// ===== REFERENCES =====
// [1] duck.ac 用户 **pdoom**，提交 **#118708** <https://duck.ac/submission/118708>
// （judge Time 539.871670 ms，14:09:45，现役 rank 1 = 本题 T）—— **本文件正文逐字节移植自它**
// （BASE32 引擎 + ALTMAX=64 替代基 + 粗 64 根打包 + 完整 NT 缓存行流）；与原文唯一差异 =
// 顶端加了本 REFERENCES/思路 两段，**正文一行未改**（md5 见 --note）。
// [2] 同作者的保留谱系（其正文 credit 段自陈，本席逐字保留）：#118374（exact BASE32 engine）·
// #112312/#117569/#118412（根打包/根槽复用/NT 流/底叶替代基）· #86352（mod65536 引擎）。
// [3] duck.ac 用户 saffah_cc_v41_agg1（本账号）：#118613（ROOT_PAD 160 + 工作区相位 928，
// 对手已按其 BASE32 递归图移植）、#118236（三 madd 调度 / 根输出融合 / C 根复用 /
// shift-blend 截断 + 延迟逆置换）、#112006/#117247。以上均在对手正文 credit 段内署名。
// [4] 学术来源（对手正文自陈）：Oded Schwartz, Noa Vaknin, SIAM J. Sci. Comput. (2023) (3.1)
// exact seven-product twelve-add alternative-basis decomposition over a ring.
// 合规/许可：duck.ac 题目页明示「你提交的代码将会被公开，所有人都可见」——对手正文属该站公开提交；
// 本人铁律 §7 明示「允许读对手代码并移植」。原提交正文无独立许可证声明。
// 本文件按 /home/yjp/duck.ac/RULES.md 第 3 节署名引用。
// ===== 思路 =====
// 【本发 = **基座交换**（不是新臂、不是仪器）：对手 pdoom 在 #118694/#118708 把实现**整体换掉**
// （源 36,878 B ↔ 我方 73,368 B；BASE 32、TILE_PAD 16、ALTMAX 64、native2x32_cache3），
// 一次拿到 541.220828 → 539.871670。我方现役 #118613 = 544.198941 ⇒ 落后对手 **4.327271 ms**。
// 【为什么发】本账号 mine 现处 **两分支皆红**（宽支 1.005·T+1 = 542.572028 < mine 544.198941，
// 严支 0.99·T+1 = 534.473953）⇒ 发射**不会毁掉任何已到手的绿**（(1302) 的 withholding 前提不成立），
// 且目标原文要求「必须第一时间提交你最先进的实现方式」。发射把缺口 **9.724988 → 5.402712 ms**。
// 【等价性证据（本机，判题机前先跑）】正文与我方现役 #118613 在**同一随机 A/B**（seed 88172645463325252）
// 下 `ck` 逐位相同 = `3323298bda9ca79b`；零输入 A/B 下亦相同 = `8e068c517f9d0383`；
// compulsory 首触页数两者同为 **49547**（A/B/C 24576 + 我方 scratch 24971）。
// 【后续】本件只是**基座**；下一棒的窗口账（TSC 自举窗）在这条新基座上做。
// =================
// New BASE32 kernel by pdoom:2x32, cache3 B vectors, full16 k-pairs.
// All8 products ready before8adds: last3 register products consume B regs,
// final memory madd consumes last A. Same21 retired instructions per pair
// as former4x16cache1 but7 load slots instead of9; B and C use32-col panels.
/*
Credit:
pdoom #118374, https://duck.ac/submission/118374 : exact BASE32 engine,
4-row simultaneous product scheduling, one fully unrolled asm body, and
coarse64 root packing with complete NT cache-line streams.
saffah_cc_v41_agg1 #118613, https://duck.ac/submission/118613 : ROOT_PAD
and workspace address phases, adapted here to the BASE32 recursive graph.
saffah_cc_v41_agg1 #118236, https://duck.ac/submission/118236 : three-madd
scheduling, fused four-quadrant root output, C root raw-input reuse, and
shift/blend truncation with deferred inverse word permutation.
Oded Schwartz and Noa Vaknin, SIAM J. Sci. Comput. (2023), (3.1): exact
seven-product, twelve-add alternative-basis decomposition over a ring.
https://epubs.siam.org/doi/10.1137/22M1502719
Retained lineage:
pdoom #86352 : mod65536 engine and pair-dot products; #112312 : fused root
packing, retired root slot reuse, complete cache-line streams and leaf pads;
#117569 : SIMD-native output and delayed root decode; #118412 : bottom-layer
alternative basis fused at both endpoints and skipping logical leaf padding.
saffah_cc_v41_agg1 #112006/#117247 : peeled initial pair, operand/output
packing, cache phases, three-row scheduling, and compiler options.
saffah_codex_6s_agg2 #110387/#102935 : fused reconstruction, constant
recursion and instruction order. saffah_cc_v41_260924 #96771 : cache phases.
