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lumbda/quantum/adder.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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;;; adder.lsp — Cuccaro ripple-carry reversible n-bit adder.
;;;
;;; Phase B step 1 of the lumbda-native point-add port.
;;;
;;; Ports the upstream Rust primitives from
;;; ~/git/ecdsafail-challenge/src/point_add/mod.rs:1027..1181
;;;
;;; MAJ(x, y, w): (cx w y) (cx w x) (ccx x y w)
;;; UMA(x, y, w): (ccx x y w) (cx w x) (cx x y)
;;;
;;; cuccaro-add!(a, acc, c-in):
;;; n = (length a) = (length acc)
;;; n=0 -> noop
;;; n=1 -> (cx c-in acc[0]) (cx a[0] acc[0])
;;; else:
;;; Forward MAJ sweep:
;;; maj(c-in, acc[0], a[0])
;;; for i in 1..n-1: maj(a[i-1], acc[i], a[i])
;;; Final sum bit:
;;; cx a[n-2] acc[n-1]
;;; cx a[n-1] acc[n-1]
;;; Reverse UMA sweep:
;;; for i in (n-2)..1: uma(a[i-1], acc[i], a[i])
;;; uma(c-in, acc[0], a[0])
;;;
;;; Invariant: (cuccaro-add! a acc c-in) leaves
;;; acc := (acc + a) mod 2^n
;;; a := a (unchanged)
;;; c-in := 0 (uncomputed cleanly)
;;;
;;; Validation: see tests/unit/test-adder.lsp. We run the resulting
;;; circuit through sim.lsp at n in {4, 8, 16} and assert the output
;;; register equals the classical (a + b) mod 2^n.
(load "quantum/gates.lsp")
;;; ── MAJ + UMA primitives ───────────────────────────────────────
(define (maj! c x-reg x-idx y-reg y-idx w-reg w-idx)
"MAJ(x, y, w): (cx w y) (cx w x) (ccx x y w)."
(gate-cx! c w-reg w-idx y-reg y-idx)
(gate-cx! c w-reg w-idx x-reg x-idx)
(gate-ccx! c x-reg x-idx y-reg y-idx w-reg w-idx))
(define (uma! c x-reg x-idx y-reg y-idx w-reg w-idx)
"UMA(x, y, w): (ccx x y w) (cx w x) (cx x y)."
(gate-ccx! c x-reg x-idx y-reg y-idx w-reg w-idx)
(gate-cx! c w-reg w-idx x-reg x-idx)
(gate-cx! c x-reg x-idx y-reg y-idx))
;;; ── mcx3_polar + ctrl_maj family ──────────────────────────────────
;;;
;;; Port of HEAD's 3-control X with per-control polarity
;;; (arith/adder.rs:1761) plus the four controlled MAJ/UMA wrappers
;;; (lines 1804-1825) that build on it.
;;;
;;; SCOPE: default path of mcx3_polar (explicit CCX uncompute of
;;; scratch). HEAD's env-gated Gidney measured-uncompute branch (toggled
;;; by `DIALOG_GCD_CTRL_LOWQ_MEASURED=1`) saves the coherent CCX at the
;;; cost of an HMR + classical CZ correction. Deferred to a follow-up
;;; sweep — would add lumbda flag `*mcx3-polar-measured-uncompute*`
;;; defaulting `#f` (matches HEAD's env-unset default).
;;;
;;; All four `ctrl-*!` wrappers use mcx3-polar with all-positive
;;; polarities (the only callers in HEAD). Polarity arguments are kept
;;; in mcx3-polar!'s signature for full HEAD-API parity.
(define (mcx3-polar! c c1-reg c1-idx p1 c2-reg c2-idx p2 c3-reg c3-idx p3
target-reg target-idx scratch-reg scratch-idx)
"target ^= (c1==p1) & (c2==p2) & (c3==p3). p1/p2/p3 are scheme
booleans (#t = positive control, #f = negative-via-X-wrap). scratch
borrowed clean (|0> in/out). Default path emits ccx(c1,c2,scratch),
ccx(scratch,c3,target), then explicit ccx(c1,c2,scratch) uncompute.
HEAD's Gidney measured-uncompute branch (env-gated) deferred."
;; X-wrap negative controls (HEAD adder.rs:1772-1780)
(cond ((not p1) (gate-x! c c1-reg c1-idx)))
(cond ((not p2) (gate-x! c c2-reg c2-idx)))
(cond ((not p3) (gate-x! c c3-reg c3-idx)))
;; Compute scratch = c1 & c2, then target ^= scratch & c3.
(gate-ccx! c c1-reg c1-idx c2-reg c2-idx scratch-reg scratch-idx)
(gate-ccx! c scratch-reg scratch-idx c3-reg c3-idx target-reg target-idx)
;; Default-path uncompute: re-emit the same CCX. (Gidney path would
;; use HMR + cz_if here — deferred.)
(gate-ccx! c c1-reg c1-idx c2-reg c2-idx scratch-reg scratch-idx)
;; X-wrap reverse — restore controls to original polarity (HEAD lines
;; 1791-1800).
(cond ((not p3) (gate-x! c c3-reg c3-idx)))
(cond ((not p2) (gate-x! c c2-reg c2-idx)))
(cond ((not p1) (gate-x! c c1-reg c1-idx))))
(define (ctrl-maj! c ctrl-reg ctrl-idx x-reg x-idx y-reg y-idx w-reg w-idx
scratch-reg scratch-idx)
"Controlled MAJ. When ctrl=|1>, computes maj(x, y, w) in place
(matches the uncontrolled maj!); when ctrl=|0>, no-op. Mirror of
HEAD's ctrl_maj (arith/adder.rs:1804)."
(gate-ccx! c ctrl-reg ctrl-idx w-reg w-idx y-reg y-idx)
(gate-ccx! c ctrl-reg ctrl-idx w-reg w-idx x-reg x-idx)
(mcx3-polar! c ctrl-reg ctrl-idx #t x-reg x-idx #t y-reg y-idx #t
w-reg w-idx scratch-reg scratch-idx))
(define (ctrl-uma! c ctrl-reg ctrl-idx x-reg x-idx y-reg y-idx w-reg w-idx
scratch-reg scratch-idx)
"Controlled UMA — inverse of ctrl-maj!. Mirror of HEAD's ctrl_uma
(arith/adder.rs:1810)."
(mcx3-polar! c ctrl-reg ctrl-idx #t x-reg x-idx #t y-reg y-idx #t
w-reg w-idx scratch-reg scratch-idx)
(gate-ccx! c ctrl-reg ctrl-idx w-reg w-idx x-reg x-idx)
(gate-ccx! c ctrl-reg ctrl-idx x-reg x-idx y-reg y-idx))
(define (ctrl-inv-maj! c ctrl-reg ctrl-idx x-reg x-idx y-reg y-idx w-reg w-idx
scratch-reg scratch-idx)
"Controlled INV-MAJ — alt inverse used in HEAD's clean-MAJ blocks.
Mirror of HEAD's ctrl_inv_maj (arith/adder.rs:1816)."
(mcx3-polar! c ctrl-reg ctrl-idx #t x-reg x-idx #t y-reg y-idx #t
w-reg w-idx scratch-reg scratch-idx)
(gate-ccx! c ctrl-reg ctrl-idx w-reg w-idx x-reg x-idx)
(gate-ccx! c ctrl-reg ctrl-idx w-reg w-idx y-reg y-idx))
(define (ctrl-inv-uma! c ctrl-reg ctrl-idx x-reg x-idx y-reg y-idx w-reg w-idx
scratch-reg scratch-idx)
"Controlled INV-UMA. Mirror of HEAD's ctrl_inv_uma
(arith/adder.rs:1822)."
(gate-ccx! c ctrl-reg ctrl-idx x-reg x-idx y-reg y-idx)
(gate-ccx! c ctrl-reg ctrl-idx w-reg w-idx x-reg x-idx)
(mcx3-polar! c ctrl-reg ctrl-idx #t x-reg x-idx #t y-reg y-idx #t
w-reg w-idx scratch-reg scratch-idx))
;;; ── Cuccaro ripple-carry adder ─────────────────────────────────
(define (cuccaro-add! c a-reg acc-reg cin-reg cin-idx n)
"Emit gates implementing acc := (acc + a) mod 2^n.
Requires (= n (register-width a-reg) (register-width acc-reg)).
cin-reg[cin-idx] starts |0>, ends |0>."
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 acc-reg 0))
(else
;; Forward MAJ sweep
(maj! c cin-reg cin-idx acc-reg 0 a-reg 0)
(let loop ((i 1))
(when (< i (- n 1))
(maj! c a-reg (- i 1) acc-reg i a-reg i)
(loop (+ i 1))))
;; Final sum bit
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
;; Reverse UMA sweep
(let loop ((i (- n 2)))
(when (>= i 1)
(uma! c a-reg (- i 1) acc-reg i a-reg i)
(loop (- i 1))))
(uma! c cin-reg cin-idx acc-reg 0 a-reg 0))))
;;; ── HEAD fast variant: HMR-uncompute carries ─────────────────────
;;;
;;; Port of HEAD's `cuccaro_add_fast` (mod.rs:1042-1092) +
;;; `cuccaro_sub_fast` (mod.rs:1658-1707). Allocates explicit carry
;;; ancillas + replaces UMA-CCX backward uncompute with HMR + push-cond +
;;; CZ + pop-cond per bit. Saves (n-1) Toffoli per call (0-Toffoli
;;; backward sweep per HEAD's design).
;;;
;;; Caller responsibility: provide `carries-name` register pre-allocated
;;; to width n-1 + clean (|0>); + a `bit-base` integer for classical bit
;;; IDs. The function uses bit IDs bit-base .. bit-base+n-2.
(define (cuccaro-add-fast! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base)
"Same algebra as cuccaro-add! but with HMR carry uncompute.
Pre: carries-name register (width n-1) allocated by caller, all |0>.
Post: carries-name returns to |0>; a-reg + cin-reg unchanged;
acc-reg := (acc + a) mod 2^n.
sweep-056: when (and *apply-phase-architecture* *cuccaro-vented*)
is #t, dispatch into cuccaro-add-fast-vented!."
(cond
((and *cuccaro-vented* *apply-phase-architecture*)
(cuccaro-add-fast-vented! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base))
((= n 0) #t)
((= n 1)
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 acc-reg 0))
(else
;; Forward sweep — MAJ-like with explicit carries
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 carries-name 0)
(gate-cx! c carries-name 0 a-reg 0)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg i acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-name i)
(gate-cx! c carries-name i a-reg i)
(loop-fwd (+ i 1))))
;; Final sum bit
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
;; Backward HMR uncompute sweep (0 Toffoli)
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-name i a-reg i)
(gate-hmr! c carries-name i (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(loop-back (- i 1))))
;; Step 0 backward
(gate-cx! c carries-name 0 a-reg 0)
(gate-hmr! c carries-name 0 bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c cin-reg cin-idx acc-reg 0))))
(define (cuccaro-sub-fast! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base)
"Same as cuccaro-add-fast! but: acc := (acc - a - cin) mod 2^n.
Mirrors HEAD's cuccaro_sub_fast (mod.rs:1658-1707).
sweep-056: vented dispatch on (and *apply-phase-architecture*
*cuccaro-vented*) #t."
(cond
((and *cuccaro-vented* *apply-phase-architecture*)
(cuccaro-sub-fast-vented! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base))
((= n 0) #t)
((= n 1)
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c cin-reg cin-idx acc-reg 0))
(else
;; Forward inv_UMA sweep
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 carries-name 0)
(gate-cx! c carries-name 0 a-reg 0)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-name i)
(gate-cx! c carries-name i a-reg i)
(loop-fwd (+ i 1))))
;; Final sum bit
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
;; Backward inv_MAJ HMR uncompute sweep
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-name i a-reg i)
(gate-hmr! c carries-name i (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg i acc-reg i)
(loop-back (- i 1))))
;; Step 0 backward
(gate-cx! c carries-name 0 a-reg 0)
(gate-hmr! c carries-name 0 bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c a-reg 0 acc-reg 0))))
;;; *cuccaro-use-fast* — substrate flag. When #t, ctrl-cuccaro-*-hosted!
;;; (mod-inv-by-dialog-gcd-host.lsp) dispatches to cuccaro-{add,sub}-fast!
;;; instead of cuccaro-{add,sub}! for the inner ops. Caller must
;;; pre-allocate carries register + reserve bit-id range.
(define *cuccaro-use-fast* #f)
;;; *cuccaro-vented* — sweep-056 apply-phase retrofit flag.
;;;
;;; When BOTH *apply-phase-architecture* AND *cuccaro-vented* are #t,
;;; cuccaro-{add,sub}-fast! & cuccaro-{add,sub}-fast-borrowed! dispatch
;;; into apply-phase-aware vented variants (defined at end of this file).
;;; The vented variants exercise the sweep-054 substrate by wrapping each
;;; call in a begin-apply-phase! / end-apply-phase! scope pair & sourcing
;;; vent-key BitIds from apply-phase-bit-next (the substrate's global
;;; allocator at 1,000,000+) instead of the caller-supplied bit-base.
;;;
;;; Algorithmic note (per sweep-056 analysis): the legacy backward
;;; uncompute sweep already emits per-iter (hmr + push-cond + cz + pop-cond)
;;; which IS the venting wire pattern. Each iter's CZ_if acts on
;;; (a[i-1], acc[i]) — operand qubits that subsequent iters MUTATE via
;;; cx a[i] -> a[i-1] & cx a[i-1] -> acc[i] before sweep end. Deferring
;;; the CZ_if to a post-sweep broadcast would therefore use stale operand
;;; values & break correctness. The vented first-cut consequently keeps
;;; the per-iter wire pattern intact but routes vent-key allocation
;;; through the substrate — exercising begin/end scope discipline +
;;; bit-allocator state-machine. Downstream peak-qubits win requires
;;; restructuring the carries lane (HEAD venting.rs:147-309 ripples on 2
;;; clean ancillas instead of n-1) which exceeds the constraint of this
;;; sweep (adder.lsp-only, no caller surgery).
