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
|
/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=8 sts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/* The xorshift128+ pseudo-random number generator. */
#ifndef mozilla_XorShift128Plus_h
#define mozilla_XorShift128Plus_h
#include "mozilla/Assertions.h"
#include "mozilla/Attributes.h"
#include "mozilla/FloatingPoint.h"
#include <inttypes.h>
namespace mozilla {
namespace non_crypto {
/*
* A stream of pseudo-random numbers generated using the xorshift+ technique
* described here:
*
* Vigna, Sebastiano (2014). "Further scramblings of Marsaglia's xorshift
* generators". arXiv:1404.0390 (http://arxiv.org/abs/1404.0390)
*
* That paper says:
*
* In particular, we propose a tightly coded xorshift128+ generator that
* does not fail systematically any test from the BigCrush suite of TestU01
* (even reversed) and generates 64 pseudorandom bits in 1.10 ns on an
* Intel(R) Core(TM) i7-4770 CPU @3.40GHz (Haswell). It is the fastest
* generator we are aware of with such empirical statistical properties.
*
* The stream of numbers produced by this method repeats every 2**128 - 1 calls
* (i.e. never, for all practical purposes). Zero appears 2**64 - 1 times in
* this period; all other numbers appear 2**64 times. Additionally, each *bit*
* in the produced numbers repeats every 2**128 - 1 calls.
*
* This generator is not suitable as a cryptographically secure random number
* generator.
*/
class XorShift128PlusRNG {
uint64_t mState[2];
public:
/*
* Construct a xorshift128+ pseudo-random number stream using |aInitial0| and
* |aInitial1| as the initial state. These MUST NOT both be zero.
*
* If the initial states contain many zeros, for a few iterations you'll see
* many zeroes in the generated numbers. It's suggested to seed a SplitMix64
* generator <http://xorshift.di.unimi.it/splitmix64.c> and use its first two
* outputs to seed xorshift128+.
*/
XorShift128PlusRNG(uint64_t aInitial0, uint64_t aInitial1) {
setState(aInitial0, aInitial1);
}
/**
* Return a pseudo-random 64-bit number.
*/
MOZ_NO_SANITIZE_UNSIGNED_OVERFLOW
uint64_t next() {
/*
* The offsetOfState*() methods below are provided so that exceedingly-rare
* callers that want to observe or poke at RNG state in C++ type-system-
* ignoring means can do so. Don't change the next() or nextDouble()
* algorithms without altering code that uses offsetOfState*()!
*/
uint64_t s1 = mState[0];
const uint64_t s0 = mState[1];
mState[0] = s0;
s1 ^= s1 << 23;
mState[1] = s1 ^ s0 ^ (s1 >> 17) ^ (s0 >> 26);
return mState[1] + s0;
}
/*
* Return a pseudo-random floating-point value in the range [0, 1). More
* precisely, choose an integer in the range [0, 2**53) and divide it by
* 2**53. Given the 2**128 - 1 period noted above, the produced doubles are
* all but uniformly distributed in this range.
*/
double nextDouble() {
/*
* Because the IEEE 64-bit floating point format stores the leading '1' bit
* of the mantissa implicitly, it effectively represents a mantissa in the
* range [0, 2**53) in only 52 bits. FloatingPoint<double>::kExponentShift
* is the width of the bitfield in the in-memory format, so we must add one
* to get the mantissa's range.
*/
static constexpr int kMantissaBits =
mozilla::FloatingPoint<double>::kExponentShift + 1;
uint64_t mantissa = next() & ((UINT64_C(1) << kMantissaBits) - 1);
return double(mantissa) / (UINT64_C(1) << kMantissaBits);
}
/*
* Set the stream's current state to |aState0| and |aState1|. These must not
* both be zero; ideally, they should have an almost even mix of zero and one
* bits.
*/
void setState(uint64_t aState0, uint64_t aState1) {
MOZ_ASSERT(aState0 || aState1);
mState[0] = aState0;
mState[1] = aState1;
}
static size_t offsetOfState0() {
return offsetof(XorShift128PlusRNG, mState[0]);
}
static size_t offsetOfState1() {
return offsetof(XorShift128PlusRNG, mState[1]);
}
};
} // namespace non_crypto
} // namespace mozilla
#endif // mozilla_XorShift128Plus_h
|
