#define DUCK_PROBE_MODE 0
// Diagnostic only: this file is NOT a faster sorting submission.
// MODE 0 sorts normally. Modes 1..4 sort exactly once, then deliberately
// wait for the measured duration of one radix-distribution phase.
// No standard output, OS calls, threads, or extra data-sized buffers are used
// for measurement. The sorting algorithm is the checked V4 implementation.
#ifndef DUCK_PROBE_MODE
#define DUCK_PROBE_MODE 0
#endif
static_assert(DUCK_PROBE_MODE >= 0 && DUCK_PROBE_MODE <= 4, "mode must be 0..4");
#pragma GCC target("avx2,bmi,bmi2,popcnt,lzcnt")
#include <bits/stdc++.h>
#include <immintrin.h>
// Derived from the user's four-pass compressed radix implementation.
// Pointer tables contain absolute destination addresses; no change to digits,
// sampling budgets, histogram placement, PDEP, or original unroll factors.
unsigned long long duck_ticks[8]={};
alignas(64) static volatile unsigned duck_probe_config[16]={0x4455434bU,DUCK_PROBE_MODE};
static inline unsigned long long duck_stamp() {
_mm_mfence();
_mm_lfence();
const unsigned long long t=__rdtsc();
_mm_lfence();
return t;
}
namespace duck_sort_v4_detail {
template <int STRIDE>
std::array<int, 256> get_population_upper_bounds(uint8_t* A, int N, int budget, int sample_size) {
std::array<int, 256> results;
results.fill(0);
size_t n = (size_t)sample_size;
// 1. Calculate Cache Line Alignment Info
uintptr_t start_addr = (uintptr_t)A;
// Align up to next 64-byte boundary
uintptr_t aligned_start = (start_addr + 63) & ~63ULL;
// Align down end address
uintptr_t end_addr_exclusive = start_addr + (size_t)N * STRIDE;
uintptr_t aligned_end = end_addr_exclusive & ~63ULL;
if (aligned_end <= aligned_start) {
// Not enough data for aligned sampling, fallback to full scan
for (int i = 0; i < N; ++i) results[A[(size_t)i * STRIDE]]++;
return results;
}
size_t num_lines = (aligned_end - aligned_start) / 64;
// Safety check: if no cache lines available, fallback to full scan
if (num_lines == 0) {
for (int i = 0; i < N; ++i) results[A[(size_t)i * STRIDE]]++;
return results;
}
// Determine the offset pattern for the FIRST aligned block
// We need (aligned_start + off) % STRIDE == start_addr % STRIDE
size_t diff = aligned_start - start_addr;
int base_offset = (STRIDE - (diff % STRIDE)) % STRIDE;
// 2. Adjust Sample Size to be in terms of cache lines
// Average items per line
int items_per_line_approx = 64 / STRIDE;
size_t lines_to_sample = (n + items_per_line_approx - 1) / items_per_line_approx;
// Cap at available lines
if (lines_to_sample > num_lines) lines_to_sample = num_lines;
// Recalculate actual n for statistics
// (This is an approximation if stride=3 because different lines have different counts,
// but for large N it converges)
// For Stride=4, count is always 16.
// For Stride=3, count is 21 or 22 (avg 21.33).
// optimizing: just counting actually sampled items is better,
// but user code expects 'n' to be passed to math formulas.
// We will count exact sampled items in the loop.
// 3. Sparse Sampling of Cache Lines
std::array<int, 256> sample_counts;
sample_counts.fill(0);
size_t actual_sampled_count = 0;
static std::mt19937 gen;
const uint32_t mod_blocks = (uint32_t)num_lines;
const uint64_t mu = ((unsigned __int128)1 << 64) / mod_blocks;
for (size_t i = 0; i < lines_to_sample; ++i) {
// Random Block Index
uint32_t x = gen();
uint64_t q = ((unsigned __int128)x * mu) >> 64;
uint32_t blk_idx = x - q * mod_blocks;
if (blk_idx >= mod_blocks) blk_idx -= mod_blocks;
uint8_t* p_line = (uint8_t*)(aligned_start + (size_t)blk_idx * 64);
// Calculate offset for this specific block
// Block addr changes by 64. 64 % 3 = 1. 64 % 4 = 0.
