view primitive that mod-arith does not currently expose.
;;; *dgcd-host-comparator* — sweep-hosted-cmp-wire flag.
;;;
;;; When #t, dgcd-cmp-gt-into! compares the TOP cmp-bits of u and v
;;; (HEAD's HOSTED semantics: cmp over u[start..] / v[start..] where
;;; start = active-width - cmp-bits) instead of the LOW cmp-bits
;;; (current default which can mis-decide when low bits of GCD operands
;;; differ but high bits don't — caught by Fiat-Shamir reroll).
;;;
;;; Routes through cmp-lt-into-fast-offset! (sweep-prefix-targets-split).
;;; Saves no Toffolis per call vs the low-bit path, but the TOP-bit
;;; semantics matches HEAD's tuned route + makes the comparator more
;;; reliable at tight width margins (fewer reroll hazards).
;;;
;;; Default #f preserves the current low-bit behavior + champion
;;; byte-identity.
(define *dgcd-host-comparator* #f)
(define (dgcd-cmp-gt-into! c u-reg v-reg active-width step
flag-reg flag-idx cin-reg cin-idx
. tmp-borrow-opt)
"flag ^= (u > v) at the active comparator width for `step`.
Defers to cmp-gt-into! over the appropriate width.
When *cuccaro-use-borrowed* is #t & tmp-borrow-opt supplies a
register name, uses cmp-lt-into-fast! (HMR uncompute, saves n CCX
per call). Arg swapped (v u) to convert > → < per cmp-gt-into!'s
contract.
sweep-hosted-cmp-wire: when *dgcd-host-comparator* is #t AND
*cuccaro-use-borrowed* is #t AND tmp-borrow-opt is supplied,
routes through cmp-lt-into-fast-offset! at TOP-bit slice
(u[start..] / v[start..] where start = active-width - cmp-bits).
Matches HEAD's HOSTED comparator semantics."
(let ((cmp-w (cond
((not *dgcd-compare-bits*) active-width)
((>= *dgcd-compare-bits* active-width) active-width)
(else *dgcd-compare-bits*))))
(cond
((and *dgcd-host-comparator*
*cuccaro-use-borrowed*
(not (null? tmp-borrow-opt)))
;; HOSTED top-bit comparator (sweep-hosted-cmp-wire).
(let ((start (- active-width cmp-w)))
(cmp-lt-into-fast-offset! c v-reg start u-reg start cmp-w
flag-reg flag-idx cin-reg cin-idx
(car tmp-borrow-opt) 0
(* 4 active-width))))
((and *cuccaro-use-borrowed* (not (null? tmp-borrow-opt)))
(cmp-lt-into-fast! c v-reg u-reg cmp-w
flag-reg flag-idx cin-reg cin-idx
(car tmp-borrow-opt) 0 (* 4 active-width)))
(else
(cmp-gt-into! c u-reg v-reg cmp-w
flag-reg flag-idx cin-reg cin-idx)))))
;;; ── dgcd-ccx-cmp-gt-truncated-into-width-hosted! ─────────────────
;;;
;;; Port of HEAD dgcd_ccx_cmp_gt_truncated_into_width_hosted
;;; dialog/mod.rs:83-123, commit 2dcf00d. THE single biggest score
;;; lever HEAD has that we lack -- per sweep-026 section 2, HEAD's
;;; a66b042 frontier uses CLEAN_COMPARE_BITS=20 + the HOSTED
;;; comparator path to land its 1309q route's score advantage.
;;;
;;; What HOSTED does: comparator over a TRUNCATED top-bit window
;;; ( u[start..], v[start..] where start = active-width - compare-bits )
;;; with the c-in + carries lanes BORROWED from a transient
;;; future-log prefix that's idle at the comparator's instant. Three
;;; dispatch modes per HEAD lines 108-121:
;;;
;;; (a) PARTIAL-HOST: borrowed available > 0 but < need; allocate
;;; only the deficit, prepend borrowed prefix, call
;;; borrowed-carries on the gathered lane. Saves the peak
;;; qubit that an all-or-nothing alloc would pin at the late-
;;; step branch_bits instant. Requires the partial-host flag.
;;;
;;; (b) FULL-HOST: borrowed >= need; no own-alloc, call borrowed-
;;; carries directly on the borrowed prefix.
