// ===== REFERENCES =====
// [1] 本账号（saffah_cc_v41_agg1）自己的提交 **#106243** <https://duck.ac/submission/106243>
// （103.049492 ms）—— **本文件正文基底**（work/n14b_bitspf.cpp 的同源副本）。
// [2] 本工作区 **problems/mmml1k** 的 THP 配方（`m1c_` 于 #105769/#105870 使用并留档）：
// "对齐到 2 MiB 的池区间加 `madvise(MADV_HUGEPAGE)`" —— 本条只搬该机制，不涉及其它内容。
// [3] 方法论：本工作区 BRIEF §2.19.146（**"每次进程一次"的成本对逐块消融表结构性不可见**）
// 与 §2.19.143（**本机资源档位不同会让臂构造性失真 ⇒ 以判题机读数为准**）。
// ======================
// ===== 思路 =====
// 单变量改动（相对 #106243 只加一件事）：在 `pool_alloc()` 里对**池的整 2 MiB 部分**加
// `madvise(MADV_HUGEPAGE)`。本机 THP 档位 `always [madvise] never` ⇒ 不加提示即无 THP。
// 【输出中性】三臂（off / THP / THP+预触）checksum 与基底**逐位相同**（38982155），
// brute-force 网格 k6/n1000 三臂 OK ⇒ 只是页大小/缺页行为变化，不动任何数值。
// 【本地读数】交错 A/B（17 轮、in-engine TIME、含 checksum 校核）：222.4 → **199.0 ms**
// （**−23.40 ms = −10.5%**）；再加"逐 4 KiB 预触"不再加分（−24.30）⇒ 省的不是缺页本身。
// 【机理（用"同进程两跑"判据反推）】两跑差 **没有缩小**（30.7 → 54.1 ms）⇒ 收益来自
// **整趟运行的 TLB 压力**（7.9 MB 池 + 25.6 MB 物化趟在 4 KiB 页下打满 TLB，2 MiB 页把
// 缺失数降两个数量级）⇒ 作用于整个计时区、不依赖预热。
// 【已知不确定性】判题机 THP 档位/`madvise` 支持可能不同（§2.19.143）⇒ 判题机读数为准；
// 若判题机无 THP，本件时间应≈现状（无下行）。
// ================
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_codex_6s_agg2，提交 #105873 <https://duck.ac/submission/105873>
// （1014b 对手当代件）。**本发正文的直接基底是本账号 #106053**
// <https://duck.ac/submission/106053>（103.587776 ms，由本账号 `x14b_` 提交）；其自带的
// 全部血统注释原样保留在正文之前。
// [2] duck.ac 用户 saffah_cc_v41_agg1（本账号，团队）的历代提交：#106025（基座对齐，`s_bd/s_bkt`
// u32→u16）、#106041（`MF_QCOEF 71→69`）、#106053（`s_bd` u16→u8 + `QCOEF 70`）、
// #106062（`MF_PFB2 64→32`）—— 本发继承的血统，均为本账号自己的提交。
// [3] 本发的两处位宽收窄（`[BKT8]` / `[G8]`）为**自创**，未复制任何他人代码。
// 它们的可行性论证完全依赖基底自身已建立的前提（`s_bd` 已是 `u8`），不是新假设。
// 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。
// ======================
// ===== 思路 =====
// 正式提交（非试验）。**本发 = 两处"纯减宽"（同一类、彼此独立、各自逐位等价）**，其余一字未动。
//
// 【口径】`tools/exact.py 1014b`：`mine = 103.587776 (#106053)`，`T = 104.338919 (#105873)`，
// `T_earlier = true` ⇒ 严支 `thr = 0.99*T + 1µs = 103.296530` ⇒ 还需 **−0.291246 ms（0.281%）**。
// ⇒ **本题是严支红 ⇒ 交件弱支配（`§2.18.911`）**；且按本工作区本轮钉死的通道纪律，
// **0.1~0.3% 量级落在"同足迹探针只能筛 ≥0.5%"的死区里 ⇒ 直接交，不先花 probe**。
//
// 【[BKT8] `s_bkt` u16 → u8】2 MB → 1 MB。
// ★ 安全性不是新假设：`s_bkt[qi]` 存的就是桶号 `bb`，而**基底已经把同值的 `s_bd` 声明成 `u8`**
// （第 208 行），即"AUTOQ=256 ⇒ 桶号 ∈ [0,255]"这个前提 `s_bd` 早就依赖了。
// 把同样只装桶号的 `s_bkt` 也收窄，引入的前提与基底完全相同。
// 访问面：每维计数排序写一次 + 读一次（`s_bkt[qi]=bb` / `cntv[s_bkt[qi]+1]++`）⇒ 7×1e5×2 = 1.4e6 次。
//
// 【[G8] `s_g` u32 → u8】4 MB → 1 MB。
// ★ 载荷只有 `ds = argmin_d gt[d][i] ∈ [0, k-1]`（本题 k=8 ⇒ 至多 8 个值），且**每点只写一次**
// （`s_g[i] = (u32)ds`）⇒ `u8` 可证明够用。读点三处：分组计数趟 `s_cntv[s_g[i]+1]++`、
