Implementation of is_probable_prime() function. Also made big_random() with range.

include/BigInt.hpp

@@ -102,6 +102,11 @@ class BigInt {
 
         // Random number generating functions:
         friend BigInt big_random(size_t);
+        friend BigInt big_random_range(BigInt UpperBound);
+
+        //is_probable_prime:
+        bool is_probable_prime(size_t certainty);
 };
 
 #endif  // BIG_INT_HPP
+

include/functions/math.hpp

@@ -10,6 +10,7 @@
 #include <string>
 
 #include "functions/conversion.hpp"
+#include "functions/random.hpp"
 
 
 /*
@@ -247,5 +248,108 @@ BigInt lcm(const std::string& num1, const BigInt& num2){
     return lcm(BigInt(num1), num2);
 }
 
+/*
+    BigInt ModPow(BigInt base, BigInt exponent, BigInt modulus)
+    --------------------
+ */
+
+BigInt ModPow(BigInt base, BigInt exponent, BigInt modulus){
+    BigInt x = 1;
+    BigInt y = base;
+    while(exponent > 0){
+        if (exponent % 2 == 1){
+            x = (x * y) % modulus;
+        }
+        y = (y * y) % modulus;
+        exponent = exponent / 2;
+    }
+    return x % modulus;
+}
+
+/*
+    BigInt isJacobian(BigInt a, BigInt n)
+    ----------------------
+    calculate jacobian
+ */
+
+BigInt findJacobian(BigInt a, BigInt n){
+    if (a == 0){
+        return BigInt(0);//(0/n) = 0
+    }
+    int ans = 1;
+    if (a < 0){
+        a = -a; //(a/n) = (-a/n)*(-1/n)
+        if (n % 4 == 3){
+            ans = -ans; // (-1/n) = -1 if n = 3 (mod 4)
+        }
+    }
+    if (a == 1) {
+        return BigInt(ans); // (1/n) = 1
+    }
+    while(a != 0){
+        if (a < 0){
+            a = -a;// (a/n) = (-a/n)*(-1/n)
+            if (n % 4 == 3){
+                ans = -ans;// (-1/n) = -1 if n = 3 (mod 4)
+            }
+        }
+        while(a % 2 == 0) {
+            a = a / 2;
+            if (n % 8 == 3 || n % 8 == 5){
+                ans = -ans;
+            }
+        }
+        //swap
+        BigInt temp = a;
+        a = n;
+        n = temp;
+        if (a % 4 == 3 && n % 4 == 3){
+            ans = -ans;
+        }
+        a = a % n;
+        if (a > n / 2){
+            a = a - n;
+        }
+    }
+    if (n == 1){
+        return BigInt(ans);
+    }
+    return BigInt(0);
+}
+
+/*
+    bool BigInt::is_probable_prime(size_t certainty)
+    -------------------
+    Using Solovay-Strassen primality test.
+    Returns "true" with probability of 1 - (2^-certainty) * 100%
+*/
+
+bool BigInt::is_probable_prime(size_t certainty){
+    if(BigInt(value) < 2 || certainty == 0 || sign == '-' || (BigInt(value) != 2 && BigInt(value) % 2 == 0)){
+        return false;
+    }
+    if(certainty < 0){ // certainty can't be negative.
+        throw std::invalid_argument("Error: certainty < 0. Please make certainty >= 0.");
+        return false;
+    }
+
+    //Actual Algorithm
+    for(size_t i = 0; i < certainty; ++i){
+        BigInt a = 0;
+        while(a == 0 || a == 1){ // get value in range [2,n - 1]
+            a = big_random_range((BigInt(value) - 1));
+            strip_leading_zeroes(a.value);
+        }
+        BigInt x = (BigInt(value) + findJacobian(a, BigInt(value))) % BigInt(value);
+        BigInt power = ModPow(a, (BigInt(value) - 1) / 2, BigInt(value));
+        if(x == 0 || power != x){
+            return false;
+        }
+    }
+    return true;
+}
+
+
 
 #endif  // BIG_INT_MATH_FUNCTIONS_HPP
+

include/functions/random.hpp

@@ -44,5 +44,53 @@ BigInt big_random(size_t num_digits = 0) {
     return big_rand;
 }
 
+/*
+    BigInt big_random_range(BigInt UpperBound)
+    ----------------------------------
+    Returns a random BigInt in range [0, UpperBound].
+ */
+
+BigInt big_random_range(BigInt UpperBound) { // range must be greater than 0
+    std::random_device rand_generator; // true random number generator
+    if(UpperBound.sign == '-'){
+        throw std::invalid_argument("Error: Please make UpperBound >= 0.");
+    }
+    BigInt big_rand;
+    big_rand.value = "";    // clear value to append digits
+
+    size_t num_digits = UpperBound.value.size();
+    bool too_big = true;
+    size_t iter = 0;
+    std::string strValue = "";
+    while (iter < num_digits){
+        int randomDigit = rand_generator() % 10;
+        if(!too_big){
+            strValue += std::to_string(randomDigit);
+            iter = iter + 1;
+        }
+        else {
+            char comp = UpperBound.value[iter];
+            int UpperboundDigit = std::atoi(&comp);
+            if(randomDigit < UpperboundDigit){
+                too_big = false;
+                strValue += std::to_string(randomDigit);
+                iter = iter + 1;
+            }
+            else if(randomDigit > UpperboundDigit){
+                too_big = true;
+                strValue = ""; //clear number because it's too big
+                iter = 0;
+            }
+            else {
+                too_big = true;
+                strValue += std::to_string(randomDigit);
+                iter = iter + 1;
+            }
+        }
+    }
+    big_rand.value = strValue;
+    return big_rand;
+}
+
 
 #endif  // BIG_INT_RANDOM_FUNCTIONS_HPP

test/functions/math.cpp

@@ -416,3 +416,27 @@ TEST_CASE("lcm()of big integers", "[functions][math][lcm][big]") {
         "533220692127153044311875258011747917053108027629278373174251200266431"
         "428784066739966");
 }
+
+
+TEST_CASE("is_probable_prime()", "[functions][math][is_probable_prime][random]") {
+    //List of first 1000 prime numbers.
+    BigInt prime_array[] = {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};
+
+    size_t numTrue = 0;
+    size_t certainty = 15;
+    for(size_t i = 0; i < 100; ++i){
+        size_t iter = std::rand() % 1000;
+        BigInt prime(prime_array[iter]);
+        if(prime.is_probable_prime(certainty)){
+            numTrue += 1;
+        }
+    }
+    double Simulation = (numTrue/100.0) * 100.0;
+    double Expected = (1.0 - (1 / std::pow(2.0,(double)(certainty)))) * 100.0;
+    REQUIRE(Simulation >= Expected);
+}
+
+
+
+
+