Upload files to "ex1F_goldbachs_conjecture"

ex1F_goldbachs_conjecture/goldbach.cpp

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+#include "goldbach.h"
+
+size_t single_goldbach(size_t k)
+{
+    const std::vector<size_t> relevant_primes = get_primes(k);
+    size_t m = relevant_primes.size();
+
+    size_t counter = 0;
+
+    for(size_t i = 0; i < m; ++i)
+    {
+        for(size_t j = i; j < m; ++j)
+        {
+            if(relevant_primes[i] + relevant_primes[j] == k)
+                counter += 1;
+        }
+    }
+
+    return counter;
+}
+
+
+std::vector<size_t> count_goldbach(size_t n)
+{
+    const std::vector<size_t> relevant_primes = get_primes(n);
+    size_t m = relevant_primes.size();
+
+    std::vector<size_t> counter_vector(n + 1, 0);
+
+
+    for(size_t i = 0; i < m; ++i)
+    {
+        for(size_t j = i; j < m; ++j)
+        {
+            size_t sum = relevant_primes[i] + relevant_primes[j];
+            if(sum <= n)
+                ++counter_vector[relevant_primes[i] + relevant_primes[j]];
+        }
+    }
+
+    return counter_vector;
+}

ex1F_goldbachs_conjecture/goldbach.h

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+#pragma once
+#include "mayer_primes.h"
+#include <iostream>
+#include <vector>
+#include <iterator>
+#include <cassert>
+
+
+/**
+  This function returns the number of possible decompositions of an integer into a sum of two prime numbers.
+  @param[in]    k            first integer
+  @param[out]   count        number of decompositions
+*/
+size_t single_goldbach(size_t k);
+
+/**
+  This function returns the number of possible decompositions into a sum of two prime numbers of all even integers in the interval [4,n].
+  @param[in]    n                   upper integer bound
+  @param[out]   count_vector        vector containing the number of decompositions for a natural number the corresponding index
+*/
+std::vector<size_t> count_goldbach(size_t n);

ex1F_goldbachs_conjecture/main.cpp

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+#include "../utils/timing.h"
+#include "goldbach.h"
+#include <iostream>
+#include <algorithm>
+using namespace std;
+
+
+int main(int argc, char **argv)
+{
+    cout << "Check: 694 has "<< single_goldbach(694) << " decompositions." << endl << "----------------------------------------" << endl;
+
+
+    for(size_t n : {10000, 100000, 400000, 1000000, 2000000})
+    {
+        tic();
+
+        auto goldbach_vector = count_goldbach(n);
+
+        auto max_it = max_element(goldbach_vector.begin(), goldbach_vector.end());
+        size_t max_number = distance(goldbach_vector.begin(), max_it);
+
+        double time = toc();
+
+        cout << "The number " <<  max_number << " has " << *max_it << " decompositions. Duration: " << time << endl;
+    }
+
+    /*
+    The number 9240 has 329 decompositions. Duration: 0.00572876
+    The number 99330 has 2168 decompositions. Duration: 0.3342
+    The number 390390 has 7094 decompositions. Duration: 4.23734
+    The number 990990 has 15594 decompositions. Duration: 29.5817
+    The number 1981980 has 27988 decompositions. Duration: 135.985
+    */
+
+
+    return 0;
+}

ex1F_goldbachs_conjecture/mayer_primes.h

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+#pragma once
+
+#include <cstring> //memset
+#include <vector>
+//using namespace std;
+
+/** \brief Determines all prime numbers in interval [2, @p max].
+ *
+ *  The sieve of Eratosthenes is used.
+ *
+ *  The implementation originates from <a href="http://code.activestate.com/recipes/576559-fast-prime-generator/">Florian Mayer</a>.
+ *
+ * \param[in]   max end of interval for the prime number search.
+ * \return  vector of prime numbers @f$2,3,5, ..., p<=max @f$.
+ *
+ * \copyright
+ * Copyright (c) 2008 Florian Mayer          (adapted by Gundolf Haase 2018)
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice shall be included in
+ * all copies or substantial portions of the Software.
+ *
+ *  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
+ * INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+ *
+ */
+template <class T>
+std::vector<T> get_primes(T max)
+{
+    std::vector<T> primes;
+    char *sieve;
+    sieve = new char[max / 8 + 1];
+    // Fill sieve with 1
+    memset(sieve, 0xFF, (max / 8 + 1) * sizeof(char));
+    for (T x = 2; x <= max; x++)
+    {
+        if (sieve[x / 8] & (0x01 << (x % 8))) {
+            primes.push_back(x);
+            // Is prime. Mark multiplicates.
+            for (T j = 2 * x; j <= max; j += x)
+            {
+                sieve[j / 8] &= ~(0x01 << (j % 8));
+			}
+        }
+	}
+    delete[] sieve;
+    return primes;
+}
+
+//---------------------------------------------------------------
+//int main()        // by  Florian Mayer
+//{g++ -O3  -std=c++14 -fopenmp main.cpp && ./a.out
+//    vector<unsigned long> primes;
+//    primes = get_primes(10000000);
+//    // return 0;
+//    // Print out result.
+//    vector<unsigned long>::iterator it;
+//    for(it=primes.begin(); it < primes.end(); it++)
+//        cout << *it << " ";
+//
+//    cout << endl;
+//    return 0;
+//}