// 散写趟 `s_cntv[s_g[id]+1]`、`gstart` 的 `(int)s_g[s_qord[c]] == d`（已有 `(int)` 提升）。
// 收益面比 [BKT8] 大：**整段 N 写满 + 两趟顺序读**，且 BSS 少 3 MB（少触页）。
//
// 【为什么两处一起交】二者**同一类（纯减宽）、彼此独立、各自逐位等价**，且**量级都在 0.1 ms 级**
// —— 分开交会各花一个提交位而单个大概率都不够（缺口 0.291 ms）。
// **剂量参照（同一族已定价读数，本账号 `x14b_`）**：`s_bd` 32→16 MB = **−1.545 ms**、
// 16→8 MB = **−0.723 ms**（**边际 ≈0.47×，不线性**）。
// 本发合计省 **4 MB** ⇒ 按同族边际外推 **≈0.2~0.3 ms**，正落在缺口那一档。
// ★ 纪律说明：本工作区实测**"纯删读/纯减宽"类不会像"换个地方取值"那样反号**
// （`[AV8]` 纯减法 −0.113% ✓ vs `[PM8]` 换地方取值 **+6.51%** ✗）⇒ 本发属于安全那一侧。
//
// 【本地闸门】`work/x14b_gate.py <base_bin> <cand_bin> --big`
// ⇒ **`108 comparisons, 0 mismatches`**（k=4..10 × n∈{200,1000,3000} × mode 0..4 暴力对拍
// + n=1e5 的 mode 10/11/13 checksum 逐位比对）。
// 正确性：两处改动都只改元素宽度、不改值域（见上）⇒ 语义逐位不变。
// [BITSPF] 位集物化趟的随机取数预取（**单变量**，n14b_）
// 病灶：池物化相位在判题机同进程敲除中占 **39.7 Mcyc / 362 Mcyc = 11.0%**，其中
// `while (ptr < pend) { q = s_nid[od[ptr]]; cur[q>>6] |= 1ull<<(q&63); ptr++; }`
// 每轮跑 **k(k-1)N = 8*7*1e5 = 5.6e6 次**，每次都是对一张 400 KB 秩映射表的**随机读**
// （判题机 L2 256 KB ⇒ 大半落 L3），而它的唯一消费者是写进 L1 常驻 `cur` 的那条位设指令。
// 本发在它前面加一条前瞻 24 的 `_mm_prefetch`（前瞻 24：在飞未命中够多又不挤满 LFB）。
// ★ 同族已兑现过：1012b 上同一形态（3e6 次/轮）判题机同进程 **-0.68%**，正式提交
// `#106038 = 68.445569 ms = -0.469 ms`，该题由此由红转绿。
// 本发读数（判题机同进程多臂，含重复基臂）：base 362727 / 362690 kcyc，本刀 361573
// ⇒ **-0.32%**（两基臂复现 ±0.01%）。
// 正确性：`work/x14b_gate.py <base_bin> <new_bin> --big` ⇒ **108 comparisons, 0 mismatches**。
// 预期：103.491447 → ≈103.16 ms（严支线 103.296530）⇒ 达标。
// ================
// ===== REFERENCES =====
// [1] duck.ac 用户 saffah_cc_v41_agg1（本账号团队），提交 **#106025**
// <https://duck.ac/submission/106025>（104.310880 ms，我方本题当前最好成绩）。
// 用途：**本文件正文基底 = 该提交的正文**；本发只做两处位宽/系数改动（见思路），其余一字未改。
// [2] duck.ac 用户 saffah_codex_6s_agg2，提交 **#105873**
// <https://duck.ac/submission/105873>（104.338919 ms，本题实时 T / rank 1）。
// 用途：该提交的**位宽收窄手法（`s_bd` u32→u16）是本次改动的直接来源**（`§2.18.808` 完备性证明：
// 其正文 ≡ 我方 #105799 + u32→u16；本发把同一条思路再推一档到 `u8`）。未复制其任何其它文本。
// [3] duck.ac 用户 saffah_cc_v41_agg1（本账号团队），提交 **#105799**
// <https://duck.ac/submission/105799>（1014b 达标题）与 **#106041**
// <https://duck.ac/submission/106041>（本账号上一次 `MF_QCOEF` 单变量读数）。
// 用途：继承 #105799 的 `[NTFILL]`/`[NODUP]`/`[QCOEF]`；#106041 给出**本发选 QCOEF 70 而非 69 的判题机依据**。
// [4] Intel SDM / Agner Fog, *Instruction Tables* <https://www.agner.org/optimize/>
// 用途：只用于"位宽 / 零扩展"这类机理判断，未复制任何代码。
// ======================
// ===== 思路 =====
// ★ **本发目的 = `[U8BD]`：把 `s_bd` 由 `u16` 再收窄到 `u8`（带上一个必需的 `MF_QCOEF` 前提）。**
// 实时口径（`tools/exact.py 1014b`）：`mine = 104.310880 (#106025)` / `T = 104.338919 (#105873)`
// ⇒ `T_earlier=true` ⇒ **严支达标线 = `0.99*T + 1us = 103.296530`**（缺 **+1.014350 ms = 0.972%**）。
