bench.cpp

// bench.cpp - comprehensive lxySort vs std::sort benchmark
// UTF-8 源码(中文)。注意: exe 输出为 UTF-8, 中文控制台请 chcp 65001
// Usage: bench [N]      N = array size, default 100000
// Build: g++ -O2 -std=c++17 -fopenmp bench.cpp -o bench

#ifdef _WIN32
#define NOMINMAX
#define WIN32_LEAN_AND_MEAN
#include <windows.h>
struct Clock { static double ms() {
    static LARGE_INTEGER f; static bool init=false;
    if(!init){ QueryPerformanceFrequency(&f); init=true; }
    LARGE_INTEGER c; QueryPerformanceCounter(&c);
    return (double)c.QuadPart * 1000.0 / (double)f.QuadPart;
}};
#else
#include <chrono>
using namespace std::chrono;
struct Clock { static double ms() {
    return (double)duration_cast<nanoseconds>(steady_clock::now().time_since_epoch()).count()/1e6;
}};
#endif

#include <algorithm>
#include <vector>
#include <string>
#include <random>
#include <cstdio>
#include <cstdlib>
#include <climits>
#include <chrono>
#include <functional>
using namespace std;

#include "lxysort.hpp"

static mt19937 rng(20240);

// ============ timing (best-of-N) ============
template<typename T>
static double timeLxy(vector<T>& v, const char** alg=nullptr) {
    bool tiny = v.size()<1000;
    int reps = tiny ? 400 : 12;
    if (tiny) {
        // warmup 50 iters (thread_local init + branch-predictor), then average 400:
        // a single best is below QPC resolution (collapses to 0) and median is
        // skewed by first-call stalls; warmup+mean is accurate and unbiased.
        for (int r=0;r<50;r++){ vector<T> c=v;
            if (r==0 && alg) { const char* a=nullptr; lxySortTrace(c,&a); if(alg)*alg=a; }
            else lxySort(c); }
        double sum=0;
        for (int r=0;r<reps;r++){ vector<T> c=v; double s=Clock::ms(); lxySort(c); double e=Clock::ms(); sum+=e-s; }
        return sum/reps;
    }
    double best=1e300;
    for (int r=0;r<reps;r++){ vector<T> c=v;
        double s=Clock::ms();
        if (r==0 && alg) { const char* a=nullptr; lxySortTrace(c,&a); if(alg)*alg=a; }
        else lxySort(c);
        double e=Clock::ms();
        double t=e-s; if (t<best) best=t;
    }
    return best;
}
template<typename T>
static double timeStd(vector<T>& v) {
    bool tiny = v.size()<1000;
    int reps = tiny ? 400 : 12;
    if (tiny) {
        for (int r=0;r<50;r++){ vector<T> c=v; sort(c.begin(),c.end()); }
        double sum=0;
        for (int r=0;r<reps;r++){ vector<T> c=v; double s=Clock::ms(); sort(c.begin(),c.end()); double e=Clock::ms(); sum+=e-s; }
        return sum/reps;
    }
    double best=1e300;
    for (int r=0;r<reps;r++){ vector<T> c=v;
        double s=Clock::ms(); sort(c.begin(),c.end()); double e=Clock::ms();
        double t=e-s; if (t<best) best=t; }
    return best;
}
template<typename T, typename Cmp>
static double timeStdCmp(vector<T>& v, Cmp cmp) {
    bool tiny = v.size()<1000;
    int reps = tiny ? 400 : 12;
    if (tiny) {
        for (int r=0;r<50;r++){ vector<T> c=v; sort(c.begin(),c.end(),cmp); }
        double sum=0;
        for (int r=0;r<reps;r++){ vector<T> c=v; double s=Clock::ms(); sort(c.begin(),c.end(),cmp); double e=Clock::ms(); sum+=e-s; }
        return sum/reps;
    }
    double best=1e300;
    for (int r=0;r<reps;r++){ vector<T> c=v;
        double s=Clock::ms(); sort(c.begin(),c.end(),cmp); double e=Clock::ms();
        double t=e-s; if (t<best) best=t; }
    return best;
}

static int gWins=0, gTotal=0;