New combination:
Use 32x32 arithmetic leaves and only N=64 alternative-basis products.
Apply the input map in raw 32x32 leaf loads, and the inverse output map in
root reconstruction. Internal arithmetic skips the 16-word physical gap;
coarse64 root streams retain it to finish every 64-byte cache line.
Use C's retired tail as the recursive workspace before final C writeback.
Every output is exact modulo65536, independently of input distribution.
Specialized to the stated n=4096 with separate aligned A, B and C buffers.
*/
#define ALTMAX 64
#define ROOT_PAD 160
#pragma GCC optimize("O3,unroll-loops,web,rename-registers")
#pragma GCC target("avx2")
#include <immintrin.h>
#include <stdint.h>
#include <string.h>
#ifndef TILE_PAD
#define TILE_PAD 16
#endif
#ifndef BASE
#define BASE (1 << 5)
#endif
using U = uint16_t;
static constexpr int MAXN = 4096;
alignas(4096) static U pa_[MAXN * MAXN + (MAXN/BASE)*(MAXN/BASE)*TILE_PAD + 8192], pb_[MAXN * MAXN + (MAXN/BASE)*(MAXN/BASE)*TILE_PAD + 8192];
alignas(4096) static U pc_[MAXN * MAXN + (MAXN/BASE)*(MAXN/BASE)*TILE_PAD + 8192], ws_[MAXN * MAXN + (MAXN/BASE)*(MAXN/BASE)*TILE_PAD + 8192];
static U *pa = pa_ + 1024, *pb = pb_ + 1024, *pc = pc_ + 0, *ws = ws_ + 1024;
static U *final_out;
static inline __m256i ld(const U *p) {
return _mm256_load_si256((const __m256i *)p);
}
static inline void st(U *p, __m256i x) {
_mm256_store_si256((__m256i *)p, x);
}
// The recursive quadrant layout makes every Strassen addition contiguous.
static const U *raw_basis_input;
static inline __m256i raw_basis32(const U *p,bool transformed) {
__m256i v=_mm256_loadu_si256((const __m256i*)p);
if(transformed) v=_mm256_add_epi16(v,_mm256_sub_epi16(
_mm256_loadu_si256((const __m256i*)(p-32*4096)),
_mm256_loadu_si256((const __m256i*)(p-32))));
return v;
}
static inline __m128i raw_basis16(const U *p,bool transformed) {
__m128i v=_mm_loadu_si128((const __m128i*)p);
if(transformed) v=_mm_add_epi16(v,_mm_sub_epi16(
_mm_loadu_si128((const __m128i*)(p-32*4096)),
_mm_loadu_si128((const __m128i*)(p-32))));
return v;
}
static void pack(U *d, const U *s, int n, int stride, bool right) {
if (n > BASE) {
int h = n / 2, q=h*h+(h/BASE)*(h/BASE)*TILE_PAD;
pack(d, s, h, stride, right);
pack(d + q, s + h, h, stride, right);
pack(d + 2*q, s + h*stride, h, stride, right);
pack(d + 3*q, s + h*stride + h, h, stride, right);
} else if (!right) {
const bool transformed=((s-raw_basis_input)&32) && ((s-raw_basis_input)&(32*4096));
for(int i=0;i<n;i+=4) for(int k=0;k<n;k+=16) {
__m256i a=raw_basis32(s+i*stride+k,transformed), b=raw_basis32(s+(i+1)*stride+k,transformed);
__m256i c=raw_basis32(s+(i+2)*stride+k,transformed), e=raw_basis32(s+(i+3)*stride+k,transformed);
__m256i t0=_mm256_unpacklo_epi32(a,b),t1=_mm256_unpacklo_epi32(c,e);
__m256i t2=_mm256_unpackhi_epi32(a,b),t3=_mm256_unpackhi_epi32(c,e);
__m256i u0=_mm256_unpacklo_epi64(t0,t1),u1=_mm256_unpackhi_epi64(t0,t1);
__m256i u2=_mm256_unpacklo_epi64(t2,t3),u3=_mm256_unpackhi_epi64(t2,t3);
st(d,_mm256_permute2x128_si256(u0,u1,0x20));
st(d+16,_mm256_permute2x128_si256(u2,u3,0x20));
st(d+32,_mm256_permute2x128_si256(u0,u1,0x31));
st(d+48,_mm256_permute2x128_si256(u2,u3,0x31));d+=64;
}
} else {
const bool transformed=((s-raw_basis_input)&32) && ((s-raw_basis_input)&(32*4096));
for(int k=0;k<n;k+=2) for(int j=0;j<n;) {
int w=32;
U *v=d+j*n+k*w;
for(int t=0;t<w;t+=16) {
if(t+16<=w) {
__m256i x=raw_basis32(s+k*stride+j+t,transformed);
__m256i y=raw_basis32(s+(k+1)*stride+j+t,transformed);
st(v,_mm256_unpacklo_epi16(x,y));
st(v+16,_mm256_unpackhi_epi16(x,y));v+=32;
} else {
__m128i x=_mm_load_si128((const __m128i*)(s+k*stride+j+t));
__m128i y=_mm_load_si128((const __m128i*)(s+(k+1)*stride+j+t));
_mm_store_si128((__m128i*)v,_mm_unpacklo_epi16(x,y));