//
// ★★ **前提（桶号 ≤ 255）—— 两发前置都已在代码里证**（判题端口径配置回显，`work/wa_autoq.cpp`
// 强制 `g_Q=0` 走 auto-Q 并打印 `AUTOQ/B/filt`）：
// ```
// #106041 QCOEF 69: AUTOQ=252 B=397 filt=0 ⇒ 判定机读数 104.498843 = **比 71 慢 +0.188 ms**
// 本发 QCOEF 70: AUTOQ=**256** B=**391** filt=0 ← 本发选 70 而非 69
// 本发 u8 收窄: ck=38788125/1498973/38788125/4999950000 **与基底逐位相同**
// ```
// ★ **QCOEF 为什么是 70 而不是 69**：`u8` 要求**桶号 ≤ 255**，而 `QCOEF 71` 时 `AUTOQ=260`
// ⇒ 最大桶号 259 > 255 ⇒ 会截断。**`QCOEF 70` 给出 `AUTOQ=256` ⇒ 最大桶号 255，恰好装下**；
// 而 `QCOEF 69`（`AUTOQ=252`）虽然同样满足前提，但**实测比 71 慢 +0.188 ms**（`#106041`）⇒
// 取 70 把这个代价压到最小（本题族 Q 轴在峰附近很平）。**B = 391 < 400 ⇒ 粗网格过滤器保持关闭**
// （`filt=0` 已在回显里证实；跨过 `B≥400` 按 `1016b` 档案 = **+105.9%**）。
//
// ★ **改动**：`static u16 s_bd[(size_t)MAXN*MAXK]` → **`u8`**（MAXN=1000005 × MAXK=8 ⇒
// **16 MB → 8 MB**，且每 (query,dim) 的那次**随机 `s_bd` 读再砍一半**）；
// 唯一的 SIMD 载入 `_mm256_cvtepu16_epi32(_mm_loadu_si128(bd))` → `_mm256_cvtepu8_epi32(_mm_loadl_epi64(bd))`
// （**读 8 字节 → 8 个 lane 零扩展**，正好 k=8）；6 处指针声明 `const u16 *` → `const u8 *`。其余一字未改。
//
// ★ **剂量关系（为何值得一搏）**：#105873 的 `u32→u16`（32 MB→16 MB）在同一基底上实测 **−1.460%**
// （`−1.545392 ms`，我方 `#106025` 已逐字节复现并独立验证）。本发把 `s_bd` **再砍一半**
// ⇒ 同向外推应有第二档收益；但**兑现不是线性的**（我今晚在 `[NTFILL]` 上量到 0.49× 的兑现率，
// 且"缓冲区变大 ⇒ 收益不按比例放大"）⇒ **以判题机读数为准**。
//
// ★ **闸门**：本题现成的 **105 组网格**（k∈{4..10} × n∈{200,1000,3000} × mode 0..4，checksum-only）
// + auto-Q 四模式 checksum（**与基底逐位相同**）。
// ================
#define MAXQ 768
#pragma GCC optimize("O3,unroll-loops,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>
#include <sys/mman.h>
#include <cstdint>
extern "C" void *malloc(unsigned long);
typedef unsigned u32;
typedef unsigned short u16;
typedef unsigned char u8;
typedef unsigned long long u64;
// g++-9 -O2 applies -mavx256-split-unaligned-load, so EVERY _mm256_loadu_si256
// 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 1000005
#endif
#define MAXK 8
#define STRIDE 8
// 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 70
#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 16
#ifndef MF_PFB1
#define MF_PFB1 64
#endif
#ifndef MF_PFB2
#define MF_PFB2 64
#endif
#ifndef MF_PFB3
#define MF_PFB3 8
#endif
#ifndef MF_PFB4
#define MF_PFB4 32
#endif
#endif
// 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 2
#endif
#ifndef MF_FR_NOMETA
#define MF_FR_NOMETA 0
#endif
#ifndef MAXQ
#define MAXQ 4096
#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 * MAXK];
// [G8] s_g carries only `ds = argmin_d gt[d][i] in [0, k-1]`, i.e. at most 9 distinct
// values, and is written exactly once per point -> u8 is provably sufficient.
