// Copyright 2018 Developers of the Rand project.
// Copyright 2013-2018 The Rust Project Developers.
//
// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or
// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license
// <LICENSE-MIT or https://opensource.org/licenses/MIT>, 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<u64>;
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<Isaac64Core>);
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 = <Isaac64Core as SeedableRng>::Seed;
fn from_seed(seed: Self::Seed) -> Self {
Isaac64Rng(BlockRng64::<Isaac64Core>::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::<Isaac64Core>::seed_from_u64(seed))
}
fn from_rng<S: RngCore>(rng: S) -> Result<Self, Error> {
BlockRng64::<Isaac64Core>::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<Self::Item>;
/// 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::Item>) {
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<u64>` 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<R: RngCore>(mut rng: R) -> Result<Self, Error> {
// 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<u8> = 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());
}
}
}