From 3a6c6d2829d66f4568e9167285b2097af97f88be Mon Sep 17 00:00:00 2001
From: acentelles <centelles.alberto@gmail.com>
Date: Mon, 26 Oct 2026 18:09:35 +0000
Subject: [PATCH] feat(challenges): static operator-norm base tables behind
 ont-static-base

Adds generated static base tables for the D64 selective-L2 operator-norm
sampler, with the generator script. The tables are compiled in only with the
ont-static-base feature, which is off by default; without it the sampler is
unchanged.
---
 crates/akita-challenges/Cargo.toml            |   3 +
 .../scripts/gen_op_norm_static_base.py        | 204 +++++++++++++
 .../akita-challenges/src/sampler/op_norm.rs   |  79 ++++-
 .../src/sampler/op_norm/static_base.rs        | 273 ++++++++++++++++++
 4 files changed, 558 insertions(+), 1 deletion(-)
 create mode 100644 crates/akita-challenges/scripts/gen_op_norm_static_base.py
 create mode 100644 crates/akita-challenges/src/sampler/op_norm/static_base.rs

diff --git a/crates/akita-challenges/Cargo.toml b/crates/akita-challenges/Cargo.toml
index 0773c9759..cfb706893 100644
--- a/crates/akita-challenges/Cargo.toml
+++ b/crates/akita-challenges/Cargo.toml
@@ -28,6 +28,9 @@ transcript-blake2b = ["akita-transcript/transcript-blake2b"]
 transcript-keccak = ["akita-transcript/transcript-keccak"]
 parallel = ["jolt-field/parallel"]
 logging-transcript = ["akita-transcript/logging-transcript"]
+# Recursion option (default off): the D64 selective-L2 operator-norm
+# table reads its base tables from generated static data (same entries).
+ont-static-base = []
 
 [lints]
 workspace = true
diff --git a/crates/akita-challenges/scripts/gen_op_norm_static_base.py b/crates/akita-challenges/scripts/gen_op_norm_static_base.py
new file mode 100644
index 000000000..6307a9f2c
--- /dev/null
+++ b/crates/akita-challenges/scripts/gen_op_norm_static_base.py
@@ -0,0 +1,204 @@
+#!/usr/bin/env python3
+"""Generate src/sampler/op_norm/static_base.rs (feature `ont-static-base`).
+
+Exact-integer transcription of `op_norm.rs` `build_tables` (with `pi_enclosure`,
+`arctan_inv`, `taylor_cos`, `taylor_sin`, `octant_reduce`, `apply_sign`,
+`downscale_round`, `imul`, `iadd`, `isub`, `fdiv`, `cdiv`, `fshr`, `cshr`) for
+the D64 selective-L2 operator-norm table: ring degree d = 64 at scale q = 48.
+Python integers are unbounded, so every intermediate that Rust keeps in `i128`
+is range-checked; a `checked_mul` overflow in Rust is a loop exit here as well.
+
+The output holds the 128-entry `base_cos` and `base_sin` tables as `i64` (the
+production path downcasts them to `i64`; the generator asserts they fit) and
+`eps_root`. The transcription is not trusted on its own: the
+`static_base_equals_build_tables` unit test compares every entry and `eps_root`
+with the Rust `build_tables` output.
