// Copyright 2018 Developers of the Rand project. // Copyright 2013-2018 The Rust Project Developers. // // Licensed under the Apache License, Version 2.0 or the MIT license // , at your // option. This file may not be copied, modified, or distributed // except according to those terms. //! The ISAAC-64 random number generator. use core::{fmt, slice}; use core::num::Wrapping as w; use rand_core::{RngCore, SeedableRng, Error, le}; use rand_core::block::{BlockRngCore, BlockRng64}; use isaac_array::IsaacArray; #[allow(non_camel_case_types)] type w64 = w; const RAND_SIZE_LEN: usize = 8; const RAND_SIZE: usize = 1 << RAND_SIZE_LEN; /// A random number generator that uses ISAAC-64, the 64-bit variant of the /// ISAAC algorithm. /// /// ISAAC stands for "Indirection, Shift, Accumulate, Add, and Count" which are /// the principal bitwise operations employed. It is the most advanced of a /// series of array based random number generator designed by Robert Jenkins /// in 1996[^1]. /// /// ISAAC-64 is mostly similar to ISAAC. Because it operates on 64-bit integers /// instead of 32-bit, it uses twice as much memory to hold its state and /// results. Also it uses different constants for shifts and indirect indexing, /// optimized to give good results for 64bit arithmetic. /// /// ISAAC-64 is notably fast and produces excellent quality random numbers for /// non-cryptographic applications. /// /// In spite of being designed with cryptographic security in mind, ISAAC hasn't /// been stringently cryptanalyzed and thus cryptographers do not not /// consensually trust it to be secure. When looking for a secure RNG, prefer /// [`Hc128Rng`] instead, which, like ISAAC, is an array-based RNG and one of /// the stream-ciphers selected the by eSTREAM contest. /// /// ## Overview of the ISAAC-64 algorithm: /// (in pseudo-code) /// /// ```text /// Input: a, b, c, s[256] // state /// Output: r[256] // results /// /// mix(a,i) = !(a ^ a << 21) if i = 0 mod 4 /// a ^ a >> 5 if i = 1 mod 4 /// a ^ a << 12 if i = 2 mod 4 /// a ^ a >> 33 if i = 3 mod 4 /// /// c = c + 1 /// b = b + c /// /// for i in 0..256 { /// x = s_[i] /// a = mix(a,i) + s[i+128 mod 256] /// y = a + b + s[x>>3 mod 256] /// s[i] = y /// b = x + s[y>>11 mod 256] /// r[i] = b /// } /// ``` /// /// This implementation uses [`BlockRng64`] to implement the [`RngCore`] methods. /// /// See for more information the documentation of [`IsaacRng`]. /// /// [^1]: Bob Jenkins, [*ISAAC and RC4*]( /// http://burtleburtle.net/bob/rand/isaac.html) /// /// [`IsaacRng`]: ../isaac/struct.IsaacRng.html /// [`Hc128Rng`]: ../../rand_hc/struct.Hc128Rng.html /// [`BlockRng64`]: ../../rand_core/block/struct.BlockRng64.html /// [`RngCore`]: ../../rand_core/trait.RngCore.html #[derive(Clone, Debug)] #[cfg_attr(feature="serde1", derive(Serialize, Deserialize))] pub struct Isaac64Rng(BlockRng64); impl RngCore for Isaac64Rng { #[inline(always)] fn next_u32(&mut self) -> u32 { self.0.next_u32() } #[inline(always)] fn next_u64(&mut self) -> u64 { self.0.next_u64() } fn fill_bytes(&mut self, dest: &mut [u8]) { self.0.fill_bytes(dest) } fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> { self.0.try_fill_bytes(dest) } } impl SeedableRng for Isaac64Rng { type Seed = ::Seed; fn from_seed(seed: Self::Seed) -> Self { Isaac64Rng(BlockRng64::::from_seed(seed)) } /// Create an ISAAC random number generator using an `u64` as seed. /// If `seed == 0` this will produce the same stream of random numbers as /// the reference implementation when used unseeded. fn seed_from_u64(seed: u64) -> Self { Isaac64Rng(BlockRng64::::seed_from_u64(seed)) } fn from_rng(rng: S) -> Result { BlockRng64::::from_rng(rng).map(|rng| Isaac64Rng(rng)) } } impl Isaac64Rng { /// Create an ISAAC-64 random number generator using an `u64` as seed. /// If `seed == 0` this will produce the same stream of random numbers as /// the reference implementation when used unseeded. #[deprecated(since="0.6.0", note="use SeedableRng::seed_from_u64 instead")] pub fn new_from_u64(seed: u64) -> Self { Self::seed_from_u64(seed) } } /// The core of `Isaac64Rng`, used with `BlockRng`. #[derive(Clone)] #[cfg_attr(feature="serde1", derive(Serialize, Deserialize))] pub struct Isaac64Core { #[cfg_attr(feature="serde1",serde(with="super::isaac_array::isaac_array_serde"))] mem: [w64; RAND_SIZE], a: w64, b: w64, c: w64, } // Custom Debug implementation that does not expose the internal state impl fmt::Debug for Isaac64Core { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f, "Isaac64Core {{}}") } } impl BlockRngCore for Isaac64Core { type Item = u64; type Results = IsaacArray; /// Refills the output buffer, `results`. See also the pseudocode desciption /// of the algorithm in the [`Isaac64Rng`] documentation. /// /// Optimisations used (similar to the reference implementation): /// /// - The loop is unrolled 4 times, once for every constant of mix(). /// - The contents of the main loop are moved to a function `rngstep`, to /// reduce code duplication. /// - We use local variables for a and b, which helps with optimisations. /// - We split the main loop in two, one that operates over 0..128 and one /// over 128..256. This way we can optimise out the addition and modulus /// from `s[i+128 mod 256]`. /// - We maintain one index `i` and add `m` or `m2` as base (m2 for the /// `s[i+128 mod 256]`), relying on the optimizer to turn it into pointer /// arithmetic. /// - We fill `results` backwards. The reference implementation reads values /// from `results` in reverse. We read them in the normal direction, to /// make `fill_bytes` a memcopy. To maintain compatibility we fill in /// reverse. /// /// [`Isaac64Rng`]: struct.Isaac64Rng.html fn generate(&mut self, results: &mut IsaacArray) { self.c += w(1); // abbreviations let mut a = self.a; let mut b = self.b + self.c; const MIDPOINT: usize = RAND_SIZE / 2; #[inline] fn ind(mem:&[w64; RAND_SIZE], v: w64, amount: usize) -> w64 { let index = (v >> amount).0 as usize % RAND_SIZE; mem[index] } #[inline] fn rngstep(mem: &mut [w64; RAND_SIZE], results: &mut [u64; RAND_SIZE], mix: w64, a: &mut w64, b: &mut w64, base: usize, m: usize, m2: usize) { let x = mem[base + m]; *a = mix + mem[base + m2]; let y = *a + *b + ind(&mem, x, 3); mem[base + m] = y; *b = x + ind(&mem, y, 3 + RAND_SIZE_LEN); results[RAND_SIZE - 1 - base - m] = (*b).0; } let mut m = 0; let mut m2 = MIDPOINT; for i in (0..MIDPOINT/4).map(|i| i * 4) { rngstep(&mut self.mem, results, !(a ^ (a << 21)), &mut a, &mut b, i + 0, m, m2); rngstep(&mut self.mem, results, a ^ (a >> 5 ), &mut a, &mut b, i + 1, m, m2); rngstep(&mut self.mem, results, a ^ (a << 12), &mut a, &mut b, i + 2, m, m2); rngstep(&mut self.mem, results, a ^ (a >> 33), &mut a, &mut b, i + 3, m, m2); } m = MIDPOINT; m2 = 0; for i in (0..MIDPOINT/4).map(|i| i * 4) { rngstep(&mut self.mem, results, !(a ^ (a << 21)), &mut a, &mut b, i + 0, m, m2); rngstep(&mut self.mem, results, a ^ (a >> 5 ), &mut a, &mut b, i + 1, m, m2); rngstep(&mut self.mem, results, a ^ (a << 12), &mut a, &mut b, i + 2, m, m2); rngstep(&mut self.mem, results, a ^ (a >> 33), &mut a, &mut b, i + 3, m, m2); } self.a = a; self.b = b; } } impl Isaac64Core { /// Create a new ISAAC-64 random number generator. fn init(mut mem: [w64; RAND_SIZE], rounds: u32) -> Self { fn mix(a: &mut w64, b: &mut w64, c: &mut w64, d: &mut w64, e: &mut w64, f: &mut w64, g: &mut w64, h: &mut w64) { *a -= *e; *f ^= *h >> 9; *h += *a; *b -= *f; *g ^= *a << 9; *a += *b; *c -= *g; *h ^= *b >> 23; *b += *c; *d -= *h; *a ^= *c << 15; *c += *d; *e -= *a; *b ^= *d >> 