Half sieve size, flip meaning of zero and one

Author: davepl

PrimeCPP/solution_2/PrimeCPP_PAR.cpp

@@ -1,7 +1,7 @@
 // ---------------------------------------------------------------------------
-// PrimeCPP.cpp : Pol Marcet's Modified version of Dave's Garage Prime Sieve
-// Some great ideas taken from Rust's implementation from Michael Barber
-// @mike-barber https://www.github.com/mike-barber (bit-storage-rotate)
+// PrimeCPP.cpp : Optimized version of Dave's Garage Prime Sieve
+// Optimization: Use a BitArray that represents only odd numbers to reduce memory usage
+// and improve cache performance.
 // ---------------------------------------------------------------------------
 
 #include <chrono>
@@ -26,83 +26,64 @@ const uint64_t DEFAULT_UPPER_LIMIT = 10'000'000LLU;
 class BitArray {
     uint8_t *array;
     size_t arrSize;
+    size_t logicalSize;
 
-    inline static size_t arraySize(size_t size) 
+    static constexpr size_t arraySize(size_t size) 
     {
         return (size >> 3) + ((size & 7) > 0);
     }
 
-    inline static size_t index(size_t n) 
+    static constexpr size_t index(size_t n) 
     {
         return (n >> 3);
     }
 
-    inline static uint8_t getSubindex(size_t n, uint8_t d) 
-    {
-        return d & uint8_t(uint8_t(0x01) << (n % 8));
-    }
-
-    inline void setFalseSubindex(size_t n, uint8_t &d) 
-    {
-        d &= ~uint8_t(uint8_t(0x01) << (n % 8));
-    }
-
 public:
-    explicit BitArray(size_t size) : arrSize(size) 
+    explicit BitArray(size_t size) : logicalSize(size)
     {
-        array = new uint8_t[arraySize(size)];
-        std::memset(array, 0xFF, arraySize(size));
+        arrSize = (size + 1) / 2; // Only store bits for odd numbers
+        array = new uint8_t[arraySize(arrSize)];
+        // Bits are left at zero default, so no need to initialize them
+        // std::memset(array, 0x00, arraySize(arrSize));
     }
 
     ~BitArray() { delete[] array; }
 
     bool get(size_t n) const 
     {
-        return (array[index(n)] & (uint8_t(1) << (n % 8))) != 0;
+        if (n % 2 == 0)
+            return false; // Even numbers > 2 are not prime
+        n = n / 2; // Map the actual number to the index in the array
+        return !(array[index(n)] & (uint8_t(1) << (n % 8)));
     }
 
-    static constexpr uint8_t rol(uint8_t x, uint8_t n)
+    void set(size_t n)
     {
-        n %= 8;
-        if (n == 0)
-            return x;
-        else
-            return (x << n) | (x >> (8 - n));
+        n = n / 2; // Map the actual number to the index in the array
+        array[index(n)] |= (uint8_t(1) << (n % 8));
     }
 
-    void setFlagsFalse(size_t n, size_t skip) 
-    {
-        auto rolling_mask = ~uint8_t(1 << n % 8);
-        auto roll_bits = skip % 8;
-        while (n < arrSize) {
-            array[index(n)] &= rolling_mask;
-            n += skip;
-            if (roll_bits != 0)
-                rolling_mask = rol(rolling_mask, roll_bits);
-        }
-    }
-    
     inline size_t size() const 
     {
-        return arrSize;
+        return logicalSize;
     }
 };
 
 
 // prime_sieve
 //
-// Represents the data comprising the sieve (an array of N bits, where N is the upper limit prime being tested)
-// as well as the code needed to eliminate non-primes from its array, which you perform by calling runSieve.
+// Represents the data comprising the sieve (an array of bits representing odd numbers starting from 3)
+// and includes the code needed to eliminate non-primes from its array by calling runSieve.
 
 class prime_sieve
 {
   private:
 
-      BitArray Bits;                                        // Sieve data, where 1==prime, 0==not
+      BitArray Bits; // Sieve data, where 0==prime, 1==not
 
    public:
 
-      prime_sieve(uint64_t n) : Bits(n)                     // Initialize all to true (potential primes)
+      prime_sieve(uint64_t n) : Bits(n) // Initialize bits to zero default
       {
       }
 