template<typename T>
static void runCase(const char* name, vector<T> v) {
    vector<T> ref=v; sort(ref.begin(), ref.end());
    const char* alg=nullptr;
    double t1=timeLxy(v,&alg);
    double t2=timeStd(v);
    vector<T> ck=v; lxySort(ck); bool ok=(ck==ref);
    bool win=t1<t2; gWins+=win; gTotal++;
    printf("[%s]\n", name);
    printf("  lxySort  : %10.6fms  [%s]\n", t1, alg?alg:"-");
    printf("  std::sort: %10.6fms\n", t2);
    printf("  -> %s  |  %.2fx %s\n", ok?"OK":"WRONG",
        (t1>0&&t2>0)?(win?(double)t2/t1:(double)t1/t2):0,
        win?"faster":"slower");
    printf("\n");
}
template<typename T, typename Cmp>
static void runCaseCmp(const char* name, vector<T> v, Cmp cmp) {
    vector<T> ref=v; sort(ref.begin(),ref.end(),cmp);
    vector<T> ck=v; lxySort(ck,cmp); bool ok=(ck==ref);
    double t1=timeLxy(v);
    double t2=timeStdCmp(v,cmp);
    bool win=t1<t2; gWins+=win; gTotal++;
    printf("[%s] (descending)\n", name);
    printf("  lxySort  : %8.3fms\n", t1);
    printf("  std::sort: %8.3fms\n", t2);
    printf("  -> %s  |  %.2fx %s\n\n", ok?"OK":"WRONG",
        (t1>0&&t2>0)?(win?(double)t2/t1:(double)t1/t2):0, win?"faster":"slower");
}

// ---- stability: lxyStableSort must preserve relative order of equal keys ----
struct BenchItem { int k, id; };
static void runStable(const char* name, vector<BenchItem> v) {
    auto byk=[](const BenchItem&x,const BenchItem&y){return x.k<y.k;};
    vector<BenchItem> ref=v; stable_sort(ref.begin(),ref.end(),byk);
    vector<BenchItem> ck=v; lxyStableSort(ck,byk);
    bool ok=true;
    for (size_t i=0;i<ref.size();i++) if (ck[i].k!=ref[i].k || ck[i].id!=ref[i].id){ok=false;break;}
    double t1=1e300,t2=1e300;
    int reps=v.size()<1000?300:8;
    {double b=1e300;for(int r=0;r<reps;r++){auto c=v;double s=Clock::ms();lxyStableSort(c,byk);double e=Clock::ms();if(e-s<b)b=e-s;}t1=b;}
    {double b=1e300;for(int r=0;r<reps;r++){auto c=v;double s=Clock::ms();stable_sort(c.begin(),c.end(),byk);double e=Clock::ms();if(e-s<b)b=e-s;}t2=b;}
    bool win=t1<t2; gWins+=win; gTotal++;
    printf("[%s] (stable)\n", name);
    printf("  lxyStableSort  : %8.3fms\n", t1);
    printf("  std::stable_sort: %7.3fms\n", t2);
    printf("  -> %s (stable OK)  |  %.2fx %s\n\n", ok?"STABLE":"UNSTABLE",
        (t1>0&&t2>0)?(win?(double)t2/t1:(double)t1/t2):0, win?"faster":"slower");
}

// ---- byKey: lxySortByKey(key-extractor) vs manual pair sort ----
template<typename T, typename KF>
static void runByKey(const char* name, vector<T> v, KF kf) {
    // reference: sort by (key, original index)
    vector<pair<long long,int>> pairs; pairs.reserve(v.size());
    for (int i=0;i<(int)v.size();i++) pairs.emplace_back((long long)kf(v[i]), i);
    stable_sort(pairs.begin(),pairs.end(),[](auto&x,auto&y){return x.first<y.first;});
    vector<T> out=v;
    lxySortByKey(out, kf, true);
    bool ok=true;
    for (size_t i=0;i<v.size();i++){
        // out[i] must equal the element whose (key,idx) is pairs[i]
        if (!(kf(out[i])==pairs[i].first)){ok=false;break;}
    }
    double t1=1e300;
    int reps=v.size()<1000?300:8;
    {double b=1e300;for(int r=0;r<reps;r++){auto c=v;double s=Clock::ms();lxySortByKey(c,kf,true);double e=Clock::ms();if(e-s<b)b=e-s;}t1=b;}
    printf("[%s] (byKey)\n", name);
    printf("  lxySortByKey : %8.3fms\n", t1);
    printf("  -> %s\n\n", ok?"OK":"WRONG");
}

int main(int argc, char** argv) {
    int N = (argc > 1) ? atoi(argv[1]) : 100000;
    printf("=== lxySort  vs  std::sort  (N=%d) ===\n\n", N);

