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Ñ� ¤�n ïŽw   Á— ¡Ò  üè ê ‹¶Î errÁìÇ ¨”¨”Ç  �¯§Üï¨ÂïK ÂïR ëü –�à ¨«é€ˆ%ƒÓ€8 Ô¿(‹ åg ¿(‹b Á—\ÍÄÁGü¿#(‹ ÒdqDÚ áèéüòv•˜„¤ €‚,ùœ™ € ¾d¾d DebugTupleÁÁdñ�dÂdÇ �dÃdä�dÄd empty_nameÁ�d“(5&àç::טC�œ“ã—nì—,ÿ'(‹“ì%*‰(‹ %º¾ßËŒú‰•Œúß˶ޠ‹Œ Œ(�(üµ'Z7ê!Ê•ŒúßËD…(ßË Ë'ˆõŒú a“ìŒú�Œú£Ïš�,Ê+ (‹“ì Ü+ß+É(‹ 'º¾ßËŒú(‹º¾ÈÈÈìüÌ*“Æ—ŒúßËlÐ+ŽŽ…Y’•“�7”¹Y‡é£=›5xNº¾ŒúßËüç*0Œú‡“ì��©,à1(‹$(‹“ì:?,ó1(‹Ìà1(‹ ™ŒúßË뻘Qœæ1 ø1 û11üÞ0� ú1î6ßË …1ë»,ø0ˆõDŒúMë» b…j-ƒ“ì{🠌úÜŒúâ뻚,‘5(‹“ì%*¤‘5(‹ œŒúS £5t—5 ¤5§5(üè4?ñ$†5 û4ˆõÓŒúÛ¦K“ìùӢƌú™ŒúŸ,é<(‹“ì%*üé<*(‹ �ŒúTLü<\‡=üï<$ ’=•=(ü¥ "zero",Áüê! i if i > 0 => "positive",ÁÄŒ _ => "negative",Á<¥ });Á­�¼± // Ranged sampling:ÁìÉ use std::f32::consts::PI;Áüç?< println!("Angle: {} radians", rand::random_range(-PI..PI));Á<§�¸¯�ü³ZW See also [The Book: Quick Start](https://rust-random.github.io/book/quick-start.html).Áü�š%https://www.rust-lang.org/favicon.icoÁ„ì9https://www.rust-lang.org/logos/rust-logo-128x128-blk.pngÁl›¼út“  ø‡²³Ýßàêìîñòóûs«t‰sÄr­µi�ùh„ص]G óµQ› �¶K� �7J ¡Ö¬9I¨Ø¶ H”Ù™G#Ûí¼FÚܼYÛÜvy|”¶ s„â hY\LÌ JM?B),lŸü˜<9 Generating random samples from probability distributionsÁÕ�ŒÙ # Quick startÁë�<ï�¸¬÷ use rand::RngExt;Áô� let mut rng = rand::rng();Á¬�ü°KH eprintln!("A letter: {}", rng.sample(rand::distr::Alphabetic) as char);Áü�ü€IF let percent_range = rand::distr::Uniform::try_from(0..=100).unwrap();ÁüÊ=: eprintln!("Percentage: {}%", rng.sample(&percent_range));Á<ˆ�¸��Ô” # `Distribution` traitÁ¯�ü³IF Abstractly, a [probability distribution] describes the probability ofÁüý1. occurrence of each value in its sample space.Á¯�ü³/, More concretely, a sampler `X` implementingÁüãNK [Distribution][]<T> is an algorithm for choosing valuesÁü²KH from the sample space `T` (or a subset of `T`) using randomness from anÁdþ [`Rng`].Áü‹ OL Typically the sampler `X` emulates some like-named probability distributionÁüÛ ,) (for example, [`Bernoulli`] emulates theÁüˆ TQ [Bernoulli distribution](https://en.wikipedia.org/wiki/Bernoulli_distribution)).ÁÝ �üá (% ## The Standard Uniform distributionÁŠ �üŽ OL The [`StandardUniform`] distribution is perhaps the most important sampler,ÁüÞ C@ representing the "default" probability distribution for a type.Áü¢ NK Its distribution is expected to be uniform. For `bool`, `char` and integerÁüñ PM types the sample space equals that of the type (i.e. any valid value of thatÁü JG type may be yielded), but for floating-point types the sample range isÁü�" arbitrarily set to `0.0..1.0`.Á°�ü´IF Implementing [`Distribution`] for [`StandardUniform`] for type `T`ÁüþIF enables sampling type `T` using [`RngExt::random`] and (by extension)Á¬È [`rand::random`].ÁÞ�üâ,) ### Other standard uniform distributionsÁ��ü“JG [`Alphanumeric`] is a simple distribution to sample random letters andÁüÞTQ numbers of the `char` type; in contrast [`StandardUniform`] may sample any validÁ\³ `char`.Á¿�üÃ\Y There's also an [`Alphabetic`] distribution which acts similarly to [`Alphanumeric`] butÁÜ  doesn't include digits.Á¼�üÀNK For floats (`f32`, `f64`), [`StandardUniform`] samples from `[0, 1)`. AlsoÁü�HE provided are [`Open01`] (samples from `(0, 1)`) and [`OpenClosed01`]ÁüØNK (samples from `(0, 1]`). No option is provided to sample from `[0, 1]`; itÁü§NK is suggested to use one of the above half-open ranges since the failure toÁüöKH sample a value which would have a low chance of being sampled anyway isÁü  rarely an issue in practice.Áã�üç*' ## Parameterized Uniform distributionsÁ’�ü–KH The [`Uniform`] distribution provides uniform sampling over a specifiedÁüâHE range on a subset of the types supported by the above distributions.Á«�ü¯52 Implementations support single-value-sampling viaÁüå74 [`Rng::random_range(Range)`](RngExt::random_range).Áü�NK Where a fixed (non-`const`) range will be sampled many times, it is likelyÁüì;8 faster to pre-construct a [`Distribution`] object usingÁü¨B? [`Uniform::new`], [`Uniform::new_inclusive`] or `From`.Áë�Üï ## Non-uniform samplingÁ‹�ü�MJ Sampling a simple true/false outcome with a given probability has a name:ÁüÝMJ the [`Bernoulli`] distribution (this is used by [`RngExt::random_bool`]).Á«�ü¯IF For weighted sampling of discrete values see the [`weighted`] module.Áù�üýJG This crate no longer includes other non-uniform distributions; insteadÁüÈGD it is recommended that you use either [`rand_distr`] or [`statrs`].Á��”�ü˜VS [probability distribution]: https://en.wikipedia.org/wiki/Probability_distributionÁüï74 [`rand_distr`]: https://crates.io/crates/rand_distrÁü§/, [`statrs`]: https://crates.io/crates/statrsÁü×# [`rand::random`]: crate::randomÁüû7¥àü³/æà¼ã [`Rng`]: crate::RngÁ,§ HX†»×Ùó¦ÚÛÈWL—"õé•Xt¢"€ê´dé"Cë™d”##í…Y$¢#ŽîëY¨#šï [4Ä#²ñ [³ñÝZdÌ#¨òÝZ©òó_Tñ#‹ ôó_Œ ôª_dý#� õª_‚ õ΂<²$È ö¶ 4Ø$” ÷ÙlüL€  õ€™d¦# íùÀ„ ¶ 4Å” ÙñØûc Ô˜W,¸GI57LÒ&´Ë\Ñ „Õ,Û ü³$ó¹¥güÞ8á’“” ’ó¹ “€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡”•˜Bÿ å $æœ ìü±*ó¹tà‚¹üõ7üõJG Construct a new `Bernoulli` with the given probability of success `p`.ÁÄ�|Ì # PrecisionÁà�üèHE For `p = 1.0`, the resulting distribution will always generate true.ÁüµIF For `p = 0.0`, the resulting distribution will always generate false.Áƒ�ü‹LI This method is accurate for any input `p` in the range `[0, 1]` which isÁüÜB? a multiple of 2-64. (Note that not all multiples ofÁü£?< 2-64 in `[0, 1]` can be represented as a `f64`.)Áüé¥Bÿ ¦h“üˆ*XüÔ!B? Construct a new `Bernoulli` with the probability of success ofÁü›"EB `numerator`-in-`denominator`. I.e. `from_ratio(2, 3)` will returnÁüå"JG a `Bernoulli` with a 2-in-3 chance, or about 67%, of returning `true`.Á´#�ü¼#JG For `numerator == denominator`, the resulting distribution will alwaysÁü‹$FC return `true`; for `numerator == 0` it will always return `false`.ÁüÖ$HE For `numerator > denominator` or `denominator == 0`, this returns anÁT£% error.Á²%�lº% # ExampleÁÌ%�<Ô%�¸üà% use rand::distr::Bernoulli;Á„&�üŒ&1. let d = Bernoulli::from_ratio(2, 3).unwrap();ÁüÂ&.+ assert!((d.p() - 2.0 / 3.0).abs() < 1e-9);Áõ&�”ý& // Edge cases:Áü”'MJ assert_eq!(Bernoulli::from_ratio(3, 3).unwrap().p(), 1.0); // always trueÁüæ'NK assert_eq!(Bernoulli::from_ratio(0, 3).unwrap().p(), 0.0); // always falseÁü¹(YV assert!(Bernoulli::from_ratio(4, 3).is_err()); // numerator > denominatorÁü—)RO assert!(Bernoulli::from_ratio(1, 0).is_err()); // denominator == 0Á<î)�¸T�*é¥Bÿ Ó­‚–é­‹–´í.üÚ-63 Returns the probability (`p`) of the distribution.Á•.�ü�.KH This value may differ slightly from the input due to loss of precision.Á ô.• •‚¹Bÿ ö. $÷.ü‰0%‚¹%üÃ064Æ0–— –‚¹ —½ðBÿŽ Þ0ÿƽð4Ö0„½ðÐ0 ½ð$ß0�7É™ Í0„‹ d�  #CŽšùÊ„ å4üëI!�$Žá8"TÃ=¬íÓ«ŒÕÌÏ@Tˆ3̤ üµNK Types (distributions) that can be used to create a random instance of `T`.Á„�üˆA> It is possible to sample from a distribution through both theÁüÊJG `Distribution` and [`RngExt`] traits, via `distr.sample(&mut rng)` andÁü•OL `rng.sample(distr)`. They also both offer the [`sample_iter`] method, whichÁüå<9 produces an iterator that samples from the distribution.Á¢�ü¦NK All implementations are expected to be immutable; this has the significantÁüõDA advantage of not needing to consider thread safety, and for mostÁüºIF distributions efficient state-less sampling algorithms are available.Á„ �üˆ KH Implementations are typically expected to be portable with reproducibleÁüÔ :7 results when used with a PRNG with fixed seed; see theÁü� NK [portability chapter](https://rust-random.github.io/book/portability.html)ÁüÞ NK of The Rust Rand Book. In some cases this does not apply, e.g. the `usize`Áü­ C@ type requires different sampling on 32-bit and 64-bit machines.Áñ �üõ .+ [`sample_iter`]: Distribution::sample_iterÁd® #�$#$ÿƶµü¤ ÂþÆ•» » #ñ„,ñ„2%')%'))'%46ü• 4üÄ LI Generate a random value of `T`, using `rng` as the source of randomness.Á4˜ ˜™ ˜¶µ ™»µ•»Bÿ#Ž&& ° #ÿÆ»µ4¨ „»µ¢  %¶µ•»»µ$± �7·  Ÿ ü™büÏ JG Create an iterator that generates random values of `T`, using `rng` asÁìž the source of randomness.ÁÀ�üÈC@ Note that this function takes `self` by value. This works sinceÁü�DA `Distribution` is impl'd for `&D` where `D: Distribution`,ÁüÙIF however borrowing is not automatic hence `distr.sample_iter(...)