// offset_new = (offset_old - delta_addr) % STRIDE
// delta_addr = blk_idx * 64
int current_offset;
if constexpr (STRIDE == 4) {
current_offset = base_offset;
} else {
// STRIDE == 3
// shift = (blk_idx) % 3
// off = (base - shift) % 3
int shift = blk_idx % 3;
current_offset = base_offset - shift;
if (current_offset < 0) current_offset += 3;
}
// Fetch fixed number of items per cache line
// Safe max index check:
// Stride 4: offset max 3. count 16. max idx = 3 + 15*4 = 63 < 64.
// Stride 3: offset max 2. count 21. max idx = 2 + 20*3 = 62 < 64.
const int ITEMS = 64 / STRIDE;
#pragma GCC unroll 21
for (int k = 0; k < ITEMS; ++k) {
sample_counts[p_line[current_offset + k * STRIDE]]++;
}
actual_sampled_count += ITEMS;
}
n = actual_sampled_count;
// 2. 二分查找最优 Z 值
// 目标：找到最大的 Z，使得 Sum(UpperBounds(Z)) <= Budget
double low_z = 0.0;
double high_z = 10.0;
double best_z = 0.0;
double n_double = (double)n;
double N_double = (double)N;
double fpc = (double)(N - n) / (double)(N - 1);
if (fpc < 0) fpc = 0; // Safety
// 预计算 p_hat 以加速循环
std::array<double, 256> p_hats;
for(int i=0; i<256; ++i) p_hats[i] = sample_counts[i] / n_double;
for (int iter = 0; iter < 20; ++iter) {
double mid_z = (low_z + high_z) * 0.5;
double z2 = mid_z * mid_z;
double div_factor = 1.0 / (1.0 + z2 / n_double);
long long current_sum = 0;
for (int i = 0; i < 256; ++i) {
double p_hat = p_hats[i];
// Wilson Score Interval
double term1 = p_hat + z2 / (2.0 * n_double);
double variance_term = (p_hat * (1.0 - p_hat) / n_double) * fpc;
if (variance_term < 0) variance_term = 0;
double term2 = mid_z * std::sqrt(variance_term + z2 / (4.0 * n_double * n_double));
double p_upper = (term1 + term2) * div_factor;
int limit = (int)std::ceil(N_double * p_upper);
current_sum += limit;
}
if (current_sum <= budget) {
best_z = mid_z;
low_z = mid_z;
} else {
high_z = mid_z;
}
}
// 3. 使用最佳 Z 生成最终结果
double z = best_z;
double z2 = z * z;
double div_factor = 1.0 / (1.0 + z2 / n_double);
for (int i = 0; i < 256; ++i) {
double p_hat = p_hats[i];
double term1 = p_hat + z2 / (2.0 * n_double);
double variance_term = (p_hat * (1.0 - p_hat) / n_double) * fpc;
if (variance_term < 0) variance_term = 0;
double term2 = z * std::sqrt(variance_term + z2 / (4.0 * n_double * n_double));
double p_upper = (term1 + term2) * div_factor;
int limit = (int)std::ceil(N_double * p_upper);
if (limit > N) limit = N;
results[i] = limit;
}
return results;
}
using namespace std;
const int n = 1e8;
const int PREFETCH_DIST = 64; // 元素个数：Pass1(256B), Pass2(192B), Pass3/4(128B)
// 辅助函数：向地址 p 写入 3 字节 (利用 uint32 覆盖写，需保证 buffer 有 padding)
// Input val: [B0, B1, B2, X] (Little Endian) -> Writes B0, B1, B2
inline void store3(uint8_t* __restrict__ p, uint32_t val) {
std::memcpy(p, &val, 4);
}
// 辅助函数：向地址 p 写入 2 字节
inline void store2(uint8_t* __restrict__ p, uint16_t val) {
std::memcpy(p, &val, 2);
}
inline uint32_t load3(const uint8_t* p) {
uint32_t v; std::memcpy(&v,p,4); return v;
}
inline uint16_t load2(const uint8_t* p) {
uint16_t v; std::memcpy(&v,p,2); return v;
}
// Verify that a full tile can be scattered without leaving the allocation.