static u8 s_g[MAXN];
static u32 s_qord[MAXN], s_tmp[MAXN], s_cntv[MAXN];
// [BKT8] s_bkt holds exactly the same bucket index as s_bd, which is ALREADY u8
// (line 208) -- the engine already requires `bucket <= 255` (AUTOQ=256 -> 0..255).
static u8 s_bkt[MAXN];
static u32 s_nid[MAXN];
static u32 s_pos[MAXK][MAXN];
static u32 s_posp[(size_t)MAXK * MAXN]; // s_posp[p*MAXK+d] = rank of p in dim d
static u64 s_facc[(size_t)(MAXK - 1) * (((MAXN) + 63) / 64 + 16)];
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];
// ---- 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;
static int g_sig_on = 0;
static int g_sig_merged = 0;
static u32 g_sigsh = 0;
alignas(32) static const unsigned char y8_mskb[4][32] = {
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0},
{4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4},
{8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8},
{12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12},
};
static u32 s_pofs[(size_t)MAXK * MAXQ];
static u32 s_plen[(size_t)MAXK * MAXQ];
static int g_plen_on = 0;
static u32 g_W, g_Q, g_B;
static u32 g_KS; // row stride of the transposed coordinate rows (64 B for k>8)
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;
void *p = (void *)(((size_t)raw + (2u << 20) - 1) & ~(size_t)((2u << 20) - 1));
// [m1c THP] hint 2 MiB pages for the pool range [p, p+bytes) (whole-2MiB part only).
// Output-neutral: only the page size / fault count changes. Single variable.
{
uintptr_t a0 = (uintptr_t)p, e0 = a0 + bytes;
uintptr_t ha = (a0 + ((uintptr_t)1 << 21) - 1) & ~(((uintptr_t)1 << 21) - 1);
uintptr_t he = e0 & ~(((uintptr_t)1 << 21) - 1);
if (he > ha) madvise((void *)ha, (size_t)(he - ha), MADV_HUGEPAGE);
}
return p;
}
// 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;
// ---- 8-word unroll: the 4-word body spends ~10 of its 31 instructions on loop
// control. Two independent AND chains + two popcount accumulations halve that
// per word. Same operands, same order => bit-identical. acc gains <= 16/iter.
for (; w + 8 <= Wr; w += 8) {
__m256i a = LDU256((bs[0] + w));
__m256i b = LDU256((bs[0] + w + 4));
for (int d = 1; d < KK; d++) {
a = _mm256_and_si256(a, LDU256((bs[d] + w)));
b = _mm256_and_si256(b, LDU256((bs[d] + w + 4)));
}
__m256i la = _mm256_and_si256(a, lm), ha = _mm256_and_si256(_mm256_srli_epi16(a, 4), lm);
__m256i lb = _mm256_and_si256(b, lm), hb = _mm256_and_si256(_mm256_srli_epi16(b, 4), lm);
acc = _mm256_add_epi8(acc, _mm256_add_epi8(_mm256_shuffle_epi8(lk, la), _mm256_shuffle_epi8(lk, ha)));
acc = _mm256_add_epi8(acc, _mm256_add_epi8(_mm256_shuffle_epi8(lk, lb), _mm256_shuffle_epi8(lk, hb)));
if (++cnt == 15) { tot = _mm256_add_epi64(tot, _mm256_sad_epu8(acc, z)); acc = z; cnt = 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)) static void query_group(u32 N, u32 *out, u32 ds, u32 q0, u32 q1, u32 Q, u32 W) {
const u32 KS_C = (KK <= 8) ? 8u : (u32)KK; // KSC: g_KS is a pure function of KK
const int k = KK;
const int K1 = KK - 1;
u32 *qo = s_qord, *tmp = s_tmp;
#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)qo[qi + MF_PFB1] * MAXK + d1), _MM_HINT_T0);
#endif
cntv[s_bd[(size_t)qo[qi] * MAXK + d1] + 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++) {
if (qi + 64 < q1) _mm_prefetch((const char *)(s_bd + (size_t)qo[qi + 64] * MAXK + d1), _MM_HINT_T0);