+
+Usage: gen_op_norm_static_base.py [OUT]   (default: ../src/sampler/op_norm/static_base.rs)
+"""
+import hashlib
+import struct
+import sys
+from pathlib import Path
+
+I128_MIN, I128_MAX = -(1 << 127), (1 << 127) - 1
+TRIG_SCALE = 61
+TRIG_ONE = 1 << TRIG_SCALE
+NTERMS = 12
+D, Q = 64, 48
+
+
+def chk(x):
+    assert I128_MIN <= x <= I128_MAX, "i128 overflow"
+    return x
+
+
+def fdiv(a, b):
+    return chk(a // b)
+
+
+def cdiv(a, b):
+    return chk(-((-a) // b))
+
+
+def fshr(x, sh):
+    return x >> sh
+
+
+def cshr(x, sh):
+    return -((-x) >> sh)
+
+
+def imul(a, b):
+    assert a[0] >= 0 and b[0] >= 0
+    return (fshr(chk(a[0] * b[0]), TRIG_SCALE), cshr(chk(a[1] * b[1]), TRIG_SCALE))
+
+
+def iadd(a, b):
+    return (chk(a[0] + b[0]), chk(a[1] + b[1]))
+
+
+def isub(a, b):
+    return (chk(a[0] - b[1]), chk(a[1] - b[0]))
+
+
+def add_remainder(s, phi2, pw, fact, next_factor):
+    next_pow = imul(pw, phi2)
+    next_fact = chk(fact * next_factor * (next_factor + 1))
+    rem = cdiv(next_pow[1], next_fact)
+    return (s[0] - rem, s[1] + rem)
+
+
+def taylor_cos(phi):
+    phi2 = imul(phi, phi)
+    s, pw, fact = (TRIG_ONE, TRIG_ONE), (TRIG_ONE, TRIG_ONE), 1
+    for n in range(1, NTERMS + 1):
+        pw = imul(pw, phi2)
+        tn = 2 * n
+        fact = chk(fact * (tn - 1) * tn)
+        term = (fdiv(pw[0], fact), cdiv(pw[1], fact))
+        s = isub(s, term) if n % 2 == 1 else iadd(s, term)
+    return add_remainder(s, phi2, pw, fact, 2 * NTERMS + 1)
+
+
+def taylor_sin(phi):
+    phi2 = imul(phi, phi)
+    s, pw, fact = phi, phi, 1
+    for n in range(1, NTERMS + 1):
+        pw = imul(pw, phi2)
+        tn = 2 * n
+        fact = chk(fact * tn * (tn + 1))
+        term = (fdiv(pw[0], fact), cdiv(pw[1], fact))
+        s = isub(s, term) if n % 2 == 1 else iadd(s, term)
+    return add_remainder(s, phi2, pw, fact, 2 * NTERMS + 2)
+
+
+def arctan_inv(x):
+    total, x_pow, x2, count, n = 0, x, x * x, 0, 0
+    while True:
+        denom = (2 * n + 1) * x_pow  # Rust: (2n+1).checked_mul(x_pow), None ends the loop
+        if not I128_MIN <= denom <= I128_MAX:
+            break
+        term = TRIG_ONE // denom  # denom > 0: truncation equals floor
+        if term == 0:
+            break
+        total = total + term if n % 2 == 0 else total - term
+        count += 1
+        n += 1
+        nxt = x_pow * x2  # Rust: x_pow.checked_mul(x2), None ends the loop
+        if not I128_MIN <= nxt <= I128_MAX:
+            break
+        x_pow = nxt
+    slack = count + 1
+    return (total - slack, total + slack)
+
+
+def pi_enclosure():
+    a5, a239 = arctan_inv(5), arctan_inv(239)
+    return (16 * a5[0] - 4 * a239[1], 16 * a5[1] - 4 * a239[0])
+
+
+def octant_reduce(t, d):
+    t %= 2 * d
+    cos_sign, sin_sign = 1, 1
+    if t > d:
+        t = 2 * d - t
+        sin_sign = -1
+    if t > d // 2:
+        t = d - t
+        cos_sign = -cos_sign
+    swap = t > d // 4
+    if swap:
+        t = d // 2 - t
+    return t, swap, cos_sign, sin_sign
+
+
+def apply_sign(v, sign):
+    return (-v[1], -v[0]) if sign < 0 else v
+
+
+def downscale_round(v, shift):
+    lo, hi = fshr(v[0], shift), cshr(v[1], shift)
+    entry = fdiv(lo + hi, 2)
+    return entry, max(entry - lo, hi - entry)
+
+
+def build_tables(d, q):
+    pi_lo, pi_hi = pi_enclosure()
+    shift = TRIG_SCALE - q
+    first_octant = []
+    for r in range(d // 4 + 1):
+        phi = (fdiv(pi_lo * r, d), cdiv(pi_hi * r, d))
+        first_octant.append((taylor_cos(phi), taylor_sin(phi)))
+    base_cos, base_sin, eps_root = [0] * (2 * d), [0] * (2 * d), 0
+    for t in range(2 * d):
+        r, swap, cos_sign, sin_sign = octant_reduce(t, d)
+        cos_phi, sin_phi = first_octant[r]
+        cos_a, sin_a = (sin_phi, cos_phi) if swap else (cos_phi, sin_phi)
+        c_val, c_err = downscale_round(apply_sign(cos_a, cos_sign), shift)