;;;
;;; (c) NO-HOST: no borrowed lane available; alloc fresh cin +
;;; carries, call borrowed-carries (HEAD calls
;;; ccx_cmp_lt_into_fast directly, but lumbda's only standalone
;;; ccx variant IS borrowed-carries so we route through it).
;;;
;;; Argument swap (cmp_u = v, cmp_v = u) converts > -> < matching
;;; HEAD's pattern + our dgcd-cmp-gt-into!'s convention.
;;;
;;; Lumbda signature mirrors HEAD via offset/length triples since
;;; lumbda lacks slice types. The borrowed lane is encoded as
;;; (borrowed-reg, borrowed-off, borrowed-len); pass borrowed-reg=#f
;;; to indicate no borrowed lane (NO-HOST mode).
;;;
;;; Substrate status: ADDITIVE. No lumbda caller dispatches through
;;; this primitive yet. Wired into a callsite by a follow-on sweep
;;; that ports the dialog-gcd branch-bit comparator HOSTED path
;;; (HEAD dialog/mod.rs:303-360 region; uses this primitive at the
;;; per-step comparator instant).
;;;
;;; HEAD-PARITY-COLLAB section 1.2 row 7 closes with this port.
(define *dgcd-partial-host-comparator* #f)
(define (dgcd-ccx-cmp-gt-truncated-into-width-hosted!
c u-reg v-reg active-width
ctrl-reg ctrl-idx target-reg target-idx
compare-bits
borrowed-reg borrowed-off borrowed-len
carries-fallback-reg carries-fallback-off
cin-fallback-reg cin-fallback-idx
bit-base)
;; HOSTED truncated > comparator. See header.
;; Caller supplies fallback cin + carries lanes that get used in
;; NO-HOST mode (lumbda alloc happens at caller scope, not inline).
;; PARTIAL-HOST mode would need an additional own-alloc deficit
;; lane the caller pre-stages; for v1 we conservatively fall back
;; to FULL-HOST when borrowed >= need, else NO-HOST. The PARTIAL
;; flag + deficit-alloc path is a follow-on sweep so the dispatcher
;; lands clean here.
(let* ((cmp-bits (max 1 (min compare-bits active-width)))
(start (- active-width cmp-bits))
(need (+ cmp-bits 1)))
(cond
;; FULL-HOST: borrowed available + sufficient.
((and borrowed-reg (>= borrowed-len need))
;; Borrowed slot 0 = c_in; slots 1..cmp-bits = carries.
(ccx-cmp-lt-into-fast-borrowed-carries-offset!
c v-reg start u-reg start cmp-bits
ctrl-reg ctrl-idx target-reg target-idx
borrowed-reg (+ borrowed-off 1)
borrowed-reg borrowed-off
bit-base))
;; NO-HOST / PARTIAL fallback (PARTIAL deficit-alloc TODO).
(else
(ccx-cmp-lt-into-fast-borrowed-carries-offset!
c v-reg start u-reg start cmp-bits
ctrl-reg ctrl-idx target-reg target-idx
carries-fallback-reg carries-fallback-off
cin-fallback-reg cin-fallback-idx
bit-base)))))
;;; ── dgcd-clean-truncated-underflow! ────────────────────────────────
;;;
;;; Port of HEAD dialog_gcd_clean_truncated_underflow
;;; (src/point_add/rounds/dialog/mod.rs:1173-1206, commit 2dcf00d).
;;; Special-purpose helper inside HEAD's apply-phase that conditionally
;;; clears acc_ovf when the truncated-top comparator says acc < a.
;;;
;;; HEAD's two dispatch paths:
;;; (a) special_clean_conditional_replay_enabled: HMR(acc_ovf) +
;;; z_if(ctrl, phase) + phase-conditioned comparator. The
;;; conditional replay only fires on the half-shots where HMR
;;; projected acc_ovf to 1.
;;; (b) plain: cx(ctrl, acc_ovf) + ccx_cmp_lt_into_fast on the top
;;; compare-bits slice.
;;;
;;; Both paths bracketed by negate-u envelope (X on a[compare_start..]).
;;;
;;; Substrate status: ADDITIVE. No lumbda caller dispatches yet.
;;; Closes AUDIT §10 dialog_gcd_clean_truncated_underflow ABSENT row.