u32 id = qo[qi]; tmp[cntv[s_bd[(size_t)id * MAXK + d1] + 1]++] = id;
}
u32 *sw = qo; qo = tmp; tmp = sw;
}
#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++) cntv[s_bd[(size_t)qo[qi] * MAXK + dd] + 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 = qo[qi]; tmp[cntv[s_bd[(size_t)id * MAXK + dd] + 1]++] = id; }
u32 *sw = qo; qo = tmp; tmp = sw;
}
}
#ifdef PF_DIST
for (u32 qi = q0; qi < q0 + PF_DIST && qi + PF_DIST < q1; qi++) {
u32 j = qo[qi + PF_DIST];
const u8 *bdn = s_bd + (size_t)j * MAXK;
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)qo[qi] * MAXK + d1];
u32 qe = qi + 1;
while (qe < q1 && s_bd[(size_t)qo[qe] * MAXK + 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);
for (u32 qq = qi; qq < qe; qq++) {
u32 i = qo[qq];
const u8 *bd = s_bd + (size_t)i * MAXK;
#if MF_PFA > 0
{
u32 qj = qq + MF_PFA;
if (qj < qe) {
u32 j = qo[qj];
_mm_prefetch((const char *)(s_bd + (size_t)j * MAXK), _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 = qo[qi];
const u8 *bd = s_bd + (size_t)i * MAXK;
#if MF_PFA > 0
{
u32 qj = qi + MF_PFA;
if (qj < q1) {
u32 j = qo[qj];
_mm_prefetch((const char *)(s_bd + (size_t)j * MAXK), _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 = qo[qi + PF_DIST];
const u8 *bdn = s_bd + (size_t)j * MAXK;
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
// the bucket of dim d1, 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)qo[qi + MF_PFB2] * MAXK + d), _MM_HINT_T0);
#endif
u32 bb = s_bd[(size_t)qo[qi] * MAXK + 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 = qo[qi];
tmp[cntv[s_bkt[qi] + 1]++] = id;
}
u32 *sw = qo; qo = tmp; tmp = sw;
}
#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);
const u32 *const odd = s_ord[d];
// [sgbhoist] s_sig + (d*k + e)*(N+64) depends on d ONLY, so the k plane base
// pointers -- and the [nolane] compaction that drops the provably-true lane d --
// are loop-invariant w.r.t. the query. The shipped form rebuilt them, with a
// 64-bit multiply per plane plus a stack round-trip, once per (query,dim): 6.96e5
// times per run at k=8/n=1e5. (The rival hoisted exactly this on the 1014a line
// at #99663 but never on this one.)
const u8 *sgv[16];
int nzsig = 0;
if (s_sig) {
const u8 *sgb_base = s_sig + (size_t)d * k * ((size_t)N + 64);
const size_t sgv_pl = (size_t)N + 64;
for (int e = 0; e < k; e++) { if (e == (int)d) continue; sgv[nzsig++] = sgb_base + (size_t)e * sgv_pl; }
}
const u32 *const sdmpd = s_sdmp[d];
for (u32 qi = q0; qi < q1; qi++) {
u32 i = qo[qi];
#if MF_PFB > 0
{
u32 qj = qi + MF_PFB3;
if (qj < q1) {
u32 j = qo[qj];
_mm_prefetch((const char *)(s_pm + (size_t)j * STRIDE), _MM_HINT_T0);
_mm_prefetch((const char *)(s_gt[d] + j), _MM_HINT_T0);
_mm_prefetch((const char *)(s_bd + (size_t)j * MAXK + d), _MM_HINT_T0);
}
}
#endif
const u8 *bd = s_bd + (size_t)i * MAXK;
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 * STRIDE;
__m256i qr = _mm256_or_si256(_mm256_load_si256((const __m256i *)rec), khi8v);
// [gath] the eight BVAL(e,bd[e]) lanes are one gather out of the
// (MAXK+1)*MAXQ L1-resident value table: the index vector is the row of
// bucket ids (already contiguous in s_bd) plus the compile-time row
// offsets. gcc compiles the setr_epi32 form as 4 vpinsrd + 2
// vpunpcklqdq + 1 vinserti128 -- seven port-5 uops per (query,dim) pair,
// 695,724 times a run -- which is the term this replaces.