;;;
;;; When *apply-phase-architecture* is #f (default), this flag is inert
;;; even if set #t — the vented path checks the architecture flag first.
(define *cuccaro-vented* #f)
;;; ── HEAD borrowed-carries variant — overlay carries on caller's free ancilla ─
;;;
;;; Port of HEAD's `cuccaro_add_fast_borrowed_carries` (mod.rs:1097-1144) +
;;; `cuccaro_sub_fast_borrowed_carries` (mirror). Same gate sequence as the
;;; -fast! variant but the carries lane is BORROWED from a caller-supplied
;;; register at the given offset. The HMR uncompute returns carries to
;;; clean |0> so caller's register is unchanged at exit.
;;;
;;; HEAD comment line 1095: "Kaliski step4 can reuse clean high `tmp` lanes
;;; without increasing peak Q." Our equivalent: ctrl-cuccaro-*-hosted!
;;; passes mod-inv-by-dialog-gcd-host!'s tmp register as the carries source
;;; — tmp is free during STEP 4 (used only by mod-double-inplace! at STEP 7+8).
(define (cuccaro-add-fast-borrowed! c a-reg acc-reg cin-reg cin-idx n
carries-reg carries-offset bit-base)
"Same as cuccaro-add-fast! but carries are borrowed from
carries-reg starting at carries-offset (uses n-1 slots).
carries-reg[carries-offset..carries-offset+n-2] must be |0>
on entry; HMR uncompute returns them to |0> on exit.
sweep-056: vented dispatch on (and *apply-phase-architecture*
*cuccaro-vented*) #t."
(cond
((and *cuccaro-vented* *apply-phase-architecture*)
(cuccaro-add-fast-borrowed-vented! c a-reg acc-reg cin-reg cin-idx n
carries-reg carries-offset bit-base))
((= n 0) #t)
((= n 1)
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 acc-reg 0))
(else
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg 0)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg i acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(loop-fwd (+ i 1))))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(gate-hmr! c carries-reg (+ carries-offset i) (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(loop-back (- i 1))))
(gate-cx! c carries-reg carries-offset a-reg 0)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c cin-reg cin-idx acc-reg 0))))
(define (cuccaro-add-fast-borrowed-no-cin! c a-reg acc-reg n
carries-reg carries-offset bit-base)
"acc += a mod 2^n with c_in PROVEN |0> by the caller. Mirrors HEAD's
cuccaro_add_fast_borrowed_carries_no_cin (arith/adder.rs:1184).
Same algebra as cuccaro-add-fast-borrowed! with the c_in qubit folded
out — saves the 4 cin-touching CX gates (2 forward, 2 reverse) and
means the caller doesn't need to alloc a c_in ancilla at all.
carries-reg[carries-offset..carries-offset+n-2] must be |0> on entry;
HMR uncompute returns them to |0> on exit.
Per HEAD's comment at adder.rs:1218-1228: the trailing reverse-step
pattern `cz_if(c_in,acc[0],m0); cx(a[0],c_in); cx(c_in,acc[0])` of
the c_in form collapses to a single `cz_if(a[0],acc[0],m0)` here
because (1) `cx(carries[0],a[0])` just restored a[0] to the frozen
c_in value so cz_if on a[0] == cz_if on c_in, and (2) the two
trailing CXs reset c_in (now |0>) and then cx c_in into acc (no-op
on |0>) — both drop out."
(cond
((= n 0) #t)
((= n 1)
;; Pure XOR — no carry lane needed when c_in == 0.
(gate-cx! c a-reg 0 acc-reg 0))
(else
;; Step 0 forward (cin folded out — a[0] takes its place as the
;; ccx control after the seed cx).
(gate-cx! c a-reg 0 acc-reg 0)
(gate-ccx! c a-reg 0 acc-reg 0 carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg 0)
;; Forward sweep [1..n-1) — unchanged from cuccaro-add-fast-borrowed!
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg i acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(loop-fwd (+ i 1))))
;; Top sum — unchanged.
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
;; Backward HMR sweep [1..n-1) reverse — unchanged.
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(gate-hmr! c carries-reg (+ carries-offset i) (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(loop-back (- i 1))))
;; Step 0 reverse — c_in folded out: just unwind carry[0] + cz_if
;; on a[0] (a[0] still carries the c_in value at this point because
;; the immediately-preceding `cx(carries[0],a[0])` restored it).
;; No trailing `cx(a[0],c_in)` + `cx(c_in,acc[0])` pair — see
;; docstring.
(gate-cx! c carries-reg carries-offset a-reg 0)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c a-reg 0 acc-reg 0)
(gate-pop-cond! c))))
(define (cuccaro-sub-fast-borrowed-no-cin! c a-reg acc-reg n
carries-reg carries-offset bit-base)
"acc -= a mod 2^n with c_in PROVEN |0>. Mirrors HEAD's
cuccaro_sub_fast_borrowed_carries_no_cin (arith/adder.rs:1241).
Same algebra as cuccaro-sub-fast-borrowed! with c_in folded out by
exactly the same pattern as the add direction; see
cuccaro-add-fast-borrowed-no-cin! docstring for the algebra rationale."
(cond
((= n 0) #t)
((= n 1)
;; Pure XOR (subtraction mod 2 == addition mod 2 for the single
;; bit case; c_in == 0 collapses the cin-fed CX away).
(gate-cx! c a-reg 0 acc-reg 0))
(else
;; Step 0 forward (cin folded out, a[0] takes its place).
(gate-ccx! c a-reg 0 acc-reg 0 carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg 0)
;; Forward sweep [1..n-1) — unchanged from cuccaro-sub-fast-borrowed!
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(loop-fwd (+ i 1))))
;; Top sum.
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
;; Backward HMR sweep [1..n-1) reverse.
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(gate-hmr! c carries-reg (+ carries-offset i) (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg i acc-reg i)
(loop-back (- i 1))))
;; Step 0 reverse — c_in folded out.
(gate-cx! c carries-reg carries-offset a-reg 0)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c a-reg 0 acc-reg 0)
(gate-pop-cond! c)
;; Final acc XOR with a[0] in the sub direction — preserved from
;; cuccaro-sub-fast-borrowed!'s sub-direction tail (the cin form
;; ended with `cx(a[0],acc[0])` after the cz_if + reset triple,
;; and the reset triple drops out per the no-cin algebra but the
;; standalone `cx(a[0],acc[0])` stays because sub's algebra
;; requires it independently of c_in folding).
(gate-cx! c a-reg 0 acc-reg 0))))
(define (cuccaro-sub-fast-borrowed! c a-reg acc-reg cin-reg cin-idx n
carries-reg carries-offset bit-base)
"Same as cuccaro-sub-fast! but carries borrowed from carries-reg.
sweep-056: vented dispatch on (and *apply-phase-architecture*
*cuccaro-vented*) #t."
(cond
((and *cuccaro-vented* *apply-phase-architecture*)
(cuccaro-sub-fast-borrowed-vented! c a-reg acc-reg cin-reg cin-idx n
carries-reg carries-offset bit-base))
((= n 0) #t)
((= n 1)
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c cin-reg cin-idx acc-reg 0))
(else
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg 0)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(loop-fwd (+ i 1))))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(gate-hmr! c carries-reg (+ carries-offset i) (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg i acc-reg i)
(loop-back (- i 1))))
(gate-cx! c carries-reg carries-offset a-reg 0)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c a-reg 0 acc-reg 0))))
;;; *cuccaro-use-borrowed* — when #t, ctrl-cuccaro-*-hosted! uses the
;;; cuccaro-fast-borrowed variants with tmp-reg as the carries source.
;;; ZERO peak qubit cost (tmp is already allocated by caller).
(define *cuccaro-use-borrowed* #f)
;;; ── sweep-cuccaro-lane-vector — multi-source borrow primitive ──────
;;;
;;; Port of HEAD's `dialog_gcd_build_composite_scratch` lane vector
;;; (compressed.rs:362-435). HEAD's body-scratch borrow is a `Vec<QubitId>`
;;; collected from MULTIPLE source slices (future-carry, current-block
;;; compressed cells, u-high, v-high). When `DIALOG_GCD_BORROW_CURRENT_BLOCK`
;;; fires (compressed.rs:416-427), the current block's own compressed cells
;;; are folded into the lanes — a pure qubit relabel that shrinks the
;;; body-scratch deficit.
;;;
;;; Lumbda's existing `cuccaro-*-fast-borrowed!` accepts a SINGLE
;;; `(carries-reg, carries-offset)` source: carry slot `i` resolves to
;;; `(carries-reg, carries-offset + i)`. The lane-vector primitive
;;; widens that signature: carry slot `i` resolves through a list of
;;; `(reg offset width)` triples, walking lanes left-to-right.
;;;
;;; Backward compatibility: a lane vector of `((carries-reg carries-offset (- n 1)))`
;;; produces a BYTE-IDENTICAL gate sequence to the single-source variant
;;; (proven by construction — see `cuccaro-lane-resolve` below).
;;;
;;; Lane-vector format: a list of triples `(reg offset width)` where
;;; - reg is a register name (symbol or string)
;;; - offset is the starting bit index within reg
;;; - width is the number of |0> carry slots this lane contributes
;;; Total width across lanes MUST be >= n-1. Each lane's slice
;;; reg[offset..offset+width] MUST be |0> on entry; the HMR uncompute
;;; restores all lanes to |0> on exit (each lane bit is HMR'd via
;;; bit-base + global-carry-index, so HMR classical bit IDs stay
;;; sequential exactly like the single-source variant).
;;;
;;; `cuccaro-lane-resolve` translates a global carry index `i` ∈ [0, n-1)
;;; to a `(reg . offset)` pair by walking lane-vec. Total Toffoli /
;;; Clifford / HMR-bit counts are IDENTICAL to single-source — only
;;; the qubit IDs the gates touch change.
(define (cuccaro-lane-resolve lane-vec global-i)
"Walk lane-vec to find the (reg . offset) for global carry index
global-i. Returns a pair (reg . offset). Errors if global-i exceeds
total lane width."
(let loop ((lanes lane-vec) (remaining global-i))
(cond
((null? lanes)
(error "cuccaro-lane-resolve: carry index out of lane-vec total width"))
(else
(let* ((lane (car lanes))
(l-reg (car lane))
(l-off (car (cdr lane)))
(l-w (car (cdr (cdr lane)))))
(cond
((< remaining l-w)
(cons l-reg (+ l-off remaining)))
(else
(loop (cdr lanes) (- remaining l-w)))))))))
(define (cuccaro-lane-total-width lane-vec)
"Sum widths across lane-vec."
(let loop ((lanes lane-vec) (acc 0))
(cond
((null? lanes) acc)
(else
(loop (cdr lanes) (+ acc (car (cdr (cdr (car lanes))))))))))
;; Sentinel: lane primitives loaded
(define *cuccaro-lane-vector-loaded* #t)
(define (cuccaro-add-fast-borrowed-lane! c a-reg acc-reg cin-reg cin-idx n
lane-vec bit-base)
"Multi-source variant of cuccaro-add-fast-borrowed!. Carries are
borrowed from a lane vector (list of `(reg offset width)` triples)
instead of a single (carries-reg, carries-offset) source. Total
lane-width must be >= n-1.
Each lane's slice reg[offset..offset+width] must be |0> on entry;
HMR uncompute restores all to |0> on exit. Consumes n-1 HMR
classical bit IDs (bit-base..bit-base+n-2), identical to the
single-source variant.
Backward compat: passing `((reg off (- n 1)))` produces a gate stream
byte-identical to cuccaro-add-fast-borrowed! at (reg, off)."
(when (< (cuccaro-lane-total-width lane-vec) (- n 1))
(error "cuccaro-add-fast-borrowed-lane!: lane-vec total width < n-1"))
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 acc-reg 0))
(else
;; Step 0 forward — lane slot 0
(let* ((slot0 (cuccaro-lane-resolve lane-vec 0))
(s0-reg (car slot0))
(s0-off (cdr slot0)))
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 s0-reg s0-off)
(gate-cx! c s0-reg s0-off a-reg 0))
;; Forward sweep i in [1, n-1)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(let* ((slot (cuccaro-lane-resolve lane-vec i))
(s-reg (car slot))
(s-off (cdr slot)))
(gate-cx! c a-reg i acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i s-reg s-off)
(gate-cx! c s-reg s-off a-reg i))
(loop-fwd (+ i 1))))
;; Top sum capture
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
;; Backward HMR uncompute sweep, n-1 iters
(let loop-back ((i (- n 2)))
(when (>= i 1)
(let* ((slot (cuccaro-lane-resolve lane-vec i))
(s-reg (car slot))
(s-off (cdr slot)))
(gate-cx! c s-reg s-off a-reg i)
(gate-hmr! c s-reg s-off (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg (- i 1) acc-reg i))
(loop-back (- i 1))))
;; Step 0 backward
(let* ((slot0 (cuccaro-lane-resolve lane-vec 0))
(s0-reg (car slot0))
(s0-off (cdr slot0)))
(gate-cx! c s0-reg s0-off a-reg 0)
(gate-hmr! c s0-reg s0-off bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c cin-reg cin-idx acc-reg 0)))))
(define (cuccaro-sub-fast-borrowed-lane! c a-reg acc-reg cin-reg cin-idx n
lane-vec bit-base)
"Multi-source variant of cuccaro-sub-fast-borrowed!. Mirror of
cuccaro-add-fast-borrowed-lane! with sub algebra. Same lane-vec
conventions; same n-1 HMR bit IDs consumed."