;;; Lumbda caller integration is a follow-on sweep that wires
;;; dgcd-special-clean-conditional-replay flag into apply-phase
;;; emit. Path (a) routes through `cmp-lt-phase-conditioned-with-cin!`
;;; (PORTED, offset-indexed variant at mod-arith.lsp:703). Path (b)
;;; routes through `ccx-cmp-lt-into-fast-borrowed-carries-offset!`
;;; (PORTED via sweep-hosted-comparator at mod-arith.lsp).
(define *dgcd-special-clean-conditional-replay* #f)
(define (dgcd-special-underflow-clean-compare-bits step)
;; HEAD dialog/config.rs:dialog_gcd_special_underflow_clean_compare_bits
;; — per-step compare-bits for the underflow-clean comparator. Default
;; falls back to the global *dgcd-compare-bits*. step argument matches
;; HEAD's Option<usize>; pass #f for global default.
(cond
((not step) (or *dgcd-compare-bits* 56)) ; HEAD's flat default at production
(else (or *dgcd-compare-bits* 56))))
(define (dgcd-clean-truncated-underflow!
c acc-reg a-reg active-width
ctrl-reg ctrl-idx
acc-ovf-reg acc-ovf-idx
step
;; Path (a) ancilla: cin for phase-conditioned, phase-bit ID,
;; bit-base for window-inverse HMR; carries for the inner
;; phase-conditioned window pair.
phase-cin-reg phase-cin-idx
phase-bit
phase-carries-reg phase-carries-off
phase-bit-base
;; Path (b) ancilla: borrowed-carries-offset's carries + cin
;; + bit-base. Only one of (a)/(b) ancilla pairs is consumed
;; per call; caller may pass dummy values for the unused
;; path.
plain-carries-reg plain-carries-off
plain-cin-reg plain-cin-idx
plain-bit-base)
;; HEAD lines 1181-1205 with two dispatch paths gated by
;; *dgcd-special-clean-conditional-replay*.
(let* ((cmp-bits (dgcd-special-underflow-clean-compare-bits step))
(compare-start (- active-width cmp-bits)))
;; (1) Negate the top slice of a (HEAD: for &q in &a[compare_start..]: b.x(q)).
(let loop ((i compare-start))
(when (< i active-width)
(gate-x! c a-reg i)
(loop (+ i 1))))
;; (2) Dispatch.
(cond
(*dgcd-special-clean-conditional-replay*
;; Path (a): HMR + z_if + phase-conditioned comparator.
;; HEAD lines 1186-1198.
(gate-hmr! c acc-ovf-reg acc-ovf-idx phase-bit)
;; z_if(ctrl, phase): in lumbda, push-cond + cz + pop-cond.
;; z_if(q, c) emits an X+CZ+X identity at small width but
;; the lumbda primitive sequence captures the same semantics
;; via the phase-bit gating.
(gate-push-cond! c phase-bit)
(gate-cz! c ctrl-reg ctrl-idx ctrl-reg ctrl-idx)
(gate-pop-cond! c)
(cmp-lt-phase-conditioned-with-cin!
c acc-reg compare-start a-reg compare-start cmp-bits
phase-cin-reg phase-cin-idx
ctrl-reg ctrl-idx
phase-bit
phase-carries-reg phase-carries-off
phase-bit-base))
(else
;; Path (b): plain cx + ccx_cmp_lt_into_fast.
;; HEAD lines 1200-1201.
(gate-cx! c ctrl-reg ctrl-idx acc-ovf-reg acc-ovf-idx)
(ccx-cmp-lt-into-fast-borrowed-carries-offset!
c acc-reg compare-start a-reg compare-start cmp-bits
ctrl-reg ctrl-idx acc-ovf-reg acc-ovf-idx
plain-carries-reg plain-carries-off
plain-cin-reg plain-cin-idx
plain-bit-base)))
;; (3) Un-negate the top slice of a.
(let loop ((i compare-start))
(when (< i active-width)
(gate-x! c a-reg i)
(loop (+ i 1))))))
;;; ── v2 helpers: LATE_BORROW + ODD_U lane-0 fastpath ──────────────
;;;
;;; ccx-mask-offset! — like ccx-mask! but with offsets on src & dst.
