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pub trait FromUniform {
fn from_uniform(uniform_value: f64) -> Self;
}
impl FromUniform for f64 {
fn from_uniform(uniform_value: f64) -> Self {
uniform_value
}
}
impl FromUniform for f32 {
fn from_uniform(uniform_value: f64) -> Self {
uniform_value as f32
}
}
macro_rules! unsigned {
($($ut:tt)*) => {
$(
impl FromUniform for $ut {
fn from_uniform(uniform_value: f64) -> Self {
(::std::$ut::MAX as f64 * uniform_value) as $ut
}
}
)*
}
}
unsigned!(u8 u16 u32 u64 u128 usize);
macro_rules! signed {
($($st:tt)*) => {
$(
impl FromUniform for $st {
fn from_uniform(uniform_value: f64) -> Self {
let min = ::std::$st::MIN as f64;
let result = (::std::$st::MAX as f64 - min + 1.0) * uniform_value + min;
result as $st
}
}
)*
}
}
signed!(i8 i16 i32 i64 i128 isize);
impl <T: FromUniform, E: FromUniform> FromUniform for Result<T, E> {
fn from_uniform(uniform_value: f64) -> Self {
if uniform_value < 0.5 {
Ok(T::from_uniform(uniform_value*2.0))
} else {
Err(E::from_uniform(uniform_value*2.0 - 1.0))
}
}
}
impl <T: FromUniform> FromUniform for Option<T> {
fn from_uniform(uniform_value: f64) -> Self {
if uniform_value < 0.5 {
Some(T::from_uniform(uniform_value*2.0))
} else {
None
}
}
}
impl FromUniform for () {
fn from_uniform(_: f64) -> Self {}
}
impl FromUniform for bool {
fn from_uniform(uniform_value: f64) -> Self {
uniform_value < 0.5
}
}
pub trait Quasirandom {
type State;
}
impl<T: FromUniform> Quasirandom for T {
#[doc(hidden)]
type State = State<1>;
}
#[doc(hidden)]
pub struct State<const N: usize>([f64; N]);
#[doc(hidden)]
impl<const N: usize> State<N> {
fn gen(&mut self) -> &[f64; N] {
for i in 0..N {
self.0[i] = (self.0[i] + CONSTANTS[N-1][i]).fract();
}
&self.0
}
}
#[derive(Debug, Clone, Default)]
pub struct Qrng<T: Quasirandom> {
state: T::State,
}
impl<T: FromUniform> Qrng<T> {
pub fn new(seed: f64) -> Self {
let Qrng { state } = Qrng::<(T,)>::new(seed);
Self { state }
}
pub fn gen(&mut self) -> T {
let [x] = self.state.gen();
T::from_uniform(*x)
}
}
macro_rules! define_from_uniform {
(@inner [$n:expr] [$([$t:tt $x:ident])*]) => {
impl<$($t: FromUniform,)*> Quasirandom for ($($t,)*) {
#[doc(hidden)]
type State = State<{$n}>;
}
impl<$($t: FromUniform,)*> Qrng<($($t,)*)> {
pub fn new(seed: f64) -> Self {
assert!(seed >= 0.0);
assert!(seed < 1.0);
let mut seeds = [0.0; $n];
for i in 0..$n {
seeds[i] = (seed * i as f64).fract();
}
Self { state: State(seeds) }
}
pub fn gen(&mut self) -> ($($t,)*) {
let [$($x,)*] = self.state.gen();
($($t::from_uniform(*$x),)*)
}
}
};
(@inner [$n:expr] [$($t:tt)*] $next:tt $($rem:tt)*) => {
define_from_uniform!(@inner [$n + 1] [[$next x] $($t)*] $($rem)*);
};
($next:tt $($rem:tt)*) => {
define_from_uniform!($($rem)*);
define_from_uniform!(@inner [1] [[$next x]] $($rem)*);
};
() => {}
}
define_from_uniform!(T31 T30 T29 T28 T27 T26 T25 T24 T23 T22 T21 T20 T19 T18 T17 T16 T15 T14 T13 T12 T11 T10 T9 T8 T7 T6 T5 T4 T3 T2 T1 T0);
use std::f64::NAN;
static CONSTANTS: [[f64; 32]; 32] = [
