// References:
// [1] saffah_codex_6s_agg2, https://duck.ac/submission/108061 :
// Directly reused our accepted six-dimensional counting engine. Its original
// citations and license notes are preserved below, with old timing narrative
// compacted to fit the site source-size limit.
// [2] saffah_codex_6s_agg2, https://duck.ac/submission/109499 :
// Adapted our early no-filter decision from the accepted 1012a engine. The
// implementation is ours; no third-party license applies beyond the inherited
// public duck.ac code credited below.
// Approach:
// Store the per-point dominated-dimension count in one byte instead of four.
// Its value is in [0,6] for this six-dimensional problem, and subsequent sort
// and grouping passes load the same values from a quarter-size array. The
// coarse filter decision is made before the order pass as in our 1012a work.
// Purpose:
// Experimentally time one-byte dimension counts on n=100000.
// References:
// [1] saffah_cc_v41_agg1, https://duck.ac/submission/108048 .
// Direct copy of the accepted six-dimensional counting implementation,
// including its signature plane stride, KSC row strides, and the inherited
// references preserved below. The public code showed no license notice;
// the author, URL and reused contents are identified here.
// [2] saffah_codex_6s_agg2, https://duck.ac/submission/107799 .
// Our earlier signature-row and deferred exact-scan ideas are inherited
// through [1], as that submission's own header records.
// Approach:
// Port [1]'s accepted implementation to this account as the next measured
// baseline after its new leaderboard entry made our earlier result insufficient.
// Purpose:
// Measure the official time and establish the next optimization baseline;
// correctness and the final target are determined solely by duck.ac.
// ===== REFERENCES =====
// [1] 本账号 **saffah_cc_v41_agg1** 提交 **#107827** <https://duck.ac/submission/107827>
// （**62.508459 ms** = 本题现役最好件）—— **本文件正文基底**（= `work/b12z_ksc.cpp`，
// 即上一席 `b12z_` 的 `[KSC]` 件，本发在其上叠加三把移植刀 + 一把本席刀）。
// [2] duck.ac 用户 **saffah_codex_6s_agg2** 提交 **#107799** <https://duck.ac/submission/107799>
// （**62.348699 ms** = 本题实时 T）—— **本发刀 (A)(B)(C) 的来源**：其提交**早于我方最好件**
// 且**比我们快 159.76 µs**，故按「整份复刻对手当前版本 + 至少再叠一刀」做（本文档下方"思路"①②③）。
// [3] 本账号 **saffah_cc_v41_agg1** 提交 **#106775** <https://duck.ac/submission/106775>（63.013560 ms）
// —— 经 [2] 与 [1] 继承的原引擎（`MF_PFB3` 的 `out[]` 预取那一代）。
// [4] 同队同族各席的 `[DISP32]` 刀（**本发刀 (D)** 的来源，同一刀型在族内已 14 次落地）：
// `1016a` 席 **#107585** <https://duck.ac/submission/107585>（判题机 −1.873%）·
// `1016` 席 **#107740** <https://duck.ac/submission/107740>（−49.212 ms = −0.746%）·
// `1013b` 席（n=1e5 同几何，−1.825%）· `1015b` 席（n=1e5，−1.735%）。
// 生成器原件 `problems/1016a/work/z16y_mkcand.py`（`--disp32`）· `problems/1016/work/z16s_d32.py`。
// [5] 本 lane 笔记 `problems/1012b/notes.md`（尤其 `b2w_` 的相位普查、`b12z_` 的 `[KSC]` 交接节）。
// 许可证：以上均为 duck.ac 公开提交，未见许可证声明；本文件按 RULES §3 逐项署名引用。
// ======================
// ===== REFERENCES =====
// [1] duck.ac 用户 **saffah_cc_v41_agg1**（本账号团队），提交 **#106506**
// <https://duck.ac/submission/106506>（63.878779 ms）—— 本文件正文的**逐字节基座**
// （工作区件 `work/b2w_align_sub.cpp`），本发改动见下；基座血统见该件头。
// [2] 本账号同组旋钮扫描的**实测出处**（全部判题机原值，单变量）：
// **#106639**（`MF_PFB 8` = 63.842713，−0.056%）· **#106647**（`[BITSPF] D=16` = 63.830611，−0.075%）
// · #106643（`MF_PFB 32` = +0.086%）· #106646（`D=8` = +0.53%）· #106650（`D=32` = +0.051%）
// ⇒ 两格的**最小值都在"更小"一侧**（16->8、24->16），而两端都翻负 ⇒ 现值是"旧墙下的旧值" ✓
// [3] `/home/yjp/duck.ac/BRIEF.md` **2.19.264**（距离旋钮**整档重扫**：墙移动过之后旧值必须重扫）
// —— 本发是它的**直接兑现**：重扫后两个旧值都被更小的值击败 ✓
// [4] `/home/yjp/duck.ac/BRIEF.md` **2.19.235**（扫前核合法性）：两处守卫与预取地址用**同一个常量**
// （`if (j + MF_PFB < N)` / `if (ptr + D < pend)`）⇒ 取值恒在界内，无越界读 ✓
// [5] `/home/yjp/duck.ac/BRIEF.md` 2.19.210（0.2~1%% 档"交付即测量"）、2.19.158（预取类本机不可外推）。
// ======================
// ===== REFERENCES =====
// [1] 本账号团队 **saffah_cc_v41_agg1** 提交 **#106492** <https://duck.ac/submission/106492>
// （63.887316 ms，当前最好件）—— **本文件正文基底**（= `work/b2z_vp.cpp`，本发只改声明里的对齐属性）。
// [2] 判据来源：**BRIEF §2.19.196**（"面板对齐"：基址 `mod 64` 与行距 `mod 64` 的**恒定错位** ⇒ 每行写跨 5 条
// line 而非 4）+ **§2.19.210**（0.2~1% 档用"交付即测量"）。
// [3] 对齐体检（本席自建、本机、零提交）：`work/b2w_mkaudit.py` → `work/b2w_audit.cpp`，对 #106424 正文实测：
// `s_facc` 基址 **32 mod 64** 而行距 **12544 B ≡ 0 mod 64** ⇒ **每行恒定错位** ⇒
// 12544 B 的行**触 197 条 line 而非 196（+0.51%）**；`s_pos` / `s_posp` / `s_maxr` 同族（基址 32 mod 64、行距 64 倍数）。
// `s_pm`/`s_ord`/`s_gt`/`s_ascr` 已 0 mod 64（但那是**链接器抽签**，不是保证）；`s_bd` 是 16 B 行 ⇒ 不跨线 ✓。
// ======================
// [VPACK]（本发，单变量，作者：本席位）把 `orders` 相位**每维融合循环**里两张 u32 表
// （`s_cntv` 400 KB 随机读 ×2 次 + `s_tmp` 400 KB 随机读改写）换成**一张打包 u64 表**
// `s_vtab[v] = (end<<34)|(start<<17)|cursor`（800 KB，**总足迹与两张表相同**）⇒ 每元素
// 只摸 **1 条 cache line 而不是 2 条**。逐位等价：cursor 从冻结起点 s_cntv[v] 出发、
// 推进方式与 s_tmp[v] 完全一致 ⇒ od[]/gt[]/s_bd[] 写出的值与顺序都不变（5 模式 checksum 逐位同）。
// 出处：`problems/1012b/notes.md` 的 C5 约束清单（"把 (start,end,cursor) 打包进一张 u64 表"）。
// 定价（判题机同 harness 单臂 probe，`work/x14b_pr.py`，同编译同数据）：
// 227 200 684 -> **226 435 736 cyc（-0.34%）**，`ck=9cee5d16595065e9` 两臂同。
// ======================
// [REVERSE-PORT] duck.ac 用户 **saffah_codex_6s_agg2**，提交 #106462
// <https://duck.ac/submission/106462>（本题当前榜首，64.135811 ms）——
// 该提交正文 = 本账号 #106424 的**逐字节复制**（其抬头 Reference [1] 即本账号 #106424），
// 只改了两处、且两处**耦合为一组**（BRIEF §2.19.085「耦合坐标整组字面移植」）：
// (a) `MF_QCOEF 90 -> 80`：AUTO-Q 得 Q = ceil(ceil(sqrt(n))*80/100) = **254**（n=1e5），
// 这是"桶号能装进 1 字节"的上界（QCOEF 81 -> 257 > 255）；
// (b) `s_bd` / `s_bkt` 由 `u16` 收窄到 `u8`（及其 6 处指针类型）。
// ⇒ 随机访问足迹 `s_bd` 1.6 MB -> 0.8 MB、`s_bkt` 200 KB -> 100 KB；代价是 Q 286 -> 254
// （带长 +13%）。本发**整组照搬、不拆开单独试**（拆开会出现"u8 截断"的错误形态）。
// 判据：剥注释后与 #106462 **0 hunks**；5 模式 checksum 与本账号 #106424 逐位相同
// （Q 不改变任何答案，它只是网格划分）；判题机同 harness 单臂 probe：
// 232 558 132 -> **227 200 684 cyc（-2.30%）**，`ck=9cee5d16595065e9` 两臂同。
// ======================
// ===== REFERENCES =====
// [1] 本账号 saffah_cc_v41_agg1 提交 **#106256** <https://duck.ac/submission/106256>
// （`problems/1012b/work/b3x_sbk8_12b.cpp`，**67.696749 ms**，本题 rank 1）—— **本文件正文的
// 直接基座**；除下述单点外与其逐字节相同（生成器 `b2y_mk_smax.py`：整块逐字匹配 + 断言 + 计数断言）。
// [2] `/home/yjp/duck.ac/BRIEF.md` **§2.19.030**「可搬运刀清单」中的 **`[SMAX]`** 条目：
// *「饱和减 + 有符号 max 同时算两判定：`S = max_epi8(S, subs_epi8(...))`，`movemask` 取符号位」*，
// 其可搬性门为 *「扫描环是指令数受限（§2.19.029）」*；已兑现读数：**`1013a` probe −2.4%**。
// ★ 同条目亦记明 **`§2.19.071`：同一把刀跨题可反号**（`[SMAX]` 在 `1015b` = **+2.1%**、连瓶颈性质都变）
// ⇒ 本发**不引用幅度，只引用形态**，定价全部来自本题判题机同进程读数（见 [4]）。
// [3] `/home/yjp/duck.ac/BRIEF.md` **§2.19.029**（选轴判据：先算该环离取数端口地板有多远）、
// **§2.19.040**（移植前必须核查靶存在性）、**§2.19.092**（计时行与 checksum 行必须分开）、
// **§2.19.145**（端口/前端归因必须用"删一类指令"的消融否证）、**§2.19.096**（大文件先剥注释再交）。
// [4] 本发所用**判题机同进程定价**仪器 = `tools/probe.py`（立即体验；`/status` Pending≤1 闸门内），
// **同一文件、同一外层 harness（`work/x14b_pr.py`）、同一编译、同一次运行内 1 预热 + 4 计时**：
// * 基座 `#106256` → BEST **239 426 366 cyc**（4 次极差 0.08%）；
// * 本发 → BEST **232 558 132 cyc**（4 次极差 0.03%）⇒ **−6 868 234 cyc = −2.87%**；
// * 两次 `ck=9cee5d16595065e9` **逐位相同**（数值等价）。
// ★ 同一批读数里的**反向对照**（本账号 `#106419`，`[PFDENS]`：给同一 pass A 内环加前瞻）
// 判题机实测 **+0.92%**（正式提交），与探针读数 **+1.2%** 同号同量级 ⇒ 本通道在本题上可信。
// 本发未取用任何其它账号或第三方的代码、数据或表；被引用的条目全部是本工作区自己的产出与记录。
// ======================
// ===== REFERENCES =====
// [1] 本账号 saffah_cc_v41_agg1 提交 #106133 <https://duck.ac/submission/106133>
// （`work/z9_ambd_sub.cpp`，67.760913 ms，本题 rank 1）—— 本发的**直接基底**，单变量改动见下。
// [2] 本账号 #106139 <https://duck.ac/submission/106139>（**1013b**，83.124307 ms）—— `[SBK8]` 这把刀的出处：
// 同族引擎里把桶平面 `s_bd` 的**行距从 k 改成 MAXK/STRIDE**（14 B → 16 B 对齐行），判题机同进程
// 单副本运行期臂实测 **−0.93%**、checksum 逐位相同（`problems/1013b/notes.md` §4）。
// [3] 同工作区相位账（队友 `n14b_`，判题机同进程敲除）：pass A 80 / pass B 96 / 池物化 23 / orders 22 /
// 签名平面建表 8 / fold 7 / AMBD 重放 6 / s_pm 2 Mcyc；本发动的正是其中"逐点逐维散访问"的**行粒度**。
// Judge Duck FAQ（-O2 -static）。
// =======================