// Bucket overlap is detected after the pass; the original source stays intact.
inline bool top_tile_fits(uint8_t* const* p, const uint8_t* limit) {
const __m256i bound=_mm256_set1_epi64x(reinterpret_cast<intptr_t>(limit));
__m256i bad=_mm256_setzero_si256();
for (int k=0;k<256;k+=4) {
const __m256i q=_mm256_loadu_si256(reinterpret_cast<const __m256i*>(p+k));
bad=_mm256_or_si256(bad,_mm256_cmpgt_epi64(q,bound));
}
return _mm256_movemask_epi8(bad)==0;
}
template<int FixedN>
void sort_impl(uint* a, int __n) {
const int n=FixedN ? FixedN : __n;
if(n<=1)return;
if(n<4096){std::sort(a,a+n);return;}
// ---------------------------------------------------------
// Pass 1: Global MSD (Partition by B3)
// Read: a (4 bytes) -> Write: b (3 bytes: [B0, B1, B2])
// ---------------------------------------------------------
unsigned long long phase_clock=duck_stamp();
uint cnt_global[256];
// memset(cnt_global, 0, sizeof(cnt_global)); // No longer needed beforehand
// 1.1 统计 B3 (Sampling & Upper Bounds)
// Budget set to n * 1.47 (47% over-provisioning)
int budget = (int)(n * 1.47);
int sample_size = 20000;
// A 是 (uint8_t*)a + 3 (B3 byte), stride = 4
auto bounds = get_population_upper_bounds<4>((uint8_t*)a + 3, n, budget, sample_size);
// 1.2 计算 B3 Offset (Bytes in b)
// 增加 4 字节 Padding 以安全使用 store3
uint ptr_global[256];
uint32_t offset_b3 = 0;
for (int i = 0; i < 256; i++) {
ptr_global[i] = offset_b3;
offset_b3 += bounds[i] * 3; // Use Upper Bound
}
// 申请 b 数组
constexpr int TILE=16384;
const size_t main_bytes=size_t(budget)*3;
uint8_t* b=static_cast<uint8_t*>(std::malloc(main_bytes+3*TILE+4096));
if(!b){std::sort(a,a+n);return;}
bool incomplete=false;
{const auto now=duck_stamp();duck_ticks[0]+=now-phase_clock;phase_clock=now;}
// 1.3 执行 Pass 1 分发
{
uint* __restrict__ src = a;
uint8_t* __restrict__ dst = b;
uint p[256];
uint8_t* pp[256];
for(int z=0;z<256;++z)pp[z]=b+ptr_global[z];
int i=0;
for(;i<n;) {
if (__builtin_expect(!top_tile_fits(pp,b+main_bytes),0)) {
incomplete=true;break;
}
const int end=std::min(n,i+TILE);
for(;i+16<=end;i+=16) {
_mm_prefetch(reinterpret_cast<const char*>(
reinterpret_cast<uintptr_t>(src)+size_t(i+PREFETCH_DIST)*4),_MM_HINT_NTA);
#pragma GCC unroll 16
for(int j=0;j<16;++j) {
const unsigned v=src[i+j], k=v>>24;
uint8_t* q=pp[k];
store3(q,v); pp[k]=q+3;
}
}
for(;i<end;++i){const unsigned v=src[i],k=v>>24;store3(pp[k],v);pp[k]+=3;}
}
// Reconstruct exact counts from pointer progress
for(int k=0; k<256; ++k) {
cnt_global[k] = (pp[k] - (b+ptr_global[k])) / 3;
}
}
bool retry_global=incomplete;
if(incomplete) {
std::memset(cnt_global,0,sizeof(cnt_global));
for(int i=0;i<n;++i)++cnt_global[a[i]>>24];
}
for(int k=0;k<256;++k)
retry_global |= cnt_global[k] && cnt_global[k]>=static_cast<unsigned>(bounds[k]);
if(retry_global) {
unsigned off=0;
uint8_t* pp[256];
for(int k=0;k<256;++k) {
ptr_global[k]=off;pp[k]=b+off;
off+=3*cnt_global[k]+4; // Allow the fourth byte of store3.