(when (< (cuccaro-lane-total-width lane-vec) (- n 1))
(error "cuccaro-sub-fast-borrowed-lane!: lane-vec total width < n-1"))
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c cin-reg cin-idx acc-reg 0))
(else
;; Step 0 forward
(let* ((slot0 (cuccaro-lane-resolve lane-vec 0))
(s0-reg (car slot0))
(s0-off (cdr slot0)))
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 s0-reg s0-off)
(gate-cx! c s0-reg s0-off a-reg 0))
;; Forward sweep
(let loop-fwd ((i 1))
(when (< i (- n 1))
(let* ((slot (cuccaro-lane-resolve lane-vec i))
(s-reg (car slot))
(s-off (cdr slot)))
(gate-cx! c a-reg (- i 1) acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i s-reg s-off)
(gate-cx! c s-reg s-off a-reg i))
(loop-fwd (+ i 1))))
;; Top borrow capture
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
;; Backward HMR uncompute sweep
(let loop-back ((i (- n 2)))
(when (>= i 1)
(let* ((slot (cuccaro-lane-resolve lane-vec i))
(s-reg (car slot))
(s-off (cdr slot)))
(gate-cx! c s-reg s-off a-reg i)
(gate-hmr! c s-reg s-off (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg i acc-reg i))
(loop-back (- i 1))))
;; Step 0 backward
(let* ((slot0 (cuccaro-lane-resolve lane-vec 0))
(s0-reg (car slot0))
(s0-off (cdr slot0)))
(gate-cx! c s0-reg s0-off a-reg 0)
(gate-hmr! c s0-reg s0-off bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c a-reg 0 acc-reg 0)))))
;;; *cuccaro-use-borrowed-lane* — when #t, ctrl-cuccaro-*-hosted! uses
;;; the lane-vector primitives instead of the single-source borrowed
;;; variants. The lane vector is supplied via *cuccaro-lane-vector-thunk*
;;; — a thunk evaluated at each callsite that returns the current
;;; lane vector (lets callers build per-iter / per-call lane vectors
;;; from currently-allocated borrow sources).
;;;
;;; Default `#f` keeps the single-source path active → byte-identity
;;; with champion preserved. When `#t` AND *cuccaro-use-borrowed* is
;;; also `#t` (so the borrowed path is selected), the lane-vector
;;; primitive fires; single-source callers degrade to a one-lane vec
;;; produced by the default thunk for byte-identity.
(define *cuccaro-use-borrowed-lane* #f)
;; Default thunk: builds a one-lane vector covering the entire single-
;; source (tmp-borrow) carries region. Caller sets this to a custom
;; thunk to inject multi-source lanes (e.g. tmp-borrow + block-k
;; compressed cells).
;;
;; Thunk signature: (lambda (n tmp-name) lane-vector) — receives the
;; adder width n and the legacy tmp-borrow register name; returns a
;; lane-vec list of (reg offset width) triples with total width >= n-1.
(define (cuccaro-lane-default-thunk n tmp-name)
(list (list tmp-name 0 (- n 1))))
(define *cuccaro-lane-vector-thunk* cuccaro-lane-default-thunk)
;;; ── HEAD specialization: cuccaro-add when acc is |0> on entry ─────
;;;
;;; Port of HEAD's `mod_add_qq_fast_from_zero` first-add specialization
;;; (mod.rs:961-1038). When the accumulator is provably |0> on entry,
;;; (acc + a) mod 2^n simplifies to a; the full Cuccaro adder reduces
;;; to n CX-copies of a into acc. Saves n-1 CCX per call vs the n-1
;;; MAJs in cuccaro-add!, & matches HEAD's lines 970-972 verbatim.
;;;
;;; Caller responsibility: acc-reg MUST be |0> on entry across all n
;;; bits. cin-reg unused (mirrors HEAD: no carry-in concept when both
;;; addends start at zero — cin would just leak into acc[0] as a CX).
;;; Pre/post: a-reg unchanged; acc-reg := a on exit.
;;;
;;; cin-reg/cin-idx parameters retained for signature parity with
;;; cuccaro-add! so the call sites in mod-add-from-zero! / mod-mul-
;;; solinas-from-zero! stay uniform.
(define (cuccaro-add-from-zero! c a-reg acc-reg cin-reg cin-idx n)
"acc := a (mod 2^n) when acc is |0> on entry. n CX-copies, 0 CCX.
cin-reg/cin-idx ignored (HEAD's specialization has no carry-in slot)."
(let loop ((i 0))
(when (< i n)
(gate-cx! c a-reg i acc-reg i)
(loop (+ i 1)))))
;;; ── HEAD low-to-ext family: source width n, acc width n+1 ─────────
;;;
;;; Port of HEAD's `cuccaro_add_fast_low_to_ext` (mod.rs:1711-1750) +
;;; `cuccaro_sub_fast_low_to_ext` (mod.rs:1754-1793). Same algebra as
;;; the non-ext fast variants but the accumulator is one bit wider than
;;; the source — the top sum bit (carry-out) is written into acc[n]
;;; instead of being discarded.
;;;
;;; Per HEAD's design, carries lane is internally caller-supplied (we
;;; expose carries-name + bit-base so the offset-aware windowed wrapper
;;; can drive these from a parent scope). carries width MUST be n.
;;; HMR bit IDs consumed: n (indices bit-base..bit-base+n-1).
;;;
;;; a-off and acc-off are starting indices into a-reg and acc-reg
;;; respectively — pass 0 for the default standalone call; the
;;; windowed top-level passes lo for per-block dispatch.
;;; ── cuccaro-add-low-to-ext-clean! + cuccaro-sub-low-to-ext-clean! ──
;;;
;;; Port of HEAD cuccaro_add_low_to_ext_clean (adder.rs:208-238) +
;;; cuccaro_sub_low_to_ext_clean (adder.rs:240-271), commit 2dcf00d.
;;; "Clean" variants: full n-step MAJ forward + UMA backward sweep,
;;; NO HMR, NO carry-lane ancilla -- "safe inside emit_inverse blocks"
;;; per HEAD's docstring. Materializes the carry-out into
;;; acc-ext[n] (the extension bit) via CX after the forward sweep.
;;;
;;; Substrate status: ADDITIVE. No lumbda caller dispatches through
;;; either primitive yet. Closes §1.1 ABSENT rows 7+8 (the last two
;;; ABSENT rows in §1.1 — the Cuccaro family now has full primitive
;;; coverage per HEAD-PARITY-COLLAB).
;;;
;;; Algorithm (HEAD lines 208-238):
;;; 1. maj(c_in, acc[0], a[0])
;;; 2. for i=1..n-1: maj(a[i-1], acc[i], a[i])
;;; 3. cx(a[n-1], acc[n]) -- carry-out into ext bit
;;; 4. for i=n-1..1: uma(a[i-1], acc[i], a[i])
;;; 5. uma(c_in, acc[0], a[0])
;;;
;;; a-reg + cin-reg preserved across the call (carry chain closes back
;;; to entry state); acc-ext-reg gets sum + carry-out. n=0 is a
;;; clean no-op except CX(c_in, acc[0]) per HEAD's degenerate path.
;;;
;;; Sub-clean uses inv-uma!/inv-maj! and reverses the sweep order;
;;; the CX(a[n-1], acc[n]) sits in the middle, self-inverse.
(define (cuccaro-add-low-to-ext-clean!
c a-reg acc-ext-reg n cin-reg cin-idx)
;; acc-ext := (a + acc-ext + cin); a-reg width >= n;
;; acc-ext-reg width >= n+1. a + cin restored.
(cond
((= n 0)
(gate-cx! c cin-reg cin-idx acc-ext-reg 0))
(else
(maj! c cin-reg cin-idx acc-ext-reg 0 a-reg 0)
(let loop ((i 1))
(when (< i n)
(maj! c a-reg (- i 1) acc-ext-reg i a-reg i)
(loop (+ i 1))))
(gate-cx! c a-reg (- n 1) acc-ext-reg n)
(let loop-back ((i (- n 1)))
(when (>= i 1)
(uma! c a-reg (- i 1) acc-ext-reg i a-reg i)
(loop-back (- i 1))))
(uma! c cin-reg cin-idx acc-ext-reg 0 a-reg 0))))
(define (cuccaro-sub-low-to-ext-clean!
c a-reg acc-ext-reg n cin-reg cin-idx)
;; acc-ext := (acc-ext - (a + cin)). Per HEAD lines 240-271: same
;; carry identity under the running ext bit; uses inv_uma + inv_maj.
(cond
((= n 0)
(gate-cx! c cin-reg cin-idx acc-ext-reg 0))
(else
(inv-uma! c cin-reg cin-idx acc-ext-reg 0 a-reg 0)
(let loop ((i 1))
(when (< i n)
(inv-uma! c a-reg (- i 1) acc-ext-reg i a-reg i)
(loop (+ i 1))))
(gate-cx! c a-reg (- n 1) acc-ext-reg n)
(let loop-back ((i (- n 1)))
(when (>= i 1)
(inv-maj! c a-reg (- i 1) acc-ext-reg i a-reg i)
(loop-back (- i 1))))
(inv-maj! c cin-reg cin-idx acc-ext-reg 0 a-reg 0))))
(define (cuccaro-add-fast-low-to-ext! c
a-reg a-off
acc-reg acc-off
cin-reg cin-idx
n
carries-reg carries-offset
bit-base)
"acc-ext := (acc-ext + a + cin) mod 2^(n+1).
a-reg slice : a-reg[a-off..a-off+n] (source, width n)
acc-reg slice: acc-reg[acc-off..acc-off+n+1] (extended, width n+1)
Top sum bit (carry-out) lands at acc-reg[acc-off+n].
carries-reg[carries-offset..carries-offset+n-1] must be |0> entry/exit.
Consumes n HMR classical bit IDs (bit-base..bit-base+n-1)."
(cond
((= n 0)
(gate-cx! c cin-reg cin-idx acc-reg acc-off))
(else
;; Forward sweep — n carries (one per source bit)
(gate-cx! c a-reg a-off acc-reg acc-off)
(gate-cx! c a-reg a-off cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg acc-off carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg a-off)
(let loop-fwd ((i 1))
(when (< i n)
(gate-cx! c a-reg (+ a-off i) acc-reg (+ acc-off i))
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-ccx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i)
carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg (+ a-off i))
(loop-fwd (+ i 1))))
;; Top sum bit captured into the extended slot acc[n]
(gate-cx! c a-reg (+ a-off (- n 1)) acc-reg (+ acc-off n))
;; Backward HMR uncompute sweep (n-1 iters)
(let loop-back ((i (- n 1)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i)
a-reg (+ a-off i))
(gate-hmr! c carries-reg (+ carries-offset i)
(+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i))
(gate-pop-cond! c)
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-cx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i))
(loop-back (- i 1))))
;; Step 0 backward
(gate-cx! c carries-reg carries-offset a-reg a-off)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg acc-off)
(gate-pop-cond! c)
(gate-cx! c a-reg a-off cin-reg cin-idx)
(gate-cx! c cin-reg cin-idx acc-reg acc-off))))
(define (cuccaro-sub-fast-low-to-ext! c
a-reg a-off
acc-reg acc-off
cin-reg cin-idx
n
carries-reg carries-offset
bit-base)
"acc-ext := (acc-ext - a - cin) mod 2^(n+1). Mirror of
cuccaro-add-fast-low-to-ext! — carries-reg + bit-base usage identical.
Consumes n HMR classical bit IDs."
(cond
((= n 0)
(gate-cx! c cin-reg cin-idx acc-reg acc-off))
(else
;; Forward inv-UMA sweep
(gate-cx! c cin-reg cin-idx acc-reg acc-off)
(gate-cx! c a-reg a-off cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg acc-off carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg a-off)
(let loop-fwd ((i 1))
(when (< i n)
(gate-cx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i))
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-ccx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i)
carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg (+ a-off i))
(loop-fwd (+ i 1))))
;; Top borrow bit captured into the extended slot acc[n]
(gate-cx! c a-reg (+ a-off (- n 1)) acc-reg (+ acc-off n))
;; Backward HMR uncompute sweep
(let loop-back ((i (- n 1)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i)
a-reg (+ a-off i))
(gate-hmr! c carries-reg (+ carries-offset i)
(+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i))
(gate-pop-cond! c)
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-cx! c a-reg (+ a-off i) acc-reg (+ acc-off i))
(loop-back (- i 1))))
;; Step 0 backward
(gate-cx! c carries-reg carries-offset a-reg a-off)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg acc-off)
(gate-pop-cond! c)
(gate-cx! c a-reg a-off cin-reg cin-idx)
(gate-cx! c a-reg a-off acc-reg acc-off))))
;;; ── low-to-ext borrowed-carries c_in-folded-out variants ──────────
;;;
;;; Ports of HEAD's `cuccaro_{add,sub}_fast_low_to_ext_borrowed_carries_no_cin`
;;; (`src/point_add/arith/adder.rs:631` + `:680`, commit 2dcf00d). Same
;;; algebra as the c_in form (cuccaro-{add,sub}-fast-low-to-ext!) with
;;; the c_in qubit folded out — saves 1 c_in ancilla + 4 trailing/leading
;;; CX gates per call when the caller proves c_in == |0>.
;;;
;;; SCOPE: ports the DEFAULT path only (HEAD's `gate_suffix` from
;;; `square_selfhost_gate_suffix_carries(n)` defaults to 0 via env var
;;; `SQUARE_SELFHOST_GATE_SUFFIX_CARRIES`). With gate_suffix=0 the
;;; hybrid borrowed/clean-MAJ scheme degenerates to pure borrowed-carries
;;; (the `for i in borrowed..n` clean-MAJ loops are empty). Hybrid scheme
;;; (env-driven gate_suffix > 0; lowers peak qubit by gate_suffix at the
;;; cost of extra Toffoli) is a separate future port — would add a
;;; lumbda flag `*cuccaro-low-ext-gate-suffix-carries*` and the maj/
;;; uma-fed clean-MAJ block. Worth doing when a lumbda caller materializes
;;; that wants the peak-qubit tradeoff.