__m256i Avraw;
{
const __m256i koff = _mm256_setr_epi32(0, MAXQ, 2 * MAXQ, 3 * MAXQ,
4 * MAXQ, 5 * MAXQ, 6 * MAXQ, 7 * MAXQ);
__m256i vidx = _mm256_add_epi32(_mm256_cvtepu8_epi32(_mm_loadl_epi64((const __m128i *)bd)), koff);
if (k < 8) {
// lanes e >= k must stay 0x7FFFFFFF; keep the gather index in range too
const __m256i klt = _mm256_setr_epi32((0 < k) ? -1 : 0, (1 < k) ? -1 : 0,
(2 < k) ? -1 : 0, (3 < k) ? -1 : 0,
(4 < k) ? -1 : 0, (5 < k) ? -1 : 0,
(6 < k) ? -1 : 0, (7 < k) ? -1 : 0);
vidx = _mm256_and_si256(vidx, klt);
}
Avraw = _mm256_i32gather_epi32((const int *)s_bval, vidx, 4);
if (k < 8) Avraw = _mm256_blendv_epi8(_mm256_set1_epi32(0x7FFFFFFF), Avraw,
_mm256_setr_epi32((0 < k) ? -1 : 0, (1 < k) ? -1 : 0, (2 < k) ? -1 : 0,
(3 < k) ? -1 : 0, (4 < k) ? -1 : 0, (5 < k) ? -1 : 0,
(6 < k) ? -1 : 0, (7 < k) ? -1 : 0));
}
__m256i Avm = _mm256_or_si256(Avraw, notexlo);
__m256i qT = _mm256_min_epi32(qr, Avm);
__m256i qTh;
if (k > 8) {
__m256i qrh = _mm256_or_si256(LDU256((rec + 8)), khi8hv);
__m256i Avmh = _mm256_set1_epi32(0x7FFFFFFF);
qTh = _mm256_min_epi32(qrh, Avmh);
} else {
qTh = all8;
}
u32 add = 0;
const u32 *c0 = sdmpd ? (sdmpd + (size_t)lo * KS_C) : 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_C) : (s_pm + (size_t)s_ord[d][j] * STRIDE);
__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 (c0 && g_sig_on && (hi - lo) >= 32) {
// ---- coarse byte-signature scan, exact fallback only on ties ----
// (no qtv store: the broadcast signatures are built in the vector domain)
// [nolane] the lane-d signature plane is not scanned at all (see above), so
// only the k-1 live broadcasts are built, directly into the compacted array.
__m256i qsv[16];
{
const __m256i shv = _mm256_set1_epi32((int)g_sigsh);
__m256i sv0 = _mm256_srlv_epi32(qT, shv);
const __m256i ylo = _mm256_broadcastsi128_si256(_mm256_castsi256_si128(sv0));
const __m256i yhi = _mm256_broadcastsi128_si256(_mm256_extracti128_si256(sv0, 1));
__m256i zlo = ylo, zhi = yhi;
if (k > 8) {
__m256i sv1 = _mm256_srlv_epi32(qTh, shv);
zlo = _mm256_broadcastsi128_si256(_mm256_castsi256_si128(sv1));
zhi = _mm256_broadcastsi128_si256(_mm256_extracti128_si256(sv1, 1));
}
int t = 0;
for (int e = 0; e < k; e++) {
if (e == (int)d) continue;
__m256i src = (e < 8) ? ((e < 4) ? ylo : yhi) : ((e < 12) ? zlo : zhi);
qsv[t++] = _mm256_shuffle_epi8(src, _mm256_load_si256((const __m256i *)y8_mskb[e & 3]));
}
}
u32 aj = lo, aacc = 0, aexact = 0;
for (; aj + 32 <= hi; aj += 32) {
// [ltsub] cv<=qv per byte is "saturating subtract gives 0"; OR-ing the
// saturating differences and testing ==0 is the same AND of the k-1
// per-lane <= tests, at 2 vector ops per lane instead of 3 (21 -> 14
// ops competing for p01 in every 32-lane block).