    // ================= int =================
    printf("---------- int ----------\n\n");
    auto R_wide  =[&](int n){vector<int>a(n);for(auto&x:a)x=(int)(rng()%1000000000);return a;};       // 0..1e9
    auto R_999999=[&](int n){vector<int>a(n);for(auto&x:a)x=rng()%1000000;return a;};                 // 0..999999
    auto R_999   =[&](int n){vector<int>a(n);for(auto&x:a)x=rng()%1000;return a;};                    // 0..999
    auto R_99    =[&](int n){vector<int>a(n);for(auto&x:a)x=rng()%100;return a;};                     // 0..99
    auto R_9     =[&](int n){vector<int>a(n);for(auto&x:a)x=rng()%10;return a;};                      // 0..9 many dup
    auto R_neg   =[&](int n){vector<int>a(n);for(auto&x:a)x=(int)(rng()%200000-100000);return a;};    // -100k..100k
    auto R_mix   =[&](int n){vector<int>a(n);for(auto&x:a)x=(int)(rng()%2000000000u-1000000000);return a;}; // mixed signs
    auto ASC     =[](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=i;return a;};                    // ascending
    auto ASCrep  =[&](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=i/4;return a;};                 // ascending+repeats
    auto DESC    =[](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=n-i;return a;};                  // descending
    auto DESCrep =[&](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=(n-i)/4;return a;};             // descending+repeats
    auto SAME    =[](int n){return vector<int>(n,42);};                                               // all same
    auto near10  =[&](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=i;for(int i=0;i<10;i++){int p=rng()%n,q=rng()%n;swap(a[p],a[q]);}return a;};
    auto near200 =[&](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=i;for(int i=0;i<200;i++){int p=rng()%n,q=rng()%n;swap(a[p],a[q]);}return a;};
    auto nearWide=[&](int n){vector<int>a(n);for(auto&x:a)x=(int)(rng()%2000000000u-1000000000);sort(a.begin(),a.end());for(int i=0;i<16;i++){int p=rng()%n,q=rng()%n;swap(a[p],a[q]);}return a;};
    auto SNAKE   =[](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=(i%2==0)?(i/2+1):(n-i/2);return a;};
    auto ZIGZAG  =[&](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=(rng()%2)?i:(n-i);return a;};
    auto rotSort =[&](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=i;int k=rng()%n;rotate(a.begin(),a.begin()+k,a.end());return a;}; // rotated sorted
    auto fewdist =[&](int n){vector<int>a(n);for(auto&x:a)x=rng()%3;return a;};                       // only 3 distinct
    auto perm    =[&](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=i;shuffle(a.begin(),a.end(),rng);return a;}; // permutation 1..n
    auto tail10  =[&](int n){vector<int>a(n);for(int i=0;i<n*0.9;i++)a[i]=i;for(int i=(int)(n*0.9);i<n;i++)a[i]=(int)(rng()%1000000);return a;}; // 90% sorted + random tail
    auto halfRand=[&](int n){vector<int>a(n);for(int i=0;i<n/2;i++)a[i]=i;for(int i=n/2;i<n;i++)a[i]=(int)(rng()%1000000);return a;}; // half sorted + random

