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A C++ implementation of a family of Xoroshiro+ generators
#ifndef XOROSHIRO_HPP_INCLUDED
#define XOROSHIRO_HPP_INCLUDED 1
/*
* A C++ implementation of a family of Xoroshiro+ generators.
*
* See:
* https://en.wikipedia.org/wiki/Xoroshiro128%2B
* http://xoroshiro.di.unimi.it/xoroshiro128plus.c
*
* Based on the design and public domain implementation of
* Xoroshiro128+ by written in 2016 by David Blackman and Sebastiano
* Vigna.
*
* Xoroshiro128+ fails PractRand and TestU01 because of weak low order
* bits. Blackman and Vigna recommend users take care to avoid
* relying on the low bits. See their original source for details.
* My test results are included below.
*
* Xoroshiro128+ is a variant on the ideas given by George Marsaglia
* for XorShift, and as such it is possible to use the same
* binary-matrix techniques to create the necessary magic constants to
* define other members of the Xoroshiro family at different bit
* sizes. In particular, Xoroshiro64+ may be sufficient for some
* applications and will run better on some 32-bit machines.
*
* The MIT License (MIT)
*
* Copyright (c) 2017 Melissa E. O'Neill
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include <cstdint>
namespace xoroshiro_detail {
template <typename itype, typename rtype,
unsigned int a, unsigned int b, unsigned int c>
class xoroshiro {
itype s0_, s1_;
static constexpr unsigned int ITYPE_BITS = 8*sizeof(itype);
static constexpr unsigned int RTYPE_BITS = 8*sizeof(rtype);
static inline itype rotl(const itype x, int k) {
return (x << k) | (x >> (ITYPE_BITS - k));
}
public:
using result_type = rtype;
static constexpr result_type min() { return 0; }
static constexpr result_type max() { return ~ result_type(0); }
xoroshiro(itype s0 = itype(0xc1f651c67c62c6e0),
itype s1 = itype(0x30d89576f866ac9f))
// Easter-egg seed value for Xoroshiro128+ to remind users that
// they should seed their PRNGs properly.
: s0_(s0), s1_((s0 || s1) ? s1 : 1)
{
// Nothing (else) to do.
}
rtype operator()()
{
const itype result = s0_ + s1_;
s1_ ^= s0_;
s0_ = rotl(s0_, a) ^ s1_ ^ (s1_ << b);
s1_ = rotl(s1_, c);
return result >> (ITYPE_BITS - RTYPE_BITS);
}
bool operator==(const xoroshiro& rhs)
{
return (s0_ == rhs.s0_) && (s1_ == rhs.s1_);
}
bool operator!=(const xoroshiro& rhs)
{
return !operator==(rhs);
}
// Not (yet) implemented:
// - arbitrary jumpahead (doable, but annoying to write).
// - I/O
// - Seeding from a seed_seq.
};
}
// 128 //
// This is the generator recommended by Vigna and Blackman. It fails
// PractRand and TestU01 although it can be considered as passing if
// the failures are ignored. (??!?!)
//
// TestU01 linear complexity results:
//
//| Testing Xoroshiro128+ (Vigna's Code) [Low bits] [Reversed]:
//| - seed_data[2] = { 0xda1ff5a1e44ba0f8, 0x511a1a4da9858f9a}
//| ***********************************************************
//| Xoroshiro128+ (Vigna's Code) [Low bits] [Reversed]
//| scomp_LinearComp test:
//| -----------------------------------------------
//| N = 1, n = 250, r = 0, s = 1
//| -----------------------------------------------
//| Number of degrees of freedom : 1
//| Chi2 statistic for size of jumps : 2.32
//| p-value of test : 0.13
//| -----------------------------------------------
//| Normal statistic for number of jumps : -0.15
//| p-value of test : 0.56
//| -----------------------------------------------
//| CPU time used : 00:00:00.00
//| ***********************************************************
//| Xoroshiro128+ (Vigna's Code) [Low bits] [Reversed]
//| scomp_LinearComp test:
//| -----------------------------------------------
//| N = 1, n = 500, r = 0, s = 1
//| -----------------------------------------------
//| Number of degrees of freedom : 2
//| Chi2 statistic for size of jumps : 1.97