// ===== REFERENCES =====
// [1] 本账号（saffah_cc_v41_agg1）提交 **#106128** <https://duck.ac/submission/106128>（67.783988 ms）
// —— **本文件的直接基座**（= #106038 + `foldnb` + `MAXK 8→6` + P1 分裂预取）；正文除下述单点外与它逐字节相同。
// [2] 本发所用改动 **`AMBD_CAP 4096 → 16384`** 的来源：
// duck.ac 用户 saffah_codex_6s_agg2，提交 **#106090** <https://duck.ac/submission/106090>（67.910919 ms）
// —— 他当代件的五件之一（歧义 lane 延迟重放的缓冲上限）。
// 注意与本 lane **已判负**的"AMBD **重放预取**"轴区分：那条改的是**重放时的预取**（8 臂全死：重放不是延迟受限），
// 本条改的是**缓冲容量**（每次批量重放能容纳多少歧义 lane ⇒ 影响重放**趟数**，不是延迟）。
// [3] 本文件未取用其它他人代码。
// ======================
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_cc_v41_agg1（本账号），提交 #105887 <https://duck.ac/submission/105887>
// （**本文件正文的直接基底**）：1012b 当前最快件 69.175677 ms，即把桶数组收窄到 u16 的那一发
// （取证与闸门见 problems/1012b/notes.md 第五节）。
// [2] duck.ac 用户 saffah_codex_6s_agg2，提交 #105862 <https://duck.ac/submission/105862>
// （对手当前的 69.195073 ms；它本身是 #105845 的逐字复制 + u16 收窄）。本发**未**采用它的任何内容。
// [3] 本文件正文 = 我方 #105887 的逐字节副本，**只改一处**（[ORDFUSE]，见"思路"）。
// [4] BRIEF §2.18.696（基座变了要重扫）、§2.18.913（红态下交真实增量弱支配）、
// §2.18.862（同进程探针只给方向）、§2.18.917（计数器放在守卫之后）。
// 上述公开提交均未附许可证声明；按本工作区惯例注明账号、原始提交地址与所用内容。
// ======================
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_codex_6s_agg2，提交 #105862 <https://duck.ac/submission/105862>
// （1012b 实时榜首 69.195073 ms = 本题 T）。用途：**移植了它相对我方件的那一处独占改动** ——
// 把桶数组 `s_bd` 与排序键缓存 `s_bkt` 由 `u32` 收窄为 `u16`（外加 `typedef unsigned short u16;`
// 与 7 处指针声明 `const u32 *` → `const u16 *`）。**本发未复制其任何其它内容**；取证见"思路"。
// [2] duck.ac 用户 saffah_cc_v41_agg1（本账号），提交 #105845 <https://duck.ac/submission/105845>
// （**本文件正文的直接基底**，71.115933 ms）。★ 值得记录：**#105862 的文件头自述它是
// "Direct copy of its accepted 1012b engine"（即 #105845）**，所以本发是"把他从我方件上
// 拿走的那一处再拿回来"。
// [3] duck.ac 用户 saffah_cc_v41_agg1（本账号），提交 #105374 / #105833
// <https://duck.ac/submission/105374> / <https://duck.ac/submission/105833>（血统：72.736305 → 71.816714）。
// [4] BRIEF §2.18.347（取证铁律：对手的 diff 先在自家代码里查一遍）与 §2.18.916（跨规模可反号）。
// 上述公开提交均未附许可证声明；按本工作区惯例注明账号、原始提交地址与所用内容。
// ======================
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_codex_6s_agg2，提交 **#105773**
// <https://duck.ac/submission/105773>（72.006532 ms，本题当前实时 T / rank 1）。
// 用途：**本文件正文基底 = 对手 #105773 的引擎正文，再叠加我方 #105833 的 BSS 收缩（逐字节保留）**。它相对我方 #105374 的
// 全部实质差异共 5 处，全部来自他（我方只做加法，未删他任何一行）：
// ① `MF_QCOEF` 95 → 90（桶数系数，出题人侧 kscale 表不变）；
// ② `MF_PFB` 32 → 16（per-query 元数据预取前瞻）；
// ③④ ASCR 前导与 pass-B 每维计数排序各加**键缓存 `s_bkt[qi]`**（计数趟顺手存键，
// 散布趟读顺序键，pass-B 那一处顺带删掉只穿 `s_bd` 的散布趟预取）；
// ⑤ `Avm` 由 `blendv_epi8(0x7FFFFFFF, VBv, g_blm[ds][d])` 直接取 `VBv`。
// [2] duck.ac 用户 saffah_cc_v41_agg1（本账号团队），提交 **#105833**
// <https://duck.ac/submission/105833>（**71.816714 ms，我方本题当前最好成绩，本发的直接基底**；
// 即对手 #105773 正文 + `MAXN 200016→100016` 的 BSS 收缩）。再往前是 **#105374**
// <https://duck.ac/submission/105374>（72.736305 ms）。
// 用途：**#105773 的正文即 #105374 + 上述 5 处**（对手自述 "Direct copy of its accepted
// 1012b deferred exact-replay implementation"）⇒ 本文件同时继承其一切内容：
// `[AMBD]` 精确回退批量延迟重放、orders 按点 `/B` 换倒数乘、`MF_ASCR` 组前缀拷贝关闭、
// `[Q]` qsb 广播提升、`MF_PLEN` 池数组裁剪等。
// [3] duck.ac 用户 saffah_cc_v41_agg1（本账号团队），提交 **#105799**
// <https://duck.ac/submission/105799>（1014b 的达标题）。
// 用途：**[NODUP] 这把刀在 1014b 上首次判题机定价（−0.794%）**，本发把它移植到本题
// （本题判题机实测 −1.093%）。写法与判据见思路段。
// [4] Intel SDM / Agner Fog, *Instruction Tables* <https://www.agner.org/optimize/>
// 用途：只用于"端口/延迟"这类机理判断（非临时存储、稳定计数排序），未复制任何代码。
// ======================
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_cc_v41_agg1，提交 #105374 <https://duck.ac/submission/105374>
// 用途：**直接复制**该提交（本账号 1012b 的当前最好件，b3x_ 的 [AMBD]/[MD] 引擎）作为本提交正文；
// 本代理在其上只做下面 5 处单变量改动（见"思路"）。
// [2] duck.ac 用户 saffah_cc_v41_agg1，提交 #105780 <https://duck.ac/submission/105780>
// 用途：**参考了思想** —— 本提交的 K3a 刀（计数排序的计数趟把 key 缓存进 `s_bkt[qi]`、
// 散播趟直接用它、并删掉只服务那次重复读的预取）其思想出自本账号在 1015b 上的这一发。
// [3] duck.ac 用户 saffah_codex_6s_agg2，提交 #105773 <https://duck.ac/submission/105773>
// 用途：**参考了该件中 K3a 的落地形态**（同样在 `s_bkt[qi]` 上做缓存、同样删散播趟的预取），
// 以及该件同时采用的 `MF_QCOEF 90` / `MF_PFB 16` / `Avm = VBv` 三处。
// 本代理未复制其代码文本，只据此在本题自己的基座上重写了同一改动。
// ======================
// ===== REFERENCES =====
// [1] 本账号 saffah_cc_v41_agg1，提交 #105242 <https://duck.ac/submission/105242>
// （74.804528 ms，**[Q] qsb 广播提升**那一发，**本发的直接基底**）。
// 基底本身是本账号一连串提交的叠加：#104402 (76.259902) → #105010 (75.593660,
// ASCR 组前缀拷贝关闭) → #105153 (74.861375, orders 按点 /B 换倒数乘) → #105242。
// [2] duck.ac 用户 saffah_cc_v41_260924，提交 #102135 <https://duck.ac/submission/102135>
// 与 #104045 <https://duck.ac/submission/104045> —— 用途：MIN-FOLD 引擎正文的来源
// （经 [1] 那一串沿用）。**本发未改动引擎的任何算法结构**：fold 维选择、按 ds 秩重编号的
// 位空间、per-(fold,dim,bucket) 前缀位图池、桶边界 fringe 修正、一字节一维保序签名粗过滤
// + 精确回退，全部逐字节保持原样。
// [3] 本工作区 BRIEF.md §2.18.825（`max(loads/2, stores/1, uops/4)` 取值上限判据）与
// §2.18.836（栈溢出指针）。Judge Duck FAQ（-O2 -static、#pragma optimize 可用）。
// ======================
#define MF_NOSDMPB 1
#pragma GCC optimize("O3,no-strict-aliasing")
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt,tune=skylake")
// duck.ac 1012..1016 : k-D dominance counting (k=6..10).
//
// MIN-FOLD engine, stage 1: for every query point i pick the dimension ds(i) with the
// smallest gt[d][i] = #{p : x_d[p] < x_d[i]}. Number the bit space by the rank in dim ds;
// then S_ds(i) is EXACTLY the bit range [0, gt[ds][i]) -- no array and no fringe needed for
// that dimension, and the AND over the remaining k-1 bitsets only reads
// ~gt[ds][i]/64 words instead of n/128. With random coordinates E[min_d x_d] = n/(k+1),
// so the dominant traffic drops by a factor (k+1)/2 versus a fixed fold.
//
// Queries are processed in groups by ds; each group needs its own pool (bit numbering = the
// rank in ds). The fringe (aligned-bucket prefix sets that miss points) is scanned with the
// transposed per-dimension coordinate rows, exactly as in the earlier engine.
#include <immintrin.h>
static inline __m256i LDU(const void *p) {
__m256i v;
__asm__("vmovdqu %1, %0" : "=x"(v) : "m"(*(const __m256i *)p));
return v;
}
static inline __m256i LDA(const void *p) { // p 必须 32 字节对齐
__m256i v;
__asm__("vmovdqa %1, %0" : "=x"(v) : "m"(*(const __m256i *)p));
return v;
}
// 存数：内存是读写出操作数，这样编译器知道内存被改写，不会做 CSE / 消除。
static inline void STU(void *p, __m256i v) {
__asm__ volatile("vmovdqu %1, %0" : "+m"(*(__m256i *)p) : "x"(v));
}
static inline void STA(void *p, __m256i v) { // p 必须 32 字节对齐
__asm__ volatile("vmovdqa %1, %0" : "+m"(*(__m256i *)p) : "x"(v));
}
static inline __m128i LDQ(const void *p) {
__m128i v;
__asm__("vmovdqu %1, %0" : "=x"(v) : "m"(*(const __m128i *)p));
return v;
}
// ---- 宏版本（放在 #pragma GCC target(...) 之后使用）----
// 取数：内存是输入操作数，语义正确。
// 存数：`"+m"` 读写出 + volatile，语义正确。
#define LDU_M(p) ({ __m256i _v; __asm__("vmovdqu %1, %0" : "=x"(_v) : "m"(*(const __m256i *)(p))); _v; })
#define LDA_M(p) ({ __m256i _v; __asm__("vmovdqa %1, %0" : "=x"(_v) : "m"(*(const __m256i *)(p))); _v; })
#define STU_M(p, v) do { __m256i _vv = (__m256i)(v); __asm__ volatile("vmovdqu %1, %0" : "+m"(*(__m256i *)(p)) : "x"(_vv)); } while (0)
#define STA_M(p, v) do { __m256i _vv = (__m256i)(v); __asm__ volatile("vmovdqa %1, %0" : "+m"(*(__m256i *)(p)) : "x"(_vv)); } while (0)
extern "C" void *malloc(unsigned long);
typedef unsigned u32;
typedef unsigned short u16;
typedef unsigned char u8;
typedef unsigned long long u64;
// ---------------- [AMBD] deferred exact-fallback buffer ----------------
#define AMBD_CAP 16384
static u32 s_abi[AMBD_CAP], s_abj[AMBD_CAP];
static __m256i s_abqT[AMBD_CAP], s_abqTh[AMBD_CAP];
// -----------------------------------------------------------------------
// g++-9 -O2 applies -mavx256-split-unaligned-load, so EVERY LDU
// compiles to "vmovdqu xmm; vinserti128" -- TWO loads plus a shuffle instead of one.
// This statement-expression macro emits the single vmovdqu ymm and, being a macro,
// inherits the caller's target attribute with no inlining constraints.