14; *d += *e; *f -= *b; *c ^= *e << 20; *e += *f; *g -= *c; *d ^= *f >> 17; *f += *g; *h -= *d; *e ^= *g << 14; *g += *h; } // These numbers are the result of initializing a...h with the // fractional part of the golden ratio in binary (0x9e3779b97f4a7c13) // and applying mix() 4 times. let mut a = w(0x647c4677a2884b7c); let mut b = w(0xb9f8b322c73ac862); let mut c = w(0x8c0ea5053d4712a0); let mut d = w(0xb29b2e824a595524); let mut e = w(0x82f053db8355e0ce); let mut f = w(0x48fe4a0fa5a09315); let mut g = w(0xae985bf2cbfc89ed); let mut h = w(0x98f5704f6c44c0ab); // Normally this should do two passes, to make all of the seed effect // all of `mem` for _ in 0..rounds { for i in (0..RAND_SIZE/8).map(|i| i * 8) { a += mem[i ]; b += mem[i+1]; c += mem[i+2]; d += mem[i+3]; e += mem[i+4]; f += mem[i+5]; g += mem[i+6]; h += mem[i+7]; mix(&mut a, &mut b, &mut c, &mut d, &mut e, &mut f, &mut g, &mut h); mem[i ] = a; mem[i+1] = b; mem[i+2] = c; mem[i+3] = d; mem[i+4] = e; mem[i+5] = f; mem[i+6] = g; mem[i+7] = h; } } Self { mem, a: w(0), b: w(0), c: w(0) } } /// Create an ISAAC-64 random number generator using an `u64` as seed. /// If `seed == 0` this will produce the same stream of random numbers as /// the reference implementation when used unseeded. #[deprecated(since="0.6.0", note="use SeedableRng::seed_from_u64 instead")] pub fn new_from_u64(seed: u64) -> Self { Self::seed_from_u64(seed) } } impl SeedableRng for Isaac64Core { type Seed = [u8; 32]; fn from_seed(seed: Self::Seed) -> Self { let mut seed_u64 = [0u64; 4]; le::read_u64_into(&seed, &mut seed_u64); // Convert the seed to `Wrapping` and zero-extend to `RAND_SIZE`. let mut seed_extended = [w(0); RAND_SIZE]; for (x, y) in seed_extended.iter_mut().zip(seed_u64.iter()) { *x = w(*y); } Self::init(seed_extended, 2) } fn seed_from_u64(seed: u64) -> Self { let mut key = [w(0); RAND_SIZE]; key[0] = w(seed); // Initialize with only one pass. // A second pass does not improve the quality here, because all of the // seed was already available in the first round. // Not doing the second pass has the small advantage that if // `seed == 0` this method produces exactly the same state as the // reference implementation when used unseeded. Self::init(key, 1) } fn from_rng(mut rng: R) -> Result { // Custom `from_rng` implementation that fills a seed with the same size // as the entire state. let mut seed = [w(0u64); RAND_SIZE]; unsafe { let ptr = seed.as_mut_ptr() as *mut u8; let slice = slice::from_raw_parts_mut(ptr, RAND_SIZE * 8); rng.try_fill_bytes(slice)?; } for i in seed.iter_mut() { *i = w(i.0.to_le()); } Ok(Self::init(seed, 2)) } } #[cfg(test)] mod test { use rand_core::{RngCore, SeedableRng}; use super::Isaac64Rng; #[test] fn test_isaac64_construction() { // Test that various construction techniques produce a working RNG. let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0]; let mut rng1 = Isaac64Rng::from_seed(seed); assert_eq!(rng1.next_u64(), 14964555543728284049); let mut rng2 = Isaac64Rng::from_rng(rng1).unwrap(); assert_eq!(rng2.next_u64(), 919595328260451758); } #[test] fn test_isaac64_true_values_64() { let seed = [1,0,0,0, 0,0,0,0, 23,0,0,0, 0,0,0,0, 200,1,0,0, 0,0,0,0, 210,30,0,0, 0,0,0,0]; let mut rng1 = Isaac64Rng::from_seed(seed); let mut results = [0u64; 10]; for i in results.iter_mut() { *i = rng1.next_u64(); } let expected = [ 15071495833797886820, 7720185633435529318, 10836773366498097981, 5414053799617603544, 12890513357046278984, 17001051845652595546, 9240803642279356310, 12558996012687158051, 14673053937227185542, 1677046725350116783]; assert_eq!