+        s_val, s_err = downscale_round(apply_sign(sin_a, sin_sign), shift)
+        base_cos[t], base_sin[t] = c_val, s_val
+        eps_root = max(eps_root, c_err, s_err)
+    return base_cos, base_sin, eps_root
+
+
+def render(base_cos, base_sin, eps_root, digest):
+    def table(name, values):
+        body = "".join(f"    {v},\n" for v in values)
+        return f"pub(super) static {name}: [i64; {len(values)}] = [\n{body}];\n"
+
+    return (
+        "//! Generated by `scripts/gen_op_norm_static_base.py`; do not edit.\n"
+        "//!\n"
+        f"//! Certified `base_cos` / `base_sin` tables of the D64 selective-L2\n"
+        f"//! operator-norm predicate (`d = {D}`, `q = {Q}`), as `i64`, and their\n"
+        "//! sound error bound. `static_base_equals_build_tables` checks every entry\n"
+        "//! against `build_tables`.\n"
+        f"//! SHA-256 of the little-endian `i64` entries (cos then sin): {digest}\n"
+        "\n"
+        f"pub(super) const D: usize = {D};\n"
+        f"pub(super) const Q: u32 = {Q};\n"
+        f"pub(super) const EPS_ROOT: i128 = {eps_root};\n"
+        "\n"
+        + table("BASE_COS", base_cos)
+        + "\n"
+        + table("BASE_SIN", base_sin)
+    )
+
+
+def main(argv):
+    out = Path(argv[1]) if len(argv) > 1 else Path(__file__).resolve().parent.parent / "src/sampler/op_norm/static_base.rs"
+    base_cos, base_sin, eps_root = build_tables(D, Q)
+    assert all(-(1 << 63) <= v < (1 << 63) for v in base_cos + base_sin), "entry does not fit i64"
+    blob = b"".join(struct.pack("<q", v) for v in base_cos + base_sin)
+    digest = hashlib.sha256(blob).hexdigest()
+    out.parent.mkdir(parents=True, exist_ok=True)
+    out.write_text(render(base_cos, base_sin, eps_root, digest))
+    print(f"entries,{len(base_cos) + len(base_sin)}")
+    print(f"eps_root,{eps_root}")
+    print(f"base_tables_sha256_le_i64,{digest}")
+    print(f"out,{out}")
+
+
+if __name__ == "__main__":
+    main(sys.argv)
diff --git a/crates/akita-challenges/src/sampler/op_norm.rs b/crates/akita-challenges/src/sampler/op_norm.rs
index ae9242bfb..18285a05b 100644
--- a/crates/akita-challenges/src/sampler/op_norm.rs
+++ b/crates/akita-challenges/src/sampler/op_norm.rs
@@ -112,7 +112,7 @@ impl OpNormTable {
             )));
         }
 
-        let (base_cos, base_sin, eps_root) = build_tables(d, q);
+        let (base_cos, base_sin, eps_root) = base_tables(d, q);
 
         let max_l1 = i128::from(max_l1);
         let max_t = i128::from(max_t);
@@ -606,6 +606,83 @@ fn arctan_inv(x: i128) -> (i128, i128) {
     (sum - slack, sum + slack)
 }
 
+// Static operator-norm base tables (feature `ont-static-base`, default off). The
+// base tables are a pure function of `(d, q)`; with the feature, the D64
+// selective-L2 table (`d = 64`, `q = 48`) reads them from generated static
+// data instead of evaluating the interval Taylor series, and every other
+// `(d, q)` still builds them. The transposed `freq_*_at` rows are still built
+// at run time. Without the feature `base_tables` is `build_tables` itself.
+#[cfg(not(feature = "ont-static-base"))]
+use self::build_tables as base_tables;
+
+#[cfg(feature = "ont-static-base")]
+mod static_base;
+
+#[cfg(feature = "ont-static-base")]
+fn base_tables(d: usize, q: u32) -> (Vec<i128>, Vec<i128>, i128) {
+    if d == static_base::D && q == static_base::Q {
+        let widen = |table: &[i64]| -> Vec<i128> { table.iter().map(|&v| i128::from(v)).collect() };
+        return (
+            widen(static_base::BASE_COS.as_slice()),
+            widen(static_base::BASE_SIN.as_slice()),
+            static_base::EPS_ROOT,
+        );
+    }
+    build_tables(d, q)
+}
+
+#[cfg(all(test, feature = "ont-static-base"))]
+mod static_base_tests {
+    use super::*;
+
+    /// The generated tables equal `build_tables` entry for entry, and the
+    /// table built through them equals the one built from `build_tables`.