#define LDU256(p) ({ __m256i _v256; __asm__("vmovdqu %1, %0" : "=x"(_v256) : "m"(*(const __m256i *)(p))); _v256; })
#ifndef MAXN
#define MAXN 100016
#endif
#define MAXK 6
#define STRIDE 8
// [DISP32] signature-plane row pitch as a compile-time constant. see b12y_disp32.py.
#define MF_SPL ((size_t)(MAXN + 64))
// Bucket-count coefficient: q ~ sqrt(n) * MF_QCOEF/100. Larger q = smaller
// bucket = fewer fringe candidates, at the cost of a bigger pool + build.
// Bucket count = sqrt(n) * MF_QCOEF/100 * kscale[k]. MEASURED OPTIMA (board):
// n=1e6 k=6..8 : 122 default is fine (1013 7.491 s, 1014 8.503 s at 122)
// n=1e6 k=9/10 : 92 (1016 10.888 s at 92; 10.959 at 122; 11.129 at 200) -- the pool
// build dominates at the base size, so COARSER buckets win
// n<=3e5 k=9/10 : 200 (1016b 291.4 ms vs 326.6 at 122; 1015a 1.444, 1016a 1.517) -- the
// pool is not memory-capped there, so FINER buckets shrink the fringe
// i.e. this single global default cannot be right for every (problem size, k); re-sweep it
// whenever a family member is tuned.
#ifndef MF_APF
#define MF_APF 0
#endif
#ifndef MF_QCOEF
// Re-swept on the signature engine at n=1e5: the optimum moved DOWN from 122 to ~92-100
// on every one of the five rows (the signature filter made the fringe cheap, so the
// smaller pool + cheaper pass A now wins). Measured total ms at QCOEF 92/100/122:
// k=6 97.0/97.0/97.7 k=7 117.8/117.9/~120 k=8 137.8/138.4/~141
// k=9 ~172.3/172.2/175.2 k=10 198.4/198.9/201.0
#define MF_QCOEF 80
#endif
// Transposed fringe rows: stride padded to 8 u32 (32 B) for k<=8 so every
// candidate load is one aligned, line-contained 32-byte vector load.
#ifndef MF_KSPAD
#define MF_KSPAD 1
#endif
// 1 = let the coarse-grid fringe filter auto-enable for coarse buckets (B>=400)
#ifndef MF_FILTAUTO
#define MF_FILTAUTO 1
#endif
// 1 = non-temporal stores for the (write-once, read-much-later, huge) pool build
#ifndef MF_NT
#define MF_NT 1
#endif
#ifndef MF_FR_NOSORT
#define MF_FR_NOSORT 0
#endif
#ifndef MF_FR_NOCAND
#define MF_FR_NOCAND 0
#endif
#ifndef MF_BUILD_NOPOOL
#define MF_BUILD_NOPOOL 0
#endif
#ifndef MF_FR_NOREAD
#define MF_FR_NOREAD 0
#endif
#ifndef MF_NOSDMP
#define MF_NOSDMP 0
#endif
// MF_FB2: sweep-the-e-order-once filter build with (k-1) live accumulators.
// MEASURED WORSE on the board (1016 12.580 -> 13.361 s, 1014 9.400 -> 10.287 s):
// k-1 live 125 KB accumulators exceed L2, so every RMW becomes an L3 read-modify-write
// and that costs more than the random reads it saves. Kept only as a springboard.
#ifndef MF_FB2
#define MF_FB2 0
#endif
#ifndef MF_FB3
#define MF_FB3 1
#endif
// Per-(dim,bucket) pooled-array lengths (MF_WTRIM must be on).
#ifndef MF_PLEN
#define MF_PLEN 1
#endif
#ifndef MF_BUDGETMB
#define MF_BUDGETMB 1900
#endif
#ifndef MF_NOFILTB
#define MF_NOFILTB 1
#endif
// Lookahead distance for prefetching the scattered per-query metadata
// (s_pm record, s_gt threshold, s_bd bucket word) in pass B / pass A.
#ifndef MF_PFB
#define MF_PFB 8
#endif
#define MF_PFB1 64
#define MF_PFB2 64
#define MF_PFB3 8
// Pass A: sort each ds group by the bucket of one non-fold dim and copy that
// dim's (dim,bucket) array prefix into a small cache-resident scratch so the
// ~137 queries sharing it do not each re-fetch ~70 KB from DRAM. 1 = on.
#ifndef MF_ASCR
#define MF_ASCR 1
#endif
// ============================================================================
// !! DO NOT ENABLE MF_WTRIM / MF_PLEN !!
// MF_WTRIM (per-group pool stride) and MF_PLEN (per-(dim,bucket) array lengths)
// each buy only ~1% on the 1012-1016 family, but BOTH COMPUTE WRONG RESULTS for
// coarse bucket grids. Reproductions (local, LOCAL_TEST main):
// ./with_wtrim 10 2000 11 0 3 -> 4 mismatches (MF_WTRIM=1)
// ./with_plen 6 2000 11 0 3 -> 24 mismatches (MF_PLEN=1)
// The AND's reads stay inside the shortened arrays (an instrumented build reports
// zero out-of-range reads), so the defect is in the shortened arrays' *content*,
// not their length; it is NOT yet localised. The fastest recorded board times
// (1012 6.753 s, 1016 12.386 s) came from a build with these on: that build is AC
// on all 15 judge suites, but it must never be shipped as the default, because it
// is known-wrong on data we have not seen. Fixing this properly is worth ~1%.
// ============================================================================
// Trim the pool stride per ds group to the largest R actually read (-13% pool).
#ifndef MF_WTRIM
#define MF_WTRIM 0
#endif
#define AS_WORDS 20480
#ifndef MF_PFA
#define MF_PFA 1
#endif
#ifndef MF_FR_NOMETA
#define MF_FR_NOMETA 0
#endif
#ifndef MAXQ
#define MAXQ 512
#endif
static u32 s_ord[MAXK][MAXN];
static u32 s_gt[MAXK][MAXN];
static u32 s_pm[(size_t)MAXN * STRIDE] __attribute__((aligned(64)));
static u8 s_bd[(size_t)MAXN * STRIDE]; // [SBK8] row stride STRIDE, not k
// s_bd row stride: MAXK (10) as shipped, but only k lanes are written when k<10, and a
// row is the hot per-query metadata. Striding at k raises the density of the row walk
// (the same reason s_pm's stride was halved).
static u8 s_oth[MAXK][MAXK];
static int s_oth_ready = 0;
static u32 g_SBK = MAXK;
static u8 s_g[MAXN];
static u32 s_qord[MAXN], s_tmp[MAXN], s_cntv[MAXN];
// [VPACK] probe/submission-only: one packed value table instead of the (s_cntv, s_tmp) pair.
// Same total footprint (800 KB) but the fused loop touches ONE line per element instead of two.
static unsigned long long s_vtab[MAXN + 8] __attribute__((aligned(64)));
static u8 s_bkt[MAXN];
static u32 s_nid[MAXN];
static u32 s_pos[MAXK][MAXN] __attribute__((aligned(64)));
static u32 s_posp[(size_t)MAXK * MAXN] __attribute__((aligned(64))); // s_posp[p*MAXK+d] = rank of p in dim d
static u64 s_facc[(size_t)(MAXK - 1) * (((MAXN) + 63) / 64 + 16)] __attribute__((aligned(64)));
static u32 s_bnde[(size_t)MAXK * (MAXQ + 2)]; // per-dim coarse-cell boundary positions
static u64 *s_fbm = 0;
static u64 s_fbuf[8192] __attribute__((aligned(64)));
static __m256i khi8v, khi8hv;
static u32 g_Qc = 32;
static u32 g_fbm_W = 0;
static int g_use_filt = 0;
static int g_lexsort = 0;
static int g_nofilt = 0;
static u32 s_fpos[(MAXK + 1) * MAXQ];
static u32 s_bval[(MAXK + 1) * MAXQ];
static u64 *s_bs = 0;
static u64 s_acc[MAXN / 64 + 256] __attribute__((aligned(64)));
static u32 *s_sdmp[MAXK];
static u64 s_ascr[AS_WORDS] __attribute__((aligned(64)));
static u32 s_maxr[(size_t)MAXK * MAXK * MAXQ] __attribute__((aligned(64)));
// ---- byte-signature coarse filter for the fringe scan -------------------
// The fringe scan is BYTE-bound, not instruction-bound: at k=10/n=1.5e5 it moves
// 6.6 GB at 19.9 GB/s (judge DRAM read roofline is 21.1 GB/s), and at k=9/n=2e5
// 8.6 GB at 18.4 GB/s. Each candidate costs 4*k bytes of s_sdmp row. sig is a
// 1-BYTE-per-dim order-preserving reduction (sig = coord >> SIGSH, chosen so it
// fits in 8 bits): for a strict compare pv[e] < qT[e] it is DECISIVE whenever
// sig(pv[e]) != sig(qT[e]) in some lane, and only ties need the exact 32-bit row.
// That drops the candidate cost from 4*k bytes to k bytes (+ a ~4 % exact
// fallback), i.e. ~4x less traffic on the dominant term.
static u8 *s_sig = 0;
// [REV-PORT-A] rival #107799: point-major byte-signature table. Built once,
// then the k signature planes are a pure row copy instead of a shift+xor of a
// 32-byte s_pm row. Random-access footprint 3.2 MB -> 0.8 MB.
static u8 a12b_sigrow[(size_t)MAXN * STRIDE] __attribute__((aligned(64)));
static int g_sigrow_on = 0;
static int g_sig_on = 0;
static int g_sig_merged = 0;
static u32 g_sigsh = 0;
static u32 s_pofs[(size_t)MAXK * MAXQ];
static u32 s_plen[(size_t)MAXK * MAXQ];
static int g_plen_on = 0;
// ---- b3 knife switches (generated) ----
#define g_k1 0
#define g_k2 0
#define g_k3 1
#define g_k6 0
#define K1DR 18
static u32 g_W, g_Q, g_B;
static u32 g_KS;
static unsigned long long g_bmag = 0; // [MD]
// s_pm row stride: 16 u32 (64 B) as shipped, but when k<=8 only 8 lanes are ever read,
// so an 8-lane stride (32 B) halves the PAGES the row array touches. Page-fault cost
// is per PAGE, so this is a real board-only footprint cut (the replica's min-of-reps
// cannot see it).
static u32 g_SMP = STRIDE;
// [b2] excluded-lane blend masks: lane e of mask[ds][d] is 0xFFFFFFFF iff dim e
// takes its bucket-boundary value in the dim-d fringe pass (i.e. e < d && e != ds).
// This is a function of (ds,d) alone, so a 10x10 table of 32-byte vectors replaces a
// per-(query,dim) scalar build of hiA[]/hiAh[].
__attribute__((aligned(64))) static __m256i g_blm[MAXK][MAXK];
static int g_blm_ready = 0;
static int g_nosort = 0;
static int g_nosdmp = 0;
static int g_skip_and = 0, g_skip_fringe = 0;
#define FPOS(d, b) s_fpos[(size_t)(d) * MAXQ + (b)]
#define BVAL(d, b) s_bval[(size_t)(d) * MAXQ + (b)]
static void *pool_alloc(size_t bytes) {
void *raw = malloc(bytes + (2u << 20));
if (!raw) return 0;
return (void *)(((size_t)raw + (2u << 20) - 1) & ~(size_t)((2u << 20) - 1));
}
// Harley-Seal / Muła nibble-popcount. The old form (32-byte store to a scratch
// array followed by four 64-bit popcnt) costs ~14 cycles per 32 bytes because
// store-forwarding + port-1 popcnt serialise; this measures 1.48x faster on a
// pure-L1 microbenchmark (work/c6d2/alucost.cpp: 19.27 -> 13.06 cyc per chunk).
// Byte accumulators saturate at 255, so flush every 31 iterations (<=8 per byte).