_mm_store_si128((__m128i*)(v+8),_mm_unpackhi_epi16(x,y));v+=16;
}
}
j+=w;
}
}
}
static void unpack(U *d, const U *s, int n, int stride) {
if (n > BASE) {
int h = n/2, q=h*h+(h/BASE)*(h/BASE)*TILE_PAD;
unpack(d,s,h,stride);
unpack(d+h,s+q,h,stride);
unpack(d+h*stride,s+2*q,h,stride);
unpack(d+h*stride+h,s+3*q,h,stride);
} else {
for (int i=0;i<n;++i) {
U *dp = d + (size_t)i*stride; const U *sp = s + (size_t)i*n;
int k=0;
for (;k+32<=n;k+=32) {
_mm256_stream_si256((__m256i*)(dp+k), _mm256_load_si256((const __m256i*)(sp+k)));
_mm256_stream_si256((__m256i*)(dp+k+16), _mm256_load_si256((const __m256i*)(sp+k+16)));
}
for (;k<n;k+=16) _mm256_storeu_si256((__m256i*)(dp+k), _mm256_loadu_si256((const __m256i*)(sp+k)));
}
}
}
// ===== s4bj_ : 叶尾改 blend 后，每个 16 字组内被 sigma 置换，decode 前先复原 =====
// sigma = [0,4,1,5,2,6,3,7 | 8,12,9,13,10,14,11,15] (new[j] = old[sigma(j)])
// sigma^-1= [0,2,4,6,1,3,5,7 | 8,10,12,14,9,11,13,15] (old[i] = new[sigma^-1(i)])
alignas(32) static const unsigned char s4bj_si[32] = {
0,1,4,5,8,9,12,13,2,3,6,7,10,11,14,15, 0,1,4,5,8,9,12,13,2,3,6,7,10,11,14,15};
static inline __m256i s4bj_fx(__m256i v) {
return _mm256_shuffle_epi8(v, _mm256_load_si256((const __m256i *)s4bj_si));
}
alignas(32) unsigned short s4aj_m16[16] = {0xFFFF,0,0xFFFF,0,0xFFFF,0,0xFFFF,0,0xFFFF,0,0xFFFF,0,0xFFFF,0,0xFFFF,0};
alignas(32) unsigned char s4ak_sh16[32] = {0,1,4,5,8,9,12,13, 0x80,0x80,0x80,0x80,0x80,0x80,0x80,0x80,0,1,4,5,8,9,12,13, 0x80,0x80,0x80,0x80,0x80,0x80,0x80,0x80};
// One explicit panel/row loop keeps exactly one copy of the large kernel.
static inline void native2x32_cache3(const U *a,const U *b,U *c) {
const U *a_final=a+1024;
intptr_t astep=8; // byte steps8,248 alternate within and across4-row A packs
asm volatile(
"3:\n\t"
"vmovdqa 0(%[b]), %%ymm8\n\t"
"vmovdqa 32(%[b]), %%ymm9\n\t"
"vmovdqa 64(%[b]), %%ymm10\n\t"
"vpbroadcastd 0(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm0\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm1\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm2\n\t"
"vpmaddwd 96(%[b]), %%ymm11, %%ymm3\n\t"
"vpbroadcastd 4(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm4\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm5\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm6\n\t"
"vpmaddwd 96(%[b]), %%ymm11, %%ymm7\n\t"
"vmovdqa 128(%[b]), %%ymm8\n\t"
"vmovdqa 160(%[b]), %%ymm9\n\t"
"vmovdqa 192(%[b]), %%ymm10\n\t"
"vpbroadcastd 16(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 224(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 20(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 224(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 256(%[b]), %%ymm8\n\t"
"vmovdqa 288(%[b]), %%ymm9\n\t"
"vmovdqa 320(%[b]), %%ymm10\n\t"
"vpbroadcastd 32(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 352(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 36(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 352(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 384(%[b]), %%ymm8\n\t"
"vmovdqa 416(%[b]), %%ymm9\n\t"
"vmovdqa 448(%[b]), %%ymm10\n\t"
"vpbroadcastd 48(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 480(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 52(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 480(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 512(%[b]), %%ymm8\n\t"
"vmovdqa 544(%[b]), %%ymm9\n\t"
"vmovdqa 576(%[b]), %%ymm10\n\t"
"vpbroadcastd 64(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 608(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 68(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 608(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 640(%[b]), %%ymm8\n\t"
"vmovdqa 672(%[b]), %%ymm9\n\t"
"vmovdqa 704(%[b]), %%ymm10\n\t"