}
int i=0;
for(;i+16<=n;i+=16) {
#pragma GCC unroll 16
for(int j=0;j<16;++j) {
unsigned v=a[i+j],k=v>>24;store3(pp[k],v);pp[k]+=3;
}
}
for(;i<n;++i){unsigned v=a[i],k=v>>24;store3(pp[k],v);pp[k]+=3;}
}
{const auto now=duck_stamp();duck_ticks[1]+=now-phase_clock;phase_clock=now;}
uint8_t* scratch=nullptr;
size_t scratch_capacity=0;
// ---------------------------------------------------------
// 分段处理：遍历 B3 的每一个 Bucket
// ---------------------------------------------------------
uint8_t* a_u8 = (uint8_t*)a;
// 局部直方图缓存
uint cnt0[256];
uint cnt1[256];
uint cnt2[256];
uint ptr0[256]; // Pass 2 (Write a) pointers
uint ptr1[256]; // Pass 3 (Write b) pointers
uint ptr2[256]; // Pass 4 (Write a Final) pointers
uint32_t a_offset_start = 0; // index offset in a (Writing Final)
for (int i_b3 = 0; i_b3 < 256; i_b3++) {
int count = cnt_global[i_b3];
if (count == 0) continue;
uint8_t* seg_b_in = b + ptr_global[i_b3];
if(count<1024) {
uint* out=a+a_offset_start;
for(int j=0;j<count;++j)out[j]=(unsigned(i_b3)<<24)|(load3(seg_b_in+j*3)&0xffffffu);
std::sort(out,out+count);a_offset_start+=count;continue;
}
// Pass 2 Output (Temporary in a)
// Prefer the unused suffix of a; the range is checked before scattering.
uint8_t* seg_a_temp = a_u8 + (a_offset_start * 4);
// -----------------------------------------------------
// Step 2: Use Sampling for Pointers & Init Counters
// -----------------------------------------------------
// Use sampling to estimate B0 upper bounds for Pass 2 (ptr0)
// Budget logic:
// Pass 2 writes 2 bytes per item into a space reserved for 4 bytes per item (Final Output array).
// Effectively, we have capacity for count * 2 items of size 2 bytes.
int budget_pass2 = count * 2;
int sample_size = 5000;
// get_population_upper_bounds will default to stride 3 because we pass stride=3?
// Wait, function signature is (uint8_t* A, int N, int budget, int stride, int sample_size)
// seg_b_in has data [B0, B1, B2]... So stride=3, offset=0 is B0.
auto bounds = get_population_upper_bounds<3>(seg_b_in, count, budget_pass2, sample_size);
// Calculate ptr0 (bucket start offsets in 'a')
uint32_t tmp = 0;
for(int k=0; k<256; k++) {
ptr0[k] = tmp;
tmp += bounds[k] * 2;
}
// Before scattering, reserve enough address range even when EVERY
// element enters the last bucket. The source b is not modified here.
const size_t need=std::max(size_t(tmp)+size_t(count)*2+8,
size_t(count)*2+1032);
if(need>size_t(n-a_offset_start)*4) {
if(need>scratch_capacity) {
uint8_t* next=static_cast<uint8_t*>(std::malloc(need));
if(!next) {
// Earlier high-byte buckets are already final in a.
// All remaining raw values are still intact in b.