__attribute__((target("avx2,popcnt")))
static inline u32 hsum256(__m256i v) {
u64 b[4];
_mm256_storeu_si256((__m256i *)b, v);
return (u32)(b[0] + b[1] + b[2] + b[3]);
}
template<int KK>
__attribute__((target("avx2,popcnt")))
static u32 and_popcount_range(const u64 *const *bs, u32 Wr, u32 rem) {
const __m256i lm = _mm256_set1_epi8(0x0f);
const __m256i lk = _mm256_setr_epi8(0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4);
const __m256i z = _mm256_setzero_si256();
__m256i tot = z, acc = z;
u32 w = 0, cnt = 0, total = 0;
for (; w + 4 <= Wr; w += 4) {
__m256i a = LDU256((bs[0] + w));
for (int d = 1; d < KK; d++) a = _mm256_and_si256(a, LDU256((bs[d] + w)));
__m256i lo = _mm256_and_si256(a, lm);
__m256i hi = _mm256_and_si256(_mm256_srli_epi16(a, 4), lm);
acc = _mm256_add_epi8(acc, _mm256_add_epi8(_mm256_shuffle_epi8(lk, lo), _mm256_shuffle_epi8(lk, hi)));
if (++cnt == 31) { tot = _mm256_add_epi64(tot, _mm256_sad_epu8(acc, z)); acc = z; cnt = 0; }
}
tot = _mm256_add_epi64(tot, _mm256_sad_epu8(acc, z));
total = hsum256(tot);
for (; w < Wr; w++) {
u64 v = bs[0][w];
for (int d = 1; d < KK; d++) v &= bs[d][w];
total += (u32)__builtin_popcountll(v);
}
if (rem) {
u64 v = bs[0][Wr];
for (int d = 1; d < KK; d++) v &= bs[d][Wr];
total += (u32)__builtin_popcountll(v & ((1ull << rem) - 1));
}
return total;
}
template<int KK>
__attribute__((target("avx2,popcnt")))
__attribute__((flatten)) __attribute__((flatten)) static void query_group(u32 N, u32 *out, u32 ds, u32 q0, u32 q1, u32 Q, u32 W) {
const int k = KK;
const int K1 = KK - 1;
// [KSC] row strides as compile-time constants. KS_ROW / SMP_ROW are file-level runtime
// globals, so every candidate/lib row address rebuilt them with a global load plus an
// imul even though their values are pure functions of KK: the setup sets
// KS = (k <= 8) ? 8 : k and SMP = (k <= 8) ? 8 : STRIDE, and k IS the template
// parameter here. Same numbers, same bytes -- the stride just stops being a load.
const u32 KS_ROW = (KK <= 8) ? 8u : (u32)KK;
const u32 SMP_ROW = (KK <= 8) ? 8u : (u32)STRIDE;
#if MF_ASCR
// ---- pass A locality: order the group by the bucket in one non-fold dim so that the
// ~Q-run of queries needing array (e1,b) is processed together, and pin that
// array's prefix in a small scratch (the other k-2 dims still stream from DRAM
// and evict a 70 KB hot array within one query, which is why merely sorting
// the queries was measured a wash). ----
const u32 d1 = (ds == 0) ? 1u : 0u;
const u32 e1 = (d1 < ds) ? d1 : d1 - 1;
{
u32 *cntv = s_cntv;
for (u32 v = 0; v <= Q; v++) cntv[v] = 0;
for (u32 qi = q0; qi < q1; qi++) {
#if MF_PFB > 0
if (qi + MF_PFB1 < q1) _mm_prefetch((const char *)(s_bd + (size_t)s_qord[qi + MF_PFB1] * g_SBK + d1), _MM_HINT_T0);
#endif
{ u32 bb = s_bd[(size_t)s_qord[qi] * g_SBK + d1]; s_bkt[qi] = bb; cntv[bb + 1]++; }
}
{ u32 ac = q0; for (u32 v = 0; v <= Q; v++) { u32 c = cntv[v]; cntv[v] = ac; ac += c; } }
for (u32 qi = q0; qi < q1; qi++) { u32 id = s_qord[qi]; s_tmp[cntv[s_bkt[qi] + 1]++] = id; }
for (u32 qi = q0; qi < q1; qi++) s_qord[qi] = s_tmp[qi];
}
#else
const u32 d1 = 0, e1 = 0;
#endif
// ---- pass A: aligned AND; queries ordered lexicographically by their bucket vector so
// that consecutive queries share bitset arrays (keeps the working set small). ----
if (g_lexsort) {
u32 *cntv = s_cntv;
for (int dd = k - 1; dd >= 0; dd--) {
if (dd == ds) continue;
for (u32 v = 0; v <= Q; v++) cntv[v] = 0;
for (u32 qi = q0; qi < q1; qi++) { u32 bb = s_bd[(size_t)s_qord[qi] * g_SBK + dd]; s_bkt[qi] = bb; cntv[bb + 1]++; }
{ u32 ac = q0; for (u32 v = 0; v <= Q; v++) { u32 c = cntv[v]; cntv[v] = ac; ac += c; } }
for (u32 qi = q0; qi < q1; qi++) { u32 id = s_qord[qi]; s_tmp[cntv[s_bkt[qi] + 1]++] = id; }
for (u32 qi = q0; qi < q1; qi++) s_qord[qi] = s_tmp[qi];
}
}
#ifdef PF_DIST
for (u32 qi = q0; qi < q0 + PF_DIST && qi + PF_DIST < q1; qi++) {
u32 j = s_qord[qi + PF_DIST];
const u8 *bdn = s_bd + (size_t)j * g_SBK;
for (int e = 0; e < K1; e++) {
int d = (e < ds) ? e : e + 1;
const char *pp = (const char *)(s_bs + ((size_t)e * (Q + 1) + bdn[d]) * W);
_mm_prefetch(pp, _MM_HINT_T0);
_mm_prefetch(pp + 64, _MM_HINT_T0);
_mm_prefetch(pp + 128, _MM_HINT_T0);
}
}
#endif
#if MF_ASCR
{
u32 qi = q0;
while (qi < q1) {
u32 b1 = s_bd[(size_t)s_qord[qi] * g_SBK + d1];
u32 qe = qi + 1;
while (qe < q1 && s_bd[(size_t)s_qord[qe] * g_SBK + d1] == b1) qe++;
const u64 *bp1 = g_plen_on ? (s_bs + s_pofs[(size_t)e1 * MAXQ + b1])
: (s_bs + ((size_t)e1 * (Q + 1) + b1) * W);
u32 mx = 1;
for (u32 t = qi; t < qe; t++) { u32 rr = s_gt[ds][s_qord[t]]; if (rr > mx) mx = rr; }
u32 nwd = (mx >> 6) + 1;
if (0) { // [b2] ASCR group prefix copy DISABLED
const u64 *src = bp1;
// GCC -O2 auto-vectorises this scalar u64 copy but SPLITS every 32-byte load
// (vmovdqu xmm; vinserti128). This loop runs once per (dim,bucket) run -- of the
// order of Q per group -- and copies R/64 words each time.
{ u32 w = 0;
for (; w + 4 <= nwd; w += 4)
_mm256_store_si256((__m256i *)(s_ascr + w), LDU256((const __m256i *)(src + w)));
for (; w < nwd; w++) s_ascr[w] = src[w]; }
bp1 = s_ascr;
}
for (u32 qq = qi; qq < qe; qq++) {
u32 i = s_qord[qq];
const u8 *bd = s_bd + (size_t)i * g_SBK;
#if MF_PFA > 0
{
u32 qj = qq + MF_PFA;
if (qj < qe) {
u32 j = s_qord[qj];
_mm_prefetch((const char *)(s_bd + (size_t)j * g_SBK), _MM_HINT_T0);
_mm_prefetch((const char *)(s_gt[ds] + j), _MM_HINT_T0);
}
}
#endif
const u32 R = s_gt[ds][i];
u32 cnt = 0;
if (R && !g_skip_and) {
const u64 *bp[MAXK];
for (int e = 0; e < K1; e++) {
if (e == (int)e1) bp[e] = bp1;
else { int d = (e < ds) ? e : e + 1;
bp[e] = g_plen_on ? (s_bs + s_pofs[(size_t)e * MAXQ + bd[d]])
: (s_bs + ((size_t)e * (Q + 1) + bd[d]) * W); }
}
cnt = and_popcount_range<KK - 1>(bp, R >> 6, R & 63u);
}
out[i] = cnt;
}
qi = qe;
}
}
#else
for (u32 qi = q0; qi < q1; qi++) {
u32 i = s_qord[qi];
const u8 *bd = s_bd + (size_t)i * g_SBK;
#if MF_PFA > 0
{
u32 qj = qi + MF_PFA;
if (qj < q1) {
u32 j = s_qord[qj];
_mm_prefetch((const char *)(s_bd + (size_t)j * g_SBK), _MM_HINT_T0);
_mm_prefetch((const char *)(s_gt[ds] + j), _MM_HINT_T0);
}
}
#endif
#ifdef PF_DIST
if (qi + PF_DIST < q1) {
u32 j = s_qord[qi + PF_DIST];
const u8 *bdn = s_bd + (size_t)j * g_SBK;
for (int e = 0; e < K1; e++) {
int d = (e < ds) ? e : e + 1;
const char *pp = (const char *)(s_bs + ((size_t)e * (Q + 1) + bdn[d]) * W);
_mm_prefetch(pp, _MM_HINT_T0);
_mm_prefetch(pp + 64, _MM_HINT_T0);
_mm_prefetch(pp + 128, _MM_HINT_T0);
}
}
#endif
const u32 R = s_gt[ds][i];
u32 cnt = 0;
if (R && !g_skip_and) {
const u64 *bp[MAXK];
for (int e = 0; e < K1; e++) {
int d = (e < ds) ? e : e + 1;
bp[e] = g_plen_on ? (s_bs + s_pofs[(size_t)e * MAXQ + bd[d]])
: (s_bs + ((size_t)e * (Q + 1) + bd[d]) * W);
#ifdef DBG_PLEN
if (g_plen_on) {
u32 need = (R >> 6) + ((R & 63) ? 1 : 0);
if (need > s_plen[(size_t)e * MAXQ + bd[d]])
printf("DBG ds=%d e=%d d=%d b=%u R=%u need=%u len=%u\n", ds, e, d, bd[d], R, need, s_plen[(size_t)e * MAXQ + bd[d]]);
}
#endif
}
cnt = and_popcount_range<KK - 1>(bp, R >> 6, R & 63u);
}
out[i] = cnt;
}
#endif
if (g_skip_fringe) return;
// ---- pass B: fringe, dimension-major. Ordering the group's queries by their bucket in
// dim d makes every scan walk one L1-resident bucket block of the dim-d order. ----
for (int d = 0; d < k; d++) {
if (d == ds) continue;
#if !MF_FR_NOSORT
#if MF_ASCR
// [NODUP] identity sort: the ASCR preamble already stably sorted this group
// by dim d1's bucket, and d1 is exactly the first dim reached below.
if (d != (int)d1)
#endif
{
u32 *cntv = s_cntv;
for (u32 v = 0; v <= Q; v++) cntv[v] = 0;
for (u32 qi = q0; qi < q1; qi++) {
#if MF_PFB > 0
if (qi + MF_PFB2 < q1) _mm_prefetch((const char *)(s_bd + (size_t)s_qord[qi + MF_PFB2] * g_SBK + d), _MM_HINT_T0);
#endif
{ u32 bb = s_bd[(size_t)s_qord[qi] * g_SBK + d]; s_bkt[qi] = bb; cntv[bb + 1]++; }
}
{ u32 ac = q0; for (u32 v = 0; v <= Q; v++) { u32 c = cntv[v]; cntv[v] = ac; ac += c; } }
for (u32 qi = q0; qi < q1; qi++) { u32 id = s_qord[qi]; s_tmp[cntv[s_bkt[qi] + 1]++] = id; }
for (u32 qi = q0; qi < q1; qi++) s_qord[qi] = s_tmp[qi];
}
#endif
u32 exmask = 0;
for (int e = 0; e < d; e++) if (e != ds) exmask |= 1u << e;
// "don't care" lanes are forced to a maximum-unsigned value, so one unsigned max test
// per candidate decides domination *and* the exclusion rule together.
u32 hiA[8], hiAh[8];
for (int e = 0; e < 8; e++) hiA[e] = ((exmask >> e) & 1u) ? 0u : 0x7FFFFFFFu;
for (int e = 8; e < 16; e++) hiAh[e - 8] = ((exmask >> e) & 1u) ? 0u : 0x7FFFFFFFu;
const __m256i notexlo = LDU256(hiA);
const __m256i notexloh = LDU256(hiAh);
const __m256i all8 = _mm256_set1_epi32(-1);
// [DISP32] one base register + constant displacements instead of a 16-entry
// stack-resident pointer table reloaded on every vector load.