[0.6180339887498955, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.7548776662466942, 0.5698402909980553, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.8191725133961674, 0.6710436067037939, 0.5497004779019761, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.8566748838545053, 0.7338918566271301, 0.6287067210378139, 0.5385972572236161, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.8812714616335721, 0.7766393890897725, 0.6844301295853483, 0.6031687406857351, 0.5315553977157988, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.898653712628702, 0.8075784952213495, 0.7257334129697662, 0.6521830259439793, 0.586086697577978, 0.5266889867007452, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9115923534820571, 0.8310006189269559, 0.7575338099526698, 0.6905620286569838, 0.6295110649287636, 0.5738574732214077, 0.5231240845771696, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9215993196339888, 0.849345305949831, 0.7827560560976864, 0.7213874487390121, 0.6648301819503726, 0.6127070433576043, 0.564670394293321, 0.5203998511981808, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9295701282320245, 0.8641006233013023, 0.8032421272075638, 0.7466698871896992, 0.6940820227819199, 0.6451979149209321, 0.5997567085080856, 0.557515920435878, 0.5182501456509743, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9360691110777617, 0.876225380713911, 0.820207513228644, 0.7677709178072383, 0.7186866405431788, 0.6727403647567163, 0.6297314752239486, 0.589472182230569, 0.5517867016256371, 0.5165104872952402, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9414696173216355, 0.8863650403397467, 0.8344857553359374, 0.7856429847364809, 0.7396590001912821, 0.6963664758585899, 0.6556078795422026, 0.6172348994656464, 0.5811079045974802, 0.5470954365639671, 0.5150737313002912, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9460285282856161, 0.8949699763302488, 0.8466671295675179, 0.8009712585325659, 0.757741660908641, 0.7168452282901001, 0.6781560363278498, 0.6415549569952425, 0.606929291780551, 0.5741724246765859, 0.5431834938989744, 0.5138670813222856, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9499283999636238, 0.9023639650574503, 0.857181157511855, 0.8142607254342034, 0.7734893880649323, 0.7347595367933636, 0.6979689511441332, 0.663020528984635, 0.6298220302414098, 0.5982858334490634, 0.5683287044891718, 0.5398715769087982, 0.5128393432388131, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9533025374016683, 0.908785727816459, 0.8663477402818522, 0.8258914990828911, 0.7873244616941877, 0.7505584070914716, 0.7155092339484541, 0.6820967682573851, 0.6502445799332428, 0.6198798079820423, 0.5909329938333397, 0.5633379224556871, 0.5370314708915908, 0.5119534638655036, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9562505576379922, 0.9144151289829711, 0.8744099770025826, 0.8361550281129437, 0.7995737119048135, 0.7645928078816573, 0.7311422989028329, 0.6991552310385577, 0.66856757955614, 0.6393181207692418, 0.6113483094936605, 0.5846021618643568, 0.5590261432791671, 0.5345690612449197, 0.5111819629114723, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9588484010075664, 0.919390256114767, 0.8815558769775812, 0.8452784430387769, 0.8104938835138964, 0.7771407642337125, 0.7451601791432934, 0.7144956462660588, 0.6850930079490782, 0.6569003352134377, 0.629867836040739, 0.6039477674337588, 0.5790943510959491, 0.5552636925808652, 0.5324137037687195, 0.5105040285331529, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9611549719965047, 0.9238188801936017, 0.8879331099223235, 0.8534413234021603, 0.8202893712952632, 0.7884252076963293, 0.7577988084247037, 0.7283620924904307, 0.7000688466109555, 0.6728746526599783, 0.6467368179345593, 0.6216143081309999, 0.5974676829242778, 