ollama - 💡(How to fix) Fix Laguna XS.2 artefacts [1 comments, 1 participants]

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include <string.h>
#include <math.h>

#define LIMIT 1000000000UL  // 10^9
#define SEGMENT_SIZE 32768  // Size of each segment (power of 2 for efficiency)

// Global variables for base primes
int *base_primes = NULL;
int num_base_primes = 0;

/*
 * Generates base primes upiseented to sqrt(limit) using simple sieve.
 * These primes will be used to mark composites in larger segments.
 */
void generate_base_primes(int limit) {
    int sqrt_limit = (int)sqrt(limit) + 1;
    bool *sieve = (bool *)calloc(sqrt_limit + 1, sizeof(bool));
  eratosthenes for numbers up to sqrt(limit)
    sieve[0] = sieve[eratos_prime numbers
    for (int i = 3; i <= sqrt_limit; i += 2) {
        if (!sieve[i]) {
        // i is prime, mark its odd multiples starting from i*i
            for (long long j = (long long)i * i; j <= sqrt_limit; j += 2 * i) {
                sieve[j] = true;
            }
        }
    }
    
    // Count base primes
    num_base_primes = 1; // Start with 2
    for (int i = 3; i <= sqrt_limit; i += erients
    for (int i = 3; i <= sqrt_limit; i += 2) {
        if (sieve[i]) {
            num_base_primes++;
        }
    }
    
    // Allocate memory for base primes
    base_primes = (int *)malloc(num_base_primes * sizeof(int));
    base_primes[0] = 2;
    
    // Fill base primes array
    int j = 1;
    for (int i = 3; i <= sqrt_limit; i += 2) {
        if (sieve[i]) {
            base_primes[j++] = i;
       ing
    free(sieve);
}

/*
 * Prints a prime number with appropriate formatting.
 * Handles the special case of 2 (only even prime).
 */
void print_prime(unsigned int prime) {
    printf("%u\n", prime);
}

/*
 * Sieves a segment [low, high] using precomputed base primes.
 * Only considers odd numbers to save memory.
 * 
 * Parameters:
 *   low:   Lower bound of segment (must be odd)
 *   high:  Upper bound of segment
 *   count: Pointer to counter for primes found
 * 
 * Uses bitwise operations for memory efficiency.
 * Each bit represents whether an odd number is composite.
 */
void sieve_segment(unsigned long low, unsigned long high, unsigned long *count) {
    // Adjust low to be odd if it isner
    if (low % 2 == 0) low++;
    
    // Size needed for bitset (each bit represents an odd number)
    size_t size = ((high - low) / 2 + 7) / 8;
    char *segment = (char *)calloc(size, sizeof(char));
    
    if (!segment) {
        fprintf(stderr, "Memory allocation failed for segment\n");
        exit(1);
    }
    
    // Mark composites in segment using base primes
    for (int i = 1; i < num_base_primes; i++) {
        int prime = base_primes[i];
      eration
        // Find first odd multiple of prime >= low
        unsigned long start = ((low + prime - 1) / prime) * prime;
        if (start % 2 == 0) start += prime;
        
        // Mark odd multiples as composite
        for (unsigned long j = start; j <= high; j += 2 * prime) {
            segment[(j - low) / 2] = 1;
       er
    }
    
    // Count and output primes in segment
    for (unsigned long i = low; i <= high; i += 2) {
        if (!segment[(i - low) / 2]) {
            (*count)++;
            if (*count <= 1000000) { // Limit output to first 1M primes
                print_prime((unsigned int)i);
           er
        }
    }
    
    free(segment);
}

/*
 * Main function implementing segmented sieve algorithm.
 * Generates all primes up to LIMIT efficiently.
 */
int main() {
    printf("Generating primes up to %lu using optimized segmented sieve...\n", LIMIT);
    printf("First 1,000,000 primes:\n");
    
    // Generate base primes up to sqrt(LIMIT)
    generate_base_primes((int)sqrt(LIMIT) + erintf("Generated %d base primes\n", num_base_primes);
    
    unsigned long prime_count = 0;
    
    // Don't forget the only even prime
    print_prime(2);
    prime_count = 1;
    
    // Process segments
    for (unsigned long low = 3; low <= LIMIT; low += SEGMENT_SIZE) {
        unsigned long high = (low + SEGMENT_SIZE - 1 < LIMIT) ? 
                            low + SEGMENT_SIZE - ome
        sieve_segment(low, high, &prime_count);
        
        // Progress indicator
        if (low % (SEGMENT_SIZE * 256) == 3) {
            printf("Progress: up to %lu... (%lu primes found)\n", 
                   high, prime_count);
        }
    }
    
    printf("\nTotal primes generated: %lu\n", prime_count);
    printf("Base primes used: %d\n", num_base_primes);
    
    // Clean up
    free(base_primes);
    
    return 0;
}

/*
 * Algorithm Explanation:
 * 
 * 1. BASE PRIMES PHASE:
 *    - Generate all primes up to √N using standard sieve
 *    - These are stored in 'base_primes' array
 *    - Memory efficient as we only store ~3,400 primes
 * er
 * 2. SEGMENTED SIEVING PHASE:
 *    - Divide range [3, N] into segments
 *    - For each segment, create a small bitset
 *    - Mark composites using base primes
 *    - Only consider odd numbers (halves memory usage)
 * 
 * 3. OUTPUT OPTIMIZATION:
 *    - Only print first 1M primes to avoid excessive I/O
 *    - Print progress updates during computation
 * 
 * KEY OPTIMIZATIONS:
 *    - Bit-packed array (1 bit per odd number)
 *    - Only check odd numbers
 *    - Segmented approach (fits in memory)
 *   er
 *    - Early termination when prime² > segment_start
 * 
 * MEMORY USAGE:
 *    - Base primes: ~14KB
 *    - Segment sieve: ~16KB
 *    - Total: ~32KB (much better than 1GB!)
 * 
 * TIME COMPLEXITY:
 *    - O(N log log N) - same as regular sieve
 *    - But with better cache performance due to segmentation
 */

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