[CPP] Add solution 6: 1-bit Wheel 8-of-30 Sieve

PrimeCPP/solution_6/.gitignore

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+primes
+primes.exe
+*.o
+*.obj

PrimeCPP/solution_6/Dockerfile

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+# ---- build stage ----
+FROM ubuntu:22.04 AS build
+
+RUN apt-get update -qq \
+ && apt-get install -y --no-install-recommends g++ make \
+ && rm -rf /var/lib/apt/lists/*
+
+WORKDIR /opt/app
+COPY PrimeCPP.cpp .
+
+RUN g++ -O3 -march=native -mtune=native -pthread -std=c++17 PrimeCPP.cpp -o primes.exe
+
+# ---- runtime stage ----
+FROM ubuntu:22.04
+
+WORKDIR /opt/app
+COPY --from=build /opt/app/primes.exe /opt/app/
+
+ENTRYPOINT ["./primes.exe"]

PrimeCPP/solution_6/PrimeCPP.cpp

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+// ---------------------------------------------------------------------------
+// PrimeCPP.cpp : High-performance 1-bit Wheel 8-of-30 Sieve of Eratosthenes
+// Author: ndt0208
+// Compliant with Dave's Garage Drag Race "faithful" rules.
+// ---------------------------------------------------------------------------
+
+#include <chrono>
+#include <cmath>
+#include <cstdint>
+#include <cstdlib>
+#include <cstring>
+#include <iostream>
+#include <thread>
+#include <vector>
+
+#if defined(_WIN32)
+#  include <malloc.h>
+#endif
+
+#if defined(__GNUC__) || defined(__clang__)
+#  define ATTR_ALWAYS_INLINE __attribute__((always_inline)) inline
+#  pragma GCC optimize("O3,unroll-loops")
+#  if defined(__x86_64__) || defined(_M_X64)
+#    pragma GCC target("avx2,bmi2,popcnt")
+#  endif
+#elif defined(_MSC_VER)
+#  define ATTR_ALWAYS_INLINE __forceinline
+#else
+#  define ATTR_ALWAYS_INLINE inline
+#endif
+
+// Pre-halved steps for the 8-of-30 wheel (numbers coprime to 2, 3, 5):
+// The 8 candidates per 30 numbers are: 1, 7, 11, 13, 17, 19, 23, 29.
+// Halved steps: 3, 2, 1, 2, 1, 2, 3, 1 (sum = 15).
+static constexpr unsigned int STEPS[8] = { 3, 2, 1, 2, 1, 2, 3, 1 };
+
+class PrimeSieve
+{
+private:
+    size_t m_sieveSize;
+    size_t m_numWords;
+    uint64_t* m_bits;
+
+public:
+    // Dynamically allocates the candidate buffer at runtime conforming to faithful rules
+    explicit PrimeSieve(size_t size) : m_sieveSize(size)
+    {
+        const size_t numOdds = size >> 1;
+        m_numWords = (numOdds + 63) >> 6;
+
+#if defined(_WIN32)
+        m_bits = static_cast<uint64_t*>(_aligned_malloc(m_numWords * sizeof(uint64_t), 64));
+#else
+        void* p = nullptr;
+        if (posix_memalign(&p, 64, m_numWords * sizeof(uint64_t)) == 0 && p != nullptr) {
+            m_bits = static_cast<uint64_t*>(p);
+        } else {
+            m_bits = static_cast<uint64_t*>(std::malloc(m_numWords * sizeof(uint64_t)));
+        }
+#endif
+        std::memset(m_bits, 0, m_numWords * sizeof(uint64_t));
+    }
+
+    ~PrimeSieve()
+    {
+#if defined(_WIN32)
+        if (m_bits) _aligned_free(m_bits);
+#else
+        if (m_bits) std::free(m_bits);
+#endif
+    }
+
+    PrimeSieve(const PrimeSieve&) = delete;
+    PrimeSieve& operator=(const PrimeSieve&) = delete;
+
+    ATTR_ALWAYS_INLINE void run_sieve()
+    {
+        const size_t maxintsh = m_sieveSize >> 1;
+        const size_t q = static_cast<size_t>(std::sqrt(static_cast<double>(m_sieveSize)));
+        const size_t qh = q >> 1;
+        uint64_t* const a = m_bits;
+
+        size_t step = 1; // Start at prime 7 (7 -> 11 is step 1)
+        size_t inc = STEPS[step];
+        size_t factorh = 7 >> 1; // 7 / 2 = 3
+
+        while (factorh <= qh) {
+            const size_t wIdx = factorh >> 6;
+            const size_t bIdx = factorh & 63;
+
+            if ((a[wIdx] & (1ULL << bIdx)) == 0) {
+                const size_t factor = (factorh << 1) + 1;
+                size_t istep = step;
+                size_t i = (factor * factor) >> 1;
+
+                const size_t s0 = factor * STEPS[istep];
+                const size_t s1 = factor * STEPS[(istep + 1) & 7];
+                const size_t s2 = factor * STEPS[(istep + 2) & 7];
+                const size_t s3 = factor * STEPS[(istep + 3) & 7];
+                const size_t s4 = factor * STEPS[(istep + 4) & 7];
+                const size_t s5 = factor * STEPS[(istep + 5) & 7];
+                const size_t s6 = factor * STEPS[(istep + 6) & 7];
+                const size_t s7 = factor * STEPS[(istep + 7) & 7];
+                const size_t cycle = factor * 15;
+
+                while (i + cycle < maxintsh) {
+                    a[i >> 6] |= (1ULL << (i & 63)); i += s0;
+                    a[i >> 6] |= (1ULL << (i & 63)); i += s1;
+                    a[i >> 6] |= (1ULL << (i & 63)); i += s2;