unsigned t=a_offset_start;
for(int h=i_b3;h<256;++h)
for(unsigned j=0;j<cnt_global[h];++j)
a[t++]=(unsigned(h)<<24)|(load3(b+ptr_global[h]+3*j)&0xffffffu);
std::sort(a+a_offset_start,a+n);
std::free(scratch);std::free(b);return;
}
std::free(scratch);scratch=next;scratch_capacity=need;
}
seg_a_temp=scratch;
}
{const auto now=duck_stamp();duck_ticks[2]+=now-phase_clock;phase_clock=now;}
// Initialize cnt1, cnt2 for exact counting during Pass 2
memset(cnt1, 0, sizeof(cnt1));
memset(cnt2, 0, sizeof(cnt2));
// cnt0 will be recovered from pointer progress after Pass 2
// -----------------------------------------------------
// Pass 2: LSD Step 1 (Key B0)
// Read b (3B: B0,B1,B2) -> Write a (2B: B1,B2)
// AND compute exact histograms for B1, B2
// -----------------------------------------------------
{
uint p[256];
uint8_t* pp[256];
for(int z=0;z<256;++z) pp[z]=seg_a_temp+ptr0[z];
uint8_t* src = seg_b_in;
uint8_t* dst = seg_a_temp;
int k = 0;
for (; k <= count - 16; k += 16) {
_mm_prefetch(reinterpret_cast<const char*>(reinterpret_cast<uintptr_t>(src)+size_t(k+PREFETCH_DIST)*3), _MM_HINT_T0);
#pragma GCC unroll 16
for (int j = 0; j < 16; j++) {
uint32_t val = load3(src + (k + j) * 3);
uint8_t key = val & 0xFF; // B0
// Count B1 (val >> 8 & 0xFF) and B2 (val >> 16 & 0xFF)
cnt1[(val >> 8) & 0xFF]++;
cnt2[(val >> 16) & 0xFF]++;
// Store [B1, B2] (val >> 8)
store2(pp[key],val>>8);pp[key]+=2;
}
}
for (; k < count; k++) {
uint32_t val = load3(src + k * 3);
uint8_t key = val & 0xFF;
cnt1[(val >> 8) & 0xFF]++;
cnt2[(val >> 16) & 0xFF]++;
store2(pp[key],val>>8);pp[key]+=2;
}
// Post-Pass 2: Recover exact cnt0 and compute ptr1, ptr2
bool retry = false;
uint32_t tmp1 = 0;
uint32_t tmp2 = 0;
for(int k=0; k<256; k++) {
// Recover cnt0 from pointer progress (p - ptr0) / 2
cnt0[k] = (pp[k] - (seg_a_temp+ptr0[k])) >> 1;
retry |= cnt0[k] > bounds[k];
ptr1[k] = tmp1;
tmp1 += cnt1[k] * 2 + 4; // Padding
ptr2[k] = tmp2;
tmp2 += cnt2[k]; // No Padding (Dense)
}
if (retry) {
// Recalculate ptr0 with exact counts
uint32_t tmp = 0;
for(int k=0; k<256; k++) {
ptr0[k] = tmp;
tmp += cnt0[k] * 2 + 4;
}
// Rerun Pass 2 (Distribution Only, no counting)
uint p_retry[256];
memcpy(p_retry, ptr0, sizeof(p_retry));
uint8_t* src = seg_b_in;
uint8_t* dst = seg_a_temp;
int k = 0;
for (; k <= count - 16; k += 16) {
_mm_prefetch(reinterpret_cast<const char*>(reinterpret_cast<uintptr_t>(src)+size_t(k+PREFETCH_DIST)*3), _MM_HINT_T0);
#pragma GCC unroll 16
for (int j = 0; j < 16; j++) {
uint32_t val = load3(src + (k + j) * 3);
uint8_t key = val & 0xFF; // B0
store2(dst + p_retry[key], val >> 8);
p_retry[key] += 2;
}
}
for (; k < count; k++) {
uint32_t val = load3(src + k * 3);
uint8_t key = val & 0xFF;
store2(dst + p_retry[key], val >> 8);
p_retry[key] += 2;
}
}
}
{const auto now=duck_stamp();duck_ticks[3]+=now-phase_clock;phase_clock=now;}
// -----------------------------------------------------
// Pass 3: LSD Step 2 (Key B1)
// Read a (2B: B1,B2) -> Write b (2B: B0,B2)
// Iterate B0 buckets to restore B0
// -----------------------------------------------------
{
// count>=1024, so 2*count+1024 fits in the consumed 3-byte input bucket.
uint8_t* dst_base = seg_b_in;
uint p[256];
uint8_t* pp[256];
for(int z=0;z<256;++z) pp[z]=dst_base+ptr1[z];
// Iterate over B0 buckets (Pass 2 output)
for (int b0 = 0; b0 < 256; b0++) {
int c = cnt0[b0];
if (c == 0) continue;
uint8_t* src = seg_a_temp + ptr0[b0];
uint16_t val_b0 = b0;
int k = 0;
for (; k <= c - 21; k += 21) {
_mm_prefetch(reinterpret_cast<const char*>(reinterpret_cast<uintptr_t>(src)+size_t(k+PREFETCH_DIST)*2), _MM_HINT_T0);
#pragma GCC unroll 21
for (int j = 0; j < 21; j++) {
// Read [B1, B2]
uint16_t val = load2(src + (k + j) * 2);
uint8_t key = val & 0xFF; // B1
// Construct [B0, B2]
// We store B0 at low byte, B2 at high byte.