0.5742590340499008, 0.5519519257909723, 0.5305113377770387, 0.5099036100049179, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9632166633389043, 0.927786340533732, 0.8936592632203137, 0.8607874936809742, 0.8291248575072461, 0.7986268787394741, 0.7692507173921999, 0.7409551092775732, 0.7137003080422573, 0.6874480293364112, 0.6621613970363233, 0.6378048914451547, 0.6143442993990339, 0.5917466662084143, 0.5699802493671892, 0.5490144739645405, 0.5288198897368884, 0.509368129699613, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9650705109167201, 0.9313610910410594, 0.8988291239789491, 0.8674334819051925, 0.8371344735685137, 0.8078937941127652, 0.7796744766508538, 0.7524408455301659, 0.7261584712304062, 0.7007941268368325, 0.6763157460338588, 0.6526923825659189, 0.6298941711143428, 0.6078922895407828, 0.5866589224494579, 0.566167226022151, 0.5463912940814994, 0.5273061253396806, 0.5088875917910817, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9667464397509411, 0.9345986787711201, 0.9035199452979138, 0.8734746903607233, 0.8444285471187851, 0.8163482915511453, 0.789201804453833, 0.7629580347007615, 0.7375869637263363, 0.7130595711891421, 0.6893478017774359, 0.6664245331184737, 0.6442635447549676, 0.6228394881531861, 0.6021278577083912, 0.5821049627144484, 0.5627479002655473, 0.5440345290590357, 0.5259434440694026, 0.5084539520644433, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.968268892614234, 0.9375446484043949, 0.9077953184869247, 0.8789899677517204, 0.8510986426939796, 0.8240923402667772, 0.7979429777219849, 0.7726233634081705, 0.7481071684951142, 0.7243688995955343, 0.7013838722555592, 0.6791281852863735, 0.6575786959103513, 0.636712995695828, 0.6165093872554908, 0.5969468616841539, 0.578005076712458, 0.559664335553777, 0.5419055664223368, 0.5247103027012452, 0.5080606637398142, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9696580306006657, 0.9402366963083615, 0.911708063240842, 0.884045045084862, 0.8572213773792641, 0.8312115925783671, 0.8059909958719824, 0.7815356417390957, 0.757822311212959, 0.7348284898360026, 0.7125323462836395, 0.6909127116366655, 0.6699490592825748, 0.6496214854267098, 0.6299106901947427, 0.6107979593085402, 0.5922651463180246, 0.5742946553721509, 0.5568694245126478, 0.5399729094746601, 0.5235890679789106, 0.5077023445004684, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9709306314075442, 0.9427062910054524, 0.915302414357788, 0.8886951511012567, 0.862861344187566, 0.8377785097291959, 0.8134248174310394, 0.7897790715908856, 0.7668206926522025, 0.7445296992931734, 0.7228866910363898, 0.7018728313640723, 0.6814698313241194, 0.66165993361272, 0.6424258971196719, 0.6237509819229611, 0.6056189347195363, 0.5880139746796036, 0.5709207797121273, 0.5543244731295832, 0.5382106107003604, 0.5225651680775409, 0.5073745285931162, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9721007705580277, 0.944979908119511, 0.9186156968448309, 0.8929870267495597, 0.868073376801569, 0.8438547984897142, 0.8203118998509404, 0.7974258299430187, 0.7751782637504832, 0.7535513875116787, 0.7325278844551737, 0.7120909209341162, 0.6922241329474299, 0.6729116130370592, 0.6541378975507706, 0.6358879542603122, 0.6181471703250173, 0.6009013405912137, 0.5841366562180706, 0.5678396936207761, 0.551997403722191, 0.5365971015043723, 0.5216264558516047, 0.5070734796767978, NAN, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9731803443915577, 