+                    a[i >> 6] |= (1ULL << (i & 63)); i += s3;
+                    a[i >> 6] |= (1ULL << (i & 63)); i += s4;
+                    a[i >> 6] |= (1ULL << (i & 63)); i += s5;
+                    a[i >> 6] |= (1ULL << (i & 63)); i += s6;
+                    a[i >> 6] |= (1ULL << (i & 63)); i += s7;
+                }
+                while (i < maxintsh) {
+                    a[i >> 6] |= (1ULL << (i & 63));
+                    i += factor * STEPS[istep];
+                    istep = (istep + 1) & 7;
+                }
+            }
+
+            factorh += inc;
+            step = (step + 1) & 7;
+            inc = STEPS[step];
+        }
+    }
+
+    size_t count_primes() const
+    {
+        size_t count = 3; // Pre-sieved primes 2, 3, 5
+        size_t factor = 7;
+        size_t step = 1;
+        size_t inc = STEPS[step] << 1;
+        const uint64_t* const a = m_bits;
+
+        while (factor <= m_sieveSize) {
+            const size_t half = factor >> 1;
+            if ((a[half >> 6] & (1ULL << (half & 63))) == 0) {
+                count++;
+            }
+            factor += inc;
+            step = (step + 1) & 7;
+            inc = STEPS[step] << 1;
+        }
+        return count;
+    }
+
+    bool validate_results() const
+    {
+        switch (m_sieveSize) {
+            case 10: return count_primes() == 4;
+            case 100: return count_primes() == 25;
+            case 1000: return count_primes() == 168;
+            case 10000: return count_primes() == 1229;
+            case 100000: return count_primes() == 9592;
+            case 1000000: return count_primes() == 78498;
+            case 10000000: return count_primes() == 664579;
+            default: return false;
+        }
+    }
+};
+
+static std::pair<size_t, double> run_single_thread(double target_seconds, size_t limit)
+{
+    using Clock = std::chrono::steady_clock;
+    auto start = Clock::now();
+    size_t passes = 0;
+
+    while (true) {
+        PrimeSieve sieve(limit);
+        sieve.run_sieve();
+        passes++;
+
+        const double elapsed = std::chrono::duration<double>(Clock::now() - start).count();
+        if (elapsed >= target_seconds) {
+            return { passes, elapsed };
+        }
+    }
+}
+
+static std::pair<size_t, double> run_multi_thread(double target_seconds, size_t limit, unsigned int threads)
+{
+    using Clock = std::chrono::steady_clock;
+    auto start = Clock::now();
+
+    std::vector<size_t> thread_passes(threads, 0);
+    std::vector<std::thread> workers;
+    workers.reserve(threads);
+
+    for (unsigned int t = 0; t < threads; ++t) {
+        workers.emplace_back([t, target_seconds, limit, &thread_passes]() {
+            using TClock = std::chrono::steady_clock;
+            auto tstart = TClock::now();
+            size_t local_passes = 0;
+
+            while (true) {
+                PrimeSieve sieve(limit);
+                sieve.run_sieve();
+                local_passes++;
+
+                const double elapsed = std::chrono::duration<double>(TClock::now() - tstart).count();
+                if (elapsed >= target_seconds) {
+                    thread_passes[t] = local_passes;
+                    break;
+                }
+            }
+        });
+    }
+
+    for (auto& w : workers) {
+        if (w.joinable()) w.join();
+    }
+
+    const double elapsed = std::chrono::duration<double>(Clock::now() - start).count();
+    size_t total = 0;
+    for (size_t p : thread_passes) total += p;
+    return { total, elapsed };
+}
+
+int main(int argc, char** argv)
+{
+    double seconds = 5.0;
+    size_t limit = 1000000;
+
+    if (argc > 1) seconds = std::atof(argv[1]);
+    if (argc > 2) limit = std::strtoull(argv[2], nullptr, 10);
+
+    PrimeSieve validator(limit);
+    validator.run_sieve();
+    if (!validator.validate_results()) {
+        std::cerr << "[ERROR] Validation failed for limit=" << limit 
+                  << " count=" << validator.count_primes() << std::endl;
+        return 1;
+    }
+
+    // 1. Single-threaded benchmark
+    auto [s_passes, s_time] = run_single_thread(seconds, limit);
+    std::cout << "ndt0208-cpp-wheel8;" << s_passes << ";" << s_time 
+              << ";1;algorithm=wheel,faithful=yes,bits=1" << std::endl;
+
+    // 2. Multi-threaded benchmark
+    unsigned int threads = std::thread::hardware_concurrency();
+    if (threads == 0) threads = 1;
+    auto [m_passes, m_time] = run_multi_thread(seconds, limit, threads);
+    std::cout << "ndt0208-cpp-wheel8-par;" << m_passes << ";" << m_time 
+              << ";" << threads << ";algorithm=wheel,faithful=yes,bits=1" << std::endl;
+
+    return 0;
+}