"vpbroadcastd 80(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 736(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 84(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 736(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 768(%[b]), %%ymm8\n\t"
"vmovdqa 800(%[b]), %%ymm9\n\t"
"vmovdqa 832(%[b]), %%ymm10\n\t"
"vpbroadcastd 96(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 864(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 100(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 864(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 896(%[b]), %%ymm8\n\t"
"vmovdqa 928(%[b]), %%ymm9\n\t"
"vmovdqa 960(%[b]), %%ymm10\n\t"
"vpbroadcastd 112(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 992(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 116(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 992(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 1024(%[b]), %%ymm8\n\t"
"vmovdqa 1056(%[b]), %%ymm9\n\t"
"vmovdqa 1088(%[b]), %%ymm10\n\t"
"vpbroadcastd 128(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 1120(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 132(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 1120(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 1152(%[b]), %%ymm8\n\t"
"vmovdqa 1184(%[b]), %%ymm9\n\t"
"vmovdqa 1216(%[b]), %%ymm10\n\t"
"vpbroadcastd 144(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 1248(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 148(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 1248(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 1280(%[b]), %%ymm8\n\t"
"vmovdqa 1312(%[b]), %%ymm9\n\t"
"vmovdqa 1344(%[b]), %%ymm10\n\t"
"vpbroadcastd 160(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 1376(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 164(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 1376(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 1408(%[b]), %%ymm8\n\t"
"vmovdqa 1440(%[b]), %%ymm9\n\t"
"vmovdqa 1472(%[b]), %%ymm10\n\t"
"vpbroadcastd 176(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 1504(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 180(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 1504(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 1536(%[b]), %%ymm8\n\t"
"vmovdqa 1568(%[b]), %%ymm9\n\t"
"vmovdqa 1600(%[b]), %%ymm10\n\t"
"vpbroadcastd 192(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 1632(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 196(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 1632(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 1664(%[b]), %%ymm8\n\t"
"vmovdqa 1696(%[b]), %%ymm9\n\t"
"vmovdqa 1728(%[b]), %%ymm10\n\t"
"vpbroadcastd 208(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 1760(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 212(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 1760(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 1792(%[b]), %%ymm8\n\t"
"vmovdqa 1824(%[b]), %%ymm9\n\t"
"vmovdqa 1856(%[b]), %%ymm10\n\t"
"vpbroadcastd 224(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 1888(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 228(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 1888(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vmovdqa 1920(%[b]), %%ymm8\n\t"
"vmovdqa 1952(%[b]), %%ymm9\n\t"
"vmovdqa 1984(%[b]), %%ymm10\n\t"
"vpbroadcastd 240(%[a]), %%ymm11\n\t"
"vpmaddwd %%ymm8, %%ymm11, %%ymm12\n\t"
"vpmaddwd %%ymm9, %%ymm11, %%ymm13\n\t"
"vpmaddwd %%ymm10, %%ymm11, %%ymm14\n\t"
"vpmaddwd 2016(%[b]), %%ymm11, %%ymm11\n\t"
"vpbroadcastd 244(%[a]), %%ymm15\n\t"
"vpmaddwd %%ymm8, %%ymm15, %%ymm8\n\t"
"vpmaddwd %%ymm9, %%ymm15, %%ymm9\n\t"
"vpmaddwd %%ymm10, %%ymm15, %%ymm10\n\t"
"vpmaddwd 2016(%[b]), %%ymm15, %%ymm15\n\t"
"vpaddd %%ymm12, %%ymm0, %%ymm0\n\t"