(define (cuccaro-add-fast-low-to-ext-borrowed-no-cin!
c a-reg a-off acc-reg acc-off n
carries-reg carries-offset bit-base)
"acc[acc-off..acc-off+n+1) += a[a-off..a-off+n) mod 2^(n+1) with c_in
PROVEN |0> by the caller. Mirror of HEAD's
cuccaro_add_fast_low_to_ext_borrowed_carries_no_cin at gate_suffix=0
(the default env path). acc top bit (carry-out) lands at
acc[acc-off+n]. carries-reg[carries-offset..carries-offset+n-1] must
be |0> on entry; HMR uncompute returns them to |0> on exit. Consumes
n HMR classical bit IDs (bit-base..bit-base+n-1)."
(cond
((= n 0) #t)
(else
;; Step 0 forward (cin folded out — a[0] takes its place).
(gate-cx! c a-reg a-off acc-reg acc-off)
(gate-ccx! c a-reg a-off acc-reg acc-off carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg a-off)
;; Forward sweep [1..n) — borrowed-carries path; clean-MAJ block
;; (HEAD's `for i in borrowed..n`) is empty under gate_suffix=0.
(let loop-fwd ((i 1))
(when (< i n)
(gate-cx! c a-reg (+ a-off i) acc-reg (+ acc-off i))
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-ccx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i)
carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg (+ a-off i))
(loop-fwd (+ i 1))))
;; Top sum lands at acc[n] — the low-to-ext extension.
(gate-cx! c a-reg (+ a-off (- n 1)) acc-reg (+ acc-off n))
;; Backward HMR uncompute sweep [1..n) reverse — borrowed pattern.
;; HEAD's reverse clean-UMA block (`for i in (borrowed..n).rev`) is
;; empty under gate_suffix=0.
(let loop-back ((i (- n 1)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i)
a-reg (+ a-off i))
(gate-hmr! c carries-reg (+ carries-offset i)
(+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i))
(gate-pop-cond! c)
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-cx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i))
(loop-back (- i 1))))
;; Step 0 reverse — c_in folded out. cz_if on a[0] (the preceding
;; cx(carries[0],a[0]) restored a[0] to c_in's frozen value). No
;; trailing cx pair (see cuccaro-add-fast-borrowed-no-cin! docstring
;; for the algebra rationale).
(gate-cx! c carries-reg carries-offset a-reg a-off)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c a-reg a-off acc-reg acc-off)
(gate-pop-cond! c))))
(define (cuccaro-sub-fast-low-to-ext-borrowed-no-cin!
c a-reg a-off acc-reg acc-off n
carries-reg carries-offset bit-base)
"acc[acc-off..acc-off+n+1) -= a[a-off..a-off+n) mod 2^(n+1) with
c_in PROVEN |0>. Mirror of HEAD's
cuccaro_sub_fast_low_to_ext_borrowed_carries_no_cin at gate_suffix=0.
See add variant docstring for the c_in folding algebra; sub retains
its trailing cx(a[0], acc[0]) per HEAD's sub-direction tail (the cz_if
pair drops out but the standalone XOR is independent of c_in)."
(cond
((= n 0) #t)
(else
;; Step 0 forward (cin folded out, sub direction has no seed CX).
(gate-ccx! c a-reg a-off acc-reg acc-off carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg a-off)
;; Forward sweep [1..n) — sub direction; clean-INV-UMA block empty
;; under gate_suffix=0.
(let loop-fwd ((i 1))
(when (< i n)
(gate-cx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i))
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-ccx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i)
carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg (+ a-off i))
(loop-fwd (+ i 1))))
;; Top sum lands at acc[n].
(gate-cx! c a-reg (+ a-off (- n 1)) acc-reg (+ acc-off n))
;; Backward HMR uncompute sweep [1..n) reverse — sub direction.
;; Clean-INV-MAJ block empty under gate_suffix=0.
(let loop-back ((i (- n 1)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i)
a-reg (+ a-off i))
(gate-hmr! c carries-reg (+ carries-offset i)
(+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i))
(gate-pop-cond! c)
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-cx! c a-reg (+ a-off i) acc-reg (+ acc-off i))
(loop-back (- i 1))))
;; Step 0 reverse — c_in folded out.
(gate-cx! c carries-reg carries-offset a-reg a-off)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c a-reg a-off acc-reg acc-off)
(gate-pop-cond! c)
;; Trailing cx(a[0], acc[0]) — sub-direction algebra requires this
;; independently of c_in folding (only the cz_if + reset triple
;; collapses; standalone CX stays).
(gate-cx! c a-reg a-off acc-reg acc-off))))
;;; ── Per-block kernel for windowed wrappers ────────────────────────
;;;
;;; cuccaro-add-fast-blk! / cuccaro-sub-fast-blk! — equal-width n add/sub
;;; with offset args plus top-bit overrides. Used by the windowed
;;; top-level for non-final blocks where the top bit of a is a fresh
;;; |0> ancilla (a-top-*) and the top bit of acc is a fresh cout
;;; ancilla (acc-top-*), each sitting in a separate register handle
;;; from the lo..hi-1 slice of the parent registers.
;;;
;;; Algebra mirrors `cuccaro_add_fast`(mod.rs:1042) but at every index
;;; i in [0,n), reads of `a[i]` and `acc[i]` resolve as:
;;; if i < n-1: (parent-reg, parent-off + i)
;;; if i = n-1: (top-reg, top-idx)
;;;
;;; carries-reg width MUST be >= n-1 starting at carries-offset.
;;; Consumes (n-1) HMR classical bit IDs.
(define (cuccaro-add-fast-blk! c
a-reg a-off a-top-reg a-top-idx
acc-reg acc-off acc-top-reg acc-top-idx
cin-reg cin-idx
n
carries-reg carries-offset
bit-base)
"Equal-width Cuccaro fast-add at width n with split top-bit operands.
a[i<n-1] = a-reg[a-off+i]; a[n-1] = a-top-reg[a-top-idx]
acc[i<n-1] = acc-reg[acc-off+i]; acc[n-1] = acc-top-reg[acc-top-idx]
Consumes (n-1) HMR classical bit IDs (bit-base..bit-base+n-2)."
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c cin-reg cin-idx acc-top-reg acc-top-idx)
(gate-cx! c a-top-reg a-top-idx acc-top-reg acc-top-idx))
(else
;; helpers: resolve "bit i of a" and "bit i of acc" via inline cond
;; (no values/multi-return needed — just emit the call directly)
;;
;; Forward sweep
;; Step 0
(gate-cx! c a-reg a-off acc-reg acc-off)
(gate-cx! c a-reg a-off cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg acc-off carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg a-off)
;; Steps i in [1, n-1) — pure parent-slice case
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg (+ a-off i) acc-reg (+ acc-off i))
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-ccx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i)
carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg (+ a-off i))
(loop-fwd (+ i 1))))
;; Final sum bit: two CXs into acc[n-1] = acc-top
;; cx(a[n-2], acc[n-1]) cx(a[n-1], acc[n-1])
(gate-cx! c a-reg (+ a-off (- n 2)) acc-top-reg acc-top-idx)
(gate-cx! c a-top-reg a-top-idx acc-top-reg acc-top-idx)
;; Backward HMR uncompute (i in (n-2)..1, descending)
;; NOTE: backward loop in cuccaro_add_fast runs i in 1..n-1 reversed
;; → i = n-2 down to 1. All such i satisfy i < n-1, so a[i],a[i-1]
;; both live in the parent slice. acc[i] also lives in parent slice.
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i)
a-reg (+ a-off i))
(gate-hmr! c carries-reg (+ carries-offset i)
(+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i))
(gate-pop-cond! c)
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-cx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i))
(loop-back (- i 1))))
;; Step 0 backward — uses cin + acc[0]
(gate-cx! c carries-reg carries-offset a-reg a-off)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg acc-off)
(gate-pop-cond! c)
(gate-cx! c a-reg a-off cin-reg cin-idx)
(gate-cx! c cin-reg cin-idx acc-reg acc-off))))
(define (cuccaro-sub-fast-blk! c
a-reg a-off a-top-reg a-top-idx
acc-reg acc-off acc-top-reg acc-top-idx
cin-reg cin-idx
n
carries-reg carries-offset
bit-base)
"Equal-width Cuccaro fast-sub at width n with split top-bit operands.
Top-bit override semantics identical to cuccaro-add-fast-blk!.
Consumes (n-1) HMR classical bit IDs."
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c a-top-reg a-top-idx acc-top-reg acc-top-idx)
(gate-cx! c cin-reg cin-idx acc-top-reg acc-top-idx))
(else
(gate-cx! c cin-reg cin-idx acc-reg acc-off)
(gate-cx! c a-reg a-off cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg acc-off carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg a-off)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i))
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-ccx! c a-reg (+ a-off (- i 1)) acc-reg (+ acc-off i)
carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg (+ a-off i))
(loop-fwd (+ i 1))))
;; Final sub bit: two CXs into acc[n-1] = acc-top
;; cx(a[n-1], acc[n-1]) cx(a[n-2], acc[n-1])
(gate-cx! c a-top-reg a-top-idx acc-top-reg acc-top-idx)
(gate-cx! c a-reg (+ a-off (- n 2)) acc-top-reg acc-top-idx)
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i)
a-reg (+ a-off i))
(gate-hmr! c carries-reg (+ carries-offset i)
(+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i))
(gate-pop-cond! c)
(gate-cx! c a-reg (+ a-off i) a-reg (+ a-off (- i 1)))
(gate-cx! c a-reg (+ a-off i) acc-reg (+ acc-off i))
(loop-back (- i 1))))
(gate-cx! c carries-reg carries-offset a-reg a-off)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg acc-off)
(gate-pop-cond! c)
(gate-cx! c a-reg a-off cin-reg cin-idx)
(gate-cx! c a-reg a-off acc-reg acc-off))))
;;; ── Windowed Cuccaro fast-add / fast-sub ──────────────────────────
;;;
;;; Port of HEAD's `cuccaro_add_fast_windowed` (mod.rs:1995-2055) +
;;; `cuccaro_sub_fast_windowed` (mod.rs:2061-2117).
;;;
;;; Threads the inter-block carry/borrow through a 1-bit extension per
;;; block. ~(n/blocks) measured-carry ancillae live at once (vs n-1 for
;;; a single cuccaro-add-fast!). ~1 Toffoli/bit; the MBUC saving is
;;; PEAK QUBITS — total Toffoli increases by O(blocks) due to per-block
;;; boundary-clear cmp_lt calls.
;;;
;;; Caller pre-allocates a `name-base` symbol scope; the windowed wrapper
;;; alloc's per-block ancillae using `(string->symbol (string-append
;;; (symbol->string name-base) "-blk-K-cout"))` and frees them in reverse.
;;;
;;; bit-base reservation: the caller MUST reserve at LEAST the following
;;; HMR bit IDs starting at bit-base:
;;; - For each non-final block of width w_blk = hi-lo:
;;; the per-block call uses (w_blk + 1) - 1 = w_blk HMR bits
;;; (cuccaro-add-fast-blk! at n = w_blk + 1, consumes n-1 = w_blk)
;;; - For the final block at width w_last (no extension):
;;; cuccaro-add-fast! at n = w_last, consumes (n-1) = w_last-1 HMR
;;; - For each non-final block's boundary clear:
;;; cmp-lt-into-fast! at width p = hi, consumes p HMR bits
;;;
;;; Caller-side simplest upper bound: reserve 4n bit IDs starting at
;;; bit-base. We document tighter accounting per block below.
(define (cuccaro-add-fast-windowed! c
a-reg acc-reg cin-reg cin-idx n
blocks
name-base bit-base)
"acc := (acc + a + cin) mod 2^n via blocks-wise dispatch.
blocks >= 1; clamped to [1, n]. blocks=1 falls back to
cuccaro-add-fast! (uses a freshly-alloc'd carries register
named (name-base)-carries-direct).
See module header for bit-base reservation rules."
(cond
((= n 0) #t)
(else
(let* ((blocks (cond ((< blocks 1) 1)
((> blocks n) n)
(else blocks))))
(cond
((= blocks 1)
;; Direct fallback: alloc carries (n-1) + delegate
(let ((carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-direct"))))
(alloc! c carries-name (- n 1))
(cuccaro-add-fast! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base)
(free! c carries-name)))
(else
;; Walk blocks, threading carry. Track (cout-name, p) pairs.
(let loop ((blk 0)
(lo 0)
(carry-reg cin-reg)
(carry-idx cin-idx)
(bit-cur bit-base)
(couts '()))
(cond
((>= blk blocks)
;; Boundary clear pass over couts (reverse order).
(windowed-clear-couts! c a-reg acc-reg
couts
name-base bit-cur
'add)
#t)
(else
(let* ((hi (quotient (* (+ blk 1) n) blocks)))
(cond
((<= hi lo)
(loop (+ blk 1) lo carry-reg carry-idx bit-cur couts))
((or (= blk (- blocks 1)) (= hi n))
;; LAST block — non-extended cuccaro_add_fast at
;; width (n - lo). Direct call into existing
;; cuccaro-add-fast! which expects a-reg/acc-reg
;; from index 0; we need an offset-aware variant.
;; Use cuccaro-add-fast-blk! with a-top-* + acc-top-*
;; pointing back into the parent at index (n-1).
(let* ((w (- n lo))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-final"))))
(cond
((= w 0) #t)
((= w 1)
;; Trivial 1-bit add at slot lo
(gate-cx! c carry-reg carry-idx acc-reg lo)
(gate-cx! c a-reg lo acc-reg lo))
(else
(alloc! c carries-name (- w 1))
(cuccaro-add-fast-blk!
c
a-reg lo
a-reg (+ lo (- w 1)) ; a-top = parent[n-1]
acc-reg lo
acc-reg (+ lo (- w 1)) ; acc-top = parent[n-1]
carry-reg carry-idx
w
carries-name 0
bit-cur)
(free! c carries-name)))
;; final block — boundary clear over outstanding couts
(windowed-clear-couts! c a-reg acc-reg
couts
name-base
(+ bit-cur (max 0 (- w 1)))
'add)))
(else
;; NON-final block — width w_blk = hi - lo, extended
;; with fresh zero (above a slice) + cout (above acc
;; slice). cuccaro-add-fast-blk! at n = w_blk + 1.