` mayÁü§EB need to be replaced with `(&distr).sample_iter(...)` to borrow orÁüñC@ `(&*distr).sample_iter(...)` to reborrow an existing reference.Á¹�lÁÚðÓ�<Û�¸üçLI use rand::distr::{Distribution, Alphanumeric, Uniform, StandardUniform};Á¸�ôÀÑÁã�¼ë // Vec of 16 x f32:Áü‡OL let v: Vec = StandardUniform.sample_iter(&mut rng).take(16).collect();ÁÛ�tã // String:Áüö  let s: String = AlphanumericÁô› .sample_iter(&mut rng)Á„¾ .take(7)ÁÄÓ .map(char::from)Áœð .collect();Áˆ�¤� // Dice-rolling:Áü©:7 let die_range = Uniform::new_inclusive(1, 6).unwrap();Áüè74 let mut roll_die = die_range.sample_iter(&mut rng);Áü¤)& while roll_die.next().unwrap() != 6 {ÁüÒ,) println!("Not a 6; rolling again!");Á,ƒ }Á<��¸\œ¶µ»µ§¶Bÿ#Ž((#þÆ»µ ¨¢‡âþƶµ,õ '¶µ•»»µ›�7 ›:<üþgü€" Map sampled values to type `S`Á§�l¯ÚðÁ�<É�¸üÕ-* use rand::distr::{Distribution, Uniform};Á‡�ü�41 let die = Uniform::new_inclusive(1, 6).unwrap();ÁüÈ2/ let even_number = die.map(|num| num % 2 == 0);Áüÿ1. while !even_number.sample(&mut rand::rng()) {Áüµ.+ println!("Still odd; rolling again!");Á,è…‘<ò�¸�¶µз¾¸Bÿ#‚*�+*+#þÆз …þÆå¼ ˆ…#з•»TÅ�#з×—å¼ Îò’,ß )¶µ•»з弜žZ%œlnhjüè;8š�-€.š-.„… íÿÆŽ»4…#Ž»•»|ó‰»/%/46 ðüª34­›œ ›‰» œ�º•»Bÿ,Ž00 Å,ÿÆ�º4½„�º· /8•»Ž»�º$Æ�7Þœ ´üÆ"R€2Ž3�4423þÆå» Ë"þÆë» Î"þÆñ» Ñ"#å»ñ»|ü"„ë»”#¢»567ÅQÆQÊQ67egac]_LŸ#$¤#11ñ»üÉ#$Ì#   ¢»£ÁBÿ1 Ñ#1 6å»ë»ñ»$Ö#ü›&-Lž&¡ ¡¢»ÎÃBÿ1 ¨&1 7å»ë»ñ»$©&üï&]€9Ž:�;9:;¹› ô&Ê› ÷&Û› ú&ì›|°'ÿ›È'¢»(*-/24üù)e€=‚>�?�@>@?=�#Û¼€Êå¼ Ü*þÆÛ¼ �*Û› „*»— ‡*ì›|»*…#Û¼€ÊTÓ*¹› þ)”¼A%AQSVX[]üå*34è*¥¦ ¥”¼ ¦µÉå¼Bÿ<ŽBB €+<ÿƵÉ4ø*„µÉò* Aå»Û¼ñ»å¼µÉ$�+�7ç¤ ï*´Ö,üÐ+! Sample or extend a [`String`]Áò+�üö+EB Helper methods to extend a [`String`] or sample a new [`String`].ÁÓ«ŒÂ,̼,dà,CCñ„üÖ,†Cñ„ñ„!DFDFDFüÖ.Wüó,)& Append `len` random chars to `string`Á¡-�ü©-JG Note: implementations may leave `string` with excess capacity. If thisÁüø-IF is undesirable, consider calling [`String::shrink_to_fit`] after thisÁ\Æ. method.ÁlÙ.§¨© §¶µ ¨ë» ©ŸÐBÿCŽEE ø.CÿÆë»4ð.ÿ›ê. Í$ù.�7ÿ.÷ä4Œ/¶¡/ ç.ü¬1Kü³//, Generate a [`String`] of `len` random charsÁç/�üï/LI Note: implementations may leave the string with excess capacity. If thisÁüÀ0Iä¤\Ž1¶¥l¯1ª« ª¶µ «ë»ŸÐBÿCŽGG Î1C·§4Æ1ÿ›À1 F¶µë»$Ï1�7ä§¶í§ ½1L� ,¡  T¨©²³´#\­ÌHJ�"tºÃHKÏ#LÊÎHL™dé#HNí¼|÷ÚHO¼ÛHOù•„HQ¶ 4š”HRÙ˜ ­ôHSœ—¶¸§©˜šdÚ��{},�]_KML§<œãtÔ4ÚLíTTñ„üãîTñ„ñ„!UVUVþÆU¶µ<ýÄ­V4ý ‚TTü“<üŠHE Helper method to combine the fraction and a constant exponent into aÁT× float.Áæ�üîJG Only the least significant bits of `self` may be set, 23 for `f32` andÁŒ½ 52 for `f64`.ÁüÓJG The resulting value will fall in a range that depends on the exponent.Áü¢30 As an example the range with exponent 0 will beÁüÚ41 [20..21), which is [1..2).ÁÄ–¶µÌ­BÿTT V¶µ$¯ŽÚDµÄÓ\à ì ã0 ò æ!, ó ô ÿ, õ8ª $ö& ú8ª $û- €$ �, ƒ8‚„& †8Ý,‡$ Œ, Ž8utyÁ�& ’8Ý,“$ ˜, š8f_scalarÁD›& £8Ý,¤$ ©, «8u_scalarÁD¬& ´8‚µ$ ·, ¾8 fraction_bitsÁl¿& Ì8²$Í$ Ñ, Ó8 exponent_biasÁlÔ& á8²$â*è ë á0-, õ ö „+ ÷ ø ƒ8ìù ü ‚, ý8ª $þ- …8$�8µL”8 ž, ¢8”²£ § Ñ8!$µ8‚ º ¼, ¾8‚¿% Á+ Ï Ð ß8þ4Ñ × Þ8¸4Ø8 í8ÌÄð ˆ œ8$‰$ �8ŽÚD�& —8Ù™(ž, ¡8‚¢ ¥ Ç8ˆ8£ÚlŒ& ™, ›8õ²Dœ ¥ » ä ¼ Ö, ½8à³l¾ Ì8ŽÚDÎ8Ø, Û8õ²DÜæ, é8¨³lê% ÷, ‰8‚Š'Œ8 from_bitsÁLŽ — ¹8$˜ �, Ÿ8”² '£8ô,¥ ª ¸8£Úl«, Ü Ý ë+ Þ ß ê8ìà ã é, ä8ª $å- ì8$ö8™dû ‡, ˆ8‚‰ ‹8 �8¼|‘ ¡ Õ$8 ¯8™4² ¸8Ž ¹& º8ù¼ À- Â8Ý,Ã È É Ü Ê8$Ë$ Ï8�7Ñ& Ô Ö8×8Ž Û(Þ, á8‚â å Ë$B8Ã!8„ÞTÇ! 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[`RngExt::random_range`] is implemented over [`Uniform`].ÁÔ �œØ  # Example usageÁì �<ð �¸¬ø ³ÁìŽ  use rand::distr::Uniform;Á¬ �ô° ÑÁüÏ2 / let side = Uniform::new(-10.0, 10.0).unwrap();Á‚ �ü†% " // sample between 1 and 10 pointsÁü¬* ' for _ in 0..rng.random_range(1..=10) {Áü×O L // sample a point from the square with sides -10 - 10 in two dimensionsÁü§: 7 let (x, y) = (rng.sample(side), rng.sample(side));Áüâ( % println!("Point: {}, {}", x, y);Á,‹ …‘<‘ �¸™ �ü� 2 / # Extending `Uniform` to support a custom typeÁÐ �üÔ K H To extend [`Uniform`] to support your own types, write a back-end whichÁü  Q N implements the [`UniformSampler`] trait, then implement the [`SampleUniform`]Áüò L I helper trait to "register" your back-end. See the `MyF32` example below.Á¿ �üà P M At a minimum, the back-end needs to store any parameters needed for samplingÁü” N K (e.g. the target range) and implement `new`, `new_inclusive` and `sample`.Áüã O L Those methods should include an assertion to check the range is valid (i.e.Áü³ C @ `low < high`). The example below merely wraps another back-end.Á÷ �üû M J The `new`, `new_inclusive`, `sample_single` and `sample_single_inclusive`ÁôÉ  functions use arguments ofÁüèG D type `SampleBorrow` to support passing in values by reference orÁü°I F by value. In the implementation of these functions, you can choose toÁüúT Q simply use the reference returned by [`SampleBorrow::borrow`], or you can chooseÁüÏF C to copy or clone the value, whatever is appropriate for your type.Á– �<š �¸Ì¢  use rand::prelude::*;Áü¼6 3 use rand::distr::uniform::{Uniform, SampleUniform,Áüó? < UniformSampler, UniformFloat, SampleBorrow, Error};Á³ �´·  struct MyF32(f32);ÁÎ �üÒ!  #[derive(Clone, Copy, Debug)]Áüô+ ( struct UniformMyF32(UniformFloat);Á  �ü¤* ' impl UniformSampler for UniformMyF32 {Á¼Ï  type X = MyF32;Áç �üë@ = fn new(low: B1, high: B2) -> ResultÁü¬4 1 where B1: SampleBorrow + Sized,Áüá3 0 B2: SampleBorrow + SizedÁL•  {ÁüŸW T UniformFloat::::new(low.borrow().0, high.borrow().0).map(UniformMyF32)ÁL÷  }Áü�J G fn new_inclusive(low: B1, high: B2) -> ResultÁüÌ4 œ„ ü�3 Ú„ Lµ –… ü¿a ^ UniformFloat::::new_inclusive(low.borrow().0, high.borrow().0).map(UniformMyF32)ÁL¡ ‰† ü«C @ fn sample(&self, rng: &mut R) -> Self::X {Áüï% " MyF32(self.0.sample(rng))ÁL• ‰† ,Ÿ …‘¥ �ü©"  impl SampleUniform for MyF32 {ÁüÌ$ ! type Sampler = UniformMyF32;Á,ñ …‘÷ �üû7 4 let (low, high) = (MyF32(17.0f32), MyF32(22.0f32));Áü³3 0 let uniform = Uniform::new(low, high).unwrap();Áüç- * let x = uniform.sample(&mut rand::rng());Á<• �¸� �ü¡; 8 [`SampleUniform`]: crate::distr::uniform::SampleUniformÁüÝ= : [`UniformSampler`]: crate::distr::uniform::UniformSamplerÁü›5 2 [`UniformInt`]: crate::distr::uniform::UniformIntÁüÑ9 6 [`UniformFloat`]: crate::distr::uniform::UniformFloatÁü‹? < [`UniformDuration`]: crate::distr::uniform::UniformDurationÁüËI F [`SampleBorrow::borrow`]: crate::distr::uniform::SampleBorrow::borrowÁ<Ç!ô…«ñó�–¸ È É ŸkdÜ Ê „…oT¬ ‡ ©´}d¸ ø ª±~\� ˆ Ø–|œ • Ùñ¹ ûcóÚ¼,Î ¶ýóÜÁtÕ òýóÝÆ<å àýóÞÇ„î …þóßù�! „óà™d¤! #óáíL³ ,· óÊ Œ/,Ǹ ôö¾/dÎ�ô÷Ä-lÜñôøá-tëóôùµL•Tôúò#TºÒôü´#\ÆÌôý�"tÓÃôþÏ#LãÎôÿùû„ô�¶ 4€”ô‚Ù,¿îðÝßÌλ½ô€®œ¤ ¢�‘~€mo,ó`bLNü�”� ° è= ¶ ’, · ¸ Ã, ¹8ª $º& ¾8ª $¿- Ä$ Å, Ç8‚È& Ê8‚Ë$ Í, Ï8”²Ð& Ó8Ý,Ô$ Ù, Û8²DÜ& ä8Ý,å$ ê, ì8õ²Dí& õ8Ý,ö$ û, ý8bits_to_discardÁ|þ& �8²$Ž*” — å=, ¡ ¢ °+ £ ¤ ¯8ì¥ ¨ ®, ©8ª $ª- ±8$»8ŸkdÀ Ì, Í8‚Î Ð Ò ¸<@ Construct, reducing `scale` as required to ensure that roundingÁüàC<, can never yield values greater than `high`.Áü°/<�ì<B Requirements: `low` and `high` must be finite with `low <= high`.ÁüüE<L `scale` must be non-negative, may be positive infinity but must not be NaN.ÁüÎO<�ª<@ Note: though it may be tempting to use a variant of this methodÁüºC<> to ensure that samples from `[low, high)` are always strictlyÁüŠA<7 less than `high`, this approach may be very slow whereÁüØ:<0 `scale.abs()` is much smaller than `high.abs()`ÁüŸ3</ (example: `low=0.99999999997819644, high=1.`).Áüß28 ž8±l\¡ ¬ Ð8»k­& °, ²8‚³$ µ8ˆÞ$·& », ½8‚¾$ À8Â8Æk,Æ& Ë, Í8‚Î(Ò8$Õ Ú ®8ì8ÀÇDð ù û, ü8‚ý ÿ'€8ô,‚ ‡ ­ 7澈8Œ, �8²D� ™, ›8²Dœ'¤8èÓ<¦% ®8$Á Æ ²8Ü8‰ï$à å ç þ8Æk,è î8ÀÇDð ù8»kû ÿ8í"<€ ‡ Œ8ˆÞ$ˆ% �8£8‰ï$¦ ª8ª« ® ¯ ± æ8,Ë% Ð8Æk,ü ‚8Æk,„ ‰8ü"|Š ™ Ÿ š8‰ï$›%  8‘ØdÅ Ñ Ò ò  Ó, Ô8‚Õ ×'Ø8ô,Ú ß ã70.0Áà ä8Á"4å ë ñ8Æk,ì% ó8Ÿkd† “  8»k•$ ˜8Æk,š, Ã Ä Ò+ Å Æ Ñ8ìÇ Ê Ð, Ë8ª $Ì- Ó8$Ý8Ä-lâ8 ð, ô8‚õ ø ° 8!$†8Í'<‹ “8Ÿkd• ¡, ¢8‚£ ¥% ¦, » ¼ Ê+ ½ ¾ É8ì¿ Â È, Ã8ª $Ä- Ë8$Õ8á-tÚ8 é8Ÿkdí ù, ú8‚û ý ÿ ß=È8!$�8” ’ ”, –8‚—% ™8 ¨8˜ « ®8ñ'¯$ ±8û'³ µ ¶ Ì8˜Õ,·& ¼8ñ'¾$ À8ªÕ4Â& È8û'Ê(Î8Ñ4Ñ ×8$Ø$ Ü8Œ/,Þ ã8$,ñ8ñ'‡& ‰8¾/d‹ —8$˜'œ8” ž Ÿ ¡8Ý,£$ ¨8û'º& ¼8¾/d¾ Ê8$Ë'Ï8” Ñ Ò Ô8Ý,Ö$ Û é ¼",8û8»kÿ ƒ …8˜Õ,† ‹8â/4Œ ’ “% ”8¦8ˆÞ$ª ¯ ±8ªÕ4² ¸8â/4¹ ¿ À% Á+ Ó Ô ê8ìÕ Ø é8¬„Ù8ü ÿ € ‘8»k� „8Ï"T… � �“ – — ©8ˆÞ$˜ œ8Ï"T� § ¨ « ï84Á8€È Ë Ü8Œ/,Ì'Ñ8õ�LÓ% Ý8�  „  …  – 8»k†  ‰ 8³"4Š  �  • 8ˆÞ$‘  ˜  Ý 84® 8€µ  ¸  Ê 8Œ/,¹ '¾ 8Þ�TÀ % Ë 8ð 8Æk,ô  ú 8ˆÞ$ü  �!8»kƒ!