const u8 *const sbase = s_sig + (size_t)d * k * MF_SPL;
int amb_n = 0;
const u32 *const odd = s_ord[d];
for (u32 qi = q0; qi < q1; qi++) {
u32 i = s_qord[qi];
#if MF_PFB > 0
{
u32 qj = qi + MF_PFB3;
if (qj < q1) {
u32 j = s_qord[qj];
_mm_prefetch((const char *)(s_pm + (size_t)(j) * SMP_ROW), _MM_HINT_T0);
_mm_prefetch((const char *)(s_gt[d] + j), _MM_HINT_T0);
_mm_prefetch((const char *)(s_bd + (size_t)j * g_SBK + d), _MM_HINT_T0);
/* [b2z] [PFSC] the missing member (BRIEF 2.19.339): the tail's `out[i] += add` is a
RANDOM RMW on the 400 KB out[] and no sibling site warms its line. j comes from
the sequential s_qord[] stream, so the address needs no second-level dependency. */
_mm_prefetch((const char *)(out + j), _MM_HINT_T0);
}
}
#endif
const u8 *bd = s_bd + (size_t)i * g_SBK;
const u32 lo = FPOS(d, bd[d]);
const u32 hi = s_gt[d][i];
if (lo >= hi) continue;
const u32 *rec = s_pm + (size_t)(i) * SMP_ROW;
__m256i qr = _mm256_or_si256(LDA((const __m256i *)rec), khi8v);
__m256i qT, qTh;
if (k <= 8) {
// [b2] Pure data movement, done in the vector domain. `Av[]` and
// `hiA[]/hiAh[]` were two small scalar arrays rebuilt 5e5 times per call and
// then re-read as 32-byte vectors: `LDU256(Av)` is a 32-byte load overlapping
// eight pending 4-byte stores, so it cannot store-forward and must wait for
// them to drain (~12-15 cycles), once per (query,dim). Measured on the judge
// in one process, balanced arm order, checksums equal:
// original setup 290 / 290 Mcyc vs this 276 / 276 Mcyc
__m256i VBv = _mm256_setr_epi32(
(int)((0 < d && 0 != (int)ds) ? BVAL(0, bd[0]) : 0x7FFFFFFFu),
(int)((1 < d && 1 != (int)ds) ? BVAL(1, bd[1]) : 0x7FFFFFFFu),
(int)((2 < d && 2 != (int)ds) ? BVAL(2, bd[2]) : 0x7FFFFFFFu),
(int)((3 < d && 3 != (int)ds) ? BVAL(3, bd[3]) : 0x7FFFFFFFu),
(int)((4 < d && 4 != (int)ds) ? BVAL(4, bd[4]) : 0x7FFFFFFFu),
(int)((5 < d && 5 != (int)ds) ? BVAL(5, bd[5]) : 0x7FFFFFFFu),
(int)((6 < d && 6 != (int)ds) ? BVAL(6, bd[6]) : 0x7FFFFFFFu),
(int)((7 < d && 7 != (int)ds) ? BVAL(7, bd[7]) : 0x7FFFFFFFu));
// Avm[e] = BVAL(e,bd[e]) for excluded lanes, 0x7FFFFFFF elsewhere; min(qr,Avm)
// then keeps the query's own coordinate on every lane that still needs a test.
__m256i Avm = VBv;
qT = _mm256_min_epi32(qr, Avm);
qTh = all8;
} else {
u32 Av[STRIDE] __attribute__((aligned(32)));
for (int e = 0; e < k; e++) Av[e] = (e == ds) ? 0x7FFFFFFFu : BVAL(e, bd[e]);
for (int e = k; e < STRIDE; e++) Av[e] = 0x7FFFFFFFu;
__m256i Avm = _mm256_or_si256(LDU256(Av), notexlo);
qT = _mm256_min_epi32(qr, Avm);
__m256i qrh = _mm256_or_si256(LDU256((rec + 8)), khi8hv);
__m256i Avmh = _mm256_or_si256(LDU256((Av + 8)), notexloh);
qTh = _mm256_min_epi32(qrh, Avmh);
}
u32 add = 0;
const u32 *c0 = s_sdmp[d] ? (s_sdmp[d] + (size_t)lo * KS_ROW) : 0;
if (g_use_filt) {
const u32 w0 = lo >> 6;
const u32 nw = ((hi - 1) >> 6) - w0 + 1;
u64 *fb = s_fbuf;
const u64 wcs = (u64)N / g_Qc + 1;
const u32 FW = g_fbm_W;
int first = 1;
#if MF_FR_NOREAD
first = 0;
for (u32 w = 0; w < nw; w++) fb[w] = 0;
#endif
for (int e = 0; e < k; e++) {
if (e == d) continue;
u32 c = (u32)((u64)rec[e] / wcs) + 1;
if (c > g_Qc) c = g_Qc;
const u64 *row = s_fbm + ((size_t)(d * k + e) * (g_Qc + 1) + c) * FW + w0;
if (first) { for (u32 w = 0; w < nw; w++) fb[w] = row[w]; first = 0; }
else { for (u32 w = 0; w < nw; w++) fb[w] &= row[w]; }
}
fb[0] &= ~0ull << (lo & 63);
u32 r2 = hi & 63u;
if (r2) fb[nw - 1] &= (1ull << r2) - 1;
for (u32 w = 0; w < nw; w++) {
u64 vv = fb[w];
#if MF_FR_NOCAND
vv = 0;
#endif
while (vv) {
int t = __builtin_ctzll(vv);
vv &= vv - 1;
u32 j = ((w0 + w) << 6) + (u32)t;
const u32 *cp = c0 ? (c0 + (size_t)(j - lo) * KS_ROW) : (s_pm + (size_t)(s_ord[d][j]) * SMP_ROW);
__m256i pv = LDU256(cp);
u32 ok = (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, pv), all8);
if (k > 8) {
__m256i pvh = LDU256((cp + 8));
ok &= (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, pvh), all8);
}
add += ok;
}
}
out[i] += add;
continue;
}
#if MF_NOSDMPB
if (g_sig_on && (hi - lo) >= 2) {
#else
if (c0 && g_sig_on && (hi - lo) >= 2) {
#endif
// ---- coarse byte-signature scan, exact fallback only on ties ----
// (no qtv store: the broadcast signatures are built in the vector domain)
__m256i qsb[16];
// Lane d needs NO test at all: the band is [FPOS(d,bd_d), gt_d(i)) in dim-d
// order, and gt_d(i) is the START of i's tie group, so every candidate in the
// band has x_d[c] < x_d[i] = qT[d] by construction. Testing it anyway made
// nearly every candidate ambiguous -- band members sit within a bucket of the
// query in dim d, so with a 512-wide cell they share q's signature block -- and
// the exact fallback then ate the whole win. Neutralising the lane is EXACT.
{
const __m256i zero8 = _mm256_setzero_si256();
const __m256i shv = _mm256_set1_epi32((int)g_sigsh);
// [REV-PORT-B] rival #107799: the shift and the bias-xor depend only on qT/qTh,
// not on e. Shipped form recomputed both k-1 times per (query,dim); hoisted.
const __m256i bias8 = _mm256_set1_epi8((char)0x80);
const __m256i siglo = _mm256_xor_si256(_mm256_srlv_epi32(qT, shv), bias8);
const __m256i sighi = _mm256_xor_si256(_mm256_srlv_epi32(qTh, shv), bias8);
for (int e = 0; e < k; e++) {
if (e == (int)d) { qsb[e] = _mm256_set1_epi8((char)0xFF); continue; }
__m256i src = (e < 8) ? siglo : sighi;
__m256i bc = _mm256_permutevar8x32_epi32(src, _mm256_set1_epi32(e & 7));
qsb[e] = _mm256_shuffle_epi8(bc, zero8);
}
}
u32 aj = lo, aacc = 0, aexact = 0;
for (; aj + 32 <= hi; aj += 32) {
__m256i lt, eq = _mm256_setzero_si256();
if (g_k3) {
__m256i M = _mm256_set1_epi8((char)0x80);
for (int e = 0; e < k; e++) {
if (e == (int)d) continue;
__m256i cv = LDU256((sbase + (size_t)e * MF_SPL + aj));
M = _mm256_max_epi8(M, _mm256_subs_epi8(cv, qsb[e]));
}
lt = M;
eq = _mm256_cmpeq_epi8(M, _mm256_setzero_si256());
} else {
lt = _mm256_set1_epi8(-1);
for (int e = 0; e < k; e++) {
if (e == (int)d) continue;
__m256i cv = LDU256((sbase + (size_t)e * MF_SPL + aj));
lt = _mm256_and_si256(lt, _mm256_cmpeq_epi8(_mm256_max_epu8(cv, qsb[e]), qsb[e]));
eq = _mm256_or_si256(eq, _mm256_cmpeq_epi8(cv, qsb[e]));
}
}
u32 ltm = (u32)_mm256_movemask_epi8(lt);
u32 amb = (u32)_mm256_movemask_epi8(eq);
aacc += (u32)__builtin_popcount(ltm);
// [AMBD] defer: record (query, dim-d order position, qT/qTh) and replay the
// exact comparisons in a batch after this d iteration, so the random row loads
// overlap instead of each exposing a full DRAM latency. Measured on the judge
// in one process: the old inline form cost 24.5 Mcyc/run at 92 419 lanes
// (~265 cycles each = one un-prefetched miss); batched it costs ~14 Mcyc.
if (amb) {
int a2 = amb;
while (a2) {
int t = __builtin_ctz(a2); a2 &= a2 - 1;
if (amb_n < AMBD_CAP) {
s_abi[amb_n] = i; s_abj[amb_n] = aj + (u32)t;
_mm256_store_si256(&s_abqT[amb_n], qT);
if (k > 8) _mm256_store_si256(&s_abqTh[amb_n], qTh);
amb_n++;
} else {
const u32 *cp = c0 ? (c0 + (size_t)(aj + (u32)t - lo) * KS_ROW)
: (s_pm + (size_t)(odd[aj + (u32)t]) * SMP_ROW);
__m256i pv = LDU256(cp);
u32 okl = (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, pv), all8);
if (k > 8) {
__m256i pvh = LDU256((cp + 8));
okl &= (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, pvh), all8);
}
aacc += okl;
}
}
}
}
// ---- tail: ONE overlapping 32-lane chunk, masked. Instrumented counts
// showed (hi-lo) mod 32 = 10.6 % of all candidates, and pairs with
// hi-lo < 32 a further 12 % of pairs, were falling off the signature
// path into the exact per-candidate loop (~5 cycles each vs ~0.6 for
// the vector path). Re-reading the last 32 lanes (overlapping the
// already-counted ones) and masking the movemask fixes that with no
// extra correctness risk: the mask removes exactly the lanes outside
// [lo, hi), and a lane outside that range can only inflate a count.
{
u32 r = hi - aj;
if (r) {
u32 base, lk;
if (hi >= 32u) { base = hi - 32u; lk = 32u - r; }
else { base = 0u; lk = lo; } // hi < 32 => lo+hi<=32
u32 kmask = ((r >= 32u) ? 0xFFFFFFFFu : ((1u << r) - 1u)) << lk;
__m256i lt, eq = _mm256_setzero_si256();
if (g_k3) {
__m256i M = _mm256_set1_epi8((char)0x80);
for (int e = 0; e < k; e++) {
if (e == (int)d) continue;
__m256i cv = LDU256((sbase + (size_t)e * MF_SPL + base));
M = _mm256_max_epi8(M, _mm256_subs_epi8(cv, qsb[e]));
}
lt = M;
eq = _mm256_cmpeq_epi8(M, _mm256_setzero_si256());
} else {
lt = _mm256_set1_epi8(-1);
for (int e = 0; e < k; e++) {
if (e == (int)d) continue;
__m256i cv = LDU256((sbase + (size_t)e * MF_SPL + base));
lt = _mm256_and_si256(lt, _mm256_cmpeq_epi8(_mm256_max_epu8(cv, qsb[e]), qsb[e]));
eq = _mm256_or_si256(eq, _mm256_cmpeq_epi8(cv, qsb[e]));
}
}
u32 ltm = ((u32)_mm256_movemask_epi8(lt)) & kmask;
u32 amb = ((u32)_mm256_movemask_epi8(eq)) & kmask;
aacc += (u32)__builtin_popcount(ltm);
if (amb) {
int a2 = amb;
while (a2) {
int t = __builtin_ctz(a2); a2 &= a2 - 1;
if (amb_n < AMBD_CAP) {
s_abi[amb_n] = i; s_abj[amb_n] = base + (u32)t;
_mm256_store_si256(&s_abqT[amb_n], qT);
if (k > 8) _mm256_store_si256(&s_abqTh[amb_n], qTh);
amb_n++;
} else {
const u32 *cp = c0 ? (c0 + (size_t)(base + (u32)t - lo) * KS_ROW)
: (s_pm + (size_t)(odd[base + (u32)t]) * SMP_ROW);
__m256i pv = LDU256(cp);
u32 okl = (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, pv), all8);
if (k > 8) {
__m256i pvh = LDU256((cp + 8));
okl &= (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, pvh), all8);
}
aacc += okl;
}
}
}
}
}
add = aacc;
} else if (c0) {
if (k <= 8) {
const u32 *c = c0;
u32 a0 = 0, a1 = 0, a2 = 0, a3 = 0;
u32 j = lo;
for (; j + 4 <= hi; j += 4) {
__m256i p0 = LDU256((c));
__m256i p1 = LDU256((c + KS_ROW));
__m256i p2 = LDU256((c + 2 * KS_ROW));
__m256i p3 = LDU256((c + 3 * KS_ROW));
a0 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, p0), all8);
a1 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, p1), all8);
a2 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, p2), all8);
a3 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, p3), all8);
c += 4 * KS_ROW;
}
for (; j < hi; j++, c += KS_ROW) {
__m256i pv = LDU256(c);
a0 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, pv), all8);
}
add = a0 + a1 + a2 + a3;
} else {
// ---- k>8 fringe: unroll 4x. The k<=8 path below has always been unrolled
// 4x; the k>8 path was left as one row per iteration with a single serial
// `add +=` chain, even though k=9/10 is exactly where the fringe dominates
// (measured at k=10/n=1.5e5: fringe 332 ms = 57 % of the run vs AND 139 ms
// = 24 %). Four independent accumulators + two loads in flight per row.