"vpaddd %%ymm13, %%ymm1, %%ymm1\n\t"
"vpaddd %%ymm14, %%ymm2, %%ymm2\n\t"
"vpaddd %%ymm11, %%ymm3, %%ymm3\n\t"
"vpaddd %%ymm8, %%ymm4, %%ymm4\n\t"
"vpaddd %%ymm9, %%ymm5, %%ymm5\n\t"
"vpaddd %%ymm10, %%ymm6, %%ymm6\n\t"
"vpaddd %%ymm15, %%ymm7, %%ymm7\n\t"
"vpslld $16, %%ymm1, %%ymm1\n\t"
"vpblendw $0xAA, %%ymm1, %%ymm0, %%ymm0\n\t"
"vmovdqu %%ymm0, 0(%[c])\n\t"
"vpslld $16, %%ymm3, %%ymm3\n\t"
"vpblendw $0xAA, %%ymm3, %%ymm2, %%ymm2\n\t"
"vmovdqu %%ymm2, 32(%[c])\n\t"
"vpslld $16, %%ymm5, %%ymm5\n\t"
"vpblendw $0xAA, %%ymm5, %%ymm4, %%ymm4\n\t"
"vmovdqu %%ymm4, 64(%[c])\n\t"
"vpslld $16, %%ymm7, %%ymm7\n\t"
"vpblendw $0xAA, %%ymm7, %%ymm6, %%ymm6\n\t"
"vmovdqu %%ymm6, 96(%[c])\n\t"
"add %[astep], %[a]\n\t"
"xor $240, %[astep]\n\t"
"add $128, %[c]\n\t"
"cmp %[a_final], %[a]\n\t"
"jb 3b\n\t"
: [a] "+&r"(a), [c] "+&r"(c), [astep] "+&r"(astep)
: [b] "r"(b), [a_final] "r"(a_final)
: "cc", "memory", "ymm0", "ymm1", "ymm2", "ymm3", "ymm4", "ymm5", "ymm6", "ymm7", "ymm8", "ymm9", "ymm10", "ymm11", "ymm12", "ymm13", "ymm14", "ymm15");
}
static void base(const U *a,const U *b,U *c,int n) {
native2x32_cache3(a,b,c);
}
static inline void emit_native(U *dst,const U *s,int stride) {
for(int row=0;row<4;++row) {
U *d=dst+(size_t)row*stride;
_mm256_stream_si256((__m256i*)(d+0),s4bj_fx(ld(s+32*row)));
_mm256_stream_si256((__m256i*)(d+16),s4bj_fx(ld(s+32*row+16)));
}
}
template<bool Sub>
static inline void combine(U *d,const U *a,const U *b,int len) {
#pragma GCC unroll 1
for(int chunk=0;chunk<len;chunk+=1024+TILE_PAD) {
#pragma GCC unroll 4
for(int j=0;j<1024;j+=16) {
int i=chunk+j;
__m256i x=ld(a+i),y=ld(b+i);
st(d+i,Sub?_mm256_sub_epi16(x,y):_mm256_add_epi16(x,y));
}
}
}
// At the root, the three completed packed quadrants can be sent straight
// to their final row-major destinations rather than materialized in pc.
template<int N>
static __attribute__((noinline)) void combine3_unpack(
U *d12,U *d21,U *d22,
const U *p6,const U *p7,const U *p5,
const U *p1,const U *p4,const U *p3,int stride) {
if constexpr (N > BASE) {
constexpr int h=N/2,q=h*h+(h/BASE)*(h/BASE)*TILE_PAD;
combine3_unpack<h>(d12,d21,d22,p6,p7,p5,p1,p4,p3,stride);
combine3_unpack<h>(d12+h,d21+h,d22+h,p6+q,p7+q,p5+q,p1+q,p4+q,p3+q,stride);
combine3_unpack<h>(d12+h*stride,d21+h*stride,d22+h*stride,
p6+2*q,p7+2*q,p5+2*q,p1+2*q,p4+2*q,p3+2*q,stride);
combine3_unpack<h>(d12+h*stride+h,d21+h*stride+h,d22+h*stride+h,
p6+3*q,p7+3*q,p5+3*q,p1+3*q,p4+3*q,p3+3*q,stride);
} else {
alignas(32) U temp[3*128];
for(int block=0;block<1024;block=block+128) {
for(int v=0;v<128;v+=16) {
int idx=block+v;
__m256i u2=_mm256_add_epi16(ld(p1+idx),ld(p6+idx));
__m256i u3=_mm256_add_epi16(u2,ld(p7+idx));
__m256i v5=ld(p5+idx);
st(temp+v,_mm256_add_epi16(_mm256_add_epi16(u2,v5),ld(p3+idx)));
st(temp+128+v,_mm256_sub_epi16(u3,ld(p4+idx)));
st(temp+256+v,_mm256_add_epi16(u3,v5));
}
size_t off=(size_t)(block/32)*stride;
emit_native(d12+off,temp,stride);
emit_native(d21+off,temp+128,stride);
emit_native(d22+off,temp+256,stride);
}
}
}
// Add the surviving P1 into the root C11 product while mapping its packed
// quadrant layout to the final row-major C11 cells.
template<int N>
static __attribute__((noinline)) void unpack_add(U *d,const U *p2,const U *p1,int stride) {
if constexpr(N>BASE) {
constexpr int h=N/2,q=h*h+(h/BASE)*(h/BASE)*TILE_PAD;
unpack_add<h>(d,p2,p1,stride);
unpack_add<h>(d+h,p2+q,p1+q,stride);
unpack_add<h>(d+h*stride,p2+2*q,p1+2*q,stride);
unpack_add<h>(d+h*stride+h,p2+3*q,p1+3*q,stride);
} else {
alignas(32) U temp[128];
for(int block=0;block<1024;block+=128) {
for(int v=0;v<128;v+=16)
st(temp+v,_mm256_add_epi16(ld(p2+block+v),ld(p1+block+v)));
emit_native(d+(size_t)(block/32)*stride,temp,stride);
}
}
}
// Strassen-Winograd: seven products, fifteen additions, two temporaries.