% †!8˜! ›! œ! ¯!8Æk,�! ¢!8Ï"T£! ­! ®! ±! õ!84Ç!8€Î! 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For (approximations of) continuous types (e.g. `f32`, `f64`),ÁüûDD A samples may equal `high` due to loss of precision but may not beÁÄÄE  greater than `high`.ÁáE �üéEL I Fails if `low >= high`, or if `low`, `high` or the range `high - low` isÁüºF; 8 non-finite. In release mode, only the range is checked.Á�G ƒì‰ìº® Bÿåñ'èû'ééèåó´!,åG �ƒìÀÐ|ÓG šµ!,ŠH �‰ìÀÐ|øG çÀЃì‰ì»kWˆÞ%W…G ‰G üäJ  üÒHL I Create a new `Uniform` instance, which samples uniformly from the closedÁü£I$ ! range `[low, high]` (inclusive).ÁÌI �üÔIK H Fails if `low > high`, or if `low`, `high` or the range `high - low` isÁü¤J; –Ô!lëJ ƒì‰ìº® Bÿåñ'ëû'ìëìåó´!,ÙK ®Ö!|ÇK šµ!,þK ÊÖ!|ìK êÀЃì‰ì»k±YˆÞ»YùJ ýJ üÎL5 ”îîµÐ! ÓL ÆÐ!lÖL ‹âï%ïüŠM3 4�M ´µ ´‹â µë»ÀÐBÿíŽðð ¥M í·§4�M ÿ›—M ïÀÐë»$¦M �7²Z ”M ôÿO üäMI F Helper trait for creating objects using the correct implementation ofÁü®N- * [`UniformSampler`] for the sampling type.ÁÜN �üàNH E See the [module documentation] on how to implement [`Uniform`] rangeÁü©O  sampling for a custom type.ÁÉO �üÍO1 . [module documentation]: crate::distr::uniformÁl‰P ññò’,˜P ñò’ò’ òòþÆò¶µüåP' óèß!ÄóP ôèß!¶µD‚Q àß!-úß!"Šà!üåP& ü¤P< 9 The `UniformSampler` implementation supporting type `X`.Á<êP ññüºT ü�Q2 / Helper trait handling actual uniform sampling.ÁÃQ �üÇQH àÜ!ü�R ²Ý!°R �ü´RL I Implementation of [`sample_single`] is optional, and is only useful whenÁü�SM J the implementation can be faster than `Self::new(low, high).sample(rng)`.ÁÏS �üÓS1 çÝ!ü…T4 1 [`sample_single`]: UniformSampler::sample_singleÁtÄT óóò’,ÔT óò’ò’ ôõøûý�ôõøûý�þÆ™¸ <‘U åä!�ûýõø4‘U üàT, ) The type sampled by this implementation.Á –U óóüôX˜ üžUW T Construct self, with inclusive lower bound and exclusive upper bound `[low, high)`.ÁúU �ü‚VL —Ñ!üÓVN íÑ!ü¦WD ÅÒ!ÄïW ’Ó!ŒX �ü”XA > Usually users should not call this directly but prefer to useÁ¬ÚX  [`Uniform::new`].Á÷X ƒì‰ì±À Bÿóñ'öû'÷ö÷óó´!,ÛY �ƒì™¸ ¬ÃY šµ!,†Z �‰ì™¸ ¬îY õ¶µƒì‰ì»kƒY ˆÞ$ŒY ûX ÿX üÁ[¢ ü’Z8 5 Construct self, with inclusive bounds `[low, high]`.ÁÏZ �ü×ZA £æ!ü�[  [`Uniform::new_inclusive`].ÁlÄ[ ƒì‰ì±À Bÿóñ'ùû'úúùóó´!,²\ ßè!¬š\ šµ!,Ý\ ûè!¬Å\ ø¶µƒì‰ì»kÚ[ ˆÞ$ã[ Ò[ Ö[ ü�]: œé\  Sample a value.Á4„] ¶· ¶¶µ ·ë»™¸ BÿóŽüü œ] ó·§4”] ÿ›Ž] ‘½ $�] �7£] ‹] üÚfâ üÁ]K H Sample a single value uniformly from a range with inclusive lower boundÁü‘^, ) and exclusive upper bound `[low, high)`.ÁÂ^ �üÊ^L —Ñ!ü›_N íÑ!üî_D ÅÒ!Ä·` ’Ó!Ô` �üÜ`( % By default this is implemented usingÁü‰aI F `UniformSampler::new(low, high).sample(rng)`. However, for some typesÁü×aJ G more optimal implementations for single usage may be provided via thisÁü¦b7 4 method (which is the case for integers and floats).Áüâb!  Results may not be identical.Áˆc �ü�cK H Note that to use this method in a generic context, the type needs to beÁüàc6 3 retrieved via `SampleUniform::Sampler` as follows:Á<›d �¸ü§d> ; use rand::distr::uniform::{SampleUniform, UniformSampler};Á´êd  # #[allow(unused)]Áü…e? < fn sample_from_range(lb: T, ub: T) -> T {ÁüÉe"  let mut rng = rand::rng();ÁüðeO L ::Sampler::sample_single(lb, ub, &mut rng).unwrap()Á,Äf …‘<Îf �¸lÝf ¸¦· ¬· ¸ë»Ó¾ BÿóŽþñ'ÿû'€þÿ€ µg ó·§4ôf ÿ›îf þƦ· ,‹h �¦· ™¸ ¬óg þƬ· ,¶h �¬· ™¸ ¬žh ý¶µë»¦· ¬· »k4_ˆÞ>_�7H_ ëf üf €g ü¾lì ü«iK Øì!üûi, ) and inclusive upper bound `[low, high]`.Á¬j �ü´j( ²î!üájH E `UniformSampler::new_inclusive(low, high).sample(rng)`. However, forÁü®kL I some types more optimal implementations for single usage may be providedÁ¤ÿk  via this method.Áü˜l! Ìð!¼Ál ¹¦· ¬· ¹ë»Ó¾ BÿóŽ‚ñ'ƒû'„‚ƒ„ £m ó·§4âl ÿ›Ül õö!,ùm †÷!¬ám š÷!,¤n «÷!¬Œn �¶µë»¦· ¬· »kÂdˆÞÌd�7Öd Ùl êl îl ü¡o7 ”††µÐ! ¦o ÆÐ!l©o ‹â‡ˆµ¶ˆ"$Tßo ,äo ……îàüøo5 Dûo ˜ãº® Bÿ…… ˆÀШþgüÞp@ ”ŠŠµÐ! ãp ÆÐ!læp ‹â‹Œµ¶Œ"$T¥q ,ªq ‰‰îàü¾qK DÁq ß㺮 Bÿ‰‰ ŒÀШÿjü”t üÈr6 3 Helper trait similar to [`Borrow`] but implementedÁüÿrB ? only for [`SampleUniform`] and references to [`SampleUniform`]ÁüÂs) & in order to resolve ambiguity issues.Áìs �üðs# [`Borrow`]: std::borrow::BorrowÁdžt �Ò/Ž�Žñ„ü”tÍ þÆÑäD«t �ñ„-ñ„3���,.ôÁu ü»tA > Immutably borrows from an owned value. See [`Borrow::borrow`]Á�u �ü‰u3 0 [`Borrow::borrow`]: std::borrow::Borrow::borrowÁ4Äu º º¶µ ºÑäBÿ� Ëu � �¶µÑä$Ìu üâuU Ò/‘‘þÆ»äDçu ñ»äl©v »ä’�’#%ìÔv 4×v » »»ä±…"Bÿ� Þv � ’»ä$ßv ü‰wV 8¼Ò/”¼”ð�"DŽw ñÑälÑw Ìä•�•#%ìüw 4ÿw ½ ½Ìä ½ÑäBÿ“ †x “ •8Ñä$‡x ÄÒ} ü²x? < Range that supports generating a single sample efficiently.Áòx �üöxO L See [`RngExt::random_range`] for examples; the method provides a convenientÁìÆy  interface over this type.Áäy �tèy # ExamplesÁ÷y �<ûy �¸üƒz* ' use rand::distr::uniform::SampleRange;Áô®z ÑÁÍz �üÑz= : // Range and InclusiveRange are supported for many types:Áü�{7 4 assert_eq!((9..10).sample_single(&mut rng), Ok(9));ÁüÇ{= : assert_eq!(('a'..='a').sample_single(&mut rng), Ok('a'));Á…| �ü‰|H E // RangeTo and RangeToInclusive are supported for unsigned integers:ÁüÒ|7 4 assert_eq!((..1u8).sample_single(&mut rng), Ok(0));ÁüŠ}? < assert!((..=10u32).sample_single(&mut rng).unwrap() <= 10);Á<Ê} �¸\Ü} –�—–—ñ„üÒ}å „… è} –ñ„$ñ„*˜š˜š˜š57ü¡~I üñ}+ ( Generate a sample from the given range.Ál¤~ ¾¶µ ¾»µ”ðBÿ–Ž™™ Î~ –‘‡4»~ ¢‡µ~ ˜¶µ•»»µ$Ã~ �7É~ ²~ Üš üð~% " Check whether the range is empty.ÁD� ¿ ¿¶µBÿ– ¦ – 𶵕»$§ ü¹? �œœàŒ ¾ ñßËlÁ ¯²ßËßËTÑ ãä�Ÿ˜šŸ�CEü�€H l�€ Àãä Àë»õÚ Bÿ›Žžž º€ ›·§4§€ ÿ›¡€ �ßËë»Wm�7bm ž€ Ô®� D±� Á ÁãäBÿ› º� › ŸßË$»� üõ�H �¡¡àŒ ú� Ñ‘"lý� á‘"T�‚ ªå¢¤˜š¤¢13üÒ‚H lÕ‚ ªå Âë»õÚ Bÿ Ž££ ÿ‚  ·§4ì‚ ÿ›æ‚ ¢ßËë»Äo�7Ïo ã‚ Ô�„ D„„ à êåBÿ  �„   ¤ßË$Ž„ üÍ„ œÚ„  î„ öŠ  ô„ ú„ , õ„ 8ª ö„ & ÷„ 8‚ø„ *ü„  ÿ„ óŠ 8$‰… 8š0\Ž…  ™… , š… 8ª ›…  œ… 8 ž… 8Æ<¢…  ©… , ª… 8ª «…  ¬…  ®… ð‡ + ¼…  ½… Ä… 8þ4¾… 8 Ò… 8º(lÕ…  â… 8Ž ã… & ä… 8ùæ… ê… - ì… 8Ý,í…  ò…  ó… …† 8$ô… $ ø… 8�7ú… & ý…  ÿ… 8€† 8Ž „† (‡† 8Ñ4І  �† , ‘† 8ª ’† $ “† 8Œ/,•†  š†  œ† ú†   ®† , ¯† 8ª °† 8²† 8Ä-lµ†  † 'Æ 8Í'<ņ '̆ 8º(lΆ  Û† ì† 7ó ܆ $ ݆ 8$߆  ㆠ8’ä† $ ç† 8�7é† + ‰‡  Ї ‘‡ 8þ4‹‡ 8 Ÿ‡ 8Å0D¢‡  ª‡ °‡  «‡ 8$¬‡ (²‡ 8Â$µ‡  º‡ æ‡ 7ó ̇ · 8$ч  Õ‡ 8’Ö‡ 8$û‡ 8š0\€ˆ  ‹ˆ , Œˆ 8ª �ˆ  Žˆ 8 �ˆ 8Ç„”ˆ  ¤ˆ , ¥ˆ 8ª ¦ˆ  §ˆ  ©ˆ íŠ + ·ˆ  ¸ˆ ¿ˆ 8þ4¹ˆ 8 ͈ 8º(lЈ  ݈ 8Ž Þˆ & ߈ 8ùáˆ åˆ - çˆ 8Ý,èˆ  íˆ  îˆ €‰ 8$ïˆ $ óˆ 8�7õˆ & øˆ  úˆ 8ûˆ 8Ž ÿˆ (‚‰ 8Ñ4…‰  ‹‰ , Œ‰ 8ª �‰ $ މ 8Œ/,�‰  •‰  —‰ ÿ‰   ©‰ , ª‰ 8ª «‰ 8­‰ 8Ä-l°‰  ½‰ '¾‰ 8Í'<À‰ 'lj 8ñ(¼É‰  à‰ ñ‰ 7ó በ$ ≠8$ä‰  è‰ 8’é‰ $ ì‰ 8�7î‰ + ŽŠ  �Š –Š 8þ4�Š 8 ¤Š 8Å0D§Š  ¯Š µŠ  °Š 8$±Š (·Š 8Â$ºŠ  ¿Š ㊠8 ,ÑŠ % ôŠ „ê!ìä Weighted (index) samplingÁ‚�ü†EB Primarily, this module houses the [`WeightedIndex`] distribution.ÁüÌPM See also [`rand_distr::weighted`] for alternative implementations supportingÁü�KH potentially-faster sampling or a more easily modifiable tree structure.Áé�üí^[ [`rand_distr::weighted`]: https://docs.rs/rand_distr/latest/rand_distr/weighted/index.htmlÁÓ«ŒÖ!ÌÐ!Dò!¨àÆñ×ûc¦§¼†l‰ŒßLÑ)”ÜtিŒŒ/,ð Æ¨ªŽ54÷ ਫù‹ „¨¬™d¢ #¨­í¾/dÌ �¨¯Ä-lÚ ñ¨°á-té ó¨±üÚ …C¨²ñ$ï ûc¨´q,õ Ÿg¨µq¢g¨µ,è ëíÚÜT„ ÍÔ” »¬´ ©«˜š‡‰|Î zLã ké ]_ü£4 ”··µÐ! ¨ ÆÐ!l« ¯²ÀÐÀÐT» Æë¸»+-üª!” üÞE B Creates a new a `WeightedIndex` [`Distribution`] using the valuesÁü¨? < in `weights`. The weights can use any type `X` for which anÁüì, ) implementation of [`Uniform`] exists.Á� �„¥ Error cases:ÁüºE B - [`Error::InvalidInput`] when the iterator `weights` is empty.Áü„K H - [`Error::InvalidWeight`] when a weight is not-a-number or negative.ÁüÔK H - [`Error::InsufficientNonZero`] when the sum of all weights is zero.Áü¤ B ? - [`Error::Overflow`] when the sum of all weights overflows.Áë �üó 2 / [`Uniform`]: crate::distr::uniform::UniformÁ±! ç¡üÐBÿ¶…¹¹¶þÆç¡ µ! ŽPç¡dü! �˨ÀÐ|›" àÀÐ4·" ¸ÀÐ硼4^¨MOŽ* ¸�º�º�ºº¸³Ïü‚5è üÂ+G D Update a subset of weights, without changing the number of weights.ÁŽ, �ü–,. + `new_weights` must be sorted by the index.ÁÉ, �üÑ,X U Using this method instead of `new` might be more efficient if only a small number ofÁü®-V S weights is modified. No allocations are performed, unless the weight type `X` usesÁÔ‰.  allocation internally.