(let* ((w-blk (- hi lo))
(n-ext (+ w-blk 1))
(cout-name
(string->symbol
(string-append (symbol->string name-base)
"-cout-"
(number->string blk))))
(zero-name
(string->symbol
(string-append (symbol->string name-base)
"-zero-"
(number->string blk))))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-"
(number->string blk)))))
(alloc! c cout-name 1)
(alloc! c zero-name 1)
(alloc! c carries-name (- n-ext 1))
(cuccaro-add-fast-blk!
c
a-reg lo
zero-name 0 ; a-top = fresh |0> ancilla
acc-reg lo
cout-name 0 ; acc-top = cout ancilla
carry-reg carry-idx
n-ext
carries-name 0
bit-cur)
(free! c carries-name)
(free! c zero-name)
(loop (+ blk 1)
hi
cout-name 0
(+ bit-cur (- n-ext 1))
(cons (list cout-name hi) couts))))))))))))))
#t)
(define (cuccaro-sub-fast-windowed! c
a-reg acc-reg cin-reg cin-idx n
blocks
name-base bit-base)
"acc := (acc - a - cin) mod 2^n via blocks-wise dispatch.
Mirror of cuccaro-add-fast-windowed! using sub kernels.
blocks=1 falls back to cuccaro-sub-fast!."
(cond
((= n 0) #t)
(else
(let ((blocks (cond ((< blocks 1) 1)
((> blocks n) n)
(else blocks))))
(cond
((= blocks 1)
(let ((carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-direct"))))
(alloc! c carries-name (- n 1))
(cuccaro-sub-fast! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base)
(free! c carries-name)))
(else
(let loop ((blk 0)
(lo 0)
(borrow-reg cin-reg)
(borrow-idx cin-idx)
(bit-cur bit-base)
(bouts '()))
(cond
((>= blk blocks)
(windowed-clear-couts! c a-reg acc-reg
bouts
name-base bit-cur
'sub)
#t)
(else
(let* ((hi (quotient (* (+ blk 1) n) blocks)))
(cond
((<= hi lo)
(loop (+ blk 1) lo borrow-reg borrow-idx bit-cur bouts))
((or (= blk (- blocks 1)) (= hi n))
(let* ((w (- n lo))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-final"))))
(cond
((= w 0) #t)
((= w 1)
(gate-cx! c a-reg lo acc-reg lo)
(gate-cx! c borrow-reg borrow-idx acc-reg lo))
(else
(alloc! c carries-name (- w 1))
(cuccaro-sub-fast-blk!
c
a-reg lo
a-reg (+ lo (- w 1))
acc-reg lo
acc-reg (+ lo (- w 1))
borrow-reg borrow-idx
w
carries-name 0
bit-cur)
(free! c carries-name)))
(windowed-clear-couts! c a-reg acc-reg
bouts
name-base
(+ bit-cur (max 0 (- w 1)))
'sub)))
(else
(let* ((w-blk (- hi lo))
(n-ext (+ w-blk 1))
(bout-name
(string->symbol
(string-append (symbol->string name-base)
"-bout-"
(number->string blk))))
(zero-name
(string->symbol
(string-append (symbol->string name-base)
"-zero-"
(number->string blk))))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-"
(number->string blk)))))
(alloc! c bout-name 1)
(alloc! c zero-name 1)
(alloc! c carries-name (- n-ext 1))
(cuccaro-sub-fast-blk!
c
a-reg lo
zero-name 0
acc-reg lo
bout-name 0
borrow-reg borrow-idx
n-ext
carries-name 0
bit-cur)
(free! c carries-name)
(free! c zero-name)
(loop (+ blk 1)
hi
bout-name 0
(+ bit-cur (- n-ext 1))
(cons (list bout-name hi) bouts))))))))))))))
#t)
;;; Internal: boundary-carry / borrow clearer for windowed-add/sub.
;;; For add: c_j := (acc[0..p] < a[0..p]) — cmp-lt-into-fast!(acc, a)
;;; For sub: b_j := (a[0..p] < acc[0..p]) after X-flipping a[0..p]
;;; i.e. (~a < acc) — cmp-lt-into-fast!(a, acc) with a inverted,
;;; then a restored.
;;; Frees each cout/bout in reverse order.
(define (windowed-clear-couts! c a-reg acc-reg couts
name-base bit-start direction)
"Clear boundary carries (direction='add) or borrows (direction='sub).
couts is a list of (name p) pairs in REVERSE processing order
(we just walk left-to-right since it's already reversed by cons).
bit-start = bit-base offset for the cmp HMRs."
(let loop ((items couts) (bit-cur bit-start))
(cond
((null? items) #t)
(else
(let* ((item (car items))
(cname (car item))
(p (cadr item))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-cmp-carries-"
(symbol->string cname))))
(cin-name
(string->symbol
(string-append (symbol->string name-base)
"-cmp-cin-"
(symbol->string cname)))))
(alloc! c carries-name p)
(alloc! c cin-name 1)
(cond
((eq? direction 'add)
;; cmp-lt-into-fast!(acc[0..p], a[0..p], cname)
(cmp-lt-into-fast! c acc-reg a-reg p
cname 0
cin-name 0
carries-name 0 bit-cur))
(else
;; sub: X-flip a[0..p], cmp-lt-into-fast!(a, acc), un-X-flip
(let loopx ((i 0))
(when (< i p) (gate-x! c a-reg i) (loopx (+ i 1))))
(cmp-lt-into-fast! c a-reg acc-reg p
cname 0
cin-name 0
carries-name 0 bit-cur)
(let loopx ((i 0))
(when (< i p) (gate-x! c a-reg i) (loopx (+ i 1))))))
(free! c cin-name)
(free! c carries-name)
(free! c cname)
(loop (cdr items) (+ bit-cur p)))))))
;;; ── Windowed Cuccaro fast-add / fast-sub — low-to-ext family ─────
;;;
;;; Port of HEAD's `cuccaro_add_fast_windowed_low_to_ext` (mod.rs:2119)
;;; + `cuccaro_sub_fast_windowed_low_to_ext` (mod.rs:2169).
;;;
;;; Same threading shape as the non-ext windowed; final block calls
;;; cuccaro-add-fast-low-to-ext! (offset-aware) instead of
;;; cuccaro-add-fast-blk!. acc-reg is (n+1)-wide, a-reg is n-wide.
;;; The block partition is over ext_n = n+1 (not n) — last block's
;;; a-slice may be shorter than its acc-slice.
;;;
;;; bit-base reservation identical to non-ext windowed plus 1 extra
;;; HMR bit per non-final block (kernel consumes n-ext-1 = w_blk bits,
;;; same as non-ext) — the final block consumes n_final HMR bits (one
;;; more than non-ext since _low_to_ext loops over n iters not n-1).
(define (cuccaro-add-fast-windowed-low-to-ext! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
"acc-ext := (acc-ext + a + cin) mod 2^(n+1) via blocks-wise dispatch.
a-reg width n; acc-reg width n+1. blocks >= 1; clamped to [1, n+1].
blocks=1 falls back to cuccaro-add-fast-low-to-ext! (alloc carries)."
(let* ((ext-n (+ n 1)))
(cond
((= ext-n 0) #t)
(else
(let ((blocks (cond ((< blocks 1) 1)
((> blocks ext-n) ext-n)
(else blocks))))
(cond
((= blocks 1)
(let ((carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-direct"))))
(alloc! c carries-name n)
(cuccaro-add-fast-low-to-ext! c
a-reg 0
acc-reg 0
cin-reg cin-idx
n
carries-name 0
bit-base)
(free! c carries-name)))
(else
(let loop ((blk 0)
(lo 0)
(carry-reg cin-reg)
(carry-idx cin-idx)
(bit-cur bit-base)
(couts '()))
(cond
((>= blk blocks)
(windowed-clear-couts-low-to-ext! c a-reg acc-reg
couts
name-base bit-cur
'add)
#t)
(else
(let* ((hi (quotient (* (+ blk 1) ext-n) blocks)))
(cond
((<= hi lo)
(loop (+ blk 1) lo carry-reg carry-idx bit-cur couts))
((or (= blk (- blocks 1)) (= hi ext-n))
;; LAST block — _low_to_ext at source-width (n - lo).
;; (acc slice is hi - lo, which equals (n+1) - lo;
;; matches _low_to_ext convention.)
(let* ((w-src (- n lo))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-final"))))
(cond
((= w-src 0)
;; degenerate: only one acc bit beyond lo
(gate-cx! c carry-reg carry-idx acc-reg lo))
(else
(alloc! c carries-name w-src)
(cuccaro-add-fast-low-to-ext!
c
a-reg lo
acc-reg lo
carry-reg carry-idx
w-src
carries-name 0
bit-cur)
(free! c carries-name)))
(windowed-clear-couts-low-to-ext!
c a-reg acc-reg
couts
name-base
(+ bit-cur w-src)
'add)))
(else
;; NON-final block — width w_blk = hi - lo. Uses
;; cuccaro-add-fast-blk! at n = w_blk + 1 with
;; zero ancilla above a-slice + cout above
;; acc-slice. (Same shape as non-ext windowed.)
(let* ((w-blk (- hi lo))
(n-ext-k (+ w-blk 1))
(cout-name
(string->symbol
(string-append (symbol->string name-base)
"-cout-"
(number->string blk))))
(zero-name
(string->symbol
(string-append (symbol->string name-base)
"-zero-"
(number->string blk))))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-"
(number->string blk)))))
(alloc! c cout-name 1)
(alloc! c zero-name 1)
(alloc! c carries-name (- n-ext-k 1))
(cuccaro-add-fast-blk!
c
a-reg lo
zero-name 0
acc-reg lo
cout-name 0
carry-reg carry-idx
n-ext-k
carries-name 0
bit-cur)
(free! c carries-name)
(free! c zero-name)
(loop (+ blk 1)
hi
cout-name 0
(+ bit-cur (- n-ext-k 1))
(cons (list cout-name hi) couts)))))))))))))))
#t)
(define (cuccaro-sub-fast-windowed-low-to-ext! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
"acc-ext := (acc-ext - a - cin) mod 2^(n+1) via blocks-wise dispatch.
Mirror of cuccaro-add-fast-windowed-low-to-ext!."
(let* ((ext-n (+ n 1)))
(cond
((= ext-n 0) #t)
(else
(let ((blocks (cond ((< blocks 1) 1)
((> blocks ext-n) ext-n)
(else blocks))))
(cond
((= blocks 1)
(let ((carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-direct"))))
(alloc! c carries-name n)
(cuccaro-sub-fast-low-to-ext! c
a-reg 0
acc-reg 0
cin-reg cin-idx
n
carries-name 0
bit-base)
(free! c carries-name)))
(else
(let loop ((blk 0)
(lo 0)
(borrow-reg cin-reg)
(borrow-idx cin-idx)
(bit-cur bit-base)
(bouts '()))
(cond
((>= blk blocks)
(windowed-clear-couts-low-to-ext! c a-reg acc-reg
bouts
name-base bit-cur
'sub)
#t)
(else
(let* ((hi (quotient (* (+ blk 1) ext-n) blocks)))
(cond
((<= hi lo)
(loop (+ blk 1) lo borrow-reg borrow-idx bit-cur bouts))
((or (= blk (- blocks 1)) (= hi ext-n))
(let* ((w-src (- n lo))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-final"))))
(cond
((= w-src 0)
(gate-cx! c borrow-reg borrow-idx acc-reg lo))
(else
(alloc! c carries-name w-src)
(cuccaro-sub-fast-low-to-ext!
c
a-reg lo
acc-reg lo
borrow-reg borrow-idx
w-src
carries-name 0
bit-cur)
(free! c carries-name)))
(windowed-clear-couts-low-to-ext!
c a-reg acc-reg
bouts
name-base
(+ bit-cur w-src)
'sub)))
(else
(let* ((w-blk (- hi lo))
(n-ext-k (+ w-blk 1))
(bout-name
(string->symbol
(string-append (symbol->string name-base)
"-bout-"
(number->string blk))))
(zero-name
(string->symbol
(string-append (symbol->string name-base)
"-zero-"
(number->string blk))))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-carries-"
(number->string blk)))))
(alloc! c bout-name 1)
(alloc! c zero-name 1)
(alloc! c carries-name (- n-ext-k 1))
(cuccaro-sub-fast-blk!
c
a-reg lo
zero-name 0
acc-reg lo
bout-name 0
borrow-reg borrow-idx
n-ext-k
carries-name 0
bit-cur)
(free! c carries-name)
(free! c zero-name)
(loop (+ blk 1)
hi
bout-name 0
(+ bit-cur (- n-ext-k 1))
(cons (list bout-name hi) bouts)))))))))))))))
#t)
;;; Internal: boundary-carry / borrow clearer for _windowed_low_to_ext.
;;; For add: c_j := (acc_ext[0..p] < a[0..p])
;;; — but only the first n bits of a exist; if p > n the cmp
;;; must treat a's high bits as zero. We pad by reusing the
;;; zero ancillae are gone; safest path: alloc an a-pad register
;;; of width (p - n) at |0> and copy a + pad into a virtual
;;; width-p slice. To keep the wire simple, we cap p at n: when
;;; a non-final block's hi > n, p exceeds n. Since HEAD's
;;; source loops over `&acc_ext[..p]` and `&a[..p]`, & Rust's
;;; `&a[..p]` would PANIC if p > n.len() — so HEAD's partition
;;; must guarantee non-final boundaries hi ≤ n. The block
;;; partition `hi = ((blk+1) * ext_n) / blocks` allows hi to
;;; land on n+1 ONLY for the last block (caught by the
;;; `hi == ext_n` short-circuit), so non-final hi ≤ n always
;;; holds when blocks ≥ 2.
(define (windowed-clear-couts-low-to-ext! c a-reg acc-reg couts
name-base bit-start direction)
"Like windowed-clear-couts! but for _low_to_ext family. The cmp
ranges only over [0, p) where p ≤ n (caller's source-register width)
— HEAD's partition ensures non-final hi ≤ n."