//| p-value of test : 0.37
//| -----------------------------------------------
//| Normal statistic for number of jumps : -7.27
//| p-value of test : 1 - 1.9e-13 *****
//| -----------------------------------------------
//| CPU time used : 00:00:00.00
//| ***********************************************************
//| Xoroshiro128+ (Vigna's Code) [Low bits] [Reversed]
//| scomp_LinearComp test:
//| -----------------------------------------------
//| N = 1, n = 1000, r = 0, s = 1
//| -----------------------------------------------
//| Number of degrees of freedom : 3
//| Chi2 statistic for size of jumps : 4.33
//| p-value of test : 0.23
//| -----------------------------------------------
//| Normal statistic for number of jumps : -17.31
//| p-value of test : 1 - eps1 *****
//| -----------------------------------------------
//| CPU time used : 00:00:00.00
//| ***********************************************************
//
// TestU01 Crush Results:
//| ========= Summary results of Crush =========
//|
//| Version: TestU01 1.2.3
//| Generator: Xoroshiro128+ (Vigna's Code) [Low bits] [Reversed]
//| Number of statistics: 144
//| Total CPU time: 00:39:57.80
//| The following tests gave p-values outside [0.001, 0.9990]:
//| (eps means a value < 1.0e-300):
//| (eps1 means a value < 1.0e-15):
//|
//| Test p-value
//| ----------------------------------------------
//| 71 LinearComp, r = 0 1 - eps1
//| ----------------------------------------------
//| All other tests were passed
//
// TestU01 BigCrush Results:
//
//| ========= Summary results of BigCrush =========
//|
//| Version: TestU01 1.2.3
//| Generator: Xoroshiro128+ (Vigna's Code) [Low bits] [Reversed]
//| Number of statistics: 160
//| Total CPU time: 04:14:51.79
//| The following tests gave p-values outside [0.001, 0.9990]:
//| (eps means a value < 1.0e-300):
//| (eps1 means a value < 1.0e-15):
//|
//| Test p-value
//| ----------------------------------------------
//| 68 MatrixRank, L=1000, r=0 eps
//| 71 MatrixRank, L=5000 eps
//| 80 LinearComp, r = 0 1 - eps1
//| ----------------------------------------------
//| All other tests were passed
//
// PractRand Results (standard: RNG_test stdin64 -tlmin 23):
//
//| RNG_test using PractRand version 0.93
//| RNG = RNG_stdin64, seed = 0x7ddef6ce
//| test set = normal, folding = standard (64 bit)
//|
//| rng=RNG_stdin64, seed=0x7ddef6ce
//| length= 8 megabytes (2^23 bytes), time= 0.2 seconds
//| no anomalies in 106 test result(s)
//|
//| rng=RNG_stdin64, seed=0x7ddef6ce
//| length= 16 megabytes (2^24 bytes), time= 1.2 seconds
//| no anomalies in 116 test result(s)
//|
//| rng=RNG_stdin64, seed=0x7ddef6ce
//| length= 32 megabytes (2^25 bytes), time= 2.3 seconds
//| Test Name Raw Processed Evaluation
//| [Low1/64]BRank(12):256(1) R= +2650 p~= 9.8e-799 FAIL !!!!!!!
//| ...and 126 test result(s) without anomalies
//
// PractRand (extended: RNG_test stdin64 -tlmaxonly -te 1 -tf 2)
//| RNG = RNG_stdin64, seed = 0x88ab2def
//| test set = expanded, folding = extra
//|
//| rng=RNG_stdin64, seed=0x88ab2def
//| length= 32 megabytes (2^25 bytes), time= 2.3 seconds
//| Test Name Raw Processed Evaluation
//| [Low1/16]BRank(18):768(1) R= +1272 p~= 5.4e-384 FAIL !!!!!!!
//| [Low1/32]BRank(18):384(1) R= +1272 p~= 5.4e-384 FAIL !!!!!!!
//| [Low1/32]BRank(18):512(1) R= +2650 p~= 9.8e-799 FAIL !!!!!!!
//| [Low1/64]BRank(18):256(2) R= +3748 p~= 3e-1129 FAIL !!!!!!!!
//| [Low1/64]BRank(18):384(1) R= +5405 p~= 3e-1628 FAIL !!!!!!!!
//| [Low4/64]BRank(18):768(1) R= +1272 p~= 5.4e-384 FAIL !!!!!!!
//| ...and 790 test result(s) without anomalies
//:
//:
//| rng=RNG_stdin64, seed=0x88ab2def
//| length= 8 terabytes (2^43 bytes), time= 519110 seconds
//| Test Name Raw Processed Evaluation
//| BRank(18):12K(8) R= +3598 p~= 2e-2310 FAIL !!!!!!!!