Á¨. �ü°.: 7 In case of error, `self` is not modified. Error cases:Áüï.E B - [`Error::InvalidInput`] when `new_weights` are not ordered byÁü¹/' $ index or an index is too large.Áüå/K ߬"üµ0K ´­"ü…1K H Note that due to floating-point loss of precision, this case is notÁüÕ1L I always correctly detected; usage of a fixed-point weight type may beÁ”¦2  preferred.Áü½2B ‰®"„3 �üŒ3P M Updates take `O(N)` time. If you need to frequently update weights, considerÁüá3c ` [`rand_distr::weighted_tree`](https://docs.rs/rand_distr/*/rand_distr/weighted_tree/index.html)ÁüÉ44 1 as an alternative where an update is `O(log N)`.Át‰5 âãä âÆë ã  äÀЕáBÿ¶ ˜5 ¶¼ŽÐÀÐ ¼ÀÐüê5# ½ÑÐÀÐ ½ÀÐüœ6# …ÀÐ,Î6 öÀÐ<â6 »ÀÐ$�5 ¢Ô€ãî5  6 ™A »�¾�¾�¾¾»ý³ü°L? Œ»L ú$À”ÁÁÀþÆ€í ÑL ñ€ílÔL ¯²€í€íTäL €íú$üöL$ ¿¿ò2ÂÎ1¨Ã÷¨ußÒ\uåëú$€íußÒ\uåëÂÃÍL ›�ttöL ¨¿¿ ú$ÄÞd M , M ¨¿¿ü±Mr 8å”ÅåÅá½" ¶M ò½"léM ‚¾"TùM Ÿg€í,†N Ÿgò€í,�N ÁìÆ gÆKMüªN8 ­N æçè æÁì ç€g€gŠ‚gê ûcƒg£üûcØ«q¢1ȡ蕘BÿÄ ±N Ä Æ8€í$²N œ¦ðü”PS 8é”ÈÈéá½" ™P ò½"lÌP ‚¾"TÜP ÁìɆÉ#%¼îP ,ñP ê êÁìÁìBÿÇ ÷P Ç É8€í$øP ü‡R„ 8ë”ËëËá½" ŒR ÌÑЀí Ì€íüÂR# ò½"lèR ‚¾"TøR …€í,…S ÁìÍÎÏÅQÆQÊQÎÏjlÆR L’S $—S ÊÊ€íü¦S( $©S ì ìÁìřǙș­É™Ê™àË™óG*¤�R{9 ÅQÁìBÿÊ ®S Ê Î8€í$³S ü¡U- L¤U í íÁìÎÃBÿÊ ®U Ê Ï8€í$¯U üÖVŒ 8î”ÑîÑá½" ÛV ÒÑЀí Ò€íüšW# ò½"lÀW ‚¾"TÐW ¼Ä",ÝW ÁìEGžW üèW< ”ÔÔµÐ! íW ÆÐ!lðW áª"T€X œ¼",�X ÆëÕ×Ù)+ü°\i ü«X8 5 Returns the weight at the given index, if it exists.ÁèX �üðX; 8 If the index is out of bounds, this will return `None`.Á°Y �l¸Y ÚðÊY �<ÒY �¸üÞY- * use rand::distr::weighted::WeightedIndex;Á�Z �ä˜Z  let weights = [0, 1, 2];Áü¹Z5 2 let dist = WeightedIndex::new(&weights).unwrap();ÁüóZ( % assert_eq!(dist.weight(0), Some(0));Áü [( % assert_eq!(dist.weight(1), Some(1));ÁüÍ[( % assert_eq!(dist.weight(2), Some(2));Áüú[% " assert_eq!(dist.weight(3), None);Á<¤\ �¸4·\ ï ïÆë»üBÿÓ ¾\ ÓÖÑÐÀÐ ÖÀÐüõ\# ÕÀÐ$¿\ ÷þù\ ü£ek ü¢`X U Returns a lazy-loading iterator containing the current weights of this distribution.Áÿ` �ü‡aV S If this distribution has not been updated since its creation, this will return theÁüâa) & same weights as were passed to `new`.Á�b �l˜b Úðªb �<²b �¸ü¾b- ÚÉ"ðb �äøb  let weights = [1, 2, 3];Áü™c9 6 let mut dist = WeightedIndex::new(&weights).unwrap();Áü×cB ? assert_eq!(dist.weights().collect::>(), vec![1, 2, 3]);Áüžd- * dist.update_weights(&[(0, &2)]).unwrap();ÁüÐdB ? assert_eq!(dist.weights().collect::>(), vec![2, 2, 3]);Á<—e �¸<ªe ð ðÆë¿¿ò2ÂÎ1¨Ã÷¨ußÒ\uåëðÀÐBÿÓ ²e ÓØÑÐÀÐ ØÀÐüêe# ×ÀÐ$³e îe ü»g üþf8 5 Returns the sum of all weights in this distribution.ÁdÂg ñ ñÆëÀÐBÿÓ Ïg Ó ÙÀÐ$Ðg üˆhY ”ÛÛµÐ! �h ÆÐ!lÆh áª"TÖh ÆëÜ%Ü"$üèh7 4ëh òó òÆë óë»BÿÚŽÝÝ ƒi Ú·§4ûh ÿ›õh ÜÀÐë»$„i �79 òh ôj Ü�Þ�Þ�ÞÞÜކìùª¼Ø´™ Bounds on a weightÁ°�ü´# See usage in [`WeightedIndex`].Á4âààñ„üØÙ…¶µ,êàñ„,—Ú" ñ„8—Ú",áâáââ„’¼ö Representation of 0Á$˜àà¶µüò =¤© Checked additionÁÂ�üÊKH Note that for floating-point formats with a representation of infinity,Áüš41 overflow-to-infinity is not considered an error.ÁÓ�üÛ85 - `Result::Ok`: On success, `v` is added to `self`Áü˜ HE - `Result::Err`: Returns an error when `Self` cannot represent theÁüå KH result of `self + v` (i.e. overflow). The value of `self` should beÁ”µ  discarded.Á”õ ôõ ô¶µ õ¶µóÕBÿà ˆ à â¶µ$� ¬ “ ä³ |À  Ð  Ó Ö  Ü , × 8ª Ø & Ù 8‚Ú *Þ  á  ê8$ë 8Ž54ð 8 ÷ , û 8ª ü  þ  ä8,Œ 8œ5$’ & – 8$˜  � 7ó Ÿ %   8 ® 8¨5”±  à  ×  Ä 8Å 8$É $ Í 8¬ Ï & Ð  Ò 8$Ó (Ù 8Ñ4Ü  â  ã  ä $ å  ç  è  é  ë  Ú8,ý 8$ƒ  ‡ 8ä–!\ˆ  “  –  ” 8¬ •  ˜  Ì 8à$®  ²  ¶ 8«� ³ *¸  »  • Õ 8$Ö  Û 8«� Ý % à 8¯ú  ü  ÿ  ý  þ 8­$«*°8€³ ¶ ¹ · ¸$ º% ë ñ „ , ò8ª ó& ô8‚õ$ ÷, ù ú �, û8ýü& þ8‚ÿ$ ‚ ƒ*† ‰ Ñ8Â5|“ ¢ £ ¦, ¤8ª ¥% §8Â5|± À Á Ê,  à Ç, Ä8ýÅ$ È É% ËôºŒÇ Ù “ ß å, à8ª á& â8‚ã*ç ê �8$ô8Ž54ù8 €, „8ª … ‡ Š8,•8œ5$›& Ÿ8$¡ ¦7�£ ¨% «8 º8¨5”½ Ï ã Ð8Ñ8$Õ$ Ù8¬ Û& Ü Þ8$ß(å8Ñ4è î ï ð$ ñ ó ô õ ÷ € Ð8$ÑÖ Ù8¬ Ú% Û8¯í ï ò ð ñ% ‘üÎ!ÇîÜôÇîç¥gçü–4™™š› ™Çî š€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡›•˜Bÿæ �æ ç$žœ ¤|…"àDäDÖDÚDüÕ" Ó«Œ¹"̳"äD”ÿ"ÛDßDÒDÖDÈDÌD\¶#ÂDÆD¦DªD\ã#ŽD’DrDvD´£$tŒ$tDlÑ$jD|®üä+( Convenience re-export of common membersÁ��ü”LI Like the standard library's prelude, this module simplifies importing ofÁüáOL common items. Unlike the standard prelude, the contents of this module mustÁ̱ be imported manually:ÁË�<Ï�¸Ì×£€ üñ+( # let mut r: StdRng = rand::make_rng();Áô� # let _: f32 = r.random();Á<¼�¸<¶™dí#ùíìŽD¢šú«–‘4ïÂû®Ý‘L½Ìü¯�K„ï¨þȹGl�ùÿÉ¢Et�ڀđL\ ´�Ê­µLÐ�ƒùÛ„„¶ 4à”…Ùص\èG† ÔߌÅLË)¬•ŒûL�:œâÓstd_rngÁœ²ܬŒÈLÎd´°Ó thread_rngÁ´�ô‰Œ÷Lý‘TâŒÈL΢#!Á®ECͺgeÙÆ‰‡å,ÈŒ®L´õ#!EC!ge.‰‡9<¿Ã”¨®°±š0\Ê –‡‰Ä-l× ñ‡Š•$ú ‡Œ™d€ #‡�í¼|Ž Ú‡Ž¼Û‡Ž…ËD¯ Êþ‡�…ËËþ‡�˜ Ä ô‡‘å,É êi‡’ùà „‡“¬² îðÝßdë Ð,ò ÂÄ®°œ¤ ‹$½ dfSUtÕ F¬· üæ!  User-level interface for RNGsÁˆ �üŒG D [`Rng`] is the `dyn`-safe implementation-level interface for RandomÁüÔN K (Number) Generators. This trait, `RngExt`, provides a user-level interfaceÁü£M J on RNGs. It is implemented automatically for any R: [Rng][].Áñ �üõL I This trait must usually be brought into scope via `use rand::RngExt;` orÁä  `use rand::prelude::*;`.Áß �œã  # Generic usageÁ÷ �üûE B The basic pattern is `fn foo(rng: &mut R)`. SomeÁüÁ!  things are worth noting here:Áã �üçJ G - Since `RngExt: Rng` and every `RngExt` implements `Rng`, it makes noÁü² G D difference whether we use `R: Rng` or `R: RngExt` for `R: Sized`.Áüú N K - Only `Rng` is dyn safe, supporting `&mut dyn Rng` and `R: Rng + ?Sized`.ÁÉ �üÍ O L An alternative pattern is possible: `fn foo(rng: R)`. This has someÁü� P M trade-offs. It allows the argument to be consumed directly without a `&mut`;Áüî  also it still works directlyÁü� N K on references (including type-erased references). Unfortunately within theÁüÞ L I function `foo` it is not known whether `rng` is a reference type or not,Áü« J G hence many uses of `rng` require an extra reference, either explicitlyÁüö O L (`distr.sample(&mut rng)`) or implicitly (`rng.random()`); one may hope theÁüÆ4 1 optimiser can remove redundant references later.Áû �dÿ Example:ÁŒ �<� �¸ä˜  use rand::{Rng, RngExt};Áµ �ü¹1 . fn foo(rng: &mut R) -> f32 {Á¤ë  rng.random()Á,€ …‘† �üŠ$ ! # let v = foo(&mut rand::rng());Á<¯ �¸4Á ””ñ„ü·Ô@ „¶µÉ ”ñ„,èˆ# ñ„8èˆ#,•—™œ�ž¡¤•—™œ�ž¡¤¡�™¤•œ—žüáP üÓC @ Return a random value via the [`StandardUniform`] distribution.Á› �l£ Úðµ �<½ �¸¬É ³Áã �ôë ÑÁôŽ  let x: u32 = rng.random();Á´±  println!("{}", x);ÁüÌ2 / println!("{:?}", rng.random::<(f64, bool)>());Á<ƒ �¸� �¼—  # Arrays and tuplesÁ³ �ü»8 5 The `rng.random()` method is able to generate arraysÁüøG D and tuples (up to 12 elements), so long as all element types can beÁtÄ generated.Á× �üßI F For arrays of integers, especially for those with small element typesÁü­I F (< 64 bit), it will likely be faster to instead use [`RngExt::fill`],Áüû2 / though note that generated values will differ.Á² �<º �¸¬Æ ³Áà �ôè ÑÁü‹I F let tuple: (u8, i32, char) = rng.random(); // arbitrary tuple supportÁÙ �üáD A let arr1: [f32; 32] = rng.random(); // array constructionÁôª  let mut arr2 = [0u8; 128];ÁüÍ9 6 rng.fill(&mut arr2); // array fillÁ<‹ �¸— �üŸ/ , [`StandardUniform`]: distr::StandardUniformÁ4ä    ¶µ•»Bÿ”�–– î ”„… ë #º¾•»|¡ •¶µ•»$ó +-ü¬‰ üè= : Return an iterator over [`random`](Self::random) variatesÁª �ü²? < This is a just a wrapper over [`RngExt::sample_iter`] usingÁüö  [`distr::StandardUniform`].Áš �ü¢0 - Note: this method consumes its argument. UseÁü×: 7 `(&mut rng).random_iter()` to avoid consuming the RNG.Á– �lž Úð° �<¸ �¸üÄ4 1 use rand::{rngs::SmallRng, RngExt, SeedableRng};Áý �ü…) & let rng = SmallRng::seed_from_u64(0);Áü³: 7 let v: Vec = rng.random_iter().take(5).collect();ÁÜò  assert_eq!(v.len(), 5);Á<’ �¸\¯ ¶µ—æBÿ”�˜˜”„… » ò’,… ù“#|¥ —¶µ•»ñ2(*ü³+n üñ / , Generate a random value in the given range.Á¥! �ü­!H E This function is optimised for the case that only a single sample isÁüú!D A made from the given range. See also the [`Uniform`] distributionÁüÃ"H E type which may be faster if sampling from the same range repeatedly.Á�# �ü˜#A > All supported types may be sampled with `low..high_exclusive`ÁüÞ#F C ([`Range`]) and `low..=high` ([`RangeInclusive`]) syntax. UnsignedÁü©$C @ integer types also support `..high_exclusive` ([`RangeTo`]) andÁüñ$, ) `..