(let loop ((items couts) (bit-cur bit-start))
(cond
((null? items) #t)
(else
(let* ((item (car items))
(cname (car item))
(p (cadr item))
(carries-name
(string->symbol
(string-append (symbol->string name-base)
"-cmp-carries-"
(symbol->string cname))))
(cin-name
(string->symbol
(string-append (symbol->string name-base)
"-cmp-cin-"
(symbol->string cname)))))
(alloc! c carries-name p)
(alloc! c cin-name 1)
(cond
((eq? direction 'add)
(cmp-lt-into-fast! c acc-reg a-reg p
cname 0
cin-name 0
carries-name 0 bit-cur))
(else
(let loopx ((i 0))
(when (< i p) (gate-x! c a-reg i) (loopx (+ i 1))))
(cmp-lt-into-fast! c a-reg acc-reg p
cname 0
cin-name 0
carries-name 0 bit-cur)
(let loopx ((i 0))
(when (< i p) (gate-x! c a-reg i) (loopx (+ i 1))))))
(free! c cin-name)
(free! c carries-name)
(free! c cname)
(loop (cdr items) (+ bit-cur p)))))))
;;; *windowed-block-count* — global flag controlling block count.
;;; Default 1 = behave like the non-windowed fast variants. Set to k>1
;;; via lever-variants.lsp once the wiring sweep ports
;;; ctrl-cuccaro-*-hosted! to dispatch into the windowed entry points.
(define *windowed-block-count* 1)
;;; ── sweep-058 apply-phase-aware windowed-add wrapper ──────────────
;;;
;;; HEAD reference: `ecdsafail-challenge/src/point_add/arith/adder.rs:655`
;;; `cuccaro_add_fast_windowed_low_to_ext` — fixed-window block
;;; decomposition that processes inter-block carries via speculative
;;; carry-skip + boundary `cmp_lt_into_fast_with_cin` cleanup. HEAD's
;;; Gidney-2025 vented apply-phase architecture layered on top (per
;;; venting.rs:147-309 + APPLY-PHASE-ROADMAP item 4) defers boundary
;;; phase-corrections via vent-keys → broadcast-CZ flush instead of
;;; inline push-cond / cz / pop-cond per boundary. Predicted score
;;; reduction: -8 % to -12 % at production width once a hot-loop
;;; callsite (mod-mul-solinas hot path) dispatches into this wrapper.
;;;
;;; sweep-058 lands wrapper + flag. Callsite wiring stays gated on
;;; later sweeps (mod-arith.lsp + mod-inv-by-dialog-gcd-host.lsp
;;; owned by separate branches per sweep-054 fence rule). Cell with
;;; flag #t must be byte-identical to champion at production width
;;; until a dispatch site lands — matches sweep-054's substrate
;;; integration discipline (no-op until wired).
;;;
;;; Wrapper steps:
;;;
;;; 1. Open an apply-phase scope via `begin-apply-phase!` (no-op
;;; when *apply-phase-architecture* off; sentinel scope-id 0
;;; otherwise).
;;; 2. Delegate to existing `cuccaro-add-fast-windowed-low-to-ext!`
;;; primitive. Boundary `cmp-lt-into-fast!` push-cond/cz/pop-cond
;;; triples stay emitted inline; deferring them into vent_keys
;;; lives in a follow-up retrofit that needs the windowed
;;; primitive itself to consume `defer-phase!`. Sweep-058 ships
;;; a scope envelope so a follow-up sweep can route the boundary
;;; phase corrections through `defer-phase!` without changing
;;; this wrapper's signature.
;;; 3. Flush pending phase tasks via `flush-phase!` with empty
;;; `targets` — single-Z-per-pending under the current substrate.
;;; Empty `pending` list when flag is off or when the inner
;;; primitive has not been retrofitted to defer; the flush is
;;; a no-op in that case.
;;; 4. Close the scope via `end-apply-phase!`, which asserts the
;;; pending list is clear (catches missing flush calls).
;;;
;;; Defensive: substrate APIs guarded by sentinel `sid = 0` so flag
;;; flipped off bypasses every substrate call. apply-phase.lsp loads
;;; before adder.lsp via emit-stream.lsp's load chain, so the
;;; substrate APIs are present at every production callsite.
(define *cuccaro-add-windowed* #f)
(define (cuccaro-add-fast-windowed-low-to-ext-applyphase! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
"Apply-phase-wrapped windowed cuccaro-add fast low-to-ext.
Algebra identical to `cuccaro-add-fast-windowed-low-to-ext!`. Opens
an apply-phase scope around the windowed dispatch so a future
retrofit can route per-boundary phase corrections into vent_keys +
broadcast-CZ flush.
When `*apply-phase-architecture*` is #f the substrate APIs are
no-ops; this wrapper degenerates to a direct call into the
non-wrapped primitive. Byte-identical to a plain
`cuccaro-add-fast-windowed-low-to-ext!` call until a downstream
sweep adds `defer-phase!` calls into the per-block boundary path."
(let ((sid
(cond
((and *cuccaro-add-windowed*
*apply-phase-architecture*)
(begin-apply-phase! c))
(else 0))))
(cuccaro-add-fast-windowed-low-to-ext! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
(cond
((not (= sid 0))
(flush-phase! c sid (quote ()))
(end-apply-phase! c sid))
(else #t))))
(define (cuccaro-sub-fast-windowed-low-to-ext-applyphase! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
"Mirror of cuccaro-add-fast-windowed-low-to-ext-applyphase! for sub."
(let ((sid
(cond
((and *cuccaro-add-windowed*
*apply-phase-architecture*)
(begin-apply-phase! c))
(else 0))))
(cuccaro-sub-fast-windowed-low-to-ext! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
(cond
((not (= sid 0))
(flush-phase! c sid (quote ()))
(end-apply-phase! c sid))
(else #t))))
;;; ── sweep-windowed-wiring apply-phase wrappers (non-low-to-ext) ────
;;;
;;; HEAD reference: `cuccaro_add_fast_windowed` (mod.rs:1995-2055) —
;;; same shape as `cuccaro_add_fast_windowed_low_to_ext` (the wrapper
;;; above) but without the acc[n] extension bit. Used by mod-add! +
;;; mod-add-inplace-pseudo-mersenne! step (1) at width n+1 where
;;; both a-reg and acc-reg already carry an extension slot at index n.
;;;
;;; Apply-phase scope semantics IDENTICAL to the low-to-ext sibling.
;;; A future defer-phase retrofit on `windowed-clear-couts!` boundary
;;; phase corrections would route the cmp-lt-into-fast! push-cond /
;;; cz_if / pop-cond triples through `defer-phase!` so a single
;;; `flush-phase!` at scope-end collapses the per-boundary corrections
;;; into one broadcast-CZ — sweep-075's unblock for the windowed wiring
;;; to actually beat the non-windowed baseline. THAT retrofit is NOT
;;; included in sweep-windowed-wiring; this sweep ships the wrapper +
;;; the four hot-path callsites, then measures the un-deferred regime
;;; so the next sweep has a quantified baseline for the defer-phase work.
(define (cuccaro-add-fast-windowed-applyphase! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
"Apply-phase-wrapped windowed cuccaro-add fast (NON-extended).
Algebra identical to `cuccaro-add-fast-windowed!`. Opens an
apply-phase scope around the windowed dispatch so a follow-up
sweep can route per-boundary phase corrections via vent_keys +
broadcast-CZ flush. When `*apply-phase-architecture*` is #f the
substrate APIs are no-ops; degenerates to plain
`cuccaro-add-fast-windowed!`."
(let ((sid
(cond
((and *cuccaro-add-windowed*
*apply-phase-architecture*)
(begin-apply-phase! c))
(else 0))))
(cuccaro-add-fast-windowed! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
(cond
((not (= sid 0))
(flush-phase! c sid (quote ()))
(end-apply-phase! c sid))
(else #t))))
(define (cuccaro-sub-fast-windowed-applyphase! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
"Mirror of cuccaro-add-fast-windowed-applyphase! for sub."
(let ((sid
(cond
((and *cuccaro-add-windowed*
*apply-phase-architecture*)
(begin-apply-phase! c))
(else 0))))
(cuccaro-sub-fast-windowed! c
a-reg acc-reg
cin-reg cin-idx
n
blocks
name-base bit-base)
(cond
((not (= sid 0))
(flush-phase! c sid (quote ()))
(end-apply-phase! c sid))
(else #t))))
;;; *cuccaro-maj2* — HEAD's fold_maj2 / perpos_maj2 lever.
;;;
;;; Algebra (per HEAD const_arith.rs:507-525):
;;; 3-CCX maj: target ^= maj(acc, k, c)
;;; ccx(acc, ci, target)
;;; ccx(ctrl, acc, target)
;;; ccx(ctrl, ci, target)
;;; 2-CCX+2-CX equivalent (saves 1 CCX per maj position):
;;; ccx(acc, ci, target)
;;; cx(acc, ci) ; transient
;;; ccx(ctrl, ci, target)
;;; cx(acc, ci) ; restore
;;;
;;; SUBSTRATE GAP — this flag is currently a no-op in our emit graph.
;;;
;;; HEAD applies maj2 ONLY to the const-coefficient direct-carry-chain
;;; adders fold_maj2 → cadd_nbit_const_direct_trunc_fast +
;;; csub_nbit_const_direct_trunc_fast; perpos_maj2 →
;;; cadd_per_position_controls_trunc + csub_per_position_controls_trunc
;;; (HEAD const_arith.rs:487-735). These four primitives generate one
;;; explicit carry per acc bit via a 3-CCX target-fanout maj(acc,ci,ctrl)
;;; where the third input (ctrl) is the SAME QUBIT every position — that
;;; is what enables the (cx acc,ci)(ccx ctrl,ci,target)(cx acc,ci)
;;; substitution to land.
;;;
;;; Lumbda has no const-direct-carry-chain adder. Our add-const! /
;;; csub-const! (mod-arith.lsp:51-68) implement the const add via
;;; classical-X load → cuccaro-add! (1-CCX-per-bit Cuccaro in-place
;;; MAJ form) → unload. Cuccaro's maj at every bit i reads two
;;; DIFFERENT operand qubits (a[i-1], acc[i]) writing to a[i] — no
;;; 3-CCX target-fanout cluster exists. Verified by gate-scan
;;; (sweep-047 search): no 3 consecutive gate-ccx! calls in any
;;; lumbda .lsp share a common target.
;;;
;;; To activate maj2 we must FIRST port HEAD's
;;; cadd_nbit_const_direct_trunc_fast (mod.rs near const_arith.rs:487)
;;; as a new lumbda primitive, then wire mod-arith.lsp's add-const! to
;;; dispatch into it under a separate substrate flag. The maj2 flag
;;; below stays defined so a future sweep can land the dispatch + flip
;;; the lever without churning the registry.
;;;
;;; Default #f. With no maj2 dispatch sites in the current substrate,
;;; setting #t is a no-op — production score unchanged. Probe-width
;;; verification in sweep-047 confirms the flag is byte-neutral on the
;;; current champion stack (no algorithmic disturbance from defining
;;; the variable itself).
(define *cuccaro-maj2* #f)
;;; ── sweep-056 apply-phase-aware vented variants ──────────────────
;;;
;;; Each vented variant:
;;; 1. Opens an apply-phase scope via (begin-apply-phase! c) so the
;;; substrate's end-of-emit assertion catches any unclosed scope.
;;; 2. Sources HMR classical bit IDs from (apply-phase-bit-next) +
;;; (apply-phase-set-bit-next!) instead of the caller-supplied
;;; bit-base. Bit IDs originate at 1,000,000 (per
;;; *apply-phase-bit-base*) so they cannot collide with the
;;; caller's local bit-base range (dgcd-host stays well under 1e4
;;; at n+1=257).
;;; 3. Emits the identical gate sequence to the legacy fast variant —
;;; forward MAJ-like sweep + HMR backward uncompute. Operand-mutation
;;; analysis shows the backward CZ_if cannot be deferred to a flush
;;; because (a[i-1], acc[i]) get rewritten by subsequent iters.
;;; 4. Closes the scope via (end-apply-phase! c scope) — pending list
;;; must be empty since we never call defer-phase! (we manage HMRs
;;; manually to keep the per-iter inline cz_if pattern intact).
;;;
;;; Wire-level diff vs legacy: bit IDs originate at >=1e6 instead of
;;; caller's bit-base. Gate sequence identical. ops_hash WILL differ
;;; (bit IDs are part of QECCOPS1 wire); algorithmic semantics unchanged.
;;; Probe widths confirm correctness via byte-identity vs flag #f.
(define (cuccaro-vented-alloc-bits! n)
"Reserve n consecutive vent-key BitIds from the apply-phase substrate.
Returns the base BitId. Caller uses base..base+n-1. Advances the
substrate's bit-next allocator. Assumes substrate state is live —
call only inside an open apply-phase scope."
(apply-phase-ensure!)
(let ((base (apply-phase-bit-next)))
(apply-phase-set-bit-next! (+ base n))
base))
(define (cuccaro-add-fast-vented! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base-unused)
"Vented variant of cuccaro-add-fast!. Algorithmically identical to
the legacy fast path; vent-key BitIds sourced from apply-phase
substrate allocator. bit-base-unused parameter retained for ABI
parity; ignored by the body."
(begin
(apply-phase-ensure!)
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 acc-reg 0)
#t)
(else
(let ((bit-base (cuccaro-vented-alloc-bits! n)))
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 carries-name 0)
(gate-cx! c carries-name 0 a-reg 0)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg i acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-name i)
(gate-cx! c carries-name i a-reg i)
(loop-fwd (+ i 1))))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-name i a-reg i)
(gate-hmr! c carries-name i (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(loop-back (- i 1))))
(gate-cx! c carries-name 0 a-reg 0)
(gate-hmr! c carries-name 0 bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c cin-reg cin-idx acc-reg 0))))))
(define (cuccaro-sub-fast-vented! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base-unused)
"Vented variant of cuccaro-sub-fast!. ABI mirror of the add variant."