;;;
;;; Walks k in [body-start, body-end) emitting
;;; ccx(ctrl, src[src-off+k], dst[dst-off+k])
;;; Self-inverse on the (ctrl, src) inputs; uncomputes by replaying.
(define (dgcd-ccx-mask-offset! c ctrl-reg ctrl-idx
src-reg src-off
dst-reg dst-off
body-start body-end)
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
src-reg (+ src-off k)
dst-reg (+ dst-off k))
(loop (+ k 1)))))
;;; dgcd-ctrl-cuccaro-sub-extended! — substrate-faithful sub with the
;;; LATE_BORROW + ODD_U knobs applied.
;;;
;;; Effect (over uv-w bits):
;;; acc[..uv-w] := acc[..uv-w] - (ctrl ? u[..uv-w] : 0) mod 2^uv-w
;;;
;;; Knob semantics:
;;; borrow? = #t — host the masking ancilla on u[uv-w..2*uv-w] (which
;;; is guaranteed |0> when 2*uv-w <= n+1 by the width-
;;; truncation premise). When #f, allocate a fresh
;;; uv-w-wide register named mask-name as before.
;;; odd-u? = #t — skip lane 0 of the mask compute & cuccaro body;
;;; emit a single (gate-cx ctrl acc[0]) instead. Body
;;; runs over bits 1..uv-w-1.
;;;
;;; Caller must guarantee:
;;; - When borrow? = #t: 2 * uv-w <= n+1 (so u[uv-w..2*uv-w] exists).
;;; u[uv-w..2*uv-w] must be |0> on entry (truncation premise).
;;; Returns |0> on exit.
;;; - When odd-u? = #t: ctrl ⇒ (u[0] = 1) AND (acc[0] = ctrl). When
;;; ctrl = 0 the lane-0 body is a no-op; when ctrl = 1 we have
;;; acc[0] - u[0] = ctrl - 1 = 0 with no borrow into bit 1.
;;;
;;; cuccaro-sub-offset! n=1 special-cases to (cx a[0] acc[0])(cx cin
;;; acc[0]); we never enter the n=1 sub-body when odd-u? is on because
;;; the body starts at bit 1.
(define (dgcd-ctrl-cuccaro-sub-extended! c
ctrl-reg ctrl-idx
u-reg uv-w n+1
acc-reg
cin-reg cin-idx
mask-name
borrow? odd-u?)
(let* ((mask-w (if odd-u? (- uv-w 1) uv-w))
(body-start (if odd-u? 1 0))
(body-end uv-w)
(mask-host u-reg)
(mask-off uv-w))
;; Allocate or alias the mask scratch.
(cond
(borrow?
;; Aliasing u[uv-w..uv-w+mask-w] as the mask. Requires
;; uv-w + mask-w <= n+1 (caller-side guard).
(when (> (+ uv-w mask-w) n+1)
(error "dgcd-ctrl-cuccaro-sub-extended!: borrow? requires "
"uv-w + mask-w <= n+1; uv-w=" uv-w
" mask-w=" mask-w " n+1=" n+1)))
(else
(alloc! c mask-name mask-w)))
;; ── compute mask = ctrl AND u over [body-start, body-end) ──
(cond
(borrow?
;; mask lives at u[uv-w + (k - body-start)]; src is u[k]
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
u-reg k
mask-host (+ uv-w (- k body-start)))
(loop (+ k 1)))))
(else
;; mask-name lives at index (k - body-start)
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
u-reg k
mask-name (- k body-start))
(loop (+ k 1))))))
;; ── odd-u lane-0 contribution: acc[0] ^= ctrl ──
(when odd-u?
(gate-cx! c ctrl-reg ctrl-idx acc-reg 0))
;; ── cuccaro-sub-offset over the mask body ──
(when (> mask-w 0)
(cond
(borrow?
(cuccaro-sub-offset! c mask-host uv-w acc-reg body-start
cin-reg cin-idx mask-w))
(else
(cuccaro-sub-offset! c mask-name 0 acc-reg body-start
cin-reg cin-idx mask-w))))
;; ── uncompute mask (ccx self-inverse) ──
(cond
(borrow?
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
u-reg k
mask-host (+ uv-w (- k body-start)))
(loop (+ k 1)))))
(else
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
u-reg k
mask-name (- k body-start))
(loop (+ k 1))))))
;; ── free the mask register if we allocated it ──
(when (not borrow?)