=high` ([`RangeToInclusive`]) syntax.Á¢% �dª% # PanicsÁ»% �üÃ%J G Panics if the range is empty, or if `high - low` overflows for floats.Á’& �lš& Úð¬& �<´& �¸¬À& ³ÁÚ& �ôâ& ÑÁ…' �´�'  // Exclusive rangeÁü¨'5 2 println!("{}", rng.random_range::(..10));Áüâ'3 0 println!("{}", rng.random_range(-40.0..1.3e5));Áš( �´¢(  // Inclusive rangeÁü½(/ , println!("{}", rng.random_range(-10..=10));Áüñ(0 - println!("{}", rng.random_range('a'..='z'));Á<¦) �¸²) �üº)( % [`Uniform`]: distr::uniform::UniformÁôç)  [`Range`]: std::ops::RangeÁüŠ*0 - [`RangeInclusive`]: std::ops::RangeInclusiveÁü¿*"  [`RangeTo`]: std::ops::RangeToÁüæ*4 1 [`RangeToInclusive`]: std::ops::RangeToInclusiveÁ¶|Ÿ+ d¶+ €¡ ¡¶µ»µ•»Bÿ”�šŽ›š› É+ ”„… Ã+ Ù’ Æ+ ñ•»lø+ –»µ•»t’, ™¶µ•»»µ$Î+ …j7PRUWü§1) üŸ-7 4 Return a bool with a probability `p` of being true.ÁÛ- �üã-C @ See also the [`Bernoulli`] distribution, which may be faster ifÁü«.2 / sampling from the same probability repeatedly.Áâ. �lê. Úðü. �<„/ �¸¬�/ ³Áª/ �ô²/ ÑÁüÕ// , println!("{}", rng.random_bool(1.0 / 3.0));Á<‰0 �¸•0 �d�0 œž#®0 �Ô¶0  If `p < 0` or `p > 1`.ÁÕ0 �üÝ0# [`Bernoulli`]: distr::BernoulliÁ¶|“1 \ª1 €¢ ¢¶µBÿ” ¶1 ” œ¶µ$»1 ¦Ù>üé9D üý2H E Return a bool with a probability of `numerator/denominator` of beingÁLÊ3  true.ÁØ3 �üà3H E That is, `random_ratio(2, 3)` has chance of 2 in 3, or about 67%, ofÁü­4J G returning true. If `numerator == denominator`, then the returned valueÁüü4F C is guaranteed to be `true`. If `numerator == 0`, then the returnedÁüÇ5& # value is guaranteed to be `false`.Áò5 �üú5C ô¦#üÂ6D A sampling from the same `numerator` and `denominator` repeatedly.Á‹7 �d“7 œž#¤7 �ü¬77 4 If `denominator == 0` or `numerator > denominator`.Áè7 �lð7 Úð‚8 �<Š8 �¸¬–8 ³Á°8 �ô¸8 ÑÁüÛ8+ ( println!("{}", rng.random_ratio(2, 3));Á<‹9 �¸—9 �üŸ9# ï©#¶|Õ9 dì9 €£ £¶µBÿ” ù9 ” �¶µ$þ9 Ó­.Gé­7Gü‘@: üº<5 2 Sample a new value, using the given distribution.Áô< �|ü< ### ExampleÁ�= �<˜= �¸¬¤= ³Áì¾= �óà= �ôè= ÑÁü‹>9 6 let x = rng.sample(Uniform::new(10u32, 15).unwrap());ÁüÉ>I F // Type annotation requires two types, the type and distribution; theÁü—?$ ! // distribution can be inferred.ÁüÀ?@ = let y = rng.sample::(Uniform::new(10, 15).unwrap());Á<…@ �¸4”@ ¤ ¤¶µŽ»•»Bÿ”�Ÿ€ Ÿ  ²@ ”„… ›@ þÆŽ» ž@ ‹™|¡@ ž¶µ•»Ž»$·@ •AJ=?9;üÙIz üô@J G Create an iterator that generates values using the given distribution.ÁÃA �üËA1 . Note: this method consumes its arguments. UseÁü�B< 9 `(&mut rng).sample_iter(..)` to avoid consuming the RNG.ÁÂB �lÊB ÚðÜB �<äB �¸¬ðB ³ÁüŠC> ; use rand::distr::{Alphanumeric, Uniform, StandardUniform};ÁÍC �ôÕC ÑÁøC �¼€D «ŒüœDQ N let v: Vec = (&mut rng).sample_iter(StandardUniform).take(16).collect();ÁòD �túD °�ü�E8 5 let s: String = (&mut rng).sample_iter(Alphanumeric)Á„ÊE ˜ŽÄßE ±ŽœüE ÒŽ”F �´œF  // Combined valuesÁü·FD A println!("{:?}", (&mut rng).sample_iter(StandardUniform).take(5)Áü€GA > .collect::>());ÁÆG �¤ÎG úŽüçG: ˜�ü¦H9 6 let mut roll_die = (&mut rng).sample_iter(die_range);ÁüäH) ��ü’I, Ð�,ÃI …‘<ÍI �¸\ÜI ¶µŽ»æ–Bÿ”�¢€£¢£”„… èI ·# ëI ‹™|®J ò’,ÍJ ¡¶µ•»Ž»?K•IK<>ACü±P+ ü…K8 5 Fill any type implementing [`Fill`] with random dataÁÂK �üÊKJ G This method is implemented for types which may be safely reinterpretedÁü™LJ G as an (aligned) `[u8]` slice then filled with random data. It is oftenÁüèLB ? faster than using [`RngExt::random`] but not value-equivalent.Á¯M �ü·MI F The distribution is expected to be uniform with portable results, butÁü…N> ; this cannot be guaranteed for third-party implementations.ÁÈN �lÐN ÚðâN �<êN �¸¬öN ³Á�O �ä˜O  let mut arr = [0i8; 20];Áü¹O# rand::rng().fill(&mut arr[..]);Á<áO �¸íO �üõO# [`fill_bytes`]: Rng::fill_bytesÁ¶|�P $´P €¥¦ ¥¶µ ¦ïùBÿ”�¥¥ ÂP ”„… ¹P ¨•»$¼P ¤¶µ•»$ÇP „˜îK13ü�Q" ާ§ÿù4›Q �ú•Q ½ð ’Q ¬ëT ü´Q, ) Support filling a slice with random dataÁáQ �üåQK H This trait allows slices of "plain data" types to be efficiently filledÁ¬±R  with random data.ÁÇR �üËRF C Implementations are expected to be portable across machines unlessÁü’S) & clearly documented otherwise (see theÁü¼SS P [Chapter on Portability](https://rust-random.github.io/book/portability.html)).Áü�TL I The implementations provided achieve this by byte-swapping on big-endianÁlÝT machines.Á$õT ¨¨ò’,ûT ¨ò’ò’ ©©©üªU? ô‡U  Fill this with random dataÁT­U §¨ § ¶µ ¨ë»Bÿ¨Žªª ÏU ¨·§4ÁU ÿ›»U ©¶µë»–™$ÉU �7ÜU ¸U „íU ¬©¬ü„V> T‡V ©ª ©ñ° ª½ðBÿ«Ž­­ ©V «ÿù4›V �ú•V ¬½ð–™‚L�7ŒL ’V Ô�W D�W ‡ÿ¼›´¶X LÃX  ÍX àe  ÓX ÔX *ÖX  ÙX ÚX % ÛX  áX ÷X 8to_leÁ,âX  çX 8plainÁ,éX , ïX 8® ðX & ñX 8Ý,òX *ùX  üX •Y , †Y 8® ‡Y  ˆY 8ÏÐ#,‰Y  ŽY �Y % –Y  œY µY 8ÏÐ#,�Y  ¢Y 8wrappingÁD¤Y , ­Y 8® ®Y & ¯Y 8Ý,°Y *·Y  ºY ßY 8…ËDÄY  ÌY ÙY , ÍY 8® ÎY  ÏY 7ó ÐY  ÑY 8ÏÐ#,ÒY  ×Y ØY % àY  æY ƒZ  8¸9TçY  ñY , óY 8ª ôY & õY 8‚öY $ øY , úY 8ÏÐ#,ûY & €Z 8ý�Z *…Z  ˆZ ÷a  8 ’Z 8¸9T•Z  ŸZ 8Ž  Z & ¡Z 8ù£Z §Z - ©Z 8Ý,ªZ  ¯Z  °Z ÏZ  8–™$±Z & µZ  ·Z 8¸Z  ¼Z ÁZ 8$½Z $ ÂZ 8�7ÄZ & ÇZ  ÉZ 8ÊZ 8Ž ÎZ  ÑZ ña 8ßZ 8–™$âZ  æZ 8¶çZ  êZ ëZ  íZ 7ó ïZ  ñZ ça 8ƒ[ 8ß$‡[ Œ[ 8˜ Ž[ '‘[ 8â\“[  ž[ £[ 8–™$Ÿ[ % ¤[ 8�7¶[  ¹[ 8 fill_bytesÁTº[  Ä[ ð` 8"4š_  ¡_ Þ` 8å,»_ 'À_ 8from_raw_parts_mutÁ”Â_  Ô_ È`  8–™$Õ_  Ù_ 8 as_mut_ptrÁTÚ_  ä_ å_ 8ƒ` †` 8‡` 8™‹` $ �` 8ß$«` % ñ` 8 ƒa 8® ‡a 8‰a 8–™$Œa  ‘a Ùa  §a 8® ¨a ªa 8÷9L¬a  µa  ¶a Æa 8ÏÐ#,·a  ¼a , ¾a 8ÏÐ#,¿a 8® Åa % Ça % øa  þa „b , ÿa 8ª €b & �b 8‚‚b *†b  ‰b “d  Šb �d 8ç9DËb  Ób Ôb % Õb 8$àb 8¬9$åb 8 êb , îb 8ª ïb  ñb ªc 8÷9Lÿb  ˆc  ‰c Ÿc 8¸9TŠc  ”c , –c 8ª —c $ ˜c 8æÐ#,šc %  c 8$µc 8¬9$ºc 8 ¿c 8…ËDÃc  Ëc , Ìc 8ª Íc  Îc  Ðc Œd 8÷9LÞc  çc  èc �d 8¸9Téc  óc , õc 8ª öc $ ÷c 8‡Ò#Dùc % ‚d % ”d  šd ­d , ›d 8ª œd & �d 8‚žd $  d , ¢d  £d «d , ¤d 8ý¥d & §d 8‚¨d $ ªd  ¬d *¯d  ²d Þe  ³d Ýe 8÷9L½d  Æd  Çd Êd , Èd 8ª Éd % Ëd 8÷9LÃe  Ìe  Íe Öe , Îe  Ïe Ôe , Ðe 8ýÑe $ Óe  Õe % ×e \´f ºf ‡\Àg Æg ‡dÈüä)& Random number generators and adaptersÁŽ�Œ’ ## GeneratorsÁ¤�ü¨85 This crate provides a small selection of generators.Áüá>; See also [Types of generators] and [Our RNGs] in the book.Á �ü¤&# ##### Non-deterministic generatorsÁË�üÏUR - [`SysRng`] is a stateless interface over the operating system's random numberÁü¥OL source. This is typically secure with some form of periodic re-seeding.ÁüõEB - [`ThreadRng`], provided by [`crate::rng()`], is a handle to aÁü»RO thread-local generator with periodic seeding from [`SysRng`]. Because thisÁüŽKH is local, it is typically much faster than [`SysRng`]. It should beÁüÚ74 secure, but see documentation on [`ThreadRng`].Á’�ì– ##### Standard generatorsÁ´�ü¸OL These use selected best-in-class algorithms. They are deterministic but notÁüˆ EB portable: the algorithms may be changed in any release and may beÁ¼Î  platform-dependent.Áæ �üê PM - [`StdRng`] is a CSPRNG chosen for good performance and trust of securityÁü» HE (based on reviews, maturity and usage). The current algorithm isÁü„ KH [`ChaCha12Rng`], which is well established and rigorously analysed.ÁüÐ KH [`StdRng`] is the deterministic generator used by [`ThreadRng`] butÁüœ B? without the periodic reseeding or thread-local management.Áüß NK - [`SmallRng`] is a relatively simple, insecure generator designed to beÁü® FC fast, use little memory, and pass various statistical tests ofÁüõ GD randomness quality. The current algorithm is one of the XoshiroÁü½A> generators below, depending on the target's pointer size.Áÿ�üƒ# ##### Named portable generatorsÁ§�ü«MJ These are similar to the [standard generators](#standard-generators), butÁüù85 with the additional [guarantees of reproducibility]:Á²�ü¶MJ - [`Xoshiro256PlusPlus`] is a very fast 64-bit insecure generator usingÁü„OL 256 bits of state with good performance in statistical tests of qualityÁüÔMJ - [`Xoshiro128PlusPlus`] is a very fast 32-bit insecure generator usingÁü¢OL 128 bits of state with good performance in statistical tests of qualityÁüòOL - [`ChaCha8Rng`], [`ChaCha12Rng`] and [`ChaCha20Rng`] are generators overÁüÂEB the ChaCha stream cipher designed by Daniel J. Bernstein[^1].Áˆ�ìŒ ### Additional generatorsÁª�ü®KH - The [`rdrand`] crate provides an interface to the RDRAND and RDSEEDÁüú<9 instructions available in modern Intel and AMD CPUs.