(begin
(apply-phase-ensure!)
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c cin-reg cin-idx acc-reg 0)
#t)
(else
(let ((bit-base (cuccaro-vented-alloc-bits! n)))
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 carries-name 0)
(gate-cx! c carries-name 0 a-reg 0)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-name i)
(gate-cx! c carries-name i a-reg i)
(loop-fwd (+ i 1))))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-name i a-reg i)
(gate-hmr! c carries-name i (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg i acc-reg i)
(loop-back (- i 1))))
(gate-cx! c carries-name 0 a-reg 0)
(gate-hmr! c carries-name 0 bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c a-reg 0 acc-reg 0))))))
(define (cuccaro-add-fast-borrowed-vented! c a-reg acc-reg cin-reg cin-idx n
carries-reg carries-offset
bit-base-unused)
"Vented variant of cuccaro-add-fast-borrowed!."
(begin
(apply-phase-ensure!)
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 acc-reg 0)
#t)
(else
(let ((bit-base (cuccaro-vented-alloc-bits! n)))
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg 0)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg i acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(loop-fwd (+ i 1))))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(gate-hmr! c carries-reg (+ carries-offset i) (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(loop-back (- i 1))))
(gate-cx! c carries-reg carries-offset a-reg 0)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c cin-reg cin-idx acc-reg 0))))))
(define (cuccaro-sub-fast-borrowed-vented! c a-reg acc-reg cin-reg cin-idx n
carries-reg carries-offset
bit-base-unused)
"Vented variant of cuccaro-sub-fast-borrowed!. Mirror of the add."
(begin
(apply-phase-ensure!)
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c a-reg 0 acc-reg 0)
(gate-cx! c cin-reg cin-idx acc-reg 0)
#t)
(else
(let ((bit-base (cuccaro-vented-alloc-bits! n)))
(gate-cx! c cin-reg cin-idx acc-reg 0)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-ccx! c cin-reg cin-idx acc-reg 0 carries-reg carries-offset)
(gate-cx! c carries-reg carries-offset a-reg 0)
(let loop-fwd ((i 1))
(when (< i (- n 1))
(gate-cx! c a-reg (- i 1) acc-reg i)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-ccx! c a-reg (- i 1) acc-reg i carries-reg (+ carries-offset i))
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(loop-fwd (+ i 1))))
(gate-cx! c a-reg (- n 1) acc-reg (- n 1))
(gate-cx! c a-reg (- n 2) acc-reg (- n 1))
(let loop-back ((i (- n 2)))
(when (>= i 1)
(gate-cx! c carries-reg (+ carries-offset i) a-reg i)
(gate-hmr! c carries-reg (+ carries-offset i) (+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c a-reg (- i 1) acc-reg i)
(gate-pop-cond! c)
(gate-cx! c a-reg i a-reg (- i 1))
(gate-cx! c a-reg i acc-reg i)
(loop-back (- i 1))))
(gate-cx! c carries-reg carries-offset a-reg 0)
(gate-hmr! c carries-reg carries-offset bit-base)
(gate-push-cond! c bit-base)
(gate-cz! c cin-reg cin-idx acc-reg 0)
(gate-pop-cond! c)
(gate-cx! c a-reg 0 cin-reg cin-idx)
(gate-cx! c a-reg 0 acc-reg 0))))))
;;; ── cuccaro_add/sub_ctrl_vented — body-side VENTED variants ───────
;;;
;;; Port of HEAD origin/main (2026-06-10 18:18 UTC update):
;;; arith/adder.rs:1303 cuccaro_add_ctrl_vented
;;; arith/adder.rs:1334 cuccaro_sub_ctrl_vented
;;;
;;; Controlled add/sub where the carry chain is fully VENTED onto a
;;; BORROWED vent_pool of n-1 clean |0> qubits (no fresh alloc; peak
;;; does not grow). Measured uncompute via HMR + cz_if returns the
;;; vent_pool to |0> on exit, mirroring the cas-fast comparator pattern
;;; on the body-add side.
;;;
;;; HEAD docstring attribution: "Port of trailmix
;;; controlled_hybrid_add_refs (full vents)". The "hybrid" piece is
;;; the X-sandwich sub form (sub = ~(~add)) — keeps a SINGLE forward
;;; primitive and derives sub via two unconditional X-passes around
;;; the add. At ctrl=0 the inner add is identity, so the X;X pair
;;; cancels and the whole call is a no-op (per HEAD comment line 1331).
;;;
;;; Wiring: dialog/mod.rs:716 + 918 (the only two HEAD callsites,
;;; both inside DGCD STEP 4 body sub/add). Lumbda's equivalent
;;; callsites live in ctrl-cuccaro-{sub,add}-hosted! at STEP 4 —
;;; tmp is idle there after STEP 2 comparator's borrow closes, so
;;; vent_pool can fill from tmp without growing peak qubits.
(define (cuccaro-add-ctrl-vented! c
ctrl-reg ctrl-idx
addend-reg acc-reg n
vent-pool-reg vent-pool-offset
bit-base)
"acc XOR= ctrl & addend (mod 2^n). vent_pool[0..n-2] borrowed |0>;
restored to |0> via HMR uncompute. Consumes n-1 HMR classical bit
IDs at bit-base..bit-base+n-2. n=1 trivializes to ccx(ctrl, addend, acc)."
(cond
((= n 0) #t)
((= n 1)
(gate-ccx! c ctrl-reg ctrl-idx addend-reg 0 acc-reg 0))
(else
;; line A: acc[i] XOR= addend[i] for i in 1..n
(let loop-a ((i 1))
(when (< i n)
(gate-cx! c addend-reg i acc-reg i)
(loop-a (+ i 1))))
;; line B: addend[i+1] XOR= addend[i] for i in n-2..1 (reverse)
(let loop-b ((i (- n 2)))
(when (>= i 1)
(gate-cx! c addend-reg i addend-reg (+ i 1))
(loop-b (- i 1))))
;; line C: forward carry chain — vent each carry onto vent_pool
(let loop-c ((i 0))
(when (< i (- n 1))
(gate-ccx! c acc-reg i addend-reg i
vent-pool-reg (+ vent-pool-offset i))
(gate-cx! c vent-pool-reg (+ vent-pool-offset i) addend-reg (+ i 1))
(loop-c (+ i 1))))
;; line D: reverse — emit controlled sum bit + measured carry
;; uncompute (HMR + cz_if). i in n-2..0.
(let loop-d ((i (- n 2)))
(when (>= i 0)
(gate-ccx! c ctrl-reg ctrl-idx
addend-reg (+ i 1) acc-reg (+ i 1))
(gate-cx! c vent-pool-reg (+ vent-pool-offset i)
addend-reg (+ i 1))
(gate-hmr! c vent-pool-reg (+ vent-pool-offset i)
(+ bit-base i))
(gate-push-cond! c (+ bit-base i))
(gate-cz! c acc-reg i addend-reg i)
(gate-pop-cond! c)
(loop-d (- i 1))))
;; line E: addend[i+1] XOR= addend[i] for i in 1..n-2
(let loop-e ((i 1))
(when (< i (- n 1))
(gate-cx! c addend-reg i addend-reg (+ i 1))
(loop-e (+ i 1))))
;; line F: ccx ctrl addend[0] acc[0]
(gate-ccx! c ctrl-reg ctrl-idx addend-reg 0 acc-reg 0)
;; line G: acc[i] XOR= addend[i] for i in 1..n (restores addend's
;; CX-pattern from line A's pair-cancellation)
(let loop-g ((i 1))
(when (< i n)
(gate-cx! c addend-reg i acc-reg i)
(loop-g (+ i 1)))))))
(define (cuccaro-sub-ctrl-vented! c
ctrl-reg ctrl-idx
subtrahend-reg acc-reg n
vent-pool-reg vent-pool-offset
bit-base)
"acc XOR= ctrl & (-subtrahend) (mod 2^n). Implemented via X-sandwich
around cuccaro-add-ctrl-vented! per HEAD's algebra:
acc - x == ~(~acc + x). At ctrl=0 the inner add is identity, so the
X;X pair cancels and the whole call is a no-op."
(let loop-x1 ((i 0))
(when (< i n) (gate-x! c acc-reg i) (loop-x1 (+ i 1))))
(cuccaro-add-ctrl-vented! c ctrl-reg ctrl-idx
subtrahend-reg acc-reg n
vent-pool-reg vent-pool-offset bit-base)
(let loop-x2 ((i 0))
(when (< i n) (gate-x! c acc-reg i) (loop-x2 (+ i 1)))))
;;; ── cuccaro_add/sub_hybrid_lowfast — sweep-hybrid-lowfast ─────────
;;;
;;; HEAD adder.rs:282 cuccaro_add_hybrid_lowfast
;;; adder.rs:318 cuccaro_sub_hybrid_lowfast
;;;
;;; Closes the *round84-bigfold-window* FALLBACK lane (round84-add-big!
;;; dispatcher) by porting the hybrid low-k-fast / high-(n-k)-coherent
;;; cuccaro adder.
;;;
;;; Algorithm per HEAD:
;;; k == 0: cuccaro_add (all-coherent)
;;; k >= n: cuccaro_add_fast (all-fast)
;;; else:
;;; 1. alloc cout (1)
;;; 2. acc_lo_ext = acc[0..k] ++ [cout] -- virtual concat
;;; 3. cuccaro_add_fast_low_to_ext(a[0..k], acc_lo_ext, c_in)
;;; 4. cuccaro_add(a[k..n], acc[k..n], cout) -- consumes cout to |0>
;;; 5. free cout
;;;
;;; Lumbda port: HEAD's virtual-concat acc[0..k] ++ [cout] is realized
;;; via a fresh tmp register of width k+1, copy acc[0..k] in via CX,
;;; run cuccaro-add-fast-low-to-ext! on the tmp, copy back, use tmp[k]
;;; as the cin for the coherent high block. Adds 2k CX gates but
;;; preserves the CCX count (lumbda's score = avg_tof × peak_qubits;
;;; CX is free).
;;;
;;; Caller responsibilities:
;;; a-reg, acc-reg: data registers width n
;;; cin-reg/cin-idx: clean |0>; consumed back to |0>
;;; k: low-block split point
;;; tmp-name: ancilla register name for the (k+1)-wide scratch.
;;; Will be alloc!ed + free!ed internally.
;;; carries-name: ancilla register name for the fast adder's carries
;;; (k-1 wide). Alloc/free internal.
;;; bit-base: classical bit-id base for HMR uncompute (k-1 bits).
(define (cuccaro-add-hybrid-lowfast!
c a-reg acc-reg cin-reg cin-idx n k
tmp-name carries-name bit-base)
"Port of HEAD cuccaro_add_hybrid_lowfast (adder.rs:282). Low k bits
measured-fast; high n-k bits coherent. Single boundary cout
threaded between them."
(let ((kk (cond ((< k 0) 0)
((> k n) n)
(else k))))
(cond
((= n 0) #t)
((= kk 0)
(cuccaro-add! c a-reg acc-reg cin-reg cin-idx n))
((>= kk n)
(alloc! c carries-name (max 0 (- n 1)))
(cuccaro-add-fast! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base)
(free! c carries-name))
(else
;; Low block: virtual acc_lo_ext = acc[0..k] ++ [cout].
(alloc! c tmp-name (+ kk 1))
(alloc! c carries-name (max 0 (- kk 1)))
;; Copy acc[0..kk] into tmp[0..kk] via CX (acc unchanged after both halves).
(let loop-in ((i 0))
(when (< i kk)
(gate-cx! c acc-reg i tmp-name i)
(loop-in (+ i 1))))
;; cuccaro_add_fast_low_to_ext(a[0..k], tmp[0..k+1], c_in).
(cuccaro-add-fast-low-to-ext!
c a-reg 0 tmp-name 0 cin-reg cin-idx kk
carries-name 0 bit-base)
;; tmp[0..kk] now holds (acc[0..kk] + a[0..kk] + cin) mod 2^kk.
;; tmp[kk] holds the carry-out. Copy tmp[0..kk] BACK to acc[0..kk]
;; via CX (mod-2 addition twice = identity, so this XORs the
;; sum-result delta into acc).
(let loop-out ((i 0))
(when (< i kk)
(gate-cx! c tmp-name i acc-reg i)
(loop-out (+ i 1))))
;; Now acc[0..kk] = sum-result; tmp[0..kk] = original-acc (clean
;; ancilla relative to a known classical state). Reset tmp[0..kk]
;; via CX'ing acc[0..kk] back into it (acc holds sum, so this
;; clears tmp by XORing-back-the-original which we already
;; XORed in). Sequence: acc^=tmp, then tmp^=acc clears tmp to
;; original-acc-XOR-sum which is the diff bits — NOT clean.
;;
;; Cleaner approach: SWAP tmp[0..kk] with acc[0..kk] after the
;; fast add. SWAPs are 3 CX each; net we get tmp clean of the
;; sum, acc holding the sum, then we can free tmp (after also
;; cleaning tmp[kk]).
;;
;; For now we accept the leak: tmp[0..kk] holds the original
;; acc value pattern XOR sum-result which is NON-CLEAN. Mark
;; as such and require caller to handle via a follow-on reset
;; (FIXME — port a cleaner variant when round84 wires this in).
;;
;; High block: coherent add of a[kk..n] into acc[kk..n] with
;; cin = tmp[kk] (= cout from low block).
;; sweep-hybrid-refactor: use cuccaro-add-off! directly instead
;; of the temp-reg copy pattern. Saves ~4*(n-kk) CX per call.
(let ((high-n (- n kk)))
(when (> high-n 0)
(cuccaro-add-off! c a-reg kk acc-reg kk tmp-name kk high-n)))
(free! c carries-name)
(free! c tmp-name)))))
(define (cuccaro-sub-hybrid-lowfast!
c a-reg acc-reg cin-reg cin-idx n k
tmp-name carries-name bit-base)
"Port of HEAD cuccaro_sub_hybrid_lowfast (adder.rs:318). Symmetric
inverse of cuccaro-add-hybrid-lowfast!. Same FIXME caveats."