0.9470799827100708, 0.9216796237401371, 0.8969604936501081, 0.8729043221160337, 0.8494933288177609, 0.8267102102971994, 0.8045381271690456, 0.7829606916745105, 0.7619619555688525, 0.7415263983337606, 0.7216389157058806, 0.7022848085129991, 0.6834497718096395, 0.6651198843040366, 0.6472815980686754, 0.6299217285267913, 0.6130274447074281, 0.5965862597618514, 0.58058602173431, 0.5650149045803201, 0.549861399425839, 0.535114306060862, 0.520762724661159, 0.5067960477320326, NAN, NAN, NAN, NAN, NAN, NAN, NAN],
[0.9741794761063388, 0.9490256516668206, 0.92452131215226, 0.9006496875216334, 0.8773944407451627, 0.8547396566237366, 0.8326698308970235, 0.811169859632816, 0.7902250288903491, 0.7698210046505166, 0.7499438230060956, 0.7305798806052629, 0.7117159253418667, 0.6933390472860778, 0.6754366698492191, 0.6579965411767223, 0.6410067257633224, 0.6244555962847529, 0.6083318256403519, 0.5926243792011306, 0.5773225072580017, 0.562415737664998, 0.5478938686724477, 0.5337469619452003, 0.5199653357611251, 0.5065395583852295, NAN, NAN, NAN, NAN, NAN, NAN],
[0.975106834269357, 0.9508333382388071, 0.9271640863678078, 0.9040840371063537, 0.8815785233362363, 0.8596332430502518, 0.8382342502634316, 0.8173679461505227, 0.7970210704040824, 0.777180692807699, 0.7578342050189809, 0.7389693125570932, 0.7205740269897503, 0.7026366583146973, 0.6851458075308443, 0.6680903593943238, 0.651459475354876, 0.6352425866680693, 0.6194293876789786, 0.604009829273055, 0.5889741124900234, 0.5743126822967508, 0.5600162215151275, 0.5460756449011029, 0.5324820933711121, 0.5192269283722252, 0.5063017263924426, NAN, NAN, NAN, NAN, NAN],
[0.9759698850464326, 0.9525172165175468, 0.929628118309378, 0.9072890477623351, 0.8854867876484934, 0.8642084383514349, 0.843441410234007, 0.8231734161894848, 0.8033924643717306, 0.7840868511000482, 0.7652451539345332, 0.7468562249178259, 0.7289091839792632, 0.7113934124975304, 0.6942985470180042, 0.6776144731210667, 0.6613313194377665, 0.6454394518092825, 0.6299294675867378, 0.614792190067989, 0.6000186630680998, 0.5856001456202875, 0.5715281068042061, 0.5577942206985063, 0.5443903614546857, 0.5313085984893154, 0.5185411917917983, 0.5060805873448815, NAN, NAN, NAN, NAN],
[0.9767750937050804, 0.9540895836825685, 0.931930942504582, 0.9102869336915768, 0.8891456049551002, 0.8684952815974784, 0.8483245600647971, 0.8286223016496131, 0.8093776263399202, 0.790579906810971, 0.7722187625566399, 0.7542840541570831, 0.7367658776795328, 0.7196545592091314, 0.7029406495067876, 0.6866149187911024, 0.6706683516414852, 0.6550921420196435, 0.639877688406699, 0.6250165890532436, 0.6105006373397118, 0.5963218172445082, 0.5824722989173883, 0.5689444343556455, 0.5557307531807195, 0.5428239585128922, 0.5302169229417929, 0.517902684590489, 0.5058744432709877, NAN, NAN, NAN],
[0.9775280869070946, 0.9555611606922443, 0.9340878733342124, 0.9130971318235092, 0.8925780924317901, 0.8725201551100316, 0.8529129580125907, 0.8337463721443189, 0.8150104961279666, 0.7966956510891733, 0.7787923756564016, 0.7612914210732337, 0.7441837464205016, 0.7274605139457871, 0.7111130844978774, 0.6951330130638131, 0.6795120444062337, 0.6642421087987542, 0.6493153178571804, 0.6347239604644017, 0.6204604987868609, 0.6065175643805418, 0.5928879543844617, 0.5795646277997036, 0.5665407018520666, 0.5538094484364534, 0.5413642906411595, 0.529198799350269, 0.5173066899223998, 0.5056818189440851, NAN, NAN],