// All operations are in Z/(2^16); truncation never changes the answer.
template<int N>
static __attribute__((noinline)) void root_fuse(
U *d11,U *d12,U *d21,U *d22,
const U *p1,const U *p2,const U *p3,const U *p4,const U *p5,const U *p6,const U *p7,int stride) {
if constexpr(N==64) {
constexpr int q=BASE*BASE+TILE_PAD;
root_fuse<32>(d11,d12,d21,d22,p1,p2,p3,p4,p5,p6,p7,stride);
alignas(32) U tmp[3*4*128];
U *dest[4]={d11,d12,d21,d22};
for(int block=0;block<1024;block+=128) {
for(int child=1;child<=3;child++) {
for(int v=0;v<128;v+=16) {
int idx=child*q+block+v;
__m256i v1=ld(p1+idx),v5=ld(p5+idx);
__m256i u2=_mm256_add_epi16(v1,ld(p6+idx));
__m256i u3=_mm256_add_epi16(u2,ld(p7+idx));
U *t=tmp+(child-1)*512;
st(t+v,_mm256_add_epi16(v1,ld(p2+idx)));
st(t+128+v,_mm256_add_epi16(_mm256_add_epi16(u2,v5),ld(p3+idx)));
st(t+256+v,_mm256_sub_epi16(u3,ld(p4+idx)));
st(t+384+v,_mm256_add_epi16(u3,v5));
}
}
for(int v=0;v<512;v+=16) {
__m256i c22=ld(tmp+1024+v);
st(tmp+v,_mm256_sub_epi16(ld(tmp+v),c22));
st(tmp+512+v,_mm256_sub_epi16(c22,ld(tmp+512+v)));
}
size_t off=(size_t)(block/32)*stride;
for(int r=0;r<4;r++) {
emit_native(dest[r]+off+32,tmp+r*128,stride);
emit_native(dest[r]+off+32*stride,tmp+512+r*128,stride);
emit_native(dest[r]+off+32*stride+32,tmp+1024+r*128,stride);
}
}
} else if constexpr (N > BASE) {
constexpr int h=N/2,q=h*h+(h/BASE)*(h/BASE)*TILE_PAD;
root_fuse<h>(d11,d12,d21,d22,p1,p2,p3,p4,p5,p6,p7,stride);
root_fuse<h>(d11+h,d12+h,d21+h,d22+h,p1+q,p2+q,p3+q,p4+q,p5+q,p6+q,p7+q,stride);
root_fuse<h>(d11+h*stride,d12+h*stride,d21+h*stride,d22+h*stride,
p1+2*q,p2+2*q,p3+2*q,p4+2*q,p5+2*q,p6+2*q,p7+2*q,stride);
root_fuse<h>(d11+h*stride+h,d12+h*stride+h,d21+h*stride+h,d22+h*stride+h,
p1+3*q,p2+3*q,p3+3*q,p4+3*q,p5+3*q,p6+3*q,p7+3*q,stride);
} else {
alignas(32) U temp[4*128];
for(int block=0;block<1024;block+=128) {
for(int v=0;v<128;v+=16) {
int idx=block+v;
__m256i u2=_mm256_add_epi16(ld(p1+idx),ld(p6+idx));
__m256i u3=_mm256_add_epi16(u2,ld(p7+idx));
__m256i v5=ld(p5+idx);
st(temp+v,_mm256_add_epi16(_mm256_add_epi16(u2,v5),ld(p3+idx)));
st(temp+128+v,_mm256_sub_epi16(u3,ld(p4+idx)));
st(temp+256+v,_mm256_add_epi16(u3,v5));
st(temp+384+v,_mm256_add_epi16(ld(p2+idx),ld(p1+idx)));
}
size_t off=(size_t)(block/32)*stride;
emit_native(d12+off,temp,stride);
emit_native(d21+off,temp+128,stride);
emit_native(d22+off,temp+256,stride);
emit_native(d11+off,temp+384,stride);
}
}
}
template<int N>
static __attribute__((noinline)) void mul(const U *a,const U *b,U *c,U *work) {
if constexpr (N<=BASE) {
base(a,b,c,N);
} else if constexpr (N<=ALTMAX) {
constexpr int h=N/2,q=h*h+(h/BASE)*(h/BASE)*TILE_PAD;
const U *a11=a,*a12=a+q,*a21=a+2*q,*a22=a+3*q;
const U *b11=b,*b12=b+q,*b21=b+2*q,*b22=b+3*q;
U *c11=c,*c12=c+q,*c21=c+2*q,*c22=c+3*q;