//| BRank(18):16K(32) R=+14990 p~= 0 FAIL !!!!!!!!
//| BRank(18):24K(8) R=+15289 p~= 4e-9814 FAIL !!!!!!!!
//| BRank(18):32K(16) R=+32644 p~= 0 FAIL !!!!!!!!
//| BRank(18):48K(4) R=+27344 p~= 0 FAIL !!!!!!!!
//| BRank(18):64K(11) R=+63622 p~= 0 FAIL !!!!!!!!
//| DC6-5x4Bytes-1 R= +6.5 p = 3.4e-4 unusual
//| [Low1/8]BRank(18):1536(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low1/8]BRank(18):2K(8) R= +7495 p~= 1e-4811 FAIL !!!!!!!!
//| [Low1/8]BRank(18):3K(2) R= +7644 p~= 3e-2302 FAIL !!!!!!!!
//| [Low1/8]BRank(18):4K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):6K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low1/8]BRank(18):8K(4) R=+38366 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):12K(1) R=+30205 p~= 1e-9093 FAIL !!!!!!!!
//| [Low1/8]BRank(18):16K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):24K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):32K(2) R=+120653 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):48K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):64K(1) R=+173490 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):768(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low1/16]BRank(18):1K(8) R= +7495 p~= 1e-4811 FAIL !!!!!!!!
//| [Low1/16]BRank(18):1536(2) R= +7644 p~= 3e-2302 FAIL !!!!!!!!
//| [Low1/16]BRank(18):2K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):3K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low1/16]BRank(18):4K(4) R=+38366 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):6K(1) R=+30205 p~= 1e-9093 FAIL !!!!!!!!
//| [Low1/16]BRank(18):8K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):12K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):16K(2) R=+120653 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):24K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):32K(2) R=+245352 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):48K(1) R=+261665 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):384(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low1/32]BRank(18):512(8) R= +7495 p~= 1e-4811 FAIL !!!!!!!!
//| [Low1/32]BRank(18):768(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low1/32]BRank(18):1K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):1536(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low1/32]BRank(18):2K(4) R=+38366 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):3K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):4K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):6K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):8K(2) R=+120653 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):12K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):16K(2) R=+245352 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):24K(1) R=+261665 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):32K(1) R=+349841 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):256(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low1/64]BRank(18):384(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low1/64]BRank(18):512(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):768(4) R=+27344 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):1K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):1536(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):2K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):3K(2) R=+89478 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):4K(4) R=+170629 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):6K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):8K(2) R=+245352 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):12K(1) R=+261665 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):16K(2) R=+494750 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):24K(1) R=+526192 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):32K(1) R=+702543 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):3K(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low4/16]BRank(18):4K(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low4/16]BRank(18):6K(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low4/16]BRank(18):8K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):12K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low4/16]BRank(18):16K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):24K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):32K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):48K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):64K(2) R=+120653 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):1536(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low4/32]BRank(18):2K(8) R= +7495 p~= 1e-4811 FAIL !!!!!!!!
//| [Low4/32]BRank(18):3K(2) R= +7644 p~= 3e-2302 FAIL !!!!!!!!
//| [Low4/32]BRank(18):4K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):6K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low4/32]BRank(18):8K(4) R=+38366 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):12K(1) R=+30205 p~= 1e-9093 FAIL !!!!!!!!
//| [Low4/32]BRank(18):16K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):24K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):32K(2) R=+120653 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):48K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):64K(1) R=+174868 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):768(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low4/64]BRank(18):1K(8) R= +7495 p~= 1e-4811 FAIL !!!!!!!!
//| [Low4/64]BRank(18):1536(2) R= +7644 p~= 3e-2302 FAIL !!!!!!!!
//| [Low4/64]BRank(18):2K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):3K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low4/64]BRank(18):4K(4) R=+38366 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):6K(1) R=+30205 p~= 1e-9093 FAIL !!!!!!!!
//| [Low4/64]BRank(18):8K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):12K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):16K(2) R=+120653 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):24K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):32K(2) R=+247300 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):48K(1) R=+351219 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):3K(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low8/32]BRank(18):4K(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low8/32]BRank(18):6K(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low8/32]BRank(18):8K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):12K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low8/32]BRank(18):16K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):24K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):32K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):48K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):64K(2) R=+120653 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):1536(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low8/64]BRank(18):2K(8) R= +7495 p~= 1e-4811 FAIL !!!!!!!!