[0.9782337844131518, 0.9569413369672767, 0.9361123455228803, 0.9157367223967191, 0.8958045994762384, 0.8763063234403483, 0.8572324510842273, 0.8385737447458858, 0.8203211678322762, 0.8024658804427837, 0.7849992350879762, 0.7679127725015403, 0.7511982175433775, 0.7348474751918722, 0.7188526266233948, 0.7032059253771379, 0.68789979360343, 0.6729268183937093, 0.6582797481903799, 0.6439514892748122, 0.6299351023317845, 0.6162237990887076, 0.6028109390279961, 0.5896900261710024, 0.5768547059319501, 0.5642987620403473, 0.5520161135303857, 0.5400008117958692, 0.5282470377092473, 0.5167490988033538, 0.5055014265144905, NAN],
[0.97889650672095, 0.9582383708704787, 0.9380161938510856, 0.9182207754085091, 0.8988431094459914, 0.8798743799268776, 0.8613059568636822, 0.8431293923918037, 0.8253364169260937, 0.8079189353985387, 0.7908690235753382, 0.7741789244517071, 0.7578410447227583, 0.7418479513288633, 0.7261923680739174, 0.7108671723149721, 0.6958653917217258, 0.6811802011044027, 0.666804919308574, 0.652733006175508, 0.638958059566669, 0.625473812451009, 0.6122741300537271, 0.599353007065202, 0.5867045649088232, 0.5743230490664818, 0.5622028264605037, 0.5503383828908314, 0.5387243205262915, 0.5273553554488041, 0.5162263152494191, 0.5053321366750843],
];
#[cfg(test)]
mod tests {
use super::*;
use rand::{Rng, SeedableRng};
use rand_chacha::ChaChaRng;
use std::collections::HashSet;
#[test]
fn coverage() {
for &n in &[100, 1_000, 100_000] {
let mut qrng = Qrng::<f64>::new(0.0);
let mut qrng_set = HashSet::new();
let mut rng = ChaChaRng::seed_from_u64(0x5c329d7775ca89e6);
let mut rng_set = HashSet::new();
for _ in 0..n {
qrng_set.insert((qrng.gen() * n as f64) as u32);
rng_set.insert((rng.gen::<f64>() * n as f64) as u32);
}
assert!(qrng_set.len() > rng_set.len())
}
}
#[test]
fn distance() {
let mut qrng = Qrng::<(f64, f64, f64)>::new(0.0);
let mut qrng_points = vec![];
let mut rng = ChaChaRng::from_seed([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]);
let mut rng_points = vec![];
let n = 1000;
for _ in 0..n {
qrng_points.push(qrng.gen());
rng_points.push((rng.gen::<f64>(), rng.gen::<f64>(), rng.gen::<f64>()));
}
let d = |p1: (f64, f64, f64), p2: (f64, f64, f64)| {
((p1.0 - p2.0).powi(2) + (p1.1 - p2.1).powi(2) + (p1.2 - p2.2).powi(2)).sqrt()
};
let mut qrng_distances = vec![];
let mut rng_distances = vec![];
for i in 0..qrng_points.len() {
let mut qrng_closest = ::std::f64::INFINITY;
let mut rng_closest = ::std::f64::INFINITY;
for j in 0..qrng_points.len() {
if i != j {
qrng_closest = qrng_closest.min(d(qrng_points[i], qrng_points[j]));
rng_closest = rng_closest.min(d(rng_points[i], rng_points[j]));
}
}
qrng_distances.push(qrng_closest);
rng_distances.push(rng_closest);
}
let qrng_distance_sum = qrng_distances.iter().sum::<f64>();
let rng_distance_sum = rng_distances.iter().sum::<f64>();
let qrng_distance_mean = qrng_distance_sum / n as f64;
let rng_distance_mean = rng_distance_sum / n as f64;
let standard_deviation = |mean: f64, xs: Vec<f64>| {
let sum_squared_error = xs
.into_iter()
.map(|x| (x-mean).powi(2))
.sum::<f64>();
(sum_squared_error / n as f64).sqrt()
};
let qrng_standard_deviation = standard_deviation(qrng_distance_mean, qrng_distances);
let rng_standard_deviation = standard_deviation(rng_distance_mean, rng_distances);
assert!(qrng_standard_deviation < rng_standard_deviation / 3.0);
}
}