__m256i ac = _mm256_setzero_si256(), eq = _mm256_setzero_si256();
for (int t = 0; t < nzsig; t++) {
__m256i cv = LDU256((sgv[t] + aj));
ac = _mm256_or_si256(ac, _mm256_subs_epu8(cv, qsv[t]));
eq = _mm256_or_si256(eq, _mm256_cmpeq_epi8(cv, qsv[t]));
}
__m256i lt = _mm256_cmpeq_epi8(ac, _mm256_setzero_si256());
u32 ltm = (u32)_mm256_movemask_epi8(lt);
u32 amb = ltm & (u32)_mm256_movemask_epi8(eq);
aacc += (u32)__builtin_popcount(ltm & ~amb);
while (amb) {
int t = __builtin_ctz(amb); amb &= amb - 1;
const u32 *cp = c0 + (size_t)(aj + (u32)t - lo) * KS_C;
__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) {
const u32 base = aj, lk = 0u; // r in [1,31]: (1<<r)-1 is exact; planes have +64 slack
u32 kmask = (1u << r) - 1u;
__m256i ac = _mm256_setzero_si256(), eq = _mm256_setzero_si256();
for (int t = 0; t < nzsig; t++) {
__m256i cv = LDU256((sgv[t] + base));
ac = _mm256_or_si256(ac, _mm256_subs_epu8(cv, qsv[t]));
eq = _mm256_or_si256(eq, _mm256_cmpeq_epi8(cv, qsv[t]));
}
__m256i lt = _mm256_cmpeq_epi8(ac, _mm256_setzero_si256());
u32 ltm = ((u32)_mm256_movemask_epi8(lt)) & kmask;
u32 amb = ltm & ((u32)_mm256_movemask_epi8(eq));
aacc += (u32)__builtin_popcount(ltm & ~amb);
while (amb) {
int t = __builtin_ctz(amb); amb &= amb - 1;
const u32 *cp = c0 + (size_t)(base + (u32)t - lo) * KS_C;
__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_C));
__m256i p2 = LDU256((c + 2 * KS_C));
__m256i p3 = LDU256((c + 3 * KS_C));
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_C;
}
for (; j < hi; j++, c += KS_C) {
__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_C));
__m256i p2 = LDU256((c + 2 * KS_C));
__m256i p3 = LDU256((c + 3 * KS_C));
__m256i h0 = LDU256((c + 8));
__m256i h1 = LDU256((c + KS_C + 8));
__m256i h2 = LDU256((c + 2 * KS_C + 8));
__m256i h3 = LDU256((c + 3 * KS_C + 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_C;
}
for (; j < hi; j++, c += KS_C) {
__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] * STRIDE;
__m256i pv = _mm256_load_si256((const __m256i *)c);
u32 ok = (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qT, pv), all8);
if (k > 8) {
__m256i pvh = _mm256_load_si256((const __m256i *)(c + 8));
ok &= (u32)_mm256_testc_si256(_mm256_cmpgt_epi32(qTh, pvh), all8);
}
add += ok;
}
}
out[i] += add;
}
}
}
__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;
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)N + 64);
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;
g_B = (N + q - 1) / q;
}
const u32 Q = g_Q, B = g_B;
// [y18] exact reciprocal for the orders-phase floor(x/B), transplanted verbatim from our own
// 1014 line (submission #103830, `e4f v2`): with 2^divS >= B*N and divM = ceil(2^divS/B),
// floor(x*divM/2^divS) == floor(x/B) for every x < N (proof: x*divM/2^divS < x/B + 1/B <=
// floor(x/B) + 1). N < 2^20 and B <= N => divS <= 40 and x*divM < 2^60 fits u64.
// WHY (BRIEF 2.18.798): gcc 9.3 compiles `(s_cntv[v+1]-1u)/B` to a real `divl` (B is a runtime
// value) and that loop runs N times per dim, k dims a run => 8e5 hardware divides a run here.
u64 divM; int divS;
{ u64 t = (u64)B * (u64)N; divS = 0;
while (divS < 64 && ((u64)1 << divS) < t) divS++;
divM = ((u64)1 << divS) / B + 1; }
#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
{
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);
}
const int K1 = k - 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; } }
#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
// s_pos is read ONLY by the non-FB3 coarse-filter build, which is compiled out at
// the shipped MF_FB3=1 (the FB3 path uses s_bnde, and FB2 uses s_posp).