    runCase("Random 0..1e9",          R_wide(N));
    runCase("Random 0..999999",       R_999999(N));
    runCase("Random 0..999",          R_999(N));
    runCase("Random 0..99",           R_99(N));
    runCase("Duplicates 0..9",        R_9(N));
    runCase("Negative -100k..100k",   R_neg(N));
    runCase("Mixed signs wide",       R_mix(N));
    runCase("Ascending",              ASC(N));
    runCase("Ascending + repeats",    ASCrep(N));
    runCase("Descending",             DESC(N));
    runCase("Descending + repeats",   DESCrep(N));
    runCase("All same",               SAME(N));
    runCase("Nearly sorted (10 swaps)", near10(N));
    runCase("Nearly sorted (200 swaps)", near200(N));
    runCase("Nearly sorted wide-range", nearWide(N));
    runCase("Snake pattern",          SNAKE(N));
    runCase("Zigzag peak-valley",     ZIGZAG(N));
    runCase("Rotated sorted",         rotSort(N));
    runCase("Few distinct (0..2)",    fewdist(N));
    runCase("Random permutation 1..n",perm(N));
    runCase("90% sorted + random tail",tail10(N));
    runCase("Half sorted + random",   halfRand(N));
    runCaseCmp("Descending (comparator)", ASC(N), greater<int>());

    // extra int patterns
    auto R_fullint =[&](int n){vector<int>a(n);for(auto&x:a)x=(int)(rng()%2000000000u)+0x40000000u;return a;}; // full-ish int32 range
    auto R_2dist   =[&](int n){vector<int>a(n);for(auto&x:a)x=(rng()%2)?INT_MAX:INT_MIN;return a;};                 // 2 extremes, max dup
    auto organ     =[](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=i<n/2?i:n-i;return a;};                       // organ-pipe
    auto expdist   =[&](int n){vector<int>a(n);for(auto&x:a){double u=(double)rng()/rng.max();x=(int)(-100.0*log(1.0-u));}return a;}; // exp dist (lots of small)
    auto intedge   =[&](int n){vector<int>a(n);for(int i=0;i<n;i++)a[i]=(i%3==0)?INT_MIN:(i%3==1)?INT_MAX:i-500000000;return a;};     // min/max/negative mix
    auto bitrev    =[&](int n){vector<int>a(n);for(int i=0;i<n;i++){unsigned x=i,y=0;for(int b=0;b<20;b++)y|=(x>>b&1)<<(19-b);a[i]=(int)y;}return a;}; // bit-reversal 0..2^20
    runCase("int32 full range",        R_fullint(N));
    runCase("2 extremes (max dup)",    R_2dist(N));
    runCase("Organ-pipe",              organ(N));
    runCase("Exponential dist",        expdist(N));
    runCase("INT_MIN/MAX/neg mix",     intedge(N));
    runCase("Bit-reversal 0..2^20",    bitrev(N));

    // uint64 / int64
    printf("---------- uint64 / int64 ----------\n\n");
    auto U64_rand=[&](int n){vector<unsigned long long>a(n);for(auto&x:a)x=((unsigned long long)rng()<<32)^rng();return a;};
    auto U64_asc =[](int n){vector<unsigned long long>a(n);for(int i=0;i<n;i++)a[i]=i;return a;};
    auto U64_desc=[](int n){vector<unsigned long long>a(n);for(int i=0;i<n;i++)a[i]=n-i;return a;};
    auto I64_rand=[&](int n){vector<long long>a(n);for(auto&x:a)x=(long long)(((unsigned long long)rng()<<32)^rng());return a;};
    auto I64_mix =[&](int n){vector<long long>a(n);for(auto&x:a)x=(long long)(rng()%2000000000u)-1000000000;return a;};
    runCase("uint64 Random",   U64_rand(N));
    runCase("uint64 Ascending",U64_asc(N));
    runCase("uint64 Descending",U64_desc(N));
    runCase("int64 Random",    I64_rand(N));
    runCase("int64 Mixed signs",I64_mix(N));

    // ================= double =================
    printf("---------- double ----------\n\n");
    auto D_wide  =[&](int n){vector<double>a(n);for(auto&x:a)x=(double)((long long)(rng()%2000000000u)-1000000000)/3.7;return a;};
    auto D_small =[&](int n){vector<double>a(n);for(auto&x:a)x=(double)(rng()%1000);return a;};
    auto D_asc   =[](int n){vector<double>a(n);for(int i=0;i<n;i++)a[i]=i;return a;};
    auto D_desc  =[](int n){vector<double>a(n);for(int i=0;i<n;i++)a[i]=n-i;return a;};
    auto D_near  =[&](int n){vector<double>a(n);for(int i=0;i<n;i++)a[i]=i;for(int i=0;i<16;i++){int p=rng()%n,q=rng()%n;swap(a[p],a[q]);}return a;};
    auto D_same  =[](int n){return vector<double>(n,3.14);};
    auto D_mix   =[&](int n){vector<double>a(n);for(auto&x:a)x=(double)((int)(rng()%2000000)-1000000)/2.5;return a;};
    runCase("double Random wide",  D_wide(N));
    runCase("double Random 0..999",D_small(N));
    runCase("double Ascending",    D_asc(N));
    runCase("double Descending",   D_desc(N));
    runCase("double Nearly sorted",D_near(N));
    runCase("double All same",     D_same(N));
    runCase("double Mixed signs",  D_mix(N));