+    #[test]
+    fn static_base_equals_build_tables() {
+        let (cos, sin, eps_root) = build_tables(static_base::D, static_base::Q);
+        assert_eq!(eps_root, static_base::EPS_ROOT);
+        assert_eq!(cos.len(), static_base::BASE_COS.len());
+        assert_eq!(sin.len(), static_base::BASE_SIN.len());
+        for (built, embedded) in cos.iter().zip(static_base::BASE_COS.iter()) {
+            assert_eq!(*built, i128::from(*embedded));
+        }
+        for (built, embedded) in sin.iter().zip(static_base::BASE_SIN.iter()) {
+            assert_eq!(*built, i128::from(*embedded));
+        }
+        assert_eq!(
+            base_tables(static_base::D, static_base::Q),
+            (cos.clone(), sin.clone(), eps_root)
+        );
+
+        let narrow = |table: &[i128]| -> Vec<i64> {
+            table.iter().map(|&v| i64::try_from(v).unwrap()).collect()
+        };
+        let (freq_cos, freq_sin) =
+            op_norm_accumulate::build_freq_at_tables(static_base::D, &narrow(&cos), &narrow(&sin));
+        let table = OpNormTable::new(static_base::D, static_base::Q, 53, 18).unwrap();
+        assert_eq!(table.freq_cos_at, freq_cos);
+        assert_eq!(table.freq_sin_at, freq_sin);
+        assert_eq!(table.eps_root, eps_root);
+        assert!(table.strict_threshold_contains_shrunken_subset(48, 4, 18, 600));
+    }
+
+    #[test]
+    fn static_base_still_validates_admitted_bounds() {
+        assert!(OpNormTable::new(64, 48, 53, 18).is_ok());
+        assert!(OpNormTable::new(64, 48, u64::MAX, 18).is_err());
+        assert!(OpNormTable::new(64, 48, 53, u64::MAX).is_err());
+        assert!(OpNormTable::new(0, 48, 53, 18).is_err());
+        assert!(OpNormTable::new(64, 0, 53, 18).is_err());
+    }
+
+    /// Every other `(d, q)` still builds its tables.
+    #[test]
+    fn static_base_falls_back_elsewhere() {
+        assert_eq!(base_tables(128, 48), build_tables(128, 48));
+        assert_eq!(base_tables(64, 40), build_tables(64, 40));
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/crates/akita-challenges/src/sampler/op_norm/static_base.rs b/crates/akita-challenges/src/sampler/op_norm/static_base.rs
new file mode 100644
index 000000000..637a94cf3
--- /dev/null
+++ b/crates/akita-challenges/src/sampler/op_norm/static_base.rs
@@ -0,0 +1,273 @@
+//! Generated by `scripts/gen_op_norm_static_base.py`; do not edit.
+//!
+//! Certified `base_cos` / `base_sin` tables of the D64 selective-L2
+//! operator-norm predicate (`d = 64`, `q = 48`), as `i64`, and their
+//! sound error bound. `static_base_equals_build_tables` checks every entry
+//! against `build_tables`.
