Completed first pass of the primegen algorithm

.gitignore

@@ -9,3 +9,4 @@
 
 # Generated by Cargo
 /target/
+Cargo.lock

Cargo.lock

@@ -2,7 +2,7 @@
 name = "pumpkin"
 version = "0.1.0"
 dependencies = [
- "num 0.1.27 (registry+https://github.com/rust-lang/crates.io-index)",
+ "ramp 0.1.8 (registry+https://github.com/rust-lang/crates.io-index)",
  "rand 0.3.11 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
 
@@ -15,18 +15,27 @@ dependencies = [
  "winapi-build 0.1.1 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
 
+[[package]]
+name = "gcc"
+version = "0.3.17"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+dependencies = [
+ "advapi32-sys 0.1.2 (registry+https://github.com/rust-lang/crates.io-index)",
+ "winapi 0.2.4 (registry+https://github.com/rust-lang/crates.io-index)",
+]
+
 [[package]]
 name = "libc"
 version = "0.1.10"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 
 [[package]]
-name = "num"
+name = "ramp"
-version = "0.1.27"
+version = "0.1.8"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 dependencies = [
+ "gcc 0.3.17 (registry+https://github.com/rust-lang/crates.io-index)",
  "rand 0.3.11 (registry+https://github.com/rust-lang/crates.io-index)",
- "rustc-serialize 0.3.16 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
 
 [[package]]
@@ -39,11 +48,6 @@ dependencies = [
  "winapi 0.2.4 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
 
-[[package]]
-name = "rustc-serialize"
-version = "0.3.16"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-
 [[package]]
 name = "winapi"
 version = "0.2.4"

Cargo.toml

@@ -4,5 +4,5 @@ version = "0.1.0"
 authors = ["Zach Dziura <zcdziura@gmail.com>"]
 
 [dependencies]
-num = "0.1.27"
+ramp = "0.1.8"
 rand = "0.3.11"

src/lib.rs

@@ -1,4 +1,8 @@
-extern crate num;
+#![feature(augmented_assignments)]
+#![feature(core)]
+
+extern crate core;
+extern crate ramp;
 extern crate rand;
 
-pub mod primes;
+pub mod prime;

src/prime.rs

@@ -0,0 +1,213 @@
+use core::ops::{Add, BitAnd, Mul, Rem, Shr, Sub};
+
+use ramp::{Int, RandomInt};
+
+use rand::{OsRng, thread_rng};
+
+use std::fmt;
+
+static SMALL_PRIMES: [u32; 999] = [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];
+
+#[derive(Debug)]
+pub struct Prime {
+    bit_length: usize,
+    num: Int
+}
+
+impl Prime {
+    pub fn new(bit_length: usize) -> Prime {
+        let one = Int::one();
+        let two = &one + &one;
+        let mut rngesus = match OsRng::new() {
+            Ok(rng) => rng,
+            Err(reason) => panic!("Error initializing RNG: {}", reason)
+        };
+        let mut candidate = rngesus.gen_uint(bit_length);
+        
+        // Make sure candidate is odd before continuing...
+        if &candidate & (&one) == 0 {
+            candidate += &one;
+        }
+        while !is_prime(&candidate) {
+            candidate += &two;
+        }
+
+        Prime {
+            bit_length: bit_length,
+            num: candidate
+        }
+    }
+
+}
+
+impl fmt::Display for Prime {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "{}", self.num)
+    }
+}
+
+
+pub fn is_prime(candidate: &Int) -> bool {
+    // First, iterate through the array of small primes and divide the
+    // candidate. If the candidate divides any of them, then we know the number
+    // is a multiple of that prime; that is, the candidate is composite.
+    let zero = Int::zero();
+
+    for p in SMALL_PRIMES.into_iter() {
+        let prime: Int = Int::from(*p);
+        let (_, r) = candidate.divmod(&prime);
+
+        if r != zero {
+            continue;
+        } else {
+            return false;
+        }
+    }
+
+    // Second, do a Fermat test on the candidate
+    if !fermat(candidate) {
+        return false;
+    }
+
+    // Finally, do a Miller-Rabin test
+    if !miller_rabin(candidate) {
+        return false;
+    }
+
+    true
+}
+
+pub fn fermat(candidate: &Int) -> bool {
+    // Perform Fermat's little theorem on the candidate to determine probable
+    // primality.
+    let one = Int::one();
+    let random = thread_rng().gen_int_range(&one, candidate);
+
+    let result = mod_exp(&random, &candidate.sub(&one), candidate);
+
+    if result == one {
+        true
+    } else {
+        false
+    }
+}
+
+pub fn miller_rabin(candidate: &Int) -> bool {
+    // Perform five iterations of the Miller-Rabin test on the candidate.
+    let (s, d) = rewrite(candidate);
+    let one = Int::one();
+    let two = (&one).add(&one);
+
+    for _ in (0..5) {
+        let basis = thread_rng().gen_int_range(&two, candidate);
+        let mut x = mod_exp(&basis, &d, candidate);
+
+        if x.eq(&one) || x.eq(&(candidate.sub(&one))) {
+            continue;
+        } else {
+            for _ in (one.clone() .. s.sub(&one)) {
+                x = mod_exp(&x, &two, candidate);
+                if x == one.clone() {
+                    return false;
+                } else if x == (candidate.sub(&one)) {
+                    break;
+                }
+            }
+            return false;
+        }
+    }
+
+    true
+}
+
+fn mod_exp(base: &Int, exponent: &Int, modulus: &Int) -> Int {
+    let (zero, one) = (Int::zero(), Int::one());
+    let mut result = one.clone();
+    let mut base = base.clone();
+    let mut exponent = exponent.clone();
+
+    while &exponent > &zero {
+        if (&exponent).bitand(&one) == (one.clone()) {
+            result = ((&result).mul(&base)).rem(modulus);
+        }
+
+        base = ((&base).mul(&base)).rem(modulus);
+        exponent = exponent.clone().shr(1);
+    }
+
+    result
+}
+
+fn rewrite(candidate: &Int) -> (Int, Int) {
+    let one = Int::one();
+
+    let mut d = candidate.sub(&one);
+    let mut s = Int::zero();
+
+    while (&d).bitand(&one) == one {
+        d = d.clone().shr(1);
+        s = (&s).add(&one);
+    }
+
+    (s, d)
+}