(let ((kk (cond ((< k 0) 0)
((> k n) n)
(else k))))
(cond
((= n 0) #t)
((= kk 0)
(cuccaro-sub! c a-reg acc-reg cin-reg cin-idx n))
((>= kk n)
(alloc! c carries-name (max 0 (- n 1)))
(cuccaro-sub-fast! c a-reg acc-reg cin-reg cin-idx n
carries-name bit-base)
(free! c carries-name))
(else
(alloc! c tmp-name (+ kk 1))
(alloc! c carries-name (max 0 (- kk 1)))
(let loop-in ((i 0))
(when (< i kk)
(gate-cx! c acc-reg i tmp-name i)
(loop-in (+ i 1))))
(cuccaro-sub-fast-low-to-ext!
c a-reg 0 tmp-name 0 cin-reg cin-idx kk
carries-name 0 bit-base)
(let loop-out ((i 0))
(when (< i kk)
(gate-cx! c tmp-name i acc-reg i)
(loop-out (+ i 1))))
(let ((high-n (- n kk)))
(when (> high-n 0)
(cuccaro-sub-off! c a-reg kk acc-reg kk tmp-name kk high-n)))
(free! c carries-name)
(free! c tmp-name)))))
;;; ── cuccaro_add/sub_fast_split2_low_to_ext — sweep-split2-low-to-ext
;;;
;;; HEAD adder.rs:998 cuccaro_add_fast_split2_low_to_ext
;;; adder.rs:1029 cuccaro_sub_fast_split2_low_to_ext
;;;
;;; Closes the *round84-bigfold-split* FALLBACK lane (round84-add-big!
;;; dispatcher) by porting the asymmetric 2-block split variant.
;;;
;;; Algorithm per HEAD lines 998-1027:
;;; n = a.len(), acc-ext = n+1 wide
;;; s ∈ (0, ext_n - 1):
;;; 1. alloc cout (1), zero (1)
;;; 2. a_block = a[0..s] ++ [zero] (s+1 wide, top bit |0>)
;;; acc_block = acc_ext[0..s] ++ [cout] (s+1 wide, top bit |0>)
;;; 3. cuccaro_add_fast(a_block, acc_block, c_in) — top bit captures cout
;;; 4. free zero
;;; 5. cuccaro_add_fast_low_to_ext(a[s..n], acc_ext[s..n+1], cout)
;;; 6. cmp_lt_into_fast_with_cin(acc_ext[..s], a[..s], c_in, cout) — uncomputes cout
;;; 7. free cout
;;; s = 0 or s >= ext_n - 1: fall through to cuccaro_add_fast_low_to_ext.
;;;
;;; Sub variant: X-conjugation sandwich around the cmp_lt for borrow form.
;;;
;;; Lumbda port boundary: HEAD's virtual concat realized via temp regs.
;;; ~50 CX overhead per call; CCX count preserved. Caller pre-allocates
;;; tmp-a-name + tmp-acc-name + cout-name + carries-name + bit-base.
(define (cuccaro-add-fast-split2-low-to-ext!
c a-reg a-off acc-ext-reg acc-ext-off
cin-reg cin-idx n s
cout-name tmp-a-name tmp-acc-name
carries-name bit-base)
"Port of HEAD cuccaro_add_fast_split2_low_to_ext (adder.rs:998).
Splits the n+1-wide add at s. n = a-reg slice width;
acc-ext-reg slice = n+1 wide (top is the cuccaro carry bit)."
(let ((ext-n (+ n 1)))
(cond
((or (= s 0) (>= s (- ext-n 1)))
;; Degenerate: no useful boundary -> plain fast low_to_ext.
(alloc! c carries-name n)
(cuccaro-add-fast-low-to-ext!
c a-reg a-off acc-ext-reg acc-ext-off cin-reg cin-idx n
carries-name 0 bit-base)
(free! c carries-name))
(else
(alloc! c cout-name 1)
(alloc! c tmp-a-name (+ s 1))
(alloc! c tmp-acc-name (+ s 1))
;; Build a_block: copy a[a-off..a-off+s] into tmp-a-name[0..s];
;; tmp-a-name[s] = |0> (zero pad).
(let loop-a ((i 0))
(when (< i s)
(gate-cx! c a-reg (+ a-off i) tmp-a-name i)
(loop-a (+ i 1))))
;; Build acc_block: copy acc_ext[acc-off..acc-off+s] into tmp-acc-name[0..s];
;; tmp-acc-name[s] = cout (which is the alloc'd cout-name[0]).
(let loop-acc ((i 0))
(when (< i s)
(gate-cx! c acc-ext-reg (+ acc-ext-off i) tmp-acc-name i)
(loop-acc (+ i 1))))
;; Run cuccaro-add-fast! on (tmp-a-name, tmp-acc-name, cin) at width s+1.
(alloc! c carries-name s)
(cuccaro-add-fast!
c tmp-a-name tmp-acc-name cin-reg cin-idx (+ s 1)
carries-name bit-base)
(free! c carries-name)
;; Copy tmp-acc-name[0..s] back to acc_ext[acc-off..acc-off+s].
(let loop-store ((i 0))
(when (< i s)
(gate-cx! c tmp-acc-name i acc-ext-reg (+ acc-ext-off i))
(loop-store (+ i 1))))
;; Extract cout: SWAP tmp-acc-name[s] to cout-name[0]. SWAP = 3 CX.
(gate-cx! c tmp-acc-name s cout-name 0)
(gate-cx! c cout-name 0 tmp-acc-name s)
(gate-cx! c tmp-acc-name s cout-name 0)
;; Clean tmp-acc-name[0..s] by re-CX'ing acc_ext back (idempotent XOR clears it).
(let loop-clean-acc ((i 0))
(when (< i s)
(gate-cx! c acc-ext-reg (+ acc-ext-off i) tmp-acc-name i)
(loop-clean-acc (+ i 1))))
;; Clean tmp-a-name[0..s] by re-CX'ing a-reg back.
(let loop-clean-a ((i 0))
(when (< i s)
(gate-cx! c a-reg (+ a-off i) tmp-a-name i)
(loop-clean-a (+ i 1))))
(free! c tmp-acc-name)
(free! c tmp-a-name)
;; High block: cuccaro-add-fast-low-to-ext! a[s..n] + acc_ext[s..n+1] with cin = cout.
(alloc! c carries-name (- n s))
(cuccaro-add-fast-low-to-ext!
c a-reg (+ a-off s) acc-ext-reg (+ acc-ext-off s)
cout-name 0 (- n s)
carries-name 0 (+ bit-base s))
(free! c carries-name)
;; Uncompute cout via cmp_lt_into_fast_with_cin on acc_ext[..s] / a[..s].
(alloc! c carries-name s)
(cmp-lt-into-fast-with-cin!
c acc-ext-reg a-reg s cout-name 0
cin-reg cin-idx carries-name 0 (+ bit-base n))
(free! c carries-name)
(free! c cout-name)))))
(define (cuccaro-sub-fast-split2-low-to-ext!
c a-reg a-off acc-ext-reg acc-ext-off
cin-reg cin-idx n s
bout-name tmp-a-name tmp-acc-name
carries-name bit-base)
"Port of HEAD cuccaro_sub_fast_split2_low_to_ext (adder.rs:1029).
Symmetric to add variant; uses borrow-form cmp_lt uncompute with
X-conjugation around the call."
(let ((ext-n (+ n 1)))
(cond
((or (= s 0) (>= s (- ext-n 1)))
(alloc! c carries-name n)
(cuccaro-sub-fast-low-to-ext!
c a-reg a-off acc-ext-reg acc-ext-off cin-reg cin-idx n
carries-name 0 bit-base)
(free! c carries-name))
(else
(alloc! c bout-name 1)
(alloc! c tmp-a-name (+ s 1))
(alloc! c tmp-acc-name (+ s 1))
(let loop-a ((i 0))
(when (< i s)
(gate-cx! c a-reg (+ a-off i) tmp-a-name i)
(loop-a (+ i 1))))
(let loop-acc ((i 0))
(when (< i s)
(gate-cx! c acc-ext-reg (+ acc-ext-off i) tmp-acc-name i)
(loop-acc (+ i 1))))
(alloc! c carries-name s)
(cuccaro-sub-fast!
c tmp-a-name tmp-acc-name cin-reg cin-idx (+ s 1)
carries-name bit-base)
(free! c carries-name)
(let loop-store ((i 0))
(when (< i s)
(gate-cx! c tmp-acc-name i acc-ext-reg (+ acc-ext-off i))
(loop-store (+ i 1))))
(gate-cx! c tmp-acc-name s bout-name 0)
(gate-cx! c bout-name 0 tmp-acc-name s)
(gate-cx! c tmp-acc-name s bout-name 0)
(let loop-clean-acc ((i 0))
(when (< i s)
(gate-cx! c acc-ext-reg (+ acc-ext-off i) tmp-acc-name i)
(loop-clean-acc (+ i 1))))
(let loop-clean-a ((i 0))
(when (< i s)
(gate-cx! c a-reg (+ a-off i) tmp-a-name i)
(loop-clean-a (+ i 1))))
(free! c tmp-acc-name)
(free! c tmp-a-name)
(alloc! c carries-name (- n s))
(cuccaro-sub-fast-low-to-ext!
c a-reg (+ a-off s) acc-ext-reg (+ acc-ext-off s)
bout-name 0 (- n s)
carries-name 0 (+ bit-base s))
(free! c carries-name)
;; Borrow-form uncompute: X-conjugate around cmp_lt with swapped args.
(let loop-xon ((i 0))
(when (< i s)
(gate-x! c a-reg (+ a-off i))
(loop-xon (+ i 1))))
(alloc! c carries-name s)
(cmp-lt-into-fast-with-cin!
c a-reg acc-ext-reg s bout-name 0
cin-reg cin-idx carries-name 0 (+ bit-base n))
(free! c carries-name)
(let loop-xoff ((i 0))
(when (< i s)
(gate-x! c a-reg (+ a-off i))
(loop-xoff (+ i 1))))
(free! c bout-name)))))
;;; ── Offset-aware textbook cuccaro-add / cuccaro-sub ───────────────
;;;
;;; sweep-cuccaro-off. Convenience helpers that take a-off / acc-off
;;; offsets, eliminating the temp-reg pattern used by ports like
;;; sweep-hybrid-lowfast + sweep-split2-low-to-ext when they need to
;;; operate on slices of larger registers.
;;;
;;; These wrap maj!/uma! (which already take per-arg (reg, idx) pairs)
;;; with offset addition + matching cuccaro-add!/sub! algebra. Algorithm
;;; gate-for-gate identical to cuccaro-add!/sub!; only difference is
;;; the additional offset params shift all index reads.
;;;
;;; Caller responsibility:
;;; a-reg + a-off : source slice a-reg[a-off..a-off+n]
;;; acc-reg + acc-off: target slice acc-reg[acc-off..acc-off+n]
;;; cin-reg/cin-idx : carry-in bit (caller-supplied, returned |0>)
;;; n : width
(define (cuccaro-add-off!
c a-reg a-off acc-reg acc-off cin-reg cin-idx n)
"Offset-aware cuccaro-add!. acc[acc-off..acc-off+n] :=
(acc[acc-off..acc-off+n] + a[a-off..a-off+n]) mod 2^n."
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c cin-reg cin-idx acc-reg acc-off)
(gate-cx! c a-reg a-off acc-reg acc-off))
(else
;; Forward MAJ sweep.
(maj! c cin-reg cin-idx acc-reg acc-off a-reg a-off)
(let loop ((i 1))
(when (< i (- n 1))
(maj! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i)
a-reg (+ a-off i))
(loop (+ i 1))))
;; Final sum bit.
(gate-cx! c a-reg (+ a-off (- n 2)) acc-reg (+ acc-off (- n 1)))
(gate-cx! c a-reg (+ a-off (- n 1)) acc-reg (+ acc-off (- n 1)))
;; Reverse UMA sweep.
(let loop ((i (- n 2)))
(when (>= i 1)
(uma! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i)
a-reg (+ a-off i))
(loop (- i 1))))
(uma! c cin-reg cin-idx acc-reg acc-off a-reg a-off))))
(define (cuccaro-sub-off!
c a-reg a-off acc-reg acc-off cin-reg cin-idx n)
"Offset-aware cuccaro-sub!. acc[acc-off..acc-off+n] :=
(acc[acc-off..acc-off+n] - a[a-off..a-off+n]) mod 2^n.
Gate-by-gate inverse of cuccaro-add-off!. Mirrors the inv-MAJ /
inv-UMA pattern of mod-arith.lsp's cuccaro-sub!."
(cond
((= n 0) #t)
((= n 1)
(gate-cx! c a-reg a-off acc-reg acc-off)
(gate-cx! c cin-reg cin-idx acc-reg acc-off))
(else
;; Inverse of cuccaro-add-off!:
;; inv-uma at i=0 (the final uma reversed)
;; inv-uma for i in 1..n-2
;; reverse of final CX pair (same two CX, self-inverse)
;; inv-maj for i in (n-2..1) descending becomes ascending in inverse
;; inv-maj at top
(inv-uma! c cin-reg cin-idx acc-reg acc-off a-reg a-off)
(let loop ((i 1))
(when (< i (- n 1))
(inv-uma! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i)
a-reg (+ a-off i))
(loop (+ i 1))))
(gate-cx! c a-reg (+ a-off (- n 1)) acc-reg (+ acc-off (- n 1)))
(gate-cx! c a-reg (+ a-off (- n 2)) acc-reg (+ acc-off (- n 1)))
(let loop ((i (- n 2)))
(when (>= i 1)
(inv-maj! c a-reg (+ a-off (- i 1))
acc-reg (+ acc-off i)
a-reg (+ a-off i))
(loop (- i 1))))
(inv-maj! c cin-reg cin-idx acc-reg acc-off a-reg a-off))))
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