@@ -122,15 +103,21 @@ class prime_sieve
 
           while (factor <= q)
           {
-              for (uint64_t num = factor; num < Bits.size(); num += 2)
+              // Find the next prime number
+              for (; factor <= q; factor += 2)
               {
-                  if (Bits.get(num))
+                  if (Bits.get(factor))
                   {
-                      factor = num;
                       break;
                   }
               }
-              Bits.setFlagsFalse(factor * factor, factor + factor);
+
+              // Mark multiples of the prime number as not prime
+              uint64_t start = factor * factor;
+              for (uint64_t num = start; num <= Bits.size(); num += factor * 2)
+              {
+                  Bits.set(num);
+              }
 
               factor += 2;            
           }
@@ -142,9 +129,9 @@ class prime_sieve
 
       size_t countPrimes() const
       {
-          size_t count = (Bits.size() >= 2);                   // Count 2 as prime if within range
-          for (int i = 3; i < Bits.size(); i+=2)
-              if (Bits.get(i))
+          size_t count = (Bits.size() >= 2); // Count 2 as prime if within range
+          for (uint64_t num = 3; num <= Bits.size(); num += 2)
+              if (Bits.get(num))
                   count++;
           return count;
       }
@@ -155,23 +142,24 @@ class prime_sieve
 
       bool isPrime(uint64_t n) const
       {
-          if (n & 1)
-              return Bits.get(n);
-          else
+          if (n == 2)
+              return true;
+          if (n < 2 || n % 2 == 0)
               return false;
+          return Bits.get(n);
       }
 
       // validateResults
       //
-      // Checks to see if the number of primes found matches what we should expect.  This data isn't used in the
+      // Checks to see if the number of primes found matches what we should expect. This data isn't used in the
       // sieve processing at all, only to sanity check that the results are right when done.
 
       bool validateResults() const
       {
           const std::map<const uint64_t, const int> resultsDictionary =
           {
-                {             10LLU, 4         },               // Historical data for validating our results - the number of primes
-                {            100LLU, 25        },               // to be found under some limit, such as 168 primes under 1000
+                {             10LLU, 4         }, // Historical data for validating our results - the number of primes
+                {            100LLU, 25        }, // to be found under some limit, such as 168 primes under 1000
                 {          1'000LLU, 168       },
                 {         10'000LLU, 1229      },
                 {        100'000LLU, 9592      },
@@ -195,8 +183,8 @@ class prime_sieve
           if (showResults)
               cout << "2, ";
 
-          size_t count = (Bits.size() >= 2);                   // Count 2 as prime if in range
-          for (uint64_t num = 3; num <= Bits.size(); num+=2)
+          size_t count = (Bits.size() >= 2); // Count 2 as prime if in range
+          for (uint64_t num = 3; num <= Bits.size(); num += 2)
           {
               if (Bits.get(num))
               {
@@ -215,7 +203,7 @@ class prime_sieve
                << "Average: " << duration/passes << ", "
                << "Limit: "   << Bits.size() << ", "
                << "Counts: "  << count << "/" << countPrimes() << ", "
-               << "Valid : "  << (validateResults() ? "Pass" : "FAIL!") 
+               << "Valid: "   << (validateResults() ? "Pass" : "FAIL!") 
                << "\n";
 
           // Following 2 lines added by rbergen to conform to drag race output format
@@ -322,7 +310,7 @@ int main(int argc, char **argv)
     }
 
     if (bOneshot)
-        cout << "Oneshot is on.  A single pass will be used to simulate a 5 second run." << endl;
+        cout << "Oneshot is on. A single pass will be used to simulate a 5 second run." << endl;
 
     if (bOneshot && (cSecondsRequested > 0 || cThreadsRequested > 1))   
     {
@@ -357,8 +345,8 @@ int main(int argc, char **argv)
     else
     {
         auto tStart       = steady_clock::now();
-        std::thread threads[cThreads];
-        uint64_t l_passes[cThreads];
+        std::vector<std::thread> threads(cThreads);
+        std::vector<uint64_t> l_passes(cThreads);
         for (unsigned int i = 0; i < cThreads; i++)
             threads[i] = std::thread([i, &l_passes, &tStart](size_t llUpperLimit)
             {