logo
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
// 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

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

// This is the default multiplier used by PCG for 64-bit state.
const MULTIPLIER: u64 = 6364136223846793005;

/// A PCG random number generator (XSH RR 64/32 (LCG) variant).
///
/// Permuted Congruential Generator with 64-bit state, internal Linear
/// Congruential Generator, and 32-bit output via "xorshift high (bits),
/// random rotation" output function.
///
/// This is a 64-bit LCG with explicitly chosen stream with the PCG-XSH-RR
/// output function. This combination is the standard `pcg32`.
///
/// Despite the name, this implementation uses 16 bytes (128 bit) space
/// comprising 64 bits of state and 64 bits stream selector. These are both set
/// by `SeedableRng`, using a 128-bit seed.
///
/// Note that two generators with different stream parameter may be closely
/// correlated.
#[derive(Clone, PartialEq, Eq)]
#[cfg_attr(feature = "serde1", derive(Serialize, Deserialize))]
pub struct Lcg64Xsh32 {
    state: u64,
    increment: u64,
}

/// [`Lcg64Xsh32`] is also officially known as `pcg32`.
pub type Pcg32 = Lcg64Xsh32;

impl Lcg64Xsh32 {
    /// Multi-step advance functions (jump-ahead, jump-back)
    ///
    /// The method used here is based on Brown, "Random Number Generation
    /// with Arbitrary Stride,", Transactions of the American Nuclear
    /// Society (Nov. 1994).  The algorithm is very similar to fast
    /// exponentiation.
    ///
    /// Even though delta is an unsigned integer, we can pass a
    /// signed integer to go backwards, it just goes "the long way round".
    ///
    /// Using this function is equivalent to calling `next_32()` `delta`
    /// number of times.
    #[inline]
    pub fn advance(&mut self, delta: u64) {
        let mut acc_mult: u64 = 1;
        let mut acc_plus: u64 = 0;
        let mut cur_mult = MULTIPLIER;
        let mut cur_plus = self.increment;
        let mut mdelta = delta;

        while mdelta > 0 {
            if (mdelta & 1) != 0 {
                acc_mult = acc_mult.wrapping_mul(cur_mult);
                acc_plus = acc_plus.wrapping_mul(cur_mult).wrapping_add(cur_plus);
            }
            cur_plus = cur_mult.wrapping_add(1).wrapping_mul(cur_plus);
            cur_mult = cur_mult.wrapping_mul(cur_mult);
            mdelta /= 2;
        }
        self.state = acc_mult.wrapping_mul(self.state).wrapping_add(acc_plus);
    }

    /// Construct an instance compatible with PCG seed and stream.
    ///
    /// Note that the highest bit of the `stream` parameter is discarded
    /// to simplify upholding internal invariants.
    ///
    /// Note that two generators with different stream parameters may be closely
    /// correlated.
    ///
    /// PCG specifies the following default values for both parameters:
    ///
    /// - `state = 0xcafef00dd15ea5e5`
    /// - `stream = 0xa02bdbf7bb3c0a7`
    // Note: stream is 1442695040888963407u64 >> 1
    pub fn new(state: u64, stream: u64) -> Self {
        // The increment must be odd, hence we discard one bit:
        let increment = (stream << 1) | 1;
        Lcg64Xsh32::from_state_incr(state, increment)
    }

    #[inline]
    fn from_state_incr(state: u64, increment: u64) -> Self {
        let mut pcg = Lcg64Xsh32 { state, increment };
        // Move away from initial 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 Lcg64Xsh32 {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "Lcg64Xsh32 {{}}")
    }
}

impl SeedableRng for Lcg64Xsh32 {
    type Seed = [u8; 16];

    /// We use a single 127-bit seed to initialise the state and select a stream.
    /// One `seed` bit (lowest bit of `seed[8]`) is ignored.
    fn from_seed(seed: Self::Seed) -> Self {
        let mut seed_u64 = [0u64; 2];
        le::read_u64_into(&seed, &mut seed_u64);

        // The increment must be odd, hence we discard one bit:
        Lcg64Xsh32::from_state_incr(seed_u64[0], seed_u64[1] | 1)
    }
}

impl RngCore for Lcg64Xsh32 {
    #[inline]
    fn next_u32(&mut self) -> u32 {
        let state = self.state;
        self.step();

        // Output function XSH RR: xorshift high (bits), followed by a random rotate
        // Constants are for 64-bit state, 32-bit output
        const ROTATE: u32 = 59; // 64 - 5
        const XSHIFT: u32 = 18; // (5 + 32) / 2
        const SPARE: u32 = 27; // 64 - 32 - 5

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

    #[inline]
    fn next_u64(&mut self) -> u64 {
        impls::next_u64_via_u32(self)
    }

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

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