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  1. //***********************************************
  2. // Author: Fritz Ammon
  3. // Date: 30 August 2014
  4. // Sieve of Eratosthenes v3
  5. // Revised: 4 February 2016
  6. // Was not optimally utilizing all bits.
  7. //***********************************************
  8.  
  9. #include <iostream>
  10. #include <cstring>
  11.  
  12. using namespace std;
  13.  
  14. typedef unsigned long long ull;
  15.  
  16. void mark(ull a[], ull i);
  17. bool check(ull a[], ull i);
  18.  
  19. const ull NUM_BYTES = 3920; // Must divide evenly with 4 so as not to corrupt mem.
  20. const ull LAST_ODD = 2 * (NUM_BYTES * 8 - 1) + 3; // 2n + 3; just determining the last odd to refine algo.
  21.  
  22. int main()
  23. {
  24. 	ull s[NUM_BYTES / 8];
  25.     ull p, i;
  26.     bool done = false;
  27.     ull count = 1;
  28.  
  29. 	if (NUM_BYTES % 8 != 0)
  30. 		return 0; // Must align to reach NUM_BYTES.
  31.  
  32.     memset(s, -1, NUM_BYTES); // Init all bits to 1 (-1 on unsigned).
  33.  
  34.     p = 3;
  35.     while (!done)
  36.     {
  37. 		i = p;
  38. 		if ((i *= i) > LAST_ODD) // Can stop once P^2 > last odd num.
  39. 		{
  40. 			done = true;
  41. 			continue;
  42. 		}
  43.  
  44. 		while (i <= LAST_ODD)
  45. 		{
  46. 			mark(s, i); // Turn bit off.
  47. 			i += (2 * p); // Continue marking multiples of p.
  48. 		}
  49.  
  50. 		while (!check(s, (p += 2)));
  51.     }
  52.  
  53.     std::ios_base::sync_with_stdio(false); // Speed up output.
  54.  
  55.     cout << "2 (1)\n";
  56.     for (ull c = 3; c <= LAST_ODD; c += 2)
  57.     {
  58.     	if (check(s, c))
  59. 			cout << c << " (" << ++count << ")\n";
  60. 	}
  61.  
  62.     return 0;
  63. }
  64.  
  65. void mark(ull a[], ull i)
  66. {
  67. 	// i - 3 comes from the formula 2n + 3 = i.
  68. 	// We use 2n + 3 = i instead of 2n + 1 = i because we start our list of odds with 3.
  69. 	// In other words, the odd number 3 should correspond to the index 0.
  70. 	// i is the actual odd number, so to get the index of that odd number in the bitwise index,
  71. 	// we need to rearrange the formula to i - 3 / 2 = n.
  72. 	// 128 comes from taking the index divided by 64, so that's (i - 3) / 2 / 64.
  73. 	// We need to divide by 64 in order to manipulate the bits of the correct element (ull) in the array.
  74.     a[(i - 3) / 128] &= ~(static_cast<ull> (1) << (63 - (((i - 3) / 2) % 64)));
  75. }
  76.  
  77. bool check(ull a[], ull i)
  78. {
  79.     return (a[(i - 3) / 128] & (static_cast<ull> (1) << (63 - (((i - 3) / 2) % 64)))) != 0;
  80. }
Runtime error #stdin #stdout 0.01s 3456KB
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5
https://ideone.com/SJvNYf
Bitwise Sieve of Eratosthenes
language:
C++14 (gcc 8.3)
created:
9 years ago
visibility:
secret

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