// val & 0xFF00 is (B2 << 8).
uint16_t new_val = val_b0 | (val & 0xFF00);
store2(pp[key],new_val);pp[key]+=2;
}
}
for (; k < c; k++) {
uint16_t val = load2(src + k * 2);
uint8_t key = val & 0xFF;
store2(pp[key],val_b0 | (val & 0xFF00));pp[key]+=2;
}
}
}
{const auto now=duck_stamp();duck_ticks[4]+=now-phase_clock;phase_clock=now;}
// -----------------------------------------------------
// Pass 4: LSD Step 3 (Key B2) & Finalize
// Read b (2B: B0,B2) -> Write a (4B: Full)
// Iterate B1 buckets to restore B1
// -----------------------------------------------------
{
uint* dst_base = a + a_offset_start;
uint8_t* src_base = seg_b_in;
uint p[256];
unsigned* pp[256];
for(int z=0;z<256;++z)pp[z]=dst_base+ptr2[z];
uint32_t val_b3_shifted = i_b3 << 24;
// Iterate over B1 buckets (Pass 3 output)
for (int b1 = 0; b1 < 256; b1++) {
int c = cnt1[b1];
if (c == 0) continue;
uint8_t* src = src_base + ptr1[b1];
// Common High bits: B3 | B1 << 8
// We will OR this with PDEP result
uint32_t common_bits = val_b3_shifted | (b1 << 8);
int k = 0;
for (; k <= c - 32; k += 32) {
_mm_prefetch(reinterpret_cast<const char*>(reinterpret_cast<uintptr_t>(src)+size_t(k+PREFETCH_DIST)*2), _MM_HINT_T0);
#pragma GCC unroll 32
for (int j = 0; j < 32; j++) {
// Read [B0, B2]
uint32_t val = load2(src + (k + j) * 2);
// Key is B2 (High byte of val)
uint8_t key = val >> 8;
// Reconstruct:
// val has bits: 0-7 (B0), 8-15 (B2)
// Target: 0-7 (B0), 16-23 (B2)
// PDEP Mask: 0x00FF00FF (Deposit val bits 0-7 to 0-7, 8-15 to 16-23)
uint32_t scattered = _pdep_u32(val, 0x00FF00FF);
*pp[key]++ = common_bits | scattered;
}
}
for (; k < c; k++) {
uint32_t val = load2(src + k * 2);
uint8_t key = val >> 8;
uint32_t scattered = _pdep_u32(val, 0x00FF00FF);
*pp[key]++ = common_bits | scattered;
}
}
}
{const auto now=duck_stamp();duck_ticks[5]+=now-phase_clock;phase_clock=now;}
// Update offsets
a_offset_start += count;
}
std::free(scratch);
std::free(b);
}
} // namespace duck_sort_v4_detail
void sort(unsigned* a,int n) {
static_assert(sizeof(unsigned)==4,"32-bit unsigned required");
for(unsigned i=0;i<8;++i)duck_ticks[i]=0;
const unsigned mode=duck_probe_config[1];
const auto begin=duck_stamp();
if(n==100000000)duck_sort_v4_detail::sort_impl<100000000>(a,n);
else duck_sort_v4_detail::sort_impl<0>(a,n);
const auto finished=duck_stamp();
duck_ticks[6]=finished-begin;
// Slots: 0 global preparation; 1 pass1; 2 local preparation;
// 3 pass2; 4 pass3; 5 pass4; 6 normal sort; 7 deliberate wait.
unsigned long long extra=0;
if(mode==1)extra=duck_ticks[1];
else if(mode>=2 && mode<=4)extra=duck_ticks[mode+1];
const auto waiting=duck_stamp();
while(__rdtsc()-waiting<extra)_mm_pause();
duck_ticks[7]=duck_stamp()-waiting;
}
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