src/primes.rs

@@ -1,108 +0,0 @@
-use num::{BigUint, FromPrimitive, One, Zero, pow};
-use num::bigint::RandBigInt;
-use num::integer::Integer;
-
-use rand::{OsRng, thread_rng};
-
-pub fn generate_prime() -> BigUint {
-    /* Generates a large prime number within the range [2^2048, 2^2049);
-     * that is, generates a large prime number between 2^2048 inclusive and
-     * 2^2049 exclusive.
-     */
-
-    // Generate the RNG, which will be sourced from the OS's secure source
-    // of entropy. Also, give it a sweet name.
-    let one: BigUint = One::one();
-    let two = one.clone() + one.clone();
-    let mut rngesus = match OsRng::new() {
-        Ok(o) => o,
-        Err(err) => panic!("Error initializing RNG: {}", err)
-    };
-
-    let lower_bound = pow(BigUint::from_u8(2).unwrap(), 2048);
-    let upper_bound = pow(BigUint::from_u8(2).unwrap(), 2049);
-
-    let mut candidate = rngesus.gen_biguint_range(&lower_bound,
-                                                     &upper_bound);
-    if candidate.is_even() {
-        candidate = candidate + one.clone();
-    }
-    while !test_prime(&candidate, 128) {
-        candidate = candidate + two.clone();
-    }
-    
-    candidate
-}
-
-fn test_prime(candidate: &BigUint, limit: u8) -> bool {
-    let (zero, one): (BigUint, BigUint) = (Zero::zero(), One::one());
-    let two = one.clone() + one.clone();
-    
-    if *candidate < two {
-        false
-    } else if *candidate == two {
-        true
-    } else if candidate.is_even() {
-        false
-    } else {
-        let (s, d) = rewrite(&(candidate - one.clone()));
-        let mut k = 0;
-
-        while k < limit {
-            let basis = thread_rng().gen_biguint_range(&two, candidate);
-            let mut v = modulo(&basis, &d, candidate);
-
-            if v != one.clone() && v != (candidate - one.clone()) {
-                let mut i = zero.clone();
-                loop {
-                    v = modulo(&v, &two, candidate);
-                    if v == (candidate - one.clone()) {
-                        break
-                    } else if v == one.clone() || i == (s.clone() - one.clone()) {
-                        return false;
-                    }
-                    
-                    i = i + one.clone();
-                }
-            }  
-
-            k = k + 2;
-        }
-
-        true
-    }
-}
-
-fn rewrite(n: &BigUint) -> (BigUint, BigUint) {
-    let mut d = n.clone();
-    let mut s: BigUint = Zero::zero();
-    let one: BigUint = One::one();
-    let two = one.clone() + one.clone();
-
-    while d.is_even() {
-        d = d.clone() / two.clone();
-        s = s.clone() + one.clone();
-    }
-
-    (s, d)
-}
-
-fn modulo(base: &BigUint, exponent: &BigUint, modulus: &BigUint) -> BigUint {
-    // Modular exponentiation function, with BigUints!
-    // Warning!! Ahead, thar be clones!
-    let (zero, one): (BigUint, BigUint) = (Zero::zero(), One::one());
-    let mut result = one.clone();
-    let mut b = base.clone();
-    let mut e = exponent.clone();
-
-    while e > zero {
-        if (exponent & one.clone()) == one {
-            result = (result * b.clone()) % modulus;
-        }
-
-        b = (b.clone() * b.clone()) % modulus;
-        e = e >> 1;
-    }
-
-    result
-}