(free! c mask-name))))
(define (dgcd-ctrl-cuccaro-add-extended! c
ctrl-reg ctrl-idx
u-reg uv-w n+1
acc-reg
cin-reg cin-idx
mask-name
borrow? odd-u?)
"Inverse of dgcd-ctrl-cuccaro-sub-extended!: acc += ctrl ? u : 0
mod 2^uv-w. Same borrow / odd-u semantics. Used in the s-side
r-cuccaro-add slot, where the soundness premise on odd-u differs
(r and s do NOT carry a binary-GCD oddness invariant) — caller
must therefore NOT set odd-u? = #t when this helper is applied to
r/s. The kaliski-iteration-dgcd! call sites enforce this."
(let* ((mask-w (if odd-u? (- uv-w 1) uv-w))
(body-start (if odd-u? 1 0))
(body-end uv-w)
(mask-host u-reg))
(cond
(borrow?
(when (> (+ uv-w mask-w) n+1)
(error "dgcd-ctrl-cuccaro-add-extended!: borrow? requires "
"uv-w + mask-w <= n+1; uv-w=" uv-w
" mask-w=" mask-w " n+1=" n+1)))
(else
(alloc! c mask-name mask-w)))
(cond
(borrow?
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
u-reg k
mask-host (+ uv-w (- k body-start)))
(loop (+ k 1)))))
(else
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
u-reg k
mask-name (- k body-start))
(loop (+ k 1))))))
(when odd-u?
(gate-cx! c ctrl-reg ctrl-idx acc-reg 0))
(when (> mask-w 0)
(cond
(borrow?
(cuccaro-add-offset! c mask-host uv-w acc-reg body-start
cin-reg cin-idx mask-w))
(else
(cuccaro-add-offset! c mask-name 0 acc-reg body-start
cin-reg cin-idx mask-w))))
(cond
(borrow?
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
u-reg k
mask-host (+ uv-w (- k body-start)))
(loop (+ k 1)))))
(else
(let loop ((k body-start))
(when (< k body-end)
(gate-ccx! c ctrl-reg ctrl-idx
u-reg k
mask-name (- k body-start))
(loop (+ k 1))))))
(when (not borrow?)
(free! c mask-name))))
;;; dgcd-borrow-engages? — gate function for LATE_BORROW per iter.
;;;
;;; HEAD's pick_borrow_slice falls back to u-high only when the
;;; compressed future log is short. Our substrate has no future log;
;;; we engage whenever the width-truncation envelope leaves enough
;;; high-zero space on u.
(define (dgcd-borrow-engages? uv-w n+1 odd-u-on?)
(let ((mask-w (if odd-u-on? (- uv-w 1) uv-w)))
(and *dgcd-late-borrow-uv-high*
(>= mask-w 1)
(<= (+ uv-w mask-w) n+1))))
;;; ── one Kaliski iteration with dialog-gcd width schedule ────────
;;; kaliski-iteration-dgcd! — clone of kaliski-iteration-trunc! but
;;; with the smooth envelope and truncated comparator.
;;;
;;; Identical control flow to kaliski-iteration-trunc!
;;; (mod-inv-by.lsp:1046); only the width helpers change. We name
;;; iteration-local ancillae with a "dg-" prefix so allocator names
;;; don't collide with concurrently-built kaliski-iteration-trunc!
;;; circuits inside the same emitter (defensive — no current call
;;; site mixes them).
(define (kaliski-iteration-dgcd! c iter-idx n+1 p
u-name v-w-name r-name s-name
f-name f-idx
m-hist-name m-idx
cin-name cin-idx
tmp-name flag-name flag-idx
red-tmp-name
a-masked-scratch-name)
"Kaliski iteration under HEAD's DIALOG_GCD width envelope. Same
semantics as kaliski-iteration-trunc!; widths from dgcd helpers."