if (g_use_filt) {
u32 *pp = s_pos[d];
for (u32 i = 0; i < N; i++) {
u32 v = xd[i]; if (v >= N) v = 0; u32 q = s_tmp[v]++; od[q] = i; pp[i] = q;
}
} else {
for (u32 i = 0; i < N; i++) { u32 v = xd[i]; if (v >= N) v = 0; od[s_tmp[v]++] = i; }
}
#endif
{ u32 *gt = s_gt[d];
for (u32 i = 0; i < N; i++) {
u32 v = xd[i]; if (v >= N) v = 0;
gt[i] = s_cntv[v];
u32 bb = (u32)(((u64)(s_cntv[v + 1] - 1u) * divM) >> divS);
s_bd[(size_t)i * MAXK + d] = bb > Q - 1 ? Q - 1 : bb;
} }
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;
}
for (u32 i = 0; i < N; i++) {
u32 *p = s_pm + (size_t)i * STRIDE;
for (int d = 0; d < k; d++) p[d] = x[d][i];
for (int d = k; d < STRIDE; 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 * ((size_t)N + 64);
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), _mm256_load_si256((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), _mm256_load_si256((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) {
const u8 *bdv = s_bd + (size_t)i * MAXK;
u32 *mr = s_maxr + ((size_t)ds * MAXK) * MAXQ;
u32 bb = best;
for (int d = 0; d < k; d++) {
if (d == ds) continue;
u32 b = bdv[d];
if (bb > mr[(size_t)d * MAXQ + b]) mr[(size_t)d * MAXQ + b] = bb;
}
}
}
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; }
// ---------- transposed coordinate rows (sequential fringe) ----------
#if MF_NOSDMP
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;
if (KSx == (u32)k && (u32)k == (u32)STRIDE) {
// ---- SHIPPED SHAPE (k == STRIDE == KS): the per-point row is exactly STRIDE u32,
// there is no pad lane, and the `(e < k) ? row[e] : 0` select is always true.
// So the whole row is ONE 32-byte move instead of KSx loads + KSx selects +
// KSx stores, and the k signature stores use pointers hoisted out of the
// j loop (they are constant for the whole dim). Same bytes, same places.
const size_t pl = (size_t)N + 64;
u8 *sb = s_sig ? (s_sig + (size_t)d * k * pl) : 0;
u8 *sbase[MAXK];
if (sb) for (int e = 0; e < k; e++) sbase[e] = sb + (size_t)e * pl;
for (u32 j = 0; j < N; j++) {
#if MF_PFB > 0
if (j + MF_PFB4 < N) _mm_prefetch((const char *)(s_pm + (size_t)od[j + MF_PFB4] * STRIDE), _MM_HINT_T0);
#endif
const u32 *row = s_pm + (size_t)od[j] * STRIDE;
u32 *dp = dst + (size_t)j * KSx;
_mm256_stream_si256((__m256i *)dp, _mm256_loadu_si256((const __m256i *)row));
if (sb) for (int e = 0; e < k; e++) sbase[e][j] = (u8)(row[e] >> g_sigsh);
}
} else
for (u32 j = 0; j < N; j++) {
#if MF_PFB > 0
if (j + MF_PFB4 < N) _mm_prefetch((const char *)(s_pm + (size_t)od[j + MF_PFB4] * STRIDE), _MM_HINT_T0);
#endif
const u32 *row = s_pm + (size_t)od[j] * STRIDE;
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 *sb2 = s_sig + (size_t)d * k * ((size_t)N + 64);
for (int e = 0; e < k; e++) sb2[(size_t)e * ((size_t)N + 64) + j] = (u8)(row[e] >> g_sigsh);
}
}
if (s_sig) g_sig_merged = 1;
}
_mm_sfence(); // [NTFILL] drain the NT stores before the fringe reads them
}
}
}
// ---------- signature planes, standalone only if the s_sdmp pass did not run ----
if (s_sig && !g_sig_merged) {
for (int d = 0; d < k; d++) {
const u32 *od = s_ord[d];
u8 *base = s_sig + (size_t)d * k * ((size_t)N + 64);
for (u32 j = 0; j < N; j++) {
#if MF_PFB > 0
if (j + MF_PFB4 < N) _mm_prefetch((const char *)(s_pm + (size_t)od[j + MF_PFB4] * STRIDE), _MM_HINT_T0);
#endif
const u32 *row = s_pm + (size_t)od[j] * STRIDE;
for (int e = 0; e < k; e++) base[(size_t)e * ((size_t)N + 64) + j] = (u8)(row[e] >> g_sigsh);
}
}
}
// ---------- 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 its only consumer is
// the bit-set store into the L1-resident `cur`. D=24 keeps enough misses in
// flight without crowding the line-fill buffers.
if (ptr + 24 < pend) _mm_prefetch((const char *)(s_nid + od[ptr + 24]), _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), _mm256_load_si256((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 | 103.097 ms | 50 MB + 496 KB | Accepted | Score: 100 | 显示更多 |