    // ================= float =================
    printf("---------- float ----------\n\n");
    auto F_wide =[&](int n){vector<float>a(n);for(auto&x:a)x=(float)((int)(rng()%2000000000u)-1000000000)/3.7f;return a;};
    auto F_small=[&](int n){vector<float>a(n);for(auto&x:a)x=(float)(rng()%1000);return a;};
    auto F_asc  =[](int n){vector<float>a(n);for(int i=0;i<n;i++)a[i]=(float)i;return a;};
    auto F_desc =[](int n){vector<float>a(n);for(int i=0;i<n;i++)a[i]=(float)(n-i);return a;};
    auto F_neg  =[&](int n){vector<float>a(n);for(auto&x:a)x=(float)((int)(rng()%2000000)-1000000)/2.5f;return a;};
    auto F_same =[](int n){return vector<float>(n,2.718f);};
    runCase("float Random wide",  F_wide(N));
    runCase("float Random 0..999",F_small(N));
    runCase("float Ascending",    F_asc(N));
    runCase("float Descending",   F_desc(N));
    runCase("float Mixed signs",  F_neg(N));
    runCase("float All same",     F_same(N));

    // ================= string (stable mode) =================
    printf("---------- string (stable mode) ----------\n\n");
    auto S_random=[&](int n){vector<string>a(n);for(auto&x:a){int L=rng()%8+1;x.reserve(L);for(int j=0;j<L;j++)x+=(char)('a'+rng()%26);}return a;};
    auto S_asc   =[&](int n){vector<string>a(n);for(int i=0;i<n;i++){char b[16];snprintf(b,16,"%012d",i);a[i]=b;}return a;};
    auto S_desc  =[&](int n){vector<string>a(n);for(int i=0;i<n;i++){char b[16];snprintf(b,16,"%012d",n-i);a[i]=b;}return a;};
    auto S_near  =[&](int n){vector<string>a(n);for(int i=0;i<n;i++){char b[16];snprintf(b,16,"%012d",i);a[i]=b;}for(int i=0;i<16;i++){int p=rng()%n,q=rng()%n;swap(a[p],a[q]);}return a;};
    auto S_few   =[&](int n){vector<string>a(n);for(auto&x:a)x="s"+to_string(rng()%8);return a;};
    runCase("string Random",   S_random(N));
    runCase("string Ascending",S_asc(N));
    runCase("string Descending",S_desc(N));
    runCase("string Nearly sorted",S_near(N));
    runCase("string Few distinct",S_few(N));

    // ================= stability & byKey =================
    printf("---------- stability (equal keys) & byKey ----------\n\n");
    auto StMany=[&](int n){vector<BenchItem>a(n);for(int i=0;i<n;i++){a[i].k=rng()%8; a[i].id=i;}return a;};   // few distinct keys, heavy dup
    auto StFew =[&](int n){vector<BenchItem>a(n);for(int i=0;i<n;i++){a[i].k=i/3;    a[i].id=i;}return a;};   // near-sorted keys
    auto StRand=[&](int n){vector<BenchItem>a(n);for(int i=0;i<n;i++){a[i].k=(int)(rng()%100000);a[i].id=i;}return a;}; // many distinct
    runStable("stable many-dup keys",   StMany(N));
    runStable("stable near-sorted keys",StFew(N));
    runStable("stable random keys",     StRand(N));

    auto BkInt=[&](int n){vector<int>a(n);for(auto&x:a)x=(int)(rng()%100000);return a;};
    auto BkDbl=[&](int n){vector<double>a(n);for(auto&x:a)x=(double)(rng()%1000000)/3.0;return a;};
    runByKey("byKey int",  BkInt(N), [](int x){return x;});
    runByKey("byKey double",BkDbl(N),[](double x){return (long long)(x*7);});