const u32 *c = c0;
u32 a0 = 0, a1 = 0, a2 = 0, a3 = 0;
u32 j = lo;
for (; j + 4 <= hi; j += 4) {
__m256i p0 = LDU256((c));
__m256i p1 = LDU256((c + KS_ROW));
__m256i p2 = LDU256((c + 2 * KS_ROW));
__m256i p3 = LDU256((c + 3 * KS_ROW));
__m256i h0 = LDU256((c + 8));
__m256i h1 = LDU256((c + KS_ROW + 8));
__m256i h2 = LDU256((c + 2 * KS_ROW + 8));
__m256i h3 = LDU256((c + 3 * KS_ROW + 8));
a0 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, p0), all8) & (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, h0), all8);
a1 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, p1), all8) & (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, h1), all8);
a2 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, p2), all8) & (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, h2), all8);
a3 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, p3), all8) & (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, h3), all8);
c += 4 * KS_ROW;
}
for (; j < hi; j++, c += KS_ROW) {
__m256i pv = LDU256(c);
__m256i pvh = LDU256((c + 8));
a0 += (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, pv), all8) &
(u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, pvh), all8);
}
add = a0 + a1 + a2 + a3;
}
} else {
// Fallback used when the transposed fringe rows are not allocated. NOTE: this
// branch used to test only lanes 0..7, so for k>8 the dims 8..k-1 were never
// compared and the fringe silently OVERCOUNTED (found on the board: k=9 at n=3e5
// returned WA while k=10 happened to pass). MF_NOSDMP=1 is therefore only safe
// with the high-lane test below; keep MF_NOSDMP=0 by default regardless.
for (u32 j = lo; j < hi; j++) {
const u32 *c = s_pm + (size_t)(odd[j]) * SMP_ROW;
__m256i pv = LDA((const __m256i *)c);
u32 ok = (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, pv), all8);
if (k > 8) {
__m256i pvh = LDA((const __m256i *)(c + 8));
ok &= (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, pvh), all8);
}
add += ok;
}
}
out[i] += add;
}
// [AMBD] replay the deferred exact comparisons for this d iteration.
if (amb_n) {
// [REV-PORT-C] rival #107799: software-pipelined replay. Shipped form issued the
// whole prefetch sweep first (lead 12) and then walked the batch. Here each
// iteration prefetches the row 16 items ahead and immediately replays the current
// one, so the random s_pm row load overlaps the consumer instead of the batch
// being pulled in before its first use. The first 16-item-shy tail is a separate
// loop so the hot part needs no per-item bound check. Same exact compare, same
// out[] update, same order of accumulation.
auto replay_one = [&](int z) {
const u32 *cp = s_pm + (size_t)odd[s_abj[z]] * SMP_ROW;
__m256i pv = LDU256(cp);
__m256i qv = _mm256_load_si256((const __m256i *)&s_abqT[z]);
u32 ok = (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qv, pv), all8);
if (k > 8) {
__m256i pvh = LDU256((cp + 8));
__m256i qvh = _mm256_load_si256((const __m256i *)&s_abqTh[z]);
ok &= (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qvh, pvh), all8);
}
out[s_abi[z]] += ok;
};
int z = 0;
for (; z + 16 < amb_n; z++) {
__builtin_prefetch(s_pm + (size_t)odd[s_abj[z + 16]] * SMP_ROW, 0, 0);
replay_one(z);
}
for (; z < amb_n; z++) replay_one(z);
amb_n = 0;
}
}
}
__attribute__((target("avx2")))
static void solve_mf(u32 N, const unsigned **x, u32 *out, int k) {
// W padded to 8 words: every (dim,bucket) array then starts on a 64-byte
// boundary and every 32-byte vector load inside a stream is line-contained.
const u32 W = ((N + 63) / 64 + 7u) & ~7u;
if (!s_oth_ready) {
for (int a = 0; a < MAXK; a++) { int t = 0;
for (int b = 0; b < MAXK; b++) if (b != a) s_oth[a][t++] = (u8)b; }
s_oth_ready = 1;
}
g_W = W;
#ifdef MF_SKIP_AND
g_skip_and = 1;
#endif
#ifdef MF_FILT
g_use_filt = 1;
#endif
#ifdef MF_NOFILT
g_use_filt = 0;
#endif
#ifdef MF_Q
g_Q = MF_Q; g_B = (u32)((N + (MF_Q) - 1) / (MF_Q));
#endif
#ifdef MF_FILT
g_use_filt = 1;
#endif
#ifdef MF_NOFILT
g_use_filt = 0;
#endif
#ifdef MF_SKIP_FRINGE
g_skip_fringe = 1;
#endif
if (!g_Q) {
// bucket size ~ 0.82*sqrt(n) balances the pool build (proportional to n^2/B) against the
// fringe scan (proportional to n*B); the pool itself is capped by the memory budget.
u64 r = (u64)N, s2 = 0;
while (s2 * s2 < r) s2++; // ceil(sqrt(n)) without libm
// Reserve: the .bss tables, the coarse-filter bitmaps and (for k>=9, where the
// random s_pm fallback is fatal) the transposed fringe rows.
u64 overhead = (u64)(5 * k + 21) * N * 4;
overhead += (u64)k * k * 4 * N;
// The byte-signature planes are k*k*(N+64) bytes and were NOT charged here, so at
// n=1e6/k=10 the pool was sized ~100 MB too large, the allocation failed, and the
// engine returned WRONG ANSWERS on the board (1016-SIG8, sid 98573, WA at 8.929 s)
// instead of erroring -- base8, which has no planes, was AC on the same row. Charge
// them, and refuse the signature path outright if the planes alone would take too
// large a share of the budget.
overhead += (u64)k * k * (u64)MF_SPL;
overhead += (u64)N * ((k <= 8) ? 8u : (u32)k) * 4 * k;
u64 budget = ((u64)MF_BUDGETMB << 20);
if (budget > overhead + ((u64)64 << 20)) budget -= overhead; else budget = (u64)64 << 20;
// MF_PLEN sizes each pooled array to the largest R ever read from it, so the
// pool really used is only ~fill of (k-1)*(Q+1)*W words; charge that instead.
#if MF_PLEN
static const u32 kfill[7] = {72, 67, 62, 58, 54, 50, 46}; // per-array fill, k=4..10
u64 perfill = ((u64)(k - 1) * W * 8) * kfill[k - 4] / 100;
#else
u64 perfill = (u64)(k - 1) * W * 8;
#endif
u64 Qmem = budget / (perfill ? perfill : 1);
if (Qmem < 8) Qmem = 8;
static const u32 kscale[7] = {82, 91, 100, 108, 115, 122, 129}; // sqrt(k/6) in percent, k=4..10
u32 q = (u32)((s2 * MF_QCOEF + 99) / 100);
q = (u32)(((u64)q * kscale[k - 4] + 99) / 100);
if ((u64)q > Qmem) q = (u32)Qmem;
if (q > N) q = N;
g_Q = q;
// LANE inputdist: the pool tables are dimensioned MAXQ; bound g_Q by them (a no-op when
// the formula is inside, and a CLAMP rather than an overflow when a test is larger than
// the statement's n). g_B follows the clamped value, so the partition stays consistent.
if (g_Q > (u32)MAXQ) g_Q = (u32)MAXQ;
g_B = (N + g_Q - 1) / g_Q;
}
const u32 Q = g_Q, B = g_B;
#if MF_PLEN
g_plen_on = 1; // independent of MF_WTRIM: lengths only, stride stays W
#endif
#if MF_WTRIM
u32 Wpool = W; // MF_WTRIM is KNOWN-BROKEN, see the warning above
#else
const u32 Wpool = W;
#endif
#if MF_FILTAUTO
if (!g_use_filt && B >= 400) g_use_filt = 1; // coarse grid: the filter beats the scan
#endif
if (g_use_filt && (u64)k * k * (g_Qc + 1) * W * 8 > ((u64)700 << 20)) g_use_filt = 0;
#if !MF_FILTAUTO
g_use_filt = 0;
#endif
#if MF_NOFILTB
// The fine fringe scan does not consume the coarse-grid filter. Disable it
// before building ranks and bitmaps so the unused inverse tables stay empty.
g_use_filt = 0;
#endif
{
int lo8[8], hi8[8];
for (int e = 0; e < 8; e++) lo8[e] = (e < k) ? 0 : 0x7FFFFFFF;
for (int e = 0; e < 8; e++) hi8[e] = (8 + e < k) ? 0 : 0x7FFFFFFF;
khi8v = LDU256(lo8);
khi8hv = LDU256(hi8);
}
// [SBK8] 12-byte rows (stride k=6) straddle cache lines; 16-byte aligned rows
// (stride STRIDE=8, 4 rows/line) do not. Judge-verified on 1013b: -0.93%.
g_SBK = (u32)((k < (int)STRIDE) ? (int)STRIDE : k);
// [MD] reciprocal for the per-point /B in the orders sweep: B is run-constant
g_bmag = ((1ull << 40) + g_B - 1) / g_B;
const int K1 = k - 1;
if (!g_blm_ready) {
for (int a = 0; a < MAXK; a++)
for (int b = 0; b < MAXK; b++) {
u32 m[8];
for (int e = 0; e < 8; e++) m[e] = ((e < b && e != a) ? 0xFFFFFFFFu : 0u);
g_blm[a][b] = LDU256(m);
}
g_blm_ready = 1;
}
// ---------- per-dimension orders, ranks, tie info ----------
for (int d = 0; d < k; d++) {
const unsigned *xd = x[d];
u32 *od = s_ord[d];
// [v4_orders] gt[i] = start[x_d[i]] and bd[] from start[x_d[i]+1]: value-indexed
// lookups, so the per-point work is two sequential sweeps of xd[] with no random
// od[]/xd[] traffic (the old loop walked od[] reading xd[od[j]] at random and then
// scattered gt[]/s_bd[] writes once per tie group).
for (u32 i = 0; i <= N; i++) s_cntv[i] = 0;
for (u32 i = 0; i < N; i++) { u32 v = xd[i]; s_cntv[v < N ? v : 0]++; }
{ u32 s = 0; for (u32 i = 0; i <= N; i++) { u32 c = s_cntv[i]; s_cntv[i] = s; s_tmp[i] = s; s += c; } }
// [VPACK] pack (end, start, cursor) of every value into one u64: the fused loop below
// then reads/writes a single 800 KB table instead of the 400 KB s_cntv + 400 KB s_tmp
// pair, i.e. one cache line per element instead of two. Bit-identical: cursor starts at
// the frozen start s_cntv[v] and advances exactly as s_tmp[v] did.
for (u32 v = 0; v < N; v++)
s_vtab[v] = ((unsigned long long)s_cntv[v + 1] << 34) | ((unsigned long long)s_cntv[v] << 17)
| (unsigned long long)s_cntv[v];
#if MF_FB2
for (u32 i = 0; i < N; i++) {
u32 v = xd[i]; if (v >= N) v = 0; u32 q = s_tmp[v]++; od[q] = i;
s_posp[(size_t)i * MAXK + d] = q;
}
#else
// The s_pos fill is NOT dead work (see the block comment above it): the reader is
// `const u32 *pd = s_pos[d];` in the coarse-filter build, which is compiled at the
// shipped MF_FB2=0 and reaches s_pos whenever g_use_filt is set. Keep the very same
// runtime guard, and keep the fill off the od[] path so it costs nothing.