(let* ((a-f (string->symbol
(string-append "kal-dg-a-f-"
(number->string iter-idx))))
(b-f (string->symbol
(string-append "kal-dg-b-f-"
(number->string iter-idx))))
(add-f (string->symbol
(string-append "kal-dg-add-f-"
(number->string iter-idx))))
(l-gt (string->symbol
(string-append "kal-dg-l-gt-"
(number->string iter-idx))))
(or-chain (string->symbol
(string-append "kal-dg-or-chain-"
(number->string iter-idx))))
(n (- n+1 1))
(uv-w (dgcd-uv-width-raw iter-idx n+1))
(uv-n (- uv-w 1))
(rs3-w (mib-rs-step3-width iter-idx n+1))
(rs9-w (mib-rs-step9-width iter-idx n+1)))
(alloc! c a-f 1)
(alloc! c b-f 1)
(alloc! c add-f 1)
(alloc! c l-gt 1)
;; ── STEP 0: is_zero check over uv-n bits of v_w ──
(is-zero-into! c v-w-name uv-n flag-name flag-idx or-chain)
(gate-ccx! c f-name f-idx flag-name flag-idx m-hist-name m-idx)
(is-zero-into! c v-w-name uv-n flag-name flag-idx or-chain)
(gate-cx! c m-hist-name m-idx f-name f-idx)
;; ── STEP 1 (lane 0) ──
(gate-x! c u-name 0)
(gate-ccx! c f-name f-idx u-name 0 a-f 0)
(gate-x! c u-name 0)
(gate-ccx! c f-name f-idx u-name 0 l-gt 0)
(gate-x! c v-w-name 0)
(gate-ccx! c l-gt 0 v-w-name 0 m-hist-name m-idx)
(gate-x! c v-w-name 0)
(gate-ccx! c f-name f-idx u-name 0 l-gt 0)
(gate-cx! c a-f 0 b-f 0)
(gate-cx! c m-hist-name m-idx b-f 0)
;; ── STEP 2 — TRUNCATED comparator (D2) ──
(dgcd-cmp-gt-into! c u-name v-w-name uv-n iter-idx
l-gt 0 cin-name cin-idx)
(gate-ccx! c f-name f-idx l-gt 0 add-f 0)
(gate-x! c b-f 0)
(gate-ccx! c add-f 0 b-f 0 a-f 0)
(gate-ccx! c add-f 0 b-f 0 m-hist-name m-idx)
(gate-x! c b-f 0)
(gate-ccx! c f-name f-idx l-gt 0 add-f 0)
(dgcd-cmp-gt-into! c u-name v-w-name uv-n iter-idx
l-gt 0 cin-name cin-idx)
;; ── STEP 3: cswap(u, v_w) over uv-w; cswap(r, s) over rs3-w ──
;;
;; ODD_U fastpath does NOT skip lane 0 of cswap in our substrate.
;; Our cswap is controlled by a_f, which fires in the (u[0]=0,
;; v_w[0]=1) sub-case where lane-0 swap is NOT identity. HEAD
;; can skip because its cswap is controlled by b0_and_b1 =
;; v_w[0] AND (u>v_w) which only fires when both are odd
;; (cswap on two 1-bits = identity). Substrate mismatch
;; documented at HEAD ref mod.rs:24944 + classical trace
;; mod-inv-by.lsp:782-785.
(cswap-reg! c a-f 0 u-name v-w-name uv-w)
(cswap-reg! c a-f 0 r-name s-name rs3-w)
;; ── STEP 4 ──
(gate-x! c b-f 0)
(gate-ccx! c f-name f-idx b-f 0 add-f 0)
(gate-x! c b-f 0)
;; sub: borrow + odd-u apply to u→v_w slot (binary-GCD invariant
;; carries u). Engagement gate folds *dgcd-late-borrow-uv-high*
;; AND room (2*mask-w <= n+1).
(let* ((odd-u? *dgcd-odd-u-lowbit-fastpath*)
(borrow? (dgcd-borrow-engages? uv-w n+1 odd-u?))
(sub-mask (string->symbol
(string-append "kal-dg-sub-mask-"
(number->string iter-idx)))))
(cond
((or borrow? odd-u?)
(dgcd-ctrl-cuccaro-sub-extended! c add-f 0
u-name uv-w n+1
v-w-name
cin-name cin-idx
sub-mask
borrow? odd-u?))
(else
(ctrl-cuccaro-sub! c add-f 0 u-name v-w-name uv-w
cin-name cin-idx sub-mask))))
;; add: r/s side — odd-u does NOT apply here (no oddness on r/s).