//| [Low8/64]BRank(18):3K(2) R= +7644 p~= 3e-2302 FAIL !!!!!!!!
//| [Low8/64]BRank(18):4K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):6K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low8/64]BRank(18):8K(4) R=+38366 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):12K(1) R=+30205 p~= 1e-9093 FAIL !!!!!!!!
//| [Low8/64]BRank(18):16K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):24K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):32K(2) R=+120653 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):48K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):64K(1) R=+174868 p~= 0 FAIL !!!!!!!!
//| ...and 1698 test result(s) without anomalies
//|
//| rng=RNG_stdin64, seed=0x88ab2def
//| length= 16 terabytes (2^44 bytes), time= 1067251 seconds
//| Test Name Raw Processed Evaluation
//| BRank(18):12K(16) R= +5089 p~= 4e-3746 FAIL !!!!!!!!
//| BRank(18):16K(64) R=+21199 p~= 0 FAIL !!!!!!!!
//| BRank(18):24K(16) R=+21622 p~= 0 FAIL !!!!!!!!
//| BRank(18):32K(32) R=+46165 p~= 0 FAIL !!!!!!!!
//| BRank(18):48K(8) R=+38670 p~= 0 FAIL !!!!!!!!
//| BRank(18):64K(22) R=+89975 p~= 0 FAIL !!!!!!!!
//| DC6-5x4Bytes-1 R= +12.4 p = 9.8e-8 very suspicious
//| [Low1/8]BRank(18):1536(8) R= +3598 p~= 2e-2310 FAIL !!!!!!!!
//| [Low1/8]BRank(18):2K(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low1/8]BRank(18):3K(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low1/8]BRank(18):4K(16) R=+32644 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):6K(4) R=+27344 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):8K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):12K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):16K(8) R=+116607 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):24K(2) R=+89478 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):32K(4) R=+170629 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):48K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low1/8]BRank(18):64K(2) R=+245352 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):768(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low1/16]BRank(18):1K(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low1/16]BRank(18):1536(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low1/16]BRank(18):2K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):3K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low1/16]BRank(18):4K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):6K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):8K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):12K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):16K(4) R=+170629 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):24K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):32K(2) R=+245352 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):48K(1) R=+261665 p~= 0 FAIL !!!!!!!!
//| [Low1/16]BRank(18):64K(1) R=+349841 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):384(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low1/32]BRank(18):512(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low1/32]BRank(18):768(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low1/32]BRank(18):1K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):1536(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low1/32]BRank(18):2K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):3K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):4K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):6K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):8K(4) R=+170629 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):12K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):16K(2) R=+245352 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):24K(1) R=+261665 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):32K(2) R=+494750 p~= 0 FAIL !!!!!!!!
//| [Low1/32]BRank(18):48K(1) R=+526192 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):256(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low1/64]BRank(18):384(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low1/64]BRank(18):512(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):768(4) R=+27344 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):1K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):1536(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):2K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):3K(2) R=+89478 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):4K(4) R=+170629 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):6K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):8K(2) R=+245352 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):12K(1) R=+261665 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):16K(2) R=+494750 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):24K(1) R=+526192 p~= 0 FAIL !!!!!!!!
//| [Low1/64]BRank(18):32K(1) R=+702543 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):3K(8) R= +3598 p~= 2e-2310 FAIL !!!!!!!!
//| [Low4/16]BRank(18):4K(32) R=+14990 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):6K(8) R=+15289 p~= 4e-9814 FAIL !!!!!!!!
//| [Low4/16]BRank(18):8K(16) R=+32644 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):12K(4) R=+27344 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):16K(16) R=+76731 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):24K(4) R=+60410 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):32K(8) R=+116607 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):48K(2) R=+89478 p~= 0 FAIL !!!!!!!!
//| [Low4/16]BRank(18):64K(5) R=+190769 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):1536(8) R= +3598 p~= 2e-2310 FAIL !!!!!!!!
//| [Low4/32]BRank(18):2K(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low4/32]BRank(18):3K(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low4/32]BRank(18):4K(16) R=+32644 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):6K(4) R=+27344 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):8K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):12K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):16K(8) R=+116607 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):24K(2) R=+89478 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):32K(4) R=+170629 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):48K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low4/32]BRank(18):64K(2) R=+247300 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):768(4) R= +2544 p~= 4e-1354 FAIL !!!!!!!!
//| [Low4/64]BRank(18):1K(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low4/64]BRank(18):1536(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low4/64]BRank(18):2K(8) R=+23082 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):3K(2) R=+19335 p~= 2e-5821 FAIL !!!!!!!!