(results, expected); let seed = [57,48,0,0, 0,0,0,0, 50,9,1,0, 0,0,0,0, 49,212,0,0, 0,0,0,0, 148,38,0,0, 0,0,0,0]; let mut rng2 = Isaac64Rng::from_seed(seed); // skip forward to the 10000th number for _ in 0..10000 { rng2.next_u64(); } for i in results.iter_mut() { *i = rng2.next_u64(); } let expected = [ 18143823860592706164, 8491801882678285927, 2699425367717515619, 17196852593171130876, 2606123525235546165, 15790932315217671084, 596345674630742204, 9947027391921273664, 11788097613744130851, 10391409374914919106]; assert_eq!(results, expected); } #[test] fn test_isaac64_true_values_32() { let seed = [1,0,0,0, 0,0,0,0, 23,0,0,0, 0,0,0,0, 200,1,0,0, 0,0,0,0, 210,30,0,0, 0,0,0,0]; let mut rng = Isaac64Rng::from_seed(seed); let mut results = [0u32; 12]; for i in results.iter_mut() { *i = rng.next_u32(); } // Subset of above values, as an LE u32 sequence let expected = [ 3477963620, 3509106075, 687845478, 1797495790, 227048253, 2523132918, 4044335064, 1260557630, 4079741768, 3001306521, 69157722, 3958365844]; assert_eq!(results, expected); } #[test] fn test_isaac64_true_values_mixed() { let seed = [1,0,0,0, 0,0,0,0, 23,0,0,0, 0,0,0,0, 200,1,0,0, 0,0,0,0, 210,30,0,0, 0,0,0,0]; let mut rng = Isaac64Rng::from_seed(seed); // Test alternating between `next_u64` and `next_u32` works as expected. // Values are the same as `test_isaac64_true_values` and // `test_isaac64_true_values_32`. assert_eq!(rng.next_u64(), 15071495833797886820); assert_eq!(rng.next_u32(), 687845478); assert_eq!(rng.next_u32(), 1797495790); assert_eq!(rng.next_u64(), 10836773366498097981); assert_eq!(rng.next_u32(), 4044335064); // Skip one u32 assert_eq!(rng.next_u64(), 12890513357046278984); assert_eq!(rng.next_u32(), 69157722); } #[test] fn test_isaac64_true_bytes() { let seed = [1,0,0,0, 0,0,0,0, 23,0,0,0, 0,0,0,0, 200,1,0,0, 0,0,0,0, 210,30,0,0, 0,0,0,0]; let mut rng = Isaac64Rng::from_seed(seed); let mut results = [0u8; 32]; rng.fill_bytes(&mut results); // Same as first values in test_isaac64_true_values as bytes in LE order let expected = [100, 131, 77, 207, 155, 181, 40, 209, 102, 176, 255, 40, 238, 155, 35, 107, 61, 123, 136, 13, 246, 243, 99, 150, 216, 167, 15, 241, 62, 149, 34, 75]; assert_eq!(results, expected); } #[test] fn test_isaac64_new_uninitialized() { // Compare the results from initializing `IsaacRng` with // `seed_from_u64(0)`, to make sure it is the same as the reference // implementation when used uninitialized. // Note: We only test the first 16 integers, not the full 256 of the // first block. let mut rng = Isaac64Rng::seed_from_u64(0); let mut results = [0u64; 16]; for i in results.iter_mut() { *i = rng.next_u64(); } let expected: [u64; 16] = [ 0xF67DFBA498E4937C, 0x84A5066A9204F380, 0xFEE34BD5F5514DBB, 0x4D1664739B8F80D6, 0x8607459AB52A14AA, 0x0E78BC5A98529E49, 0xFE5332822AD13777, 0x556C27525E33D01A, 0x08643CA615F3149F, 0xD0771FAF3CB04714, 0x30E86F68A37B008D, 0x3074EBC0488A3ADF, 0x270645EA7A2790BC, 0x5601A0A8D3763C6A, 0x2F83071F53F325DD, 0xB9090F3D42D2D2EA]; assert_eq!(results, expected); } #[test] fn test_isaac64_clone() { let seed = [1,0,0,0, 0,0,0,0, 23,0,0,0, 0,0,0,0, 200,1,0,0, 0,0,0,0, 210,30,0,0, 0,0,0,0]; let mut rng1 = Isaac64Rng::from_seed(seed); let mut rng2 = rng1.clone(); for _ in 0..16 { assert_eq!(rng1.next_u64(), rng2.next_u64()); } } #[test] #[cfg(feature="serde1")] fn test_isaac64_serde() { use bincode; use std::io::{BufWriter, BufReader}; let seed = [1,0,0,0, 23,0,0,0, 200,1,0,0, 210,30,0,0, 57,48,0,0, 0,0,0,0, 0,0,0,0, 0,0,0,0]; let mut rng = Isaac64Rng::from_seed(seed); let buf: Vec = Vec::new(); let mut buf = BufWriter::new(buf); bincode::serialize_into(&mut buf, &rng).expect("Could not serialize"); let buf = buf.into_inner().unwrap(); let mut read = BufReader::new(&buf[..]); let mut deserialized: Isaac64Rng = bincode::deserialize_from(&mut read).expect("Could not deserialize"); for _ in 0..300 { // more than the 256 buffered results assert_eq!(rng.next_u64(), deserialized.next_u64()); } } }