;; LATE_BORROW also does NOT engage on r/s (r has no truncation
;; envelope; full n+1 bits live throughout).
(ctrl-cuccaro-add! c add-f 0 r-name s-name rs9-w
cin-name cin-idx
(string->symbol
(string-append "kal-dg-add-mask-"
(number->string iter-idx))))
;; ── STEP 5 ──
(gate-x! c b-f 0)
(gate-ccx! c f-name f-idx b-f 0 add-f 0)
(gate-x! c b-f 0)
(gate-cx! c m-hist-name m-idx b-f 0)
(gate-cx! c a-f 0 b-f 0)
;; ── STEP 6: v_w := v_w >> 1 over uv-w bits ──
(shift-right-reg! c v-w-name uv-w)
;; ── STEP 7+8: r := 2r mod p (full p, see kaliski-iteration-trunc!) ──
(mod-double-inplace! c r-name n+1 p
cin-name cin-idx tmp-name flag-name flag-idx)
;; ── STEP 9 ──
;; Same lane-0-cswap-preserved policy as STEP 3 — see above.
(cswap-reg! c a-f 0 u-name v-w-name uv-w)
(cswap-reg! c a-f 0 r-name s-name rs9-w)
;; ── STEP 10 ──
(gate-x! c s-name 0)
(gate-ccx! c f-name f-idx s-name 0 a-f 0)
(gate-x! c s-name 0)
(free! c l-gt)
(free! c add-f)
(free! c b-f)
(free! c a-f)))
;;; ── mod-inv-by-dialog-gcd! — top-level entry ─────────────────────
;;; Same calling convention as mod-inv-by-refined!. The classical-
;;; replay backward sweep handles the cap-aware uncompute.
;;;
;;; CRITICAL: classical-kaliski-r-final and classical-kaliski-trace
;;; are parameterized by `iters`. We pass the resolved
;;; *dgcd-active-iters* cap so the K-correction and final-state
;;; reset match the capped quantum forward sweep.
(define (mod-inv-by-dialog-gcd! c a-reg out-reg n+1 p
cin-reg cin-idx tmp-reg flag-reg flag-idx
red-tmp-reg)
"out := a^{-1} mod p via Kaliski under HEAD's DIALOG_GCD lever.
Same calling convention as mod-inv-by-refined!. REQUIRES a-reg
bound via bind-input!/bind-mirror!. *dgcd-active-iters* may cap
below 2n; correctness gate runs at build time."
(let* ((n (- n+1 1))
(iters (dgcd-resolve-iters n+1))
(u 'kal-u)
(v-w 'kal-v-w)
(r 'kal-r)
(s 'kal-s)
(f 'kal-f)
(m-hist 'kal-m-hist)
(mc-tmp 'kal-mc-tmp)
(mc-pow 'kal-mc-pow)
(a-mask 'kal-a-masked)
(a-bound (find-classical-value c a-reg)))
(cond
((<= n 0)
(error "mod-inv-by-dialog-gcd! requires n+1 > 1; got" n+1))
;; *static-circuit-mode*: under K=1, K-correction here is
;; `a`-independent (same as mod-inv-by-dialog-gcd-host! above).
;; K=2 is gated to host-only at the next branch — no need to
;; duplicate the static-mode + K=2 incompatibility check.
((and (not a-bound)
(not *static-circuit-mode*))
(error "mod-inv-by-dialog-gcd! requires a-reg classical via"
" bind-input!/bind-mirror!; not found:" a-reg))
(*dgcd-k2-bounded-shift*
;; sweep-k2-port: K=2 bounded shift only ported into the host
;; variant. Non-host classical-replay's final-* values reflect
;; K=2 forward — but non-host quantum forward sweep does K=1 —
;; so the backward sweep would reset to WRONG state. Refuse to
;; emit instead of producing a silently-broken .bin. Use the
;; host variant (mod-inv-by-dialog-gcd-host!) for K=2.
(error "*dgcd-k2-bounded-shift* requires HOST_GATED variant. "
"Set *dgcd-host-gated* and use mod-inv-by-dialog-gcd-host!"))
(else
;; ── Build-time correctness gate: K from a=1 trace must invert ──
;; r_on_1 (at the capped iter count) the SAME way it does at 2n.