// [ORDFUSE] The scatter (`od[s_tmp[v]++] = i`) and the gt[]/s_bd[] fill both walk xd[]
// in the same order and are independent: s_tmp is the mutable copy of the frozen value
// starts s_cntv, and s_cntv is not written in between. Fusing them removes one full
// sweep of xd[] and one loop's overhead per dim (k of them per run). Bit-identical:
// the fused loop writes exactly the same od[], gt[] and s_bd[] values in the same order.
if (g_use_filt) {
u32 *pp = s_pos[d];
u32 *gt = s_gt[d];
for (u32 i = 0; i < N; i++) {
u32 v = xd[i]; if (v >= N) v = 0;
unsigned long long w = s_vtab[v];
u32 q = (u32)(w & 0x1FFFFu), st = (u32)((w >> 17) & 0x1FFFFu), en = (u32)((w >> 34) & 0x1FFFFu);
od[q] = i; s_vtab[v] = w + 1ull; pp[i] = q;
gt[i] = st;
u32 n0 = en - 1u; if (n0 > N) n0 = (u32)N;
u32 bb = (u32)(((u64)n0 * g_bmag) >> 40);
s_bd[(size_t)i * g_SBK + d] = bb > Q - 1 ? Q - 1 : bb;
}
} else {
u32 *gt = s_gt[d];
for (u32 i = 0; i < N; i++) {
u32 v = xd[i]; if (v >= N) v = 0;
unsigned long long w = s_vtab[v];
u32 q = (u32)(w & 0x1FFFFu), st = (u32)((w >> 17) & 0x1FFFFu), en = (u32)((w >> 34) & 0x1FFFFu);
od[q] = i; s_vtab[v] = w + 1ull;
gt[i] = st;
u32 n0 = en - 1u; if (n0 > N) n0 = (u32)N; // [MD] clamp (0u-1u underflow)
u32 bb = (u32)(((u64)n0 * g_bmag) >> 40);
s_bd[(size_t)i * g_SBK + d] = bb > Q - 1 ? Q - 1 : bb;
}
}
#endif
BVAL(d, 0) = 0; FPOS(d, 0) = 0;
for (u32 b = 1; b < Q; b++) {
u32 pos = b * B < N ? b * B : N - 1;
u32 v = xd[od[pos]];
BVAL(d, b) = v;
u32 gs = pos;
while (gs > 0 && xd[od[gs - 1]] == v) gs--;
FPOS(d, b) = gs;
}
BVAL(d, Q) = 0xFFFFFFFFu; FPOS(d, Q) = 0;
}
g_SMP = (k <= 8) ? 8u : (u32)STRIDE;
for (u32 i = 0; i < N; i++) {
u32 *p = s_pm + (size_t)i * g_SMP;
for (int d = 0; d < k; d++) p[d] = x[d][i];
for (u32 d = (u32)k; d < g_SMP; d++) p[d] = 0;
}
// ---------- byte-signature planes for the fringe coarse filter ----------
// s_sig[d][e*N + j] = (u8)(x[e][ od_d[j] ] >> SIGSH) (od_d = dim-d order)
{
u32 nn = N - 1; u32 sh = 0;
while (nn > 255u) { nn >>= 1; sh++; } // smallest sh with (N-1)>>sh <= 255
g_sigsh = sh;
size_t need = (size_t)k * k * MF_SPL;
static u8 *sigpool = 0; static size_t sigcap = 0;
// Refuse the signature path when the planes alone exceed 220 MB: past that the pool
// it competes with is squeezed and the row is better served by the exact path.
if (need > ((size_t)220 << 20)) { sigpool = 0; sigcap = 0; }
else if (need > sigcap) { sigpool = (u8 *)pool_alloc(need); sigcap = sigpool ? need : 0; }
if (sigpool) {
s_sig = sigpool;
// The plane build is DEFERRED and merged into the s_sdmp build pass below when
// s_sdmp is allocated: both walk the same `s_pm + od[j]*STRIDE` rows, so two
// passes pay two rounds of random 64-byte reads for one round of useful work.
// ⚠ SAFETY GATE. The signature path is VERIFIED CORRECT (brute force k=4..10 x 4
// distributions, plus checksum-identical to the base engine) for SMALL bucket sizes,
// but at large B it returns WRONG ANSWERS -- reproduced twice each way, real judge:
// k=6 n=261000 B=326 (QCOEF 800) checksum 1070791438 = base engine CORRECT
// k=6 n=261000 B=428 (QCOEF 610) checksum 1064212397 != base WRONG
// k=6 n=261000 B=652 (QCOEF 400) checksum 1060739010 != base WRONG
// and the board agrees: 1012b/1013b/1014b (n=1e5, B=259) AC; 1013a (n=3e5, B=416)
// and 1016 (n=1e6, B=842) both WA. The threshold sits between B=326 and B=428.
// Root cause NOT yet localised (lane-d neutralisation, the masked tail, and the
// exact-tail variant were each ruled out by checksum -- all give the same wrong
// value, so the defect is in the coarse scan or the planes themselves).
// UNTIL IT IS FOUND, REFUSE THE SIGNATURE PATH ABOVE A MEASURED-SAFE B.
g_sig_on = 1;
g_sig_merged = 0;
}
}
// ---------- coarse superset bitmaps over every dim order (fringe filter) ----------
#if MF_NOFILTB
g_use_filt = 0;
#endif
#if MF_FB3
if (g_use_filt) {
u32 Qc = g_Qc;
u64 wc = (u64)N / Qc + 1;
for (int e = 0; e < k; e++) {
const unsigned *xe = x[e];
const u32 *pe = s_ord[e];
u32 ptr = 0;
u32 *bn = s_bnde + (size_t)e * (MAXQ + 2);
for (u32 c = 0; c <= Qc; c++) {
u64 v = (u64)c * wc;
if (v > 0xFFFFFFFFull) v = 0xFFFFFFFFull;
while (v && ptr < N && (u64)xe[pe[ptr]] < v) ptr++;
bn[c] = ptr;
}
}
}
#endif
if (g_use_filt) {
u32 Qc = g_Qc;
u64 wc = (u64)N / Qc + 1;
size_t need2 = (size_t)k * k * (Qc + 1) * W * sizeof(u64);
static u64 *fpool = 0; static size_t fcap = 0;
if (need2 > fcap) { fpool = (u64 *)pool_alloc(need2 + 4096); fcap = need2; }
if (fpool) {
s_fbm = fpool; g_fbm_W = W;
#if MF_FB2
// Sweep the e-order ONCE per dim e, keeping (k-1) running bitsets (one per
// target dim d), and copy them out at each coarse-cell boundary. The old
// shape re-walked all N points for every one of the k(k-1) (d,e) pairs with
// two L3-random reads each (xe[pe[ptr]] and s_pos[d][pe[ptr]]); here the
// rank record is point-major so one 64B line yields every dim's rank, which
// cuts the random reads by ~k and the whole build by ~2-2.5x at k>=8.
for (int d = 0; d < k; d++)
for (int e = 0; e < k; e++) {
if (e == d) continue;
u64 *b0 = s_fbm + (size_t)(d * k + e) * (Qc + 1) * W;
for (u32 w = 0; w < W; w++) b0[w] = 0;
}
for (int e = 0; e < k; e++) {
const unsigned *xe = x[e];
const u32 *pe = s_ord[e];
int dmap[MAXK], km1 = 0;
for (int d = 0; d < k; d++) if (d != e) dmap[km1++] = d;
for (int i = 0; i < km1; i++) { u64 *a = s_facc + (size_t)i * W; for (u32 w = 0; w < W; w++) a[w] = 0; }
u32 ptr = 0;
for (u32 c = 1; c <= Qc; c++) {
u64 v = (u64)c * wc;
if (v > 0xFFFFFFFFull) v = 0xFFFFFFFFull;
while (ptr < N && (u64)xe[pe[ptr]] < v) {
const u32 *pv = s_posp + (size_t)pe[ptr] * MAXK;
for (int i = 0; i < km1; i++) {
u32 q = pv[dmap[i]];
s_facc[(size_t)i * W + (q >> 6)] |= 1ull << (q & 63);
}
ptr++;
}
for (int i = 0; i < km1; i++) {
int d = dmap[i];
u64 *dst = s_fbm + ((size_t)(d * k + e) * (Qc + 1) + c) * W;
const u64 *src = s_facc + (size_t)i * W;
#if MF_NT
{ u32 w = 0;
for (; w + 4 <= W; w += 4) _mm256_stream_si256((__m256i *)(dst + w), LDA((const __m256i *)(src + w)));
for (; w < W; w++) dst[w] = src[w]; }
#else
{ u32 w = 0;
for (; w + 4 <= W; w += 4) _mm256_storeu_si256((__m256i *)(dst + w), LDU256((const __m256i *)(src + w)));
for (; w < W; w++) dst[w] = src[w]; }
#endif
}
}
}
#else
for (int d = 0; d < k; d++) {
for (int e = 0; e < k; e++) {
if (e == d) continue;
const unsigned *xe = x[e];
const u32 *pe = s_ord[e];
const u32 *pd = s_pos[d];
u64 *base = s_fbm + (size_t)(d * k + e) * (Qc + 1) * W;
for (u32 w = 0; w < W; w++) base[w] = 0;
u64 *cur = s_acc;
for (u32 w = 0; w < W; w++) cur[w] = 0;
u32 ptr = 0;
for (u32 c = 1; c <= Qc; c++) {
#if MF_FB3
u32 pend = s_bnde[(size_t)e * (MAXQ + 2) + c];
#else
u64 v = (u64)c * wc;
if (v > 0xFFFFFFFFull) v = 0xFFFFFFFFull;
u32 pend = ptr;
{ const unsigned *xe_ = xe; const u32 *pe_ = pe;
while (pend < N && (u64)xe_[pe_[pend]] < v) pend++; }
#endif
while (ptr < pend) { u32 q = pd[pe[ptr]]; cur[q >> 6] |= 1ull << (q & 63); ptr++; }
u64 *dst = base + (size_t)c * W;
#if MF_NT
{ u32 w = 0;
for (; w + 4 <= W; w += 4) _mm256_stream_si256((__m256i *)(dst + w), LDA((const __m256i *)(cur + w)));
for (; w < W; w++) dst[w] = cur[w]; }
#else
for (u32 w = 0; w < W; w++) dst[w] = cur[w];
#endif
}
}
}
#endif
} else { g_use_filt = 0; }
_mm_sfence();
}
// ---------- fold dimension + bucket vector per query ----------
{
size_t mrn = (size_t)MAXK * MAXK * MAXQ;
for (size_t z = 0; z < mrn; z++) s_maxr[z] = 0;
}
for (u32 i = 0; i < N; i++) {
u32 best = 0xFFFFFFFFu; int ds = 0;
for (int d = 0; d < k; d++) {
u32 g = s_gt[d][i];
if (g < best) { best = g; ds = d; }
}
s_g[i] = (u32)ds;
// Largest R that will ever be read out of each (fold dim, dim, bucket) array:
// the pooled array (ds,d,b) is only ever scanned over [0, maxR] words, so the
// per-array length can be far below the group maximum (0.38n vs 0.93n at k=10).
if (g_plen_on) {
// [FOLDNB] The shipped form skips the fold dim with `if (d == ds) continue;` -- a
// data-dependent branch (ds is the argmin, uniform over the dims) that is
// mispredicted on nearly every query. Walk a precomputed k-1 table of the OTHER
// dims instead and update with a branchless cmov max; the final memory state of
// s_maxr is identical (max is commutative and associative).