U *x=work+0,*y=work+2*q+704,*next=work+4*q+640;
mul<h>(a12,b21,c11,next); // m2
mul<h>(a22,b22,c22,next); // m4
combine<false>(x,a21,a22,q);
combine<false>(y,b21,b22,q);
mul<h>(x,y,c12,next); // m5
combine<true>(x,a22,a12,q);
combine<true>(y,b22,b12,q);
mul<h>(x,y,c21,next); // m6
for(int chunk=0;chunk<q;chunk+=1024+TILE_PAD)
_Pragma("GCC unroll 4")
for(int i=chunk;i<chunk+1024;i+=16)
st(c22+i,_mm256_sub_epi16(_mm256_add_epi16(ld(c12+i),ld(c21+i)),_mm256_add_epi16(ld(c11+i),ld(c22+i))));
mul<h>(a11,b11,x,next); // m1
combine<false>(c11,c11,x,q);
combine<true>(y,b22,b11,q);
mul<h>(a21,y,x,next); // m3
combine<false>(c21,c21,x,q);
combine<true>(x,a22,a11,q);
mul<h>(x,b12,y,next); // m7
combine<true>(c12,c12,y,q);
} else {
constexpr int h=N/2,q=h*h+(h/BASE)*(h/BASE)*TILE_PAD;
const U *a11=a,*a12=a+q,*a21=a+2*q,*a22=a+3*q;
const U *b11=b,*b12=b+q,*b21=b+2*q,*b22=b+3*q;
U *c11=c,*c12=c+q,*c21=c+2*q,*c22=c+3*q;
U *x=work+192,*y=work+q+512,*next=work+q+q+512;
combine<true>(y,b22,b12,q);
combine<true>(x,a11,a21,q);
mul<h>(x,y,c21,next); // P7
combine<false>(x,a21,a22,q);
combine<true>(y,b12,b11,q);
mul<h>(x,y,c22,next); // P5
combine<true>(x,x,a11,q);
combine<true>(y,b22,y,q);
mul<h>(x,y,c12,next); // P6
combine<true>(x,a12,x,q);
mul<h>(x,b22,c11,next); // P3
combine<true>(y,y,b21,q);
mul<h>(a22,y,x,next); // P4
mul<h>(a11,b11,y,next); // P1
if constexpr (N == 4096) {
combine3_unpack<2048>(final_out+2048,
final_out+(size_t)2048*4096,
final_out+(size_t)2048*4096+2048,
c12,c21,c22,y,x,c11,4096);
} else {
for(int chunk=0;chunk<q;chunk+=1024+TILE_PAD) for(int i=chunk;i<chunk+1024;i+=16) {
__m256i u2=_mm256_add_epi16(ld(y+i),ld(c12+i));
__m256i u3=_mm256_add_epi16(u2,ld(c21+i));
__m256i p5=ld(c22+i);
st(c12+i,_mm256_add_epi16(_mm256_add_epi16(u2,p5),ld(c11+i)));
st(c21+i,_mm256_sub_epi16(u3,ld(x+i)));
st(c22+i,_mm256_add_epi16(u3,p5));
}
}
mul<h>(a12,b21,c11,next); // P2
if constexpr (N == 4096) unpack_add<2048>(final_out,c11,y,4096);
else combine<false>(c11,c11,y,q);
}
}
static constexpr int RQ=2048*2048+(2048/BASE)*(2048/BASE)*TILE_PAD,RS=RQ+ROOT_PAD;
alignas(4096) static U root_mem[15*RS+4096];
alignas(4096) static U root_tile[4*(64*64+(64/BASE)*(64/BASE)*TILE_PAD)];
template<bool Right>
static void pack_root(const U*s,int n,int offset,U *dest,U *destq,int voff) {
if(n>64){int h=n/2,q=h*h+(h/BASE)*(h/BASE)*TILE_PAD;
pack_root<Right>(s,h,offset,dest,destq,voff);
pack_root<Right>(s+h,h,offset+q,dest,destq,voff);
pack_root<Right>(s+h*4096,h,offset+2*q,dest,destq,voff);
pack_root<Right>(s+h*4096+h,h,offset+3*q,dest,destq,voff);
}else{
pack(root_tile,s,64,4096,Right);
pack(root_tile+(64*64+(64/BASE)*(64/BASE)*TILE_PAD),s+2048,64,4096,Right);
pack(root_tile+2*(64*64+(64/BASE)*(64/BASE)*TILE_PAD),s+2048*4096,64,4096,Right);
pack(root_tile+3*(64*64+(64/BASE)*(64/BASE)*TILE_PAD),s+2048*4096+2048,64,4096,Right);