//| [Low4/64]BRank(18):4K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):6K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):8K(4) R=+82453 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):12K(1) R=+63271 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):16K(4) R=+170629 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):24K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):32K(2) R=+247300 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):48K(1) R=+351219 p~= 0 FAIL !!!!!!!!
//| [Low4/64]BRank(18):64K(1) R=+527569 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):3K(8) R= +3598 p~= 2e-2310 FAIL !!!!!!!!
//| [Low8/32]BRank(18):4K(32) R=+14990 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):6K(8) R=+15289 p~= 4e-9814 FAIL !!!!!!!!
//| [Low8/32]BRank(18):8K(16) R=+32644 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):12K(4) R=+27344 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):16K(16) R=+76731 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):24K(4) R=+60410 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):32K(8) R=+116607 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):48K(2) R=+89478 p~= 0 FAIL !!!!!!!!
//| [Low8/32]BRank(18):64K(5) R=+190769 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):1536(8) R= +3598 p~= 2e-2310 FAIL !!!!!!!!
//| [Low8/64]BRank(18):2K(16) R=+10600 p~= 3e-7802 FAIL !!!!!!!!
//| [Low8/64]BRank(18):3K(4) R=+10811 p~= 1e-5750 FAIL !!!!!!!!
//| [Low8/64]BRank(18):4K(16) R=+32644 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):6K(4) R=+27344 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):8K(8) R=+54257 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):12K(2) R=+42716 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):16K(8) R=+116607 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):24K(2) R=+89478 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):32K(4) R=+170629 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):48K(1) R=+129402 p~= 0 FAIL !!!!!!!!
//| [Low8/64]BRank(18):64K(2) R=+247300 p~= 0 FAIL !!!!!!!!
//| ...and 1738 test result(s) without anomalies
//
// (it is, perhaps, worth noting that XorShift* 64/32, a generator half the
// size of Xoroshiro128+ does not suffer these kinds of failures)
// - 128 state bits, uint64_t output, period 2^128 - 1
using xoroshiro128plus64 =
xoroshiro_detail::xoroshiro<uint64_t, uint64_t, 55, 14, 36>;
// This is a variation on the above generator which avoids the
// problems with weak low-order bits by discarding the low-order bits,
// to return only 32 bits. It passes PractRand and TestU01.
// - 128 state bits, uint32_t output, period 2^128 - 1
using xoroshiro128plus32 =
xoroshiro_detail::xoroshiro<uint64_t, uint32_t, 55, 14, 36>;
//// Variations ////
// These are variations on the above theme. The constants are
// mathematically correct and are designed to have a similar size
// relationships to the constants for Xoroshiro128+. Empirical
// testing shows them to be acceptable, but it is possible that there
// are even better constants.
// These variations have similar properties to the ones above. The
// first variant fails statistical tests due to weak low-order bits,
// and the second should pass stringent statistical tests.
// 256 //
// - 256 state bits, __uint128_t output, period 2^256 - 1
using xoroshiro256plus128 =
xoroshiro_detail::xoroshiro<__uint128_t, __uint128_t, 105, 36, 70>;
// - 256 state bits, uint64_t output, period 2^256 - 1
using xoroshiro256plus64 =
xoroshiro_detail::xoroshiro<__uint128_t, uint64_t, 105, 36, 70>;
// 64 //
// - 64 state bits, uint32_t output, period 2^64 - 1
using xoroshiro64plus32 =
xoroshiro_detail::xoroshiro<uint32_t, uint32_t, 27, 7, 20>;
// - 64 state bits, uint16_t output, period 2^64 - 1
using xoroshiro64plus16 =
xoroshiro_detail::xoroshiro<uint32_t, uint16_t, 27, 7, 20>;
// 32 //
// - 32 state bits, uint16_t output, period 2^32 - 1
using xoroshiro32plus16 =
xoroshiro_detail::xoroshiro<uint16_t, uint16_t, 13, 5, 10>;
// - 32 state bits, uint8_t output, period 2^32 - 1
using xoroshiro32plus8 =
xoroshiro_detail::xoroshiro<uint16_t, uint8_t, 13, 5, 10>;
// 16 //
// - 16 state bits, uint8_t output, period 2^16 - 1
using xoroshiro16plus8 =
xoroshiro_detail::xoroshiro<uint8_t, uint8_t, 4, 7, 3>;
#endif // XOROSHIRO_HPP_INCLUDED
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