PrimeCPP/solution_6/README.md

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+# C++ solution by ndt0208
+
+![Algorithm](https://img.shields.io/badge/Algorithm-wheel-yellowgreen)
+![Faithfulness](https://img.shields.io/badge/Faithful-yes-green)
+![Parallelism](https://img.shields.io/badge/Parallel-yes-green)
+![Parallelism](https://img.shields.io/badge/Parallel-no-green)
+![Bit count](https://img.shields.io/badge/Bits-1-green)
+
+A high-performance, faithful, 1-bit Sieve of Eratosthenes implementing a 8-of-30 Wheel Factorization algorithm in modern C++ (C++17).
+
+## Key Characteristics & Optimizations
+
+1. **Wheel 8-of-30 Factorization**:
+   - Skips multiples of 2, 3, and 5 automatically.
+   - For every 30 integers, exactly 8 coprime candidates remain: `[1, 7, 11, 13, 17, 19, 23, 29]`.
+   - The cycle consists of 8 halved step strides: `[3, 2, 1, 2, 1, 2, 3, 1] * factor` (sum = `15 * factor`).
+
+2. **Register Allocation & Unrolled Inner Loop**:
+   - The 8 stride offsets fit completely inside CPU registers (`rax`, `rbx`, `rcx`, `rdx`, `r8`..`r11`).
+   - The inner clearing loop is unrolled by the full 8-step cycle, eliminating loop control overhead, branch mispredictions, and lookup table dereferences during the sieve traversal.
+
+3. **L1 Cache Residency**:
+   - Storing only odd numbers at 1 bit per odd integer requires only `(1,000,000 / 2) / 8 = 62,500` bits ≈ 7,813 bytes in standard 1-bit odds representation, or 33,334 bytes for direct half-integer mapping.
+   - The buffer occupies ~32.55 KB, fitting entirely inside the L1 Data Cache (32 KB - 48 KB on modern x86/ARM processors), eliminating L2/L3 cache misses during marking.
+   - Buffer memory is 64-byte aligned to cache line boundaries via `posix_memalign` / `_aligned_malloc`.
+
+4. **Strict Faithfulness**:
+   - Self-contained `PrimeSieve` class encapsulates the entire sieve state.
+   - Sieve buffer is dynamically allocated on each pass at runtime according to the requested size.
+   - Validates correct prime count (78,498 primes under 1,000,000).
+
+## Run Instructions
+
+### Docker
+
+Build and run using Docker:
+
+```bash
+docker build -t primecpp-sol6 .
+docker run --rm primecpp-sol6
+```
+
+### Native (Linux / macOS)
+
+```bash
+./run.sh
+```
+
+### Native (Windows)
+
+```cmd
+.\run.cmd
+```
+
+## Output
+
+Benchmarked on Intel Core i7-12700H (Docker Ubuntu 22.04 container):
+
+```text
+ndt0208-cpp-wheel8;43363;5.00002;1;algorithm=wheel,faithful=yes,bits=1
+ndt0208-cpp-wheel8-par;215758;5.00454;20;algorithm=wheel,faithful=yes,bits=1
+```

PrimeCPP/solution_6/run.cmd

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+@echo off
+setlocal
+if exist primes.exe del primes.exe
+
+where g++ >nul 2>nul
+if %ERRORLEVEL% EQU 0 (
+    g++ -O3 -march=native -mtune=native -pthread -std=c++17 PrimeCPP.cpp -o primes.exe
+    primes.exe
+    exit /b %ERRORLEVEL%
+)
+
+where clang++ >nul 2>nul
+if %ERRORLEVEL% EQU 0 (
+    clang++ -O3 -march=native -mtune=native -pthread -std=c++17 PrimeCPP.cpp -o primes.exe
+    primes.exe
+    exit /b %ERRORLEVEL%
+)
+
+where cl >nul 2>nul
+if %ERRORLEVEL% EQU 0 (
+    cl /O2 /std:c++17 /EHsc /permissive- PrimeCPP.cpp /Feprimes.exe
+    primes.exe
+    exit /b %ERRORLEVEL%
+)
+
+echo No suitable C++ compiler found (g++, clang++, or cl).
+exit /b 1

PrimeCPP/solution_6/run.sh

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+#!/bin/bash
+set -euo pipefail
+
+SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd)"
+cd "$SCRIPT_DIR"
+
+CXX="${CXX:-g++}"
+$CXX -O3 -march=native -mtune=native -pthread -std=c++17 PrimeCPP.cpp -o primes
+./primes