Áü·IF - The [`rand_jitter`] crate provides a user-space implementation ofÁü�JG entropy harvesting from CPU timer jitter, but is very slow and hasÁüÌJG [security issues](https://github.com/rust-random/rand/issues/699).Áü—LI - The [`rand_pcg`] crate provides portable implementations of a subsetÁüä96 of the [PCG] family of small, insecure generatorsÁüžKH - The [`rand_xoshiro`] crate provides portable implementations of theÁüê63 [xoshiro] family of small, insecure generatorsÁ¡�ü¥1. For more, search [crates with the `rng` tag].Á×�üÛ ## Traits and functionalityÁû�üÿEB All generators implement [`TryRng`]. Most implement [`Rng`] (i.e.ÁüÅEB `TryRng`) and thus also implement [`RngExt`].Áü‹52 See also the [Random Values] chapter in the book.ÁÁ�üÅC@ Secure RNGs may additionally implement the [`CryptoRng`] trait.Á‰�ü�@= Use the [`rand_core`] crate when implementing your own RNGs.ÁÎ�üÒYV [^1]: D. J. Bernstein, [*ChaCha, a variant of Salsa20*](https://cr.yp.to/chacha.html)Á¬�ü°YV [guarantees of reproducibility]: https://rust-random.github.io/book/crate-reprod.htmlÁüŠLI [Types of generators]: https://rust-random.github.io/book/guide-gen.htmlÁü×B? [Our RNGs]: https://rust-random.github.io/book/guide-rngs.htmlÁüšIF [Random Values]: https://rust-random.github.io/book/guide-values.htmlÁìä [`RngExt`]: crate::RngExtÁì‚  [`TryRng`]: crate::TryRngÁ¼  çáü¸ # [`CryptoRng`]: crate::CryptoRngÁüÜ '$ [`SeedableRng`]: crate::SeedableRngÁü„!/, [`rdrand`]: https://crates.io/crates/rdrandÁü´!96 [`rand_jitter`]: https://crates.io/crates/rand_jitterÁüî!30 [`rand_pcg`]: https://crates.io/crates/rand_pcgÁü¢";8 [`rand_xoshiro`]: https://crates.io/crates/rand_xoshiroÁüÞ"?< [crates with the `rng` tag]: https://crates.io/keywords/rngÁüž#*' [chacha]: https://cr.yp.to/chacha.htmlÁüÉ#&# [PCG]: https://www.pcg-random.org/Áüð#(% [xoshiro]: https://prng.di.unimi.it/Á$гÄÙï€ìŽDÇ%š«Â�”í%¦¬¬�”�&´­–‘4á&®ݑLž'̯SysErrorÁD¹( ±SysRngÁ4Ã(¬²»‰$­²Lš$,ž$²¸š› InfallibleÁT� ¸Ä³´ص\© G³¶�¶4¶ �³·Ìþ BL� 13 "Dä ÆÔ«!ÜÆ üÀ# é ³Ú÷ìÏ Üõº¼¾HIJ¼¾L¯ $´ ¹¹¢¶À üà& Lã HÜõÜõBÿ¹¹ ¼Öµì„¼  ³ü‚$ l… ÜõBÿ¹¹ ¾ƒBêÄÞ ÜõÀÁÂÑ’“”ÃÂÁTý ,‚ ¿¿�‡ü±5 d´ Ö ÖÜõкBÿ¿ Á ¿ Á$Æ ü¨ 5 d« × ×ÜõÔ¼Bÿ¿ ¸ ¿ Â$½ üŸ!G t¢! ØÙ ØÜõ Ùñ°³¿Bÿ¿ ±! ¿ Ã$¶! „˜Dè´¥$”©$²¦ù‰$T÷¸ÄÄÅص\“GÄÇ�¶4 �ÄÈš!,¨2ÄÉÌèVL‡EG46#%ü‹'ÝöËÍÐHIJÐÍL¹$¾Êʳ²ÊüÖ 2üÔKH Create a new `Xoshiro128PlusPlus`. If `seed` is entirely 0, it will beÁü¤  mapped to a different seed.ÁLÙ ³²ÝöBÿÊÊ ÍÖµ²áî $ò Í�Ï�Ï�ÏÏÍÈÌüó (üé 85 Create a new `Xoshiro128PlusPlus` from a `u64` seed.Á¦ �ü® 2/ This uses the SplitMix64 generator internally.Álö ÝöBÿÊÊ Ðƒ,ˆt¦¬Ä ãÐÐü¸"ÝöÔÕÖב’“”ÕÖ×Tá,æÓÓ�‡ü�5d�á áÝöкBÿÓ �Ó Õ$¢üÝ5dàâ âÝöÔ¼BÿÓ íÓ Ö$òüÔFt×ãä ãÝö äñ°³¿BÿÓ æÓ ׆ʴú ÏÊ×�Ø�Ø�ØØ×¯ú´½$”Á$²´ù‰$T÷¸ÄÙÚص\“GÙÜ�¶4 �ÙÝš!,¨2ÙÞÌèVL‡EG46#%ü‹'Ú÷àâåHIJâåL¹$¾ßߢ¶ÊüÖ 2üÔKH Create a new `Xoshiro256PlusPlus`. If `seed` is entirely 0, it will beÁü¤ ›’$LÙ ¢¶Ú÷Bÿßß âÖµ.Äî $ò â�ä�ä�ääâ×�üó (üé 85 Create a new `Xoshiro256PlusPlus` from a `u64` seed.Á¦ �ü® 2³”$lö Ú÷Bÿßß åƒ,ˆt¦¬Ù ãååü�"Ú÷éêìí‘’“”ìêíTª,¯èè�‡üÖ5dÙì ìÚ÷кBÿè æè ê$ë,•ê�ë�ë�ëëêå¶üÈ5dËí íÚ÷Ô¼Bÿè Øè ì$ÝüšFt�îï îÚ÷ ïñ°³¿Bÿè ¬è íϪ´új¯�í�î�î�îîíʾ<ò$Ó¥ó"œÜ$ÜÖ$ö$²ÂÃù‰$T�¸Äïðص\©Gïòóµd¶›ïó�¶4Ä�ïôùëžïõÌþmL�\^KM9;¬Ò,´Ž×ø÷øùú‘’“”øùúT«,°öö�‡üß5dâö ö×øкBÿö ïö ø$ôüÖ5dÙ÷ ÷×øÔ¼Bÿö æö ù$ëüÍFtÐøù ø×ø ùñ°³¿Bÿö ßö ú$ä´úª¦ÜÂ×øüþHIþL $¥ûû¢¶±üÑ&LÔH×ø×øBÿûû þÖµj¦ä¨×ø¬š%Óæó"´�%ôû$4©%‘’“”¡ÌдçTŸ“2€‚ù‰$T´¸Ä€ƒñʾ,€„ÉÜãI€…Ödéµ€†¡‰$D„ €ˆ±»‰$4ެ€‰²»‰$­€‰²ص\¦G€ŠýÑDʦ€Œ GeneratorÁLÔ€�óµdð›€��¶4þ�€�$’„™3œ«$DÅ\ÓŒäù,üèêÒÔ´›¦„·—™}Läpr^`üÍ !´Ó €Lø $ý €¸ÓdÅ<Ê€ ¸Ó¤òlù€×ùqxÎò"i�D•\�,�€””¸Óü� ×ù—˜  ˜\Ä4É––à¬$üö-Dùúû ú×ù ûà¬$Bÿ– ‚– ˜$‡ŽÒ4¥”Ã×ùšœüþ,4�€ü ü×ùÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´Òw  ¡Œ/¢ó ý!.]+'Bÿ™ ˆ™ š$�DÙš�›�›�››š›¸ÓUÿÍäÜ£l¦€ý ý×ùBÿ™ ´™Îà$¹tà(Œúžüä)0üõ($! Immediately reseed the generatorÁž)�ü¦)96 This discards any remaining random data in the cache.Á4ë)ÿ ÿŒú¬¯$Bÿ� ò)� ž$÷)ì»,ü…,52 Debug implementation does not leak internal stateÁŒú  g üß,6â,€�‚ €Œú �€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡‚•˜BÿŸ æ,Ÿ  $ç,ñí,̆7ü�1,) Access a fast, pre-initialized generatorÁ¼1�üÀ10- This is a handle to the local [`ThreadRng`].Áñ1�üõ1.+ See also [`crate::rngs`] for alternatives.Á¤2�l¨2Úð¶2�<º2�¸ÌÂ2£€ Ü2�Œà2 # fn main() {Áò2�üö2&# let mut numbers = [1, 2, 3, 4, 5];Áü�3&# numbers.shuffle(&mut rand::rng());ÁüÄ3%" println!("Numbers: {numbers:?}");Áê3�üî3JG // Using a local binding avoids an initialization-check on each usage:Áô¹4ÑÁØ4�üÜ485 println!("True or false: {}", rng.random::());Áü•5B? println!("A simulated die roll: {}", rng.random_range(1..=6));Á<Ø5 # }Á<à5�¸è5�tì5 # SecurityÁû5�üÿ5$! Refer to [`ThreadRng#Security`].Á¤6�d¨6œž#µ6�ü¹6LI This method panics in case of [`SysRng`] failure during initial seeding.Á�7ŒúBÿ“ìÄ7¡�¢�¢�¢¢¡¢ äçäçUÿÔí7Œú¤÷¤ÌŽ8<‘8ŒúBÿ££ ¤ÌÁ8Œú¦§¨©‘’“”§¨©Tá8,æ8¥¥�‡ü•95d˜9ƒ ƒŒúкBÿ¥ ¥9¥ §$ª9ü¶;5d¹;„ „ŒúÔ¼Bÿ¥ Æ;¥ ¨$Ë;üß=Gtâ=…† …Œú †ñ°³¿Bÿ¥ ñ=¥ ©$ö=„˜h¢ü‹@Œú¬º%jüÙ%&_ü‰&&TŒÖ&Ó¥ó"œ¸&ܲ&\¼�'Óæó"´ï&ôé&dL¤(Ósys_rngÁœ†(Ü€(,°(Ó…Â$jÓ…Â$.,}\Öüé" Sequence-related functionalityÁŒ�Ì� This module provides:Áª�ü®GD * [`IndexedRandom`] for sampling slices and other indexable listsÁüöRO * [`IndexedMutRandom`] for sampling slices and other mutably indexable listsÁüÉ+( * [`SliceRandom`] for mutating slicesÁüõ1. * [`IteratorRandom`] for sampling iteratorsÁü§GD * [`index::sample`] low-level API to choose multiple indices fromÁœï `0..length`Áƒ�l‡ Also see:Á•�ü™MJ * [`crate::distr::weighted::WeightedIndex`] distribution which providesÁüç  weighted index sampling.Áˆ�üŒMJ In order to make results reproducible across 32-64 bit architectures, allÁüÚKH `usize` indices are sampled as a `u32` where possible (also providing aÁü¦+( small performance boost in some cases).ÁÞ´ÁÓêÕË WeightErrorÁ\¨ ÆÃ¢EtÇ ÚÄø’t€ ØÅŠN|Î ÑÆ�K„ï ¨È¹Gl� ùÉ‘L\� ´Ê„Ód׳¶ùô„´µTíüú%\ŒŽ··þƽð ˜�ú›‚ÿwLkßôü˸¹º*,T¦ª¶¶½ðT¶,¶´¶¶¤ø|ø´¶¶Ü‘޼¼ÃÌ$ –�ú™‚ÿ½¾¿ÀÔ³º½ð‚ÿBÿ»» ½½ð�7�§üÃ9¬Ê‡ ‡‚ÿBÿ» à» ¾½ð$嚉¥üˆ :d‹ ´ˆ ˆ‚ÿBÿ» ˜ »â�$� ¤ § šœüÞ%.dá%´‰ ‰‚ÿBÿ» î%»ó€$ó%™ ý%´å”é³ÅÐùõ„Áö 4ú”ÁÄÙ,í24 üõ+Œ‡ŽÆÆÃÌ$ ™�úœ”©¾Yœ$¿‰ÇÈÉÊ,.T§«ÅŽð4· ·ÁÅÅT™,™ÁÅÅœ©|©ÁÅÅüÁ!ŽÌÌÃÌ$ Æ�úÉ”©ÍÎüÑ"ؽð”©BÿËË Í½ð�7D•¤C•ü´ %T» Š Š”©BÿË Æ Ë Î½ð‰‹¨Î�Ï�Ï�ÏÏÎá¯ü…+œˆÁé¾Bÿ Уåˆüß#,èÁé¾BÿŠÓ£8†Ĭ<²Áé¾dýD� ³Ú¹Gl›ùÓÔÉŸB\öÓÕùÜ„Ó×¶ 4á”ÓØÙü”…CÓÙ¤”uü® c,ÔTV@B|ˆÓ«ŒðÌêBüŠ*üšDA Extension trait on iterators, providing random sampling methods.Áß�üãNK This trait is implemented on all iterators `I` where `I: Iterator + Sized`Áä² and provides methods forÁüÏ=: choosing one or more elements. You must `use` this trait:Á��<‘�¸ü™" use rand::seq::IteratorRandom;Á¼�üÀ+( let faces = "😀😎ðŸ˜�😕😠😢";ÁüìJG println!("I am {}!", faces.chars().choose(&mut rand::rng()).unwrap());Á<·�¸ü¿'$ Example output (non-deterministic):Á\ç ```noneÁtó I am 😀!Á<‚�¸t”ÚÚò’,¯ÄQ¶µD¤Úò’*ÈÝ$ ò’6ÈÝ$,ÛÝàâäæÛÝàâäæÛÝâàäæü¦\ü»  Uniformly sample one elementÁà�üèEB Assuming that the [`Iterator::size_hint`] is correct, this methodÁü² HE returns one uniformly-sampled random element of the slice, or `None`Áüÿ GD only if the slice is empty. Incorrect bounds on the `size_hint` mayÁüË IF cause this method to incorrectly return `None` if fewer elements thanÁü™ HE the advertised `lower` bound are present and may prevent sampling ofÁüæ KH elements beyond an advertised `upper` bound (i.e. incorrect `size_hint`Áü¶ B? is memory-safe, but may result in unexpected `None` result andÁôý  non-uniform distribution).Á  �ü¨ KH With an accurate [`Iterator::size_hint`] and where [`Iterator::nth`] isÁüø HE a constant-time operation, this method can offer `O(1)` performance.ÁÌÅ Where no size hint isÁüãEB available, complexity is `O(n)` where `n` is the iterator length.Áü­?< Partial hints (where `lower > 0`) also improve performance.Áñ�üùJG Note further that [`Iterator::size_hint`] may affect the number of RNGÁüÈJG samples used as well as the result (while remaining uniform sampling).Áü—EB Consider instead using [`IteratorRandom::choose_stable`] to avoidÁüáLI [`Iterator`] combinators which only change size hints from affecting theÁd² results.ÁÃ�lËÚðÝ�<å�¸üñ"öÙ$˜�ü 41 let words = "Mary had a little lamb".split(' ');ÁüÙ<9 println!("{}", words.choose(&mut rand::rng()).unwrap());Á<š�¸4©‹¶µ ‹ë»°íBÿÚŽÜÜ ÂÚ·§4ûÿ›õ Û¶µë»$·�7ý~ °ü´,cüê!)