+//! SHA-256 of the little-endian `i64` entries (cos then sin): fd2c192c42aa43710ef7c9947d0d8626a5fc621b87912b28e19ccc52c45b826f
+
+pub(super) const D: usize = 64;
+pub(super) const Q: u32 = 48;
+pub(super) const EPS_ROOT: i128 = 1;
+
+pub(super) static BASE_COS: [i64; 128] = [
+    281474976710656,
+    281135927774059,
+    280119597762857,
+    278428435105064,
+    276066513959653,
+    273039524401542,
+    269354758713710,
+    265021093819447,
+    260048969897066,
+    254450365228603,
+    248238767343085,
+    241429140523889,
+    234037889758477,
+    226082821217338,
+    217583099357370,
+    208559200753021,
+    199032864766430,
+    189027041175396,
+    178565834885358,
+    167674447858561,
+    156379118400326,
+    144707057948671,
+    132686385519576,
+    120346059965811,
+    107715810212517,
+    94826063637631,
+    81707872769660,
+    68392840479422,
+    54913043845964,
+    41300956880066,
+    27589372291508,
+    13811322488556,
+    0,
+    -13811322488557,
+    -27589372291509,
+    -41300956880067,
+    -54913043845965,
+    -68392840479423,
+    -81707872769661,
+    -94826063637632,
+    -107715810212518,
+    -120346059965811,
+    -132686385519577,
+    -144707057948672,
+    -156379118400327,
+    -167674447858562,
+    -178565834885359,
+    -189027041175397,
+    -199032864766431,
+    -208559200753022,
+    -217583099357371,
+    -226082821217339,
+    -234037889758478,
+    -241429140523890,
+    -248238767343086,
+    -254450365228604,
+    -260048969897067,
+    -265021093819448,
+    -269354758713711,
+    -273039524401543,
+    -276066513959654,
+    -278428435105065,
+    -280119597762858,
+    -281135927774060,
+    -281474976710656,
+    -281135927774060,
+    -280119597762858,
+    -278428435105065,
+    -276066513959654,
+    -273039524401543,
+    -269354758713711,
+    -265021093819448,
+    -260048969897067,
+    -254450365228604,
+    -248238767343086,
+    -241429140523890,
+    -234037889758478,
+    -226082821217339,
+    -217583099357371,
+    -208559200753022,
+    -199032864766431,
+    -189027041175397,
+    -178565834885359,
+    -167674447858562,
+    -156379118400327,
+    -144707057948672,
+    -132686385519577,
+    -120346059965811,
+    -107715810212518,
+    -94826063637632,
+    -81707872769661,
+    -68392840479423,
+    -54913043845965,
+    -41300956880067,
+    -27589372291509,
+    -13811322488557,
+    0,
+    13811322488556,
+    27589372291508,
+    41300956880066,
+    54913043845964,
+    68392840479422,
+    81707872769660,
+    94826063637631,
+    107715810212517,
+    120346059965811,
+    132686385519576,
+    144707057948671,
+    156379118400326,
+    167674447858561,
+    178565834885358,
+    189027041175396,
+    199032864766430,
+    208559200753021,
+    217583099357370,
+    226082821217338,
+    234037889758477,
+    241429140523889,
+    248238767343085,
+    254450365228603,
+    260048969897066,
+    265021093819447,
+    269354758713710,
+    273039524401542,
+    276066513959653,
+    278428435105064,
+    280119597762857,
+    281135927774059,
+];
+
+pub(super) static BASE_SIN: [i64; 128] = [
+    0,
+    13811322488556,
+    27589372291508,
+    41300956880066,
+    54913043845964,
+    68392840479422,
+    81707872769660,
+    94826063637631,
+    107715810212517,
+    120346059965811,
+    132686385519576,
+    144707057948671,
+    156379118400326,
+    167674447858561,
+    178565834885358,
+    189027041175396,
+    199032864766430,
+    208559200753021,
+    217583099357370,
+    226082821217338,
+    234037889758477,
+    241429140523889,
+    248238767343085,
+    254450365228603,
+    260048969897066,
+    265021093819447,
+    269354758713710,
+    273039524401542,
+    276066513959653,
+    278428435105064,
+    280119597762857,
+    281135927774059,
+    281474976710656,
+    281135927774059,
+    280119597762857,
+    278428435105064,
+    276066513959653,
+    273039524401542,
+    269354758713710,
+    265021093819447,
+    260048969897066,
+    254450365228603,
+    248238767343085,
+    241429140523889,
+    234037889758477,
+    226082821217338,
+    217583099357370,
+    208559200753021,
+    199032864766430,
+    189027041175396,
+    178565834885358,
+    167674447858561,
+    156379118400326,
+    144707057948671,
+    132686385519576,
+    120346059965811,
+    107715810212517,
+    94826063637631,
+    81707872769660,
+    68392840479422,
+    54913043845964,
+    41300956880066,
+    27589372291508,
+    13811322488556,
+    0,
+    -13811322488557,
+    -27589372291509,
+    -41300956880067,
+    -54913043845965,
+    -68392840479423,
+    -81707872769661,
+    -94826063637632,
+    -107715810212518,
+    -120346059965811,
+    -132686385519577,
+    -144707057948672,
+    -156379118400327,
+    -167674447858562,
+    -178565834885359,
+    -189027041175397,
+    -199032864766431,
+    -208559200753022,
+    -217583099357371,
+    -226082821217339,
+    -234037889758478,
+    -241429140523890,
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