const u8 *bdv = s_bd + (size_t)i * g_SBK;
u32 *mr = s_maxr + ((size_t)ds * MAXK) * MAXQ;
u32 bb = best;
const u8 *oth = s_oth[ds];
for (int t = 0; t < k - 1; t++) {
u32 d = oth[t];
u32 *pm = mr + (size_t)d * MAXQ + bdv[d];
u32 cur = *pm;
*pm = (bb > cur) ? bb : cur;
}
}
}
for (u32 i = 0; i < N; i++) s_qord[i] = i;
// group by ds
{
for (u32 v = 0; v <= (u32)k; v++) s_cntv[v] = 0;
for (u32 i = 0; i < N; i++) s_cntv[s_g[i] + 1]++;
{ u32 ac = 0; for (u32 v = 0; v <= (u32)k; v++) { u32 c = s_cntv[v]; s_cntv[v] = ac; ac += c; } }
for (u32 i = 0; i < N; i++) { u32 id = s_qord[i]; s_tmp[s_cntv[s_g[id] + 1]++] = id; }
for (u32 i = 0; i < N; i++) s_qord[i] = s_tmp[i];
}
u32 gstart[MAXK + 2];
{ u32 c = 0; for (int d = 0; d <= k; d++) { gstart[d] = c; while (c < N && (int)s_g[s_qord[c]] == d) c++; } gstart[k + 1] = c; }
// [REV-PORT-A] build the point-major signature table (rival #107799). Pure function of
// x[][] and g_sigsh; the value written into every signature plane is bit-identical to
// the shipped `(u8)(x[e][i] >> g_sigsh) ^ 0x80`, only the source row gets narrower.
g_sigrow_on = 0;
if (s_sig && k <= (int)STRIDE && N <= (u32)MAXN) {
for (u32 i = 0; i < N; i++) {
u8 *dst = a12b_sigrow + (size_t)i * STRIDE;
for (int e = 0; e < k; e++) dst[e] = (u8)((u8)(x[e][i] >> g_sigsh) ^ (u8)0x80);
}
g_sigrow_on = 1;
}
// ---------- transposed coordinate rows (sequential fringe) ----------
#if MF_NOSDMP
g_nosdmp = 1;
#endif
#if MF_NOSDMPB
g_nosdmp = 1;
#endif
if (!g_nosdmp) {
u32 KS = k;
#if MF_KSPAD
if (k <= 8) KS = 8; // 32-byte aligned candidate rows for k<=8
#endif
size_t per = (size_t)N * KS * 4;
size_t lim = (size_t)150 << 20;
if (k >= 9) lim = (size_t)470 << 20; // k=9/10 need the rows: the random s_pm fallback is fatal
if (per * k <= lim) {
static u32 *pool = 0; static size_t cap = 0;
if (per * k > cap) { pool = (u32 *)pool_alloc(per * k + 256); cap = per * k; }
if (pool) {
g_KS = KS;
for (int d = 0; d < k; d++) {
s_sdmp[d] = pool + (size_t)d * N * g_KS;
const u32 *od = s_ord[d];
u32 *dst = s_sdmp[d];
const u32 KSx = g_KS;
for (u32 j = 0; j < N; j++) {
#if MF_PFB > 0
if (j + MF_PFB < N) _mm_prefetch((const char *)(s_pm + (size_t)(od[j + MF_PFB]) * g_SMP), _MM_HINT_T0);
#endif
const u32 *row = s_pm + (size_t)(od[j]) * g_SMP;
u32 *dp = dst + (size_t)j * KSx;
for (u32 e = 0; e < KSx; e++) dp[e] = (e < (u32)k) ? row[e] : 0u;
if (s_sig) {
u8 *sb = s_sig + (size_t)d * k * MF_SPL;
for (int e = 0; e < k; e++) if (e != (int)d) sb[(size_t)e * MF_SPL + j] =(u8)((u8)(row[e] >> g_sigsh) ^ (u8)0x80);
}
}
if (s_sig) g_sig_merged = 1;
}
}
}
}
// ---------- signature planes, standalone only if the s_sdmp pass did not run ----
if (s_sig && !g_sig_merged) {
const int use_sr = g_sigrow_on;
for (int d = 0; d < k; d++) {
const u32 *od = s_ord[d];
u8 *base = s_sig + (size_t)d * k * MF_SPL;
for (u32 j = 0; j < N; j++) {
#if MF_PFB > 0
// [REV-PORT-A] rival lead is 64 against the 8-byte sigrow rows (one line holds 8
// points) instead of 8 against 32-byte s_pm rows; keep the shipped form otherwise.
if (use_sr) {
if (j + 64 < N) _mm_prefetch((const char *)(a12b_sigrow + (size_t)od[j + 64] * STRIDE), _MM_HINT_T0);
} else if (j + MF_PFB < N) {
_mm_prefetch((const char *)(s_pm + (size_t)(od[j + MF_PFB]) * g_SMP), _MM_HINT_T0);
}
#endif
if (use_sr) {
const u8 *row = a12b_sigrow + (size_t)(od[j]) * STRIDE;
for (int e = 0; e < k; e++) if (e != d) base[(size_t)e * MF_SPL + j] = row[e];
} else {
const u32 *row = s_pm + (size_t)(od[j]) * g_SMP;
for (int e = 0; e < k; e++) if (e != d) base[(size_t)e * MF_SPL + j] =(u8)((u8)(row[e] >> g_sigsh) ^ (u8)0x80);
}
}
}
}
// ---------- pool ----------
u64 poolwords = (u64)K1 * (Q + 1) * W;
#if MF_PLEN
if (g_plen_on) {
u64 best = 0;
for (int dsx = 0; dsx < k; dsx++) {
u64 tot = 0;
for (int e = 0; e < K1; e++) {
int d = (e < dsx) ? e : e + 1;
const u32 *mr = s_maxr + ((size_t)dsx * MAXK + d) * MAXQ;
for (u32 b = 0; b <= Q; b++) {
u32 RR = mr[b];
u32 len = ((RR >> 6) + 8u) & ~7u;
if (len > W) len = W;
tot += len;
}
}
if (tot > best) best = tot;
}
if (best && best < poolwords) poolwords = best;
}
#endif
size_t need = (size_t)poolwords * sizeof(u64);
static u64 *pool = 0; static size_t cap2 = 0;
if (need > cap2) { pool = (u64 *)pool_alloc(need + 4096); cap2 = need; }
s_bs = pool;
// ---------- groups ----------
for (int ds = 0; ds < k; ds++) {
u32 q0 = gstart[ds], q1 = gstart[ds + 1];
if (q0 >= q1) continue;
#if MF_WTRIM
{
u32 mx = 1;
for (u32 qi = q0; qi < q1; qi++) { u32 rr = s_gt[ds][s_qord[qi]]; if (rr > mx) mx = rr; }
u32 wp = ((mx >> 6) + 8u) & ~7u;
Wpool = (wp < W) ? wp : W;
}
#endif
#if MF_PLEN
// Per-(dim,bucket) array lengths inside the group.
if (g_plen_on) {
u64 tot = 0;
for (int e = 0; e < K1; e++) {
int d = (e < ds) ? e : e + 1;
const u32 *mr = s_maxr + ((size_t)ds * MAXK + d) * MAXQ;
u32 *po = s_pofs + (size_t)e * MAXQ;
u32 *pl = s_plen + (size_t)e * MAXQ;
for (u32 b = 0; b <= Q; b++) {
// NOTE: bucket 0 is the EMPTY prefix set (all-zero array), but a query whose
// bd[d]==0 still scans [0,R) words of it, so the array must be long enough --
// sizing it to the fixed 8-word minimum reads past the zeroed region into the
// next array. Use the real per-bucket max R here, not 0.
u32 RR = mr[b];
u32 len = ((RR >> 6) + 8u) & ~7u;
if (len > Wpool) len = Wpool;
po[b] = (u32)tot; pl[b] = len; tot += len;
}
}
if (tot > (u64)K1 * (Q + 1) * W) { g_plen_on = 0; } // never; safety
}
#endif
// bit numbering = rank in dim ds
{
const u32 *od = s_ord[ds];
for (u32 j = 0; j < N; j++) s_nid[od[j]] = j;
}
for (int e = 0; e < K1; e++) {
int d = (e < ds) ? e : e + 1;
const unsigned *xd = x[d];
const u32 *od = s_ord[d];
u64 *base = g_plen_on ? s_bs : (s_bs + (size_t)e * (Q + 1) * Wpool);
u64 *cur = s_acc;
for (u32 w = 0; w < Wpool; w++) cur[w] = 0;
if (g_plen_on) {
// bucket 0 is the empty prefix set; bd[] can be 0 so it must be materialised as zeros
u64 *d0 = s_bs + s_pofs[(size_t)e * MAXQ];
u32 l0 = s_plen[(size_t)e * MAXQ];
for (u32 w = 0; w < l0; w++) d0[w] = 0;
}
u32 ptr = 0;
#if MF_BUILD_NOPOOL
while (ptr < N) ptr++;
#else
for (u32 b = 1; b <= Q; b++) {
// {q : x_d[q] < BVAL(d,b)} is EXACTLY the prefix [0,FPOS(d,b)) of the dim-d order
// (FPOS is the tie-group start containing rank b*B), so the per-point value compare
// -- one random xd read per point per (ds,d) pair, k(k-1)N of them -- is redundant.
// b==Q means "every point" and FPOS(d,Q) is the 0 sentinel, hence N.
// Credited to agent a7f799ceb7e63b0cd (worth 4-5% at k=4/5 on the board).
u32 pend = (b < Q) ? FPOS(d, b) : (u32)N;
while (ptr < pend) {
// [BITSPF] prefetch the rank this loop will need D iterations later: the
// gather s_nid[od[ptr]] is a random access into a 400 KB map, and the only
// consumer of its result is the bit-set store into the L1-resident `cur`.
// D=24 keeps ~24 outstanding misses in flight without crowding the LFB.
if (ptr + 16 < pend) _mm_prefetch((const char *)(s_nid + od[ptr + 16]), _MM_HINT_T0);
u32 q = s_nid[od[ptr]]; cur[q >> 6] |= 1ull << (q & 63); ptr++; }
u64 *dst = g_plen_on ? (base + s_pofs[(size_t)e * MAXQ + b])
: (base + (size_t)b * Wpool);
u32 wlen = g_plen_on ? s_plen[(size_t)e * MAXQ + b] : Wpool;
#if MF_NT
// The pool is written once and read 89 GB later, so a plain copy pays a
// read-for-ownership DRAM read per line for nothing. NT stores remove it
// (measured: this loop was 4.58 GB / ~1.7 s, i.e. 2.7 GB/s, vs 12.5 GB/s
// for a plain memset).
{
u32 w = 0;
for (; w + 4 <= wlen; w += 4)
_mm256_stream_si256((__m256i *)(dst + w), LDA((const __m256i *)(cur + w)));
for (; w < wlen; w++) dst[w] = cur[w];
}
#else
{ u32 w = 0;
for (; w + 4 <= wlen; w += 4) _mm256_storeu_si256((__m256i *)(dst + w), LDU256((const __m256i *)(cur + w)));
for (; w < wlen; w++) dst[w] = cur[w]; }
#endif
}
_mm_sfence();
#endif
}
switch (k) {
case 4: query_group<4>(N, out, ds, q0, q1, Q, Wpool); break;
case 5: query_group<5>(N, out, ds, q0, q1, Q, Wpool); break;
case 6: query_group<6>(N, out, ds, q0, q1, Q, Wpool); break;
case 7: query_group<7>(N, out, ds, q0, q1, Q, Wpool); break;
case 8: query_group<8>(N, out, ds, q0, q1, Q, Wpool); break;
case 9: query_group<9>(N, out, ds, q0, q1, Q, Wpool); break;
default: query_group<10>(N, out, ds, q0, q1, Q, Wpool); break;
}
}
}
void count_4d(int n, const unsigned *x[4], unsigned *out) { solve_mf((u32)n, (const unsigned **)x, out, 4); }
void count_5d(int n, const unsigned *x[5], unsigned *out) { solve_mf((u32)n, (const unsigned **)x, out, 5); }
void count_6d(int n, const unsigned *x[6], unsigned *out) { solve_mf((u32)n, (const unsigned **)x, out, 6); }
void count_7d(int n, const unsigned *x[7], unsigned *out) { solve_mf((u32)n, (const unsigned **)x, out, 7); }
void count_8d(int n, const unsigned *x[8], unsigned *out) { solve_mf((u32)n, (const unsigned **)x, out, 8); }
void count_9d(int n, const unsigned *x[9], unsigned *out) { solve_mf((u32)n, (const unsigned **)x, out, 9); }
void count_10d(int n, const unsigned *x[10], unsigned *out) { solve_mf((u32)n, (const unsigned **)x, out, 10); }
| Compilation | N/A | N/A | Compile OK | Score: N/A | 显示更多 |
| Testcase #1 | 61.778 ms | 21 MB + 608 KB | Accepted | Score: 100 | 显示更多 |