U *r0=destq+offset,*r1=r0+RS,*r2=r1+RS,*v7=dest+offset+voff*RS,*v5=v7+RS,*v6=v5+RS,*v34=v6+RS;
for(int i=0;i<(64*64+(64/BASE)*(64/BASE)*TILE_PAD);i+=32){
__m256i a=ld(root_tile+i),b=ld(root_tile+(64*64+(64/BASE)*(64/BASE)*TILE_PAD)+i),c=ld(root_tile+2*(64*64+(64/BASE)*(64/BASE)*TILE_PAD)+i),d=ld(root_tile+3*(64*64+(64/BASE)*(64/BASE)*TILE_PAD)+i);
__m256i aa=ld(root_tile+i+16),bb=ld(root_tile+(64*64+(64/BASE)*(64/BASE)*TILE_PAD)+i+16),cc=ld(root_tile+2*(64*64+(64/BASE)*(64/BASE)*TILE_PAD)+i+16),dd=ld(root_tile+3*(64*64+(64/BASE)*(64/BASE)*TILE_PAD)+i+16);
_mm256_stream_si256((__m256i*)(r0+i),a);_mm256_stream_si256((__m256i*)(r0+i+16),aa);
_mm256_stream_si256((__m256i*)(r1+i),Right?c:b);_mm256_stream_si256((__m256i*)(r1+i+16),Right?cc:bb);
_mm256_stream_si256((__m256i*)(r2+i),d);_mm256_stream_si256((__m256i*)(r2+i+16),dd);
__m256i x7=Right?_mm256_sub_epi16(d,b):_mm256_sub_epi16(a,c);
__m256i xx7=Right?_mm256_sub_epi16(dd,bb):_mm256_sub_epi16(aa,cc);
_mm256_stream_si256((__m256i*)(v7+i),x7);_mm256_stream_si256((__m256i*)(v7+i+16),xx7);
__m256i x5=Right?_mm256_sub_epi16(b,a):_mm256_add_epi16(c,d);
__m256i xx5=Right?_mm256_sub_epi16(bb,aa):_mm256_add_epi16(cc,dd);
_mm256_stream_si256((__m256i*)(v5+i),x5);_mm256_stream_si256((__m256i*)(v5+i+16),xx5);
__m256i x6=Right?_mm256_sub_epi16(d,x5):_mm256_sub_epi16(x5,a);
__m256i xx6=Right?_mm256_sub_epi16(dd,xx5):_mm256_sub_epi16(xx5,aa);
_mm256_stream_si256((__m256i*)(v6+i),x6);_mm256_stream_si256((__m256i*)(v6+i+16),xx6);
__m256i x34=Right?_mm256_sub_epi16(x6,c):_mm256_sub_epi16(b,x6);
__m256i xx34=Right?_mm256_sub_epi16(xx6,cc):_mm256_sub_epi16(bb,xx6);
_mm256_stream_si256((__m256i*)(v34+i),x34);_mm256_stream_si256((__m256i*)(v34+i+16),xx34);
}
}
}
void matrix_multiply(int n,const short*A,const short*B,short*C){
U *cq=(U*)C; // 借调用方 C 区（题面: 非 const、启动初值 0）作 3 个纯输入根槽
U *ar=root_mem,*br=ar+4*RS,*pr=br+7*RS; // root_mem 15 -> 12 槽
U *work=cq+3*RS+928;
raw_basis_input=(const U*)A;
pack_root<false>((const U*)A,2048,0,ar,cq,0);
raw_basis_input=(const U*)B;
pack_root<true>((const U*)B,2048,0,br,br,3);
_mm_mfence();
const U *a11=cq,*a12=cq+RS,*a22=cq+2*RS,*s7=ar,*s5=ar+RS,*s6=ar+2*RS,*s3=ar+3*RS;
const U *b11=br,*b21=br+RS,*b22=br+2*RS,*t7=br+3*RS,*t5=br+4*RS,*t6=br+5*RS,*t4=br+6*RS;
U *p1=ar+2*RS,*p2=br+5*RS,*p3=ar+RS,*p4=br+4*RS,*p5=ar,*p6=br+3*RS,*p7=pr;
mul<2048>(s7,t7,p7,work);mul<2048>(s5,t5,p5,work);mul<2048>(s6,t6,p6,work);
mul<2048>(s3,b22,p3,work);mul<2048>(a22,t4,p4,work);mul<2048>(a11,b11,p1,work);mul<2048>(a12,b21,p2,work);
U *out=(U*)C;
root_fuse<2048>(out,out+2048,out+2048*4096,out+2048*4096+2048,p1,p2,p3,p4,p5,p6,p7,4096);_mm_sfence();
}
| Compilation | N/A | N/A | Compile OK | Score: N/A | 显示更多 |
| Testcase #1 | 539.887 ms | 129 MB + 568 KB | Accepted | Score: 100 | 显示更多 |