    // ================= different sizes =================
    printf("---------- 不同规模 (Random 0..999999) ----------\n\n");
    // sizes that cross dispatch boundaries: 16(insertion),17,128(introsort),
    // 129(radix), then large
    for (int n : {16, 17, 100, 128, 129, 1000, 10000, 100000, 1000000}) {
        runCase(("N="+to_string(n)).c_str(), R_999999(n));
    }

    // ================= C-style array test =================
    printf("---------- C-style array (lxySort(arr)) ----------\n\n");
    {
        int carr[] = {5, 2, 8, 1, 9, 3, 7, 4, 6, 0};
        int n = sizeof(carr)/sizeof(carr[0]);
        vector<int> ref(carr, carr+n); sort(ref.begin(), ref.end());
        lxySort(carr);
        bool ok = true;
        for (int i = 0; i < n; ++i) if (carr[i] != ref[i]) { ok = false; break; }
        printf("  lxySort(arr) : %s\n\n", ok ? "OK" : "WRONG");
    }
    {
        double darr[] = {3.14, 2.71, 1.41, 0.57, 1.73};
        int n = sizeof(darr)/sizeof(darr[0]);
        vector<double> ref(darr, darr+n); sort(ref.begin(), ref.end());
        lxySort(darr);
        bool ok = true;
        for (int i = 0; i < n; ++i) if (darr[i] != ref[i]) { ok = false; break; }
        printf("  lxySort(darr) : %s\n\n", ok ? "OK" : "WRONG");
    }
    {
        const char* sarr[] = {"delta", "alpha", "epsilon", "beta", "gamma"};
        int n = sizeof(sarr)/sizeof(sarr[0]);
        vector<const char*> ref(sarr, sarr+n); sort(ref.begin(), ref.end());
        lxySort(sarr);
        bool ok = true;
        for (int i = 0; i < n; ++i) if (strcmp(sarr[i], ref[i]) != 0) { ok = false; break; }
        printf("  lxySort(sarr) : %s\n\n", ok ? "OK" : "WRONG");
    }

    // ================= parallel vs serial vs std =================
    printf("---------- 并行排序 (lxySortParallel, 比较型/CPU密集) ----------\n\n");
    for (int n : {1000000, 3000000}) {
        struct S { int a,b; };
        vector<S> v(n); for(auto&x:v){x.a=(int)(rng()%100000); x.b=(int)(rng()%1000);}
        auto cmp = [](const S&x,const S&y){return x.a<y.a;};
        double seq=0, par=0, st=0;
        // true serial: disable auto-parallel so the parallel speedup is real
        { double b=1e300;for(int r=0;r<2;r++){auto c=v; lxy_detail::parDepth()=1; double s=Clock::ms(); lxySort(c,cmp); double e=Clock::ms(); lxy_detail::parDepth()=0; if(e-s<b)b=e-s;} seq=b; }
        { double b=1e300;for(int r=0;r<5;r++){auto c=v;double s=Clock::ms();lxySortParallel(c,cmp);double e=Clock::ms();if(e-s<b)b=e-s;}par=b; }
        { double b=1e300;for(int r=0;r<5;r++){auto c=v;double s=Clock::ms();sort(c.begin(),c.end(),cmp);double e=Clock::ms();if(e-s<b)b=e-s;}st=b; }
        printf("[Struct sort(by a) N=%d]\n", n);
        printf("  lxySort(串行)   : %8.3fms\n", seq);
        printf("  lxySortParallel : %8.3fms   -> %.2fx vs 串行\n", par, seq/par);
        printf("  std::sort       : %8.3fms   -> lxyParallel %.2fx faster\n\n", st, st/par);
    }
    printf("  注: 算术 radix / 计数 / string(MSD radix) 为内存带宽瓶颈, 并行无增益;\n");
    printf("      并行主要利好 CPU 密集的比较型/自定义比较器路径 (如上方 struct)。\n\n");

    printf("=== Summary: lxySort won %d/%d cases ===\n", gWins, gTotal);
    return 0;
}