1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
// Copyright 2018 Developers of the Rand project.
// Copyright 2017 Paul Dicker.
// Copyright 2014-2017 Melissa O'Neill and PCG Project contributors
//
// 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.

//! PCG random number generators

// This is the default multiplier used by PCG for 128-bit state.
const MULTIPLIER: u128 = 0x2360_ED05_1FC6_5DA4_4385_DF64_9FCC_F645;

use core::fmt;
use rand_core::{le, Error, RngCore, SeedableRng};
#[cfg(feature = "serde1")] use serde::{Deserialize, Serialize};

/// A PCG random number generator (XSL RR 128/64 (LCG) variant).
///
/// Permuted Congruential Generator with 128-bit state, internal Linear
/// Congruential Generator, and 64-bit output via "xorshift low (bits),
/// random rotation" output function.
///
/// This is a 128-bit LCG with explicitly chosen stream with the PCG-XSL-RR
/// output function. This combination is the standard `pcg64`.
///
/// Despite the name, this implementation uses 32 bytes (256 bit) space
/// comprising 128 bits of state and 128 bits stream selector. These are both
/// set by `SeedableRng`, using a 256-bit seed.
#[derive(Clone, PartialEq, Eq)]
#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
pub struct Lcg128Xsl64 {
    state: u128,
    increment: u128,
}

/// [`Lcg128Xsl64`] is also officially known as `pcg64`.
pub type Pcg64 = Lcg128Xsl64;

impl Lcg128Xsl64 {
    /// Construct an instance compatible with PCG seed and stream.
    ///
    /// Note that PCG specifies default values for both parameters:
    ///
    /// - `state = 0xcafef00dd15ea5e5`
    /// - `stream = 0xa02bdbf7bb3c0a7ac28fa16a64abf96`
    pub fn new(state: u128, stream: u128) -> Self {
        // The increment must be odd, hence we discard one bit:
        let increment = (stream << 1) | 1;
        Lcg128Xsl64::from_state_incr(state, increment)
    }

    #[inline]
    fn from_state_incr(state: u128, increment: u128) -> Self {
        let mut pcg = Lcg128Xsl64 { state, increment };
        // Move away from inital value:
        pcg.state = pcg.state.wrapping_add(pcg.increment);
        pcg.step();
        pcg
    }

    #[inline]
    fn step(&mut self) {
        // prepare the LCG for the next round
        self.state = self
            .state
            .wrapping_mul(MULTIPLIER)
            .wrapping_add(self.increment);
    }
}

// Custom Debug implementation that does not expose the internal state
impl fmt::Debug for Lcg128Xsl64 {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "Lcg128Xsl64 {{}}")
    }
}

/// We use a single 255-bit seed to initialise the state and select a stream.
/// One `seed` bit (lowest bit of `seed[8]`) is ignored.
impl SeedableRng for Lcg128Xsl64 {
    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);
        let state = u128::from(seed_u64[0]) | (u128::from(seed_u64[1]) << 64);
        let incr = u128::from(seed_u64[2]) | (u128::from(seed_u64[3]) << 64);

        // The increment must be odd, hence we discard one bit:
        Lcg128Xsl64::from_state_incr(state, incr | 1)
    }
}

impl RngCore for Lcg128Xsl64 {
    #[inline]
    fn next_u32(&mut self) -> u32 {
        self.next_u64() as u32
    }

    #[inline]
    fn next_u64(&mut self) -> u64 {
        self.step();
        output_xsl_rr(self.state)
    }

    #[inline]
    fn fill_bytes(&mut self, dest: &mut [u8]) {
        fill_bytes_impl(self, dest)
    }

    #[inline]
    fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
        self.fill_bytes(dest);
        Ok(())
    }
}


/// A PCG random number generator (XSL 128/64 (MCG) variant).
///
/// Permuted Congruential Generator with 128-bit state, internal Multiplicative
/// Congruential Generator, and 64-bit output via "xorshift low (bits),
/// random rotation" output function.
///
/// This is a 128-bit MCG with the PCG-XSL-RR output function, also known as
/// `pcg64_fast`.
/// Note that compared to the standard `pcg64` (128-bit LCG with PCG-XSL-RR
/// output function), this RNG is faster, also has a long cycle, and still has
/// good performance on statistical tests.
#[derive(Clone, PartialEq, Eq)]
#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
pub struct Mcg128Xsl64 {
    state: u128,
}

/// A friendly name for [`Mcg128Xsl64`] (also known as `pcg64_fast`).
pub type Pcg64Mcg = Mcg128Xsl64;

impl Mcg128Xsl64 {
    /// Construct an instance compatible with PCG seed.
    ///
    /// Note that PCG specifies a default value for the parameter:
    ///
    /// - `state = 0xcafef00dd15ea5e5`
    pub fn new(state: u128) -> Self {
        // Force low bit to 1, as in C version (C++ uses `state | 3` instead).
        Mcg128Xsl64 { state: state | 1 }
    }
}

// Custom Debug implementation that does not expose the internal state
impl fmt::Debug for Mcg128Xsl64 {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "Mcg128Xsl64 {{}}")
    }
}

/// We use a single 126-bit seed to initialise the state and select a stream.
/// Two `seed` bits (lowest order of last byte) are ignored.
impl SeedableRng for Mcg128Xsl64 {
    type Seed = [u8; 16];

    fn from_seed(seed: Self::Seed) -> Self {
        // Read as if a little-endian u128 value:
        let mut seed_u64 = [0u64; 2];
        le::read_u64_into(&seed, &mut seed_u64);
        let state = u128::from(seed_u64[0])  |
                    u128::from(seed_u64[1]) << 64;
        Mcg128Xsl64::new(state)
    }
}

impl RngCore for Mcg128Xsl64 {
    #[inline]
    fn next_u32(&mut self) -> u32 {
        self.next_u64() as u32
    }

    #[inline]
    fn next_u64(&mut self) -> u64 {
        self.state = self.state.wrapping_mul(MULTIPLIER);
        output_xsl_rr(self.state)
    }

    #[inline]
    fn fill_bytes(&mut self, dest: &mut [u8]) {
        fill_bytes_impl(self, dest)
    }

    #[inline]
    fn try_fill_bytes(&mut self, dest: &mut [u8]) -> Result<(), Error> {
        self.fill_bytes(dest);
        Ok(())
    }
}

#[inline(always)]
fn output_xsl_rr(state: u128) -> u64 {
    // Output function XSL RR ("xorshift low (bits), random rotation")
    // Constants are for 128-bit state, 64-bit output
    const XSHIFT: u32 = 64; // (128 - 64 + 64) / 2
    const ROTATE: u32 = 122; // 128 - 6

    let rot = (state >> ROTATE) as u32;
    let xsl = ((state >> XSHIFT) as u64) ^ (state as u64);
    xsl.rotate_right(rot)
}

#[inline(always)]
fn fill_bytes_impl<R: RngCore + ?Sized>(rng: &mut R, dest: &mut [u8]) {
    let mut left = dest;
    while left.len() >= 8 {
        let (l, r) = { left }.split_at_mut(8);
        left = r;
        let chunk: [u8; 8] = rng.next_u64().to_le_bytes();
        l.copy_from_slice(&chunk);
    }
    let n = left.len();
    if n > 0 {
        let chunk: [u8; 8] = rng.next_u64().to_le_bytes();
        left.copy_from_slice(&chunk[..n]);
    }
}