& Uniformly sample one element (stable)Á˜"�ü "DA This method is very similar to [`choose`] except that the resultÁüé"IF only depends on the length of the iterator and the values produced byÁü·#HE `rng`. Notably for any iterator of a given length this will make theÁü„$JG same requests to `rng` and if the same sequence of values are producedÁüÓ$JG the same index will be selected from `self`. This may be useful if youÁü¢%KH need consistent results no matter what type of iterator you are workingÁüò%>; with. If you do not need this stability prefer [`choose`].Áµ&�ü½&DA Note that this method still uses [`Iterator::size_hint`] to skipÁü†'IF constructing elements where possible, however the selection and `rng`ÁüÔ'GD calls are the same in the face of this optimization. If you want toÁü (IF force every element to be created regardless call `.inspect(|e| ())`.Áî(�üö(&# [`choose`]: IteratorRandom::chooseÁl·,Œ¶µ Œë»°íBÿÚŽÞÞ ×,Ú·§4�-ÿ›Š- ݶµë»$Ì,�7Ev Å,$é1Ý�ß�ß�ßßÝïøü‰=lüš7=: Uniformly sample `amount` distinct elements into a bufferÁÜ7�üä7FC Collects values at random from the iterator into a supplied bufferÁü¯8  until that buffer is filled.ÁÔ8�üÜ8IF Although the elements are selected randomly, the order of elements inÁüª9HE the buffer is neither stable nor fully random. If random ordering isÁü÷9  desired, shuffle the result.Áœ:�ü¤:NK Returns the number of elements added to the buffer. This equals the lengthÁü÷:NK of the buffer unless the iterator contains insufficient elements, in whichÁüÊ;63 case this equals the number of elements available.Á…<�ü� Complexity is `O(n)` where `n` is the length of the iterator.ÁüÓ<1. For slices, prefer [`IndexedRandom::sample`].Á\Œ=�޶µ �ë» ŽΠBÿÚŽáá ª=Ú·§4î=ÿ›è=ã¼$Ÿ=�7ƒn£ü~n ˜=ü�HhüÓB>; Uniformly sample `amount` distinct elements into a [`Vec`]Á–C�üžCC@ This is equivalent to `sample_fill` except for the result type.ÁæC�üîCIðö$ü¼DHÃ÷$ü‰E •ø$®E�ü¶EIF The length of the returned vector equals `amount` unless the iteratorÁü„FIF contains insufficient elements, in which case it equals the number ofÁ¼ÒF elements available.ÁîF�üöFAÇú$ü¼G1’û$Ó«ŒøGÌòG4“H�¶µ �뻣§BÿÚŽãã ¬HÚ·§4ñHÿ›ëH§¾$¡H�7eŽ£e šHüÂNqüÅM1. Deprecated: use [`Self::sample_fill`] insteadÁ0.10.0ÁRenamed to `sample_fill`ÁÔ¡NüûMB¤ÅN¦‚%°‚%-�‘¶µ �ë» ‘ΠBÿÚŽåå èNÚ·§4¬Oÿ›¦O 䶵뻫c�7©c£ü¨c ÚNüùPmüèO,) Deprecated: use [`Self::sample`] insteadÁÓ«ŒŸPÌ™P¦‚%Renamed to `sample`Á¬ÝPü·P=|üP¦‚%å„%-’¶µ ’뻣§BÿÚŽçç šQÚ·§4ßQÿ›ÙQ æ¶µë»d�7dŽ£d ŒQü—R6…ééþÆîú,ÈRÄQîúD½Rîú œRL‹ ,� ³ù¨´ÑØÝCŒÀÅêë÷,ÞËêì¾/d›�êîÄ-l©ñêïçÉ$\ùÆêñŽ54†àêòù›„êô¶ 4 ”êõÙIndexÁ,¹Žýê÷IndexMutÁDÀ¨#êøü¥,êd×Û¬ƒÓ«ŒëÌåßÓ«ðÝÓ«(&î´×Ó«Œ¿̹,ðÓ«òÓ«+),“õ÷áãL­Ëͱ³üÄ%üÌJG Extension trait on indexable lists, providing random sampling methods.Á—�ü›JG This trait is implemented on `[T]` slice types. Other types supportingÁüæMJ [`std::ops::Index`] may implement this (only [`Self::len`] must beÁ|´ specified).ÁlÎùùñ„üĈOŽý¶µdÝùñ„0ó�% ñ„<ó�%,úûüþ‚„‰�™ž ¤úûüþë‚„‰�왞 ¤þÆë¶µë»88øóå#ÄQòŽ%ôêÅQòŽ% 8êÁ¤óêŽ%5”�%(¤�%þ€ 8¶µ*^ 8ë»4ÓřǙș­É™Ê™àË™óG*¤�R{9 òŽ%Ž^þÆì¶µë»з½îÃî88ø€�7#ÄQÊ�%ô’7ÅQÊ�% 8êÁ¤›7Â�%5ø�%(ˆ‘%�• 8¶µ»A 8ë»4â6з ú6ÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´ÒwÊ�%Çî4B  ‚þë‰ú�ìž„ü™¤û¼ƒtð The lengthÁ†“ “¶µBÿù Šùñ¿$‹ÔÓü   True when the length is zeroÁDÖ” ”¶µBÿù ßù¨Á$àü‘ \ü“ ÈÝ$¸ �üÀ B? Returns a reference to one uniformly-sampled random element ofÁü‡ /, the slice, or `None` if the slice is empty.Á» �üà %" For slices, complexity is `O(1)`.Áí �lõ Úð‡ �<� �¸ü› ! use rand::seq::IndexedRandom;ÁÁ �üÉ '$ let choices = [1, 2, 4, 8, 16, 32];Áôõ ÑÁü˜ /, println!("{:?}", choices.choose(&mut rng));ÁüÌ 41 assert_eq!(choices[..0].choose(&mut rng), None);Á<… �¸4” •– •¶µ –ë»Å™Ç™È™­É™Ê™àË™óG*¤�R{9  •êÁBÿùŽýý ž ù·§4æ ÿ›à  ü¶µë»$Ÿ �7¨j › üµwü€A> Return an iterator which samples from `self` with replacementÁÆ�üÎ41 Returns `None` if and only if `self.is_empty()`.Á‡�l�Úð¡�<©�¸üµ!ð•%Û�üã'§–%ô�ÑÁü²B? for choice in choices.choose_iter(&mut rng).unwrap().take(3) {Áüù! println!("{:?}", choice);Á,Ÿ…‘<©�¸\¸—˜ —¶µ ˜ë»Å™Ç™È™­É™Ê™àË™óG*¤�R{9 붵뻗˜BÿùŽÿÿ Çù·§4¥ÿ›Ÿ þ¶µë»yc�7f ÄZþ8î8íîíþÌŠÌŠëYÏŠ�Њœ“D^)c˜þOþŽŽ…Y’•“�7”¹Y‡é£=›5xNÑÉã�%�¶µë»ÅÀ°�%UÿÖ�%þÆ€¶µë»88W ÄQÉ¡%S ÅQÉ¡%°�%L Á¡%€ ç¡%t ö¡%a þ þ�������þŽÊüà™üº96 Uniformly sample `amount` distinct elements from selfÁø�ü€KH Chooses `amount` elements from the slice at random, without repetition,ÁüÐFC and in random order. The returned iterator is appropriate both forÁü›IF collection into a `Vec` and filling an existing buffer (see example).ÁüéA> If `amount > self.len()`, all available elements are sampled.Á¯�ü·IF In case this API is not sufficiently flexible, use [`index::sample`].Á…�ü�<9 For slices, complexity is the same as [`index::sample`].ÁÎ�lÖÚð<è�¸üô!ð•%š�ü¢# let mut rng = &mut rand::rng();ÁüÊ/, let sample = "Hello, audience!".as_bytes();Áþ�ü†)& // collect the results into a vector:Áü´C@ let v: Vec = sample.sample(&mut rng, 3).cloned().collect();Áü�Ì„ // store in a buffer:ÁÜ¢ let mut buf = [0u8; 5];ÁüÂMJ for (b, slot) in sample.sample(&mut rng, buf.len()).zip(buf.iter_mut()) {Áœ” *slot = *b;Á,¬…‘<¶�¸Ó«ŒÈÌÂ4㙚 ™¶µ šë»ØØø’ÜåêÝ®“êÞ¾“ꛫj‚N©òï™¶µêÁBÿùŽƒƒ íù·§4òþÆêÁ,Úÿ›ìħ$î�7hŽ£h êü´$›üóFC Uniformly sample a fixed-size array of distinct elements from selfÁ¾ �üÆ FC Chooses `N` elements from the slice at random, without repetition,Áü‘!JG and in random order. Returns `None` if (and only if) `N > self.len()`.Áà!�üè!B? For slices, complexity is the same as [`index::sample_array`].Á¯"�l·"Úð<É"�¸üÕ"!ð•%û"�üƒ##…§%ü«#/²§%ß#�üç#<9 let a: [u8; 3] = sample.sample_array(&mut rng).unwrap();Á<¨$�¸d·$›œ ›¶µ œë»åæBÿùޅІ…† ×$ù·§4È%ŠtÇ$¦­%,°%…êÁ,¨%ÿ›Â%‰©dc�7ùe Ä$E Í$<¬&„�ˆ�ˆ�ˆˆ„—ãü¥0—üÕ&# Biased sampling for one elementÁý&�ü…'FC Returns a reference to one element of the slice, sampled accordingÁäÐ' to the provided weights.Áñ'�üù'DA The specified function `weight` maps each item `x` to a relativeÁüÂ(JG likelihood `weight(x)`. The probability of each item being selected isÁü‘)GD therefore `weight(x) / s`, where `s` is the sum of all `weight(x)`.ÁÝ)�üå)30 For slices of length `n`, complexity is `O(n)`.Áü�*85 For more information about the underlying algorithm,ÁüÚ*+( see the [`WeightedIndex`] distribution.ÁŠ+�ü’+%" See also [`choose_weighted_mut`].Á¼+�lÄ+ÚðÖ+�<Þ+�¸Ìê+£€ ˆ,�ü�,;8 let choices = [('a', 2), ('b', 1), ('c', 1), ('d', 0)];ÁôÐ,ÑÁüó,QN // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c',ÁüÉ-$! // and 'd' will never be printedÁüò-RO println!("{:?}", choices.choose_weighted(&mut rng, |item| item.1).unwrap().0);Á<É.�¸üÕ.%" [`choose`]: IndexedRandom::chooseÁüÿ.B? [`choose_weighted_mut`]: IndexedMutRandom::choose_weighted_mutÁüÆ/<9 [`WeightedIndex`]: crate::distr::weighted::WeightedIndexÁÓ«Œ�0̇0|¨0žŸ ž¶µ Ÿë»зÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´Òw žêÁÇîBÿùŽŠ‚‹þŒ”��‹ŠŒ Í0ù ·§4Ã1ª— »0þÆ½î ¾0þÆÃî Á0ÿ›½1�…#з �êÁ´Ö1��#з÷À%½î ë1�½îÃî|ù1ñÃîl•2àÃî4¥2¯²ÃîÃîl®2 ‰¶µë»з½îÃîHa�7pd¦4nd ¸0øúôöðòüÏ2%lç2,±3‰�������‰‡ïü¡6²üþ3$! Biased sampling with replacementÁ§4�ü¯4KH Returns an iterator which samples elements from `self` according to theÁüÿ4C@ given weights with replacement (i.e. elements may be repeated).ÁÇ5�üÏ5/, See also doc for [`Self::choose_weighted`].ÁÓ«Œ‰6̃6¤¤6¡¢ ¡¶µ ¢ë»зÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´Òwì¶µë»з½îÃî¡¢ÇîBÿùŽ‘‚’þ“””‘”’“ Î6ù ·§4Ú7ª— ¼6½À% ¿6ÎÀ% Â6ÿ›Ô7 …#з  êÁ´í7 �#з¸È%½î ‚8©Á%|�8½Á%l¬8ÍÁ%4¼8ÝÁ%lÅ8 �¶µë»з½îÃî*[�7›]¦4™] ¹6½¿ÂÄÇÉ�8ð8ïðï�ÌŠÌŠëYÏŠ�Њœ“D^)c˜þOþŽŽ…Y’•“�7”¹Y‡é£=›5xNßòÇ‘%˜¶µë»з½îÃîÅÀ”‘%Uÿº‘%þÆ•¶µë»з½îÃî88—ÄQáË%“ÅQáË%”‘%ŒÙË%À‹Ì%´šÌ%¡�üæ8%lþ8,È9��—�—�——�ú�‹:��˜�˜�˜˜�µ‡ü´G¨ü¥:1. Biased sampling of `amount` distinct elementsÁÛ:�üã:;8 Similar to [`sample`], but where the likelihood of eachÁü£;EB element's inclusion in the output may be specified. Zero-weightedÁüí;GD elements are never returned; the result may therefore contain fewerÁü¹= amount`. The elementsÁü‡=41 are returned in an arbitrary, unspecified order.ÁÀ=�üÈ=Dï´%ü‘>J½µ%üà>G‘¶%¬?�ü´?MJ This implementation uses `O(length + amount)` space and `O(length)` time.Áü†@/, See [`index::sample_weighted`] for details.