primes_dynamic.h

// for memset
#include <string.h>

int PRIMES[78550];
int last_calculated_prime = -1;
const int BASIC_PRIMES[] =  {2, 3, 5, 7, 11, 13, 17, 19, 
23, 29, 31, 37, 41, 43, 47, 53, 
59, 61, 67, 71, 73, 79, 83, 89, 
97, 101, 103, 107, 109, 113, 127, 131, 
137, 139, 149, 151, 157, 163, 167, 173, 
179, 181, 191, 193, 197, 199, 211, 223, 
227, 229, 233, 239, 241, 251, 257, 263, 
269, 271, 277, 281, 283, 293, 307, 311, 
313, 317, 331, 337, 347, 349, 353, 359, 
367, 373, 379, 383, 389, 397, 401, 409, 
419, 421, 431, 433, 439, 443, 449, 457, 
461, 463, 467, 479, 487, 491, 499, 503, 
509, 521, 523, 541, 547, 557, 563, 569, 
571, 577, 587, 593, 599, 601, 607, 613, 
617, 619, 631, 641, 643, 647, 653, 659, 
661, 673, 677, 683, 691, 701, 709, 719, 
727, 733, 739, 743, 751, 757, 761, 769, 
773, 787, 797, 809, 811, 821, 823, 827, 
829, 839, 853, 857, 859, 863, 877, 881, 
883, 887, 907, 911, 919, 929, 937, 941, 
947, 953, 967, 971, 977, 983, 991, 997, 
1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 
1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 
1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 
1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 
1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 
1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 
1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 
1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 
1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 
1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 
1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 
1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 
1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 
1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 
1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 
1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 
1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 
2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 
2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 
2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 
2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 
2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 
2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 
2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 
2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 
2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 
2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 
2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 
2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 
2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 
2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 
2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 
2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 
3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 
3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 
3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 
3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 
3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 
3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 
3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 
3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 
3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 
3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 
3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 
3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 
3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 
3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 
3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 
4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 
4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 
4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 
4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 
4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 
4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 
4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 
4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 
4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 
4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 
4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 
4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 
4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 
4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 
4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 
5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 
5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 
5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 
5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 
5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 
5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 
5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 
5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 
5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 
5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 
5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 
5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 
5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 
5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 
6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 
6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 
6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 
6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 
6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 
6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 
6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 
6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 
6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 
6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 
6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 
6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 
6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 
6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 
6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 
7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 
7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 
7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 
7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 
7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 
7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 
7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 
7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 
7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 
7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 
7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 
7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 
7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 
8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 
8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 
8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 
8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 
8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 
8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 
8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 
8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 
8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 
8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 
8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 
8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 
8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 
8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 
9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 
9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 
9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 
9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 
9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 
9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 
9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 
9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 
9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 
9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 
9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 
9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 
9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 
9931, 9941, 9949, 9967, 9973};
#include "types.h"
#include "hw_templates.h"
#define BIGEST_KNOWN_PRIME PRIMES[last_calculated_prime]
#define BIGEST_PRIME_INDEX last_calculated_prime
#define MAX_PRIME sizeof(PRIMES)/sizeof(int)
void add_prime(const int prime);
long prime_sieve(const long max_num);

long iterative_prime(const long max_num, bool return_if_not_prime);
void init_primes();
int iz_prime(const int number) {
    if(last_calculated_prime<0)
        init_primes();
    if(number>BIGEST_KNOWN_PRIME) {
        //log_info("Generating new primes for %d.", number);
        return iterative_prime(number, true)==0;
    }
    int prime_index = 0;
    for(;prime_index<=last_calculated_prime; ++prime_index) {
        if(PRIMES[prime_index] == number)
            return true;
    }
    return false;
}

void init_primes() {
    const int predefinedPrimes = (sizeof(BASIC_PRIMES)/sizeof(int));
    if(last_calculated_prime+1>=predefinedPrimes)
        return;
    int i=0;
    for(;i<predefinedPrimes; ++i) {
        PRIMES[i] = BASIC_PRIMES[i];
    }
    last_calculated_prime = i-1;
}