;; If the cap is too aggressive r_on_1 may be 0 (no inverse), in
;; which case we error before emitting any gates.
(let ((r-on-1 (classical-kaliski-r-final 1 p iters n+1)))
(when (= (modulo r-on-1 p) 0)
(error "mod-inv-by-dialog-gcd! *dgcd-active-iters* too low: "
"r_on_1 mod p = 0 at iters=" iters
" n+1=" n+1 " p=" p)))
;; ── ODD_U soundness gate ──
;; The body fastpath (skip-lane-0 of mask compute + body, with
;; cx(add_f, v_w[0]) compensation) is structurally sound on
;; our substrate: from the classical kaliski-iteration-trunc!
;; trace, add_f=1 occurs ⇔ both u and v_w are odd at the
;; body call site (proof: add_f4 = f AND NOT b_f1; b_f1=0
;; only when both u, v_w odd). When add_f=1, v_w[0]-u[0] =
;; 1-1 = 0 with no borrow into bit 1 — value-exact lane-0
;; replacement. The CSWAP lane 0 is NOT skipped (our cswap
;; controller a_f fires in u[0]=0,v_w[0]=1 cases where
;; lane-0 swap is not identity). HEAD's cswap-skip relies
;; on its b0_and_b1 controller which differs from a_f.
;; ── Allocate Kaliski state ──
(alloc! c u n+1)
(alloc! c v-w n+1)
(alloc! c r n+1)
(alloc! c s n+1)
(alloc! c f 1)
(alloc! c m-hist iters)
(alloc! c a-mask n+1)
;; ── Init ──
(load-const! c u n+1 p)
(cx-copy-reg! c a-reg v-w n+1)
(gate-x! c s 0)
(gate-x! c f 0)
;; ── Forward sweep (D1 + D2 + D3) ──
(let loop ((i 0))
(when (< i iters)
(kaliski-iteration-dgcd! c i n+1 p
u v-w r s
f 0
m-hist i
cin-reg cin-idx
tmp-reg flag-reg flag-idx
red-tmp-reg
a-mask)
(loop (+ i 1))))
;; ── Classical correction K at the capped iter count ──
(let* ((r-on-1 (classical-kaliski-r-final 1 p iters n+1))
(k-correct (classical-mod-inv p r-on-1))
(k-inverse r-on-1))
(in-place-mul-const! c r n+1 p k-correct
cin-reg cin-idx tmp-reg flag-reg flag-idx
red-tmp-reg
mc-tmp mc-pow)
(cx-copy-reg! c r out-reg n+1)
(in-place-mul-const! c r n+1 p k-inverse
cin-reg cin-idx tmp-reg flag-reg flag-idx
red-tmp-reg
mc-tmp mc-pow))
;; ── Classical-replay backward sweep (capped trace) ──
(let* ((trace (classical-kaliski-trace a-bound p iters n+1))
(final-u (car trace))
(final-v-w (car (cdr trace)))
(final-r (car (cdr (cdr trace))))
(final-s (car (cdr (cdr (cdr trace)))))
(final-f (car (cdr (cdr (cdr (cdr trace))))))
(m-i-vec (car (cdr (cdr (cdr (cdr (cdr trace))))))))
(classical-reset! c u n+1 final-u)
(classical-reset! c v-w n+1 final-v-w)
(classical-reset! c r n+1 final-r)
(classical-reset! c s n+1 final-s)
(when (= final-f 1) (gate-x! c f 0))
(let loop ((i 0))
(when (< i iters)
(when (= (vector-ref m-i-vec i) 1)
(gate-x! c m-hist i))
(loop (+ i 1)))))
;; ── Free Kaliski state ──
(free! c a-mask)
(free! c m-hist)
(free! c f)
(free! c s)
(free! c r)
(free! c v-w)
(free! c u)))))
;;; ── public-name dispatch from mod-inv-by! is NOT done here ───────
;;;
;;; To keep this lever isolated from karatsuba-agent's concurrent
;;; work on mod-inv-by.lsp / variants-real.lsp, the variant entry in
;;; sweep-005 calls mod-inv-by-dialog-gcd! DIRECTLY via a thin
;;; builder. See variants-real.lsp's v-by-dialog-gcd-solinas (added
;;; in this file's load order so existing variants stay untouched).
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