// First parameter is the max argument of the modified sieve algorithm
// Second parameter determines, that instead of finding all primes up to
// max_num, we're happy with finding any prime that can divide it
// In that case, sieve might return much sooner and might not populate all
// primes up to max num
long iterative_prime(const long max_num, bool return_if_not_prime) {
    if(last_calculated_prime<0)
        init_primes();
    // Skipping next direct number since it's even
    int current = BIGEST_KNOWN_PRIME+2;
    // If max_num is current-1 it must be even number, therefore divisible by 2
    if(max_num == current-1)
        return 2;

    int last_succesful_denominator = 0;
    log_info("Iterator start <%d, %ld>; Primes %d of max %d", current, max_num, last_calculated_prime, MAX_PRIME);
    for(;current<=max_num;) {
        // Loop over all primes. If any of them divides current, current is not a prime
        int prime_index = 0;
        last_succesful_denominator = 0;
        bool current_iz_prime = true;
        //log_info("  Dividing %d with all known primes.", current);
        for(;prime_index<=last_calculated_prime; ++prime_index) {
            if(current % PRIMES[prime_index] == 0) {
                current_iz_prime = false;
                last_succesful_denominator = PRIMES[prime_index];
                log_info("   - %d sucesfully divided by %d (%dth prime)", current, PRIMES[prime_index], prime_index);
                break;
            }
        }

        if(current_iz_prime) {
            // Register new prime
            add_prime(current);
            // If given number turned out to be prime
            if(current == max_num)
                return 0;
            // if given number can be divided by new prime
            // and we're looking for that
            if(max_num % current) {
                last_succesful_denominator = current;
                log_info("    -- this prime divides our target %ld.", max_num);
                break;
            }
                
        }
        // Jump to next number, jumping by 2 since every second number is even
        ++current;
        // Don't skip the required number tho (this if should always be true)
        if(current<max_num)
            ++current;
        else {
            //printf("Fatal error: Did you just give me even number to test?!");
            //exit(13);
        }
    }
    log_info("Loop over, %ld ain't a prime and was divided by %d.", max_num, last_succesful_denominator);
    return last_succesful_denominator;
}
// This is modified sieve algorithm that works from any x to any y value
long prime_sieve(const long max_num) {
    if(last_calculated_prime<0)
        init_primes();
    // Skipping next direct number since it's even
    const long current = BIGEST_KNOWN_PRIME+2;
    log_info("Sieve start <%ld, %ld>; Primes %d of max %d", current, max_num, last_calculated_prime, MAX_PRIME);
    // If max_num is current-1 it must be even number, therefore divisible by 2
    if(max_num == current-1)
        return 2;
    // number of numbers to investigate
    const int no_numbers = max_num - current;
    bool* numbers = calloc(no_numbers+1, sizeof(bool));
    memset(numbers, true, no_numbers*sizeof(bool));
    // Well access array by base_index+[current number]
    // therefore inital number + base_index must be 0
    const long base_index = -1*current;
    log_info("  Iterating over %d numbers. ", no_numbers);
    // First cross out any number that can be divided by current set of primes
    // count number of identified non-primes
    int non_primes = 0;
    for(long i=current; i<=max_num; ++i) {
        for(int prime_index = 0; prime_index<=BIGEST_PRIME_INDEX; ++prime_index) {
            if(i % PRIMES[prime_index] == 0) {
                numbers[base_index + i] = false;
                ++non_primes;
                //log_info("     %ld not a prime, divided by %d.", i, PRIMES[prime_index]);
                break;
            }
        }
    }
    log_info("  Crossed out %d numbers, %d remains", non_primes, no_numbers - non_primes);
    // Any further operations only make sense if any primes were left...
    if(non_primes < no_numbers) {
        int non_primes_2 = 0;
        // Now loop and mark numbers
        for(long p=current; p<=max_num; ++p) {
            const int current_index = base_index + p;
            if(!numbers[current_index])
                continue;
            long p_tmp = p*p;
            if(p_tmp > max_num) {
                log_info("  Crossing terminated at %ld since %ld^2 > %ld", p, p, max_num);
                break;
            }
            log_info("  Crossing out multiples of %ld, starting at %ld.", p, p_tmp);
            for(;p_tmp<=max_num; p_tmp+=p) {
                numbers[p_tmp + base_index] = false;
                ++non_primes_2;
            }
        }
        int primes = 0;
        // Any unmarked numbers are primes
        for(int i=0; i<no_numbers; ++i) {
            if(numbers[i]) {
                add_prime(i - base_index);
                ++primes;
            }
        }
        log_info("  Found %d primes.", primes);
    }
    else {
        log_info("  No potential primes left...");
    }
    free(numbers);
    return 0;
}
void add_prime(const int prime) {
    // Register new prime
    //log_info("  Registering prime %d, %d out of %d.", prime, last_calculated_prime+1, MAX_PRIME);
    ++last_calculated_prime;
    if(last_calculated_prime>=MAX_PRIME) {
        chyba("Fatal error: no more memory available for prime numbers. Halt.", 11);
    }
    PRIMES[last_calculated_prime] = prime;
    //log_info("    -- added to list.");
}