Áº@�lÂ@ÚðÔ@�<Ü@�¸Ìè@£€ †A�üŽA1. let choices = [('a', 2), ('b', 1), ('c', 1)];ÁôÄAÑÁüçA,) // First Draw * Second Draw = total oddsÁô˜B // -----------------------Áü»B^[ // (50% * 50%) + (25% * 67%) = 41.7% chance that the output is `['a', 'b']` in some order.ÁüžC^[ // (50% * 50%) + (25% * 67%) = 41.7% chance that the output is `['a', 'c']` in some order.Áü�D^[ // (25% * 33%) + (25% * 33%) = 16.6% chance that the output is `['b', 'c']` in some order.ÁüäDgd println!("{:?}", choices.sample_weighted(&mut rng, 2, |item| item.1).unwrap().collect::>());Á<ÐE�¸üÜE%" [`sample`]: IndexedRandom::sampleÁÓ‰|žG¼˜G|·G¤¥ ¤¶µ ¥ë»зÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´ÒwØØø’ÜåêÝ®“êÞ¾“ꛫj‚N©ò虜µêÁÇîBÿùŽš‚›”œ›šœ ÙGù·§4œIª— ÊGþÆ„– ÍG¦­%,„Iÿ›–I£…#з £êÁ´¯I£�#зàÛ%„– ÄI©„–LÒI¶ª²Z�7+^Ž£+^¦4)^ ÇG¬®¨ª,éK™�������™Æ–üòMÁüáL,ž„%Ó«Œ˜MÌ’M¦‚%å„%¬ÖMü°M=|õM¦‚%å„%-¦§ ¦¶µ §ë»ØØø’ÜåêÝ®“êÞ¾“ꛫj‚N©ò禮µêÁBÿùŽŸŸ ‘Nù·§4¬O¦­%,”Oÿ›¦O ž¶µë»$’N�7Ë[Ž£Ë[ …NüåP¤üæO2/ Deprecated: use [`Self::sample_array`] insteadÁ¦‚%Renamed to `sample_array`ÁÜÃPü�PC¬èP¦‚%Þß%-¨© ¨¶µ ©ë»åæBÿùޡТ¡¢ ‘Qù·§4‚R€³%t�Q¦­%,êQ–³%,âQÿ›üQ  ¶µë»Š$’Q�7]\ þPM ‡QüÛS±üºR52 Deprecated: use [`Self::sample_weighted`] insteadÁÓ‰|úR¼ôR¦‚%Renamed to `sample_weighted`Áô¶Sü�SFÄÞS¦‚%Èâ%-«¬ «¶µ ¬ë»зÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´ÒwØØø’ÜåêÝ®“êÞ¾“ꛫj‚N©òï«¶µêÁÇîBÿùŽ¥‚¦”§§¥¦ ‰Tù·§4ÌUª— úS¯Û% ýS¦­%,´Uÿ›ÆUª…#з ªêÁ´ßUª�#зëæ%„– ôU’Ü%L‚V ¤¶µë»з„–$ŠT�7^Ž£^¦4^ ÷Sª¬¯±üžX;üÎVJ³Š%™W�ü�WGD This trait is implemented automatically for every type implementingÁüåW85 [`IndexedRandom`] and [`std::ops::IndexMut`].Á„¨X¨¨ñ„üžX�ù¶µlºX¨#¶µ|ÊX¨ñ„?Üé%3ìé%&ñ„QÜé%Eìé%8©«©«©«üÈZhüàX&# Uniformly sample one element (mut)Á‹Y�ü“YJG Returns a mutable reference to one uniformly-sampled random element ofÁüâY/Ê”%–Z�üžZ%�•%TËZ­® ­¶µ ®ë»Å™Ç™È™­É™Ê™àË™óG*¤�R{9  ­êÁBÿ¨Žªª ÙZ¨·§4©[ÿ›£[ ©¶µë»$ÞZ�7ž^ ÖZü«c£üâ\)& Biased sampling for one element (mut)Á�]�ü˜]NK Returns a mutable reference to one element of the slice, sampled accordingÁäë]½´%Œ^�ü”^Dï´%üÝ^J½µ%ü¬_G‘¶%ø_�ü€`3î¶%ü¸`8«·%üõ`+í·%¥a�ü­a! See also [`choose_weighted`].ÁÓa�üÛa0- [`choose_mut`]: IndexedMutRandom::choose_mutÁü�b74 [`choose_weighted`]: IndexedRandom::choose_weightedÁüÌb<ç¼%Ó«Œ“cÌ�cœ®c°± °¶µ ±ë»зÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´Òw °êÁÇîBÿ¨Ž¬‚­þ®”¯®¬­¯ ×c¨ ·§4Õdª— Åc½À% ÈcÎÀ% Ëcÿ›Ïd¯…#з ¯êÁ´èd¯�#зšô%½î ýd©Á%|‹e½Á%l§eÍÁ%4·eÝÁ%lÀe «¶µë»з½îÃî�X�7K[¦4I[ Âc½¿ÂÄÇÉdáedðe¼þelˆf,Óf«�³�³�³³«‡´üßk'ü½g;8 Extension trait on slices, providing shuffling methods.Áùg�üýgIF This trait is implemented on all `[T]` slice types, providing severalÁüÇhKH methods for choosing and shuffling elements. You must `use` this trait:Á“i�<—i�¸üŸi use rand::seq::SliceRandom;Á¿i�ôÃiÑÁüâi>; let mut bytes = "Hello, random!".to_string().into_bytes();Áä¡j bytes.shuffle(&mut rng);Áü¾j0- let str = String::from_utf8(bytes).unwrap();ÁÄïj println!("{}", str);Á<ˆk�¸ü�k'ÄÛ$\¸kôÛ$”Äk l,nmroHado !leÁ<×k�¸\ék´´ñ„üßkÿ¨¶µ„ök´ñ„,Êû% ñ„8Êû%,µ·µ·µ·üõoHü�l%" Shuffle a mutable slice in place.Á·l�ü¿l3î¶%ü÷l\Y The resulting permutation is picked uniformly from the set of all possible permutations.ÁØm�làmÚðòm�<úm�¸ü†nÓ÷%ªn�ô²nÑÁüÕn  let mut y = [1, 2, 3, 4, 5];Áüún$! println!("Unshuffled: {:?}", y);ÁÄ£o y.shuffle(&mut rng);ÁüÀo$! println!("Shuffled: {:?}", y);Á<éo�¸<øo²³ ²¶µ ³ë»Bÿ´Ž¶¶ ƒp´·§4¶pÿ›°p µ¶µë»$ˆp�7Žp €pü“yÉüÃp%" Sample `amount` shuffled elementsÁíp�üõpLI Shuffles `amount` random elements into the end of the slice (`n..` whereÁüÆqJG `n = self.len() - amount`). The rest of the slice (`..n`) contains theÁü•rB? remaining elements in a permuted but not fully shuffled order.ÁÜr�üärFC Returns a tuple of the sampled elements (`&mut self[n..]`) and theÁü¯s*' remaining elements (`&mut self[..n]`).ÁÞs�üæsJG This is an efficient method to select `amount` elements at random fromÁüµt1. the slice, provided the slice may be mutated.Áët�üót85 For slices, complexity is `O(m)` where `m = amount`.Áü°uFC If `amount >= self.len()` this is equivalent to [`Self::shuffle`].Áûu�lƒvÚð•v�<�v�¸ü©vÓ÷%Ív�ôÕvÑÁüøv ®ý%ü�w:7 let (shuffled, rest) = y.partial_shuffle(&mut rng, 3);ÁüÜw" assert_eq!(shuffled.len(), 3);Áôƒx assert_eq!(rest.len(), 2);Áü¦x$! let sampled = shuffled.to_vec();ÁüÏx# assert_eq!(&sampled, &y[2..5]);Á<÷x�¸/\ƒy|–y´µ ´¶µ µë» ´ êÁªŠ&Bÿ´Ž¸¸ ²y´·§4Õz¦­%,½zÿ›Ïz ·¶µë»$·y�7ÅyŽ£4Úy ¦yìàz�ººàŒ åzûú»ú»´„{‡{¶ ¶ûúBÿ¹ ‹{¹ »ßË$Œ{ü¹{JôL½½ÿƇû4ä{ù‡ûlÂ{¨#‡û|Ò{‡û¾{܈|�¿¿àŒ �|ûúÀµ·À üª|H<­|·¸ ·ûú ¸ë»Bÿ¾ŽÁÁ ¸|¾·§4ë|ÿ›å| ÀßËë»$½|�7d µ|üÂ~w|Å~¹º ¹ûú ºë»Æ�&Æ�&Bÿ¾ŽÃà Ø~¾·§4²ÿ›¬ ÂßËë»$Ý~�7ZUŽ£ZU Õ~ü†‹`Ó«ŒòŠÌìŠú$Å�Æ�ÇÇÅÆ�ýîûñ»TŸ‹Û› º‹ŽýîûÄ’‹ÿÆîû4­‹îûú$¶‹ñ»ú$½‹ŸûÈÉËÅQÆQÊQËÉ‹‹ �‹Å‡‰ÅLí‹$ò‹ÄÄ ú$ñ»ü…Œ($ˆŒ¾ ¾ŸûřǙș­É™Ê™àË™óG*¤�R{9 ÅQŸûBÿÄ �ŒÄ Éú$îûñ»ªL™�É�Ê�Ê�ÊÊÉ€øü¸�-L»�¿ ¿ŸûÎÃBÿÄ Å�Ä Ëú$îûñ»$Æ�üÂŽmÓ«Œ®Ž̨Žú$Í�Î�ÏÎÏÍ¢‘&TÛŽÛ› öŽÄ‘&ÄÎŽÙ‘&4éŽë‘&òŽû‘&ùŽŸûÐ�QÐÇŽ ËŽÍRTÍ´¶�¹�À ÀŸûBÿÌ ½�Ì Ðú$îûñ»$¾�ü�‘"üó�-* Deprecated: renamed to [`IndexedSamples`]ÁÓ«Œ§�Ì¡�¦‚%Renamed to `IndexedSamples`Áìá�ü»�E|Š‘¦‚%ê—&ú$Ò�Ó�ÔÓÒÔþÆîû ž‘Û› ¡‘Ÿûš‘TÆ Ó«Œ� Ì— 4Ê ³Œ“—¯²´Àäïú–$œÐ=Õ×ü¢…CÕØå,²êiÕÙ‘$ÊûhÕÛ‘�iÕÛ AddAssignÁLÕŽÐÕÜçÉ$\ÂÆÕÝÃÄ-lêñÕÞ™dŒ#Õàí΂<šÈ Õáöù°„Õã¶ 4µ”ÕäÙ“<ê“ ÕåT�/–!$\¬$½TÄ tÐá”»Ó‰|¥¼ŸãüÓ$ÑdýÂÄ­¯,¨œžˆŠÌØÓ‰|¼¼Šl  •üçèéêíÔè ü´ ! Returns the number of indicesÁï Å Å•üBÿæ ó æ ç$ô ôê ü± &# Returns `true` if the length is 0.ÁDñ Æ Æ•üBÿæ ú æ è$û üè*üÁ*' Return the value at the given `index`.Áð�üøFC (Note: we cannot implement [`std::ops::Index`] because of lifetimeÁ”à restrictions.)Á,ïÇ Ç•üBÿæ õæ é$ö÷Á7ü²#üÕJG Return result as a `Vec`. Conversion may or may not be trivial.ÁD¹•üϺBÿææ êÎ%Ÿê�ë�ë�ëëꟿœê�ì�ì�ììêÀ¹ü›&üÌ<9 Iterate over the indices as a sequence of `usize` valuesÁ$¢È È•üïñò‚”óóôõš”öó­gY7ÐâÔÄÈBÿæ §æ í$¨ô–•üïðñ�P�P‘Pñl»DÀîLá$æîîüÙ&üùMJ Convert into an iterator over the indices as a sequence of `usize` valuesÁLÜ•üˆ€Bÿîî ñÈÜæ•üóù±óüˆ&‹ÉÊ É•ü Ê•üBÿò Žò ó$�î ,•t½D’ó�õ�õ�õõóõˆÝ ì™UÿD×ó�ö�ö�ööóöì™ˆÝ Uÿü“ •üø®øäÈ $Ë �ý•üBÿ÷÷ ø¬�ü­! ÆÔ«!Ü�!ü‰!#•üú®úäâ!$å!‡þ•üBÿùù ú¬›ü„$"8ÎΧÿüý�ÅQÆQÊQ�ýL­$$²$ûûüÓ$#$Ö$Ï Ï§ÿéÂBÿû Û$û ý8$à$”…%Ú%ý�ÿ�ÿ�ÿÿýê£Å&ý�€�€�€€ý¤üú&-Lý&РЧÿÎÃBÿû ‡'û �8$ˆ'üè(+8Ñѧÿü�+"ˆ€„…‰ÅQÆQÊQ…‰Lª+$¯+ƒƒüÐ+($Ó+Ö Öˆ€Å™Ç™È™­É™Ê™àË™óG*¤�R{9 ÅQˆ€Bÿƒ Ø+ƒ …$Ý+´‡,Ú,…�‡�‡�‡‡…ÁǾ-…�ˆ�ˆ�ˆˆ…ŒÈüò--Lõ-× ×ˆ€ÎÃBÿƒ ÿ-ƒ ‰$€.´®.üë/+ˆ€üÐ8bü›0KH Randomly sample exactly `amount` distinct indices from `0..length`, andÁüç01. return them in random order (fully shuffled).Á™1�ü�1LI This method is used internally by the slice sampling methods, but it canÁüê1MJ sometimes be useful to have the indices themselves so this is provided asÁœ¸2 an alternative.ÁÌ2�üÐ2IF The implementation used is not specified; we automatically select theÁüš3HE fastest available algorithm for the `length` and `amount` parametersÁüã3LI (based on detailed profiling on an Intel Haswell CPU). Roughly speaking,Áü°4NK complexity is `O(amount)`, except that when `amount` is small, performanceÁüÿ4KH is closer to `O(amount^2)`, and when `length` is close to `amount` thenÁ„Ë5 `O(length)`.ÁÜ5�üà5NK Note that performance is significantly better over `u32` indices than overÁü¯6HE `u64` indices. Because of this we hide the underlying type behind anÁäø6 abstraction, `IndexVec`.Á•7�ü™7HE If an allocation-free `no_std` function is required, it is suggestedÁüâ785 to adapt the internal `sample_floyd` implementation.Á›8�üŸ8  Panics if `amount > length`.Á¶|À84×8€Ø ؽð•üBÿŽ�� æ8ÿù4«9�ú¥9 Œ½ð�7Wï¤âWWï Þ8´£? ©?ÕÐÕ ³? ·?ŒúB €CÕÑÕ ‰CüÙLÍü�E>; Randomly sample `amount` distinct indices from `0..length`ÁÏE�üÓENK The result may contain less than `amount` indices if insufficient non-zeroÁü¢FOL weights are available. Results are returned in an arbitrary order (there isÁüòF+( no guarantee of shuffling or ordering).ÁžG�ü¢GGD Function `weight` is called once for each index to provide weights.ÁêG�üîGLд&ü»HM¦µ&œ‰Iüµ&�I�„¡Iö«"ü²IQN - [`WeightError::InvalidWeight`] when a weight is not-a-number or negative,Áü„JLI or when infinite weights fill the reservoir before all elements haveÁüÑJLI been processed (this always happens with more than `amount` infiniteÁüžKPM weights, and may also happen with exactly `amount`, depending on order).ÁïK�üóKMüÐ%Ó‰|ÇL¼ÁL|àLÙ Ù½ðÛ¼œ¡BÿŽ”‚•”–•–” ƒMÿù4öM�  óLþÆïê öL�úðM…#Û¼ÅÀt…N�#Û¼ÅÀïê ’N©ïêLœN “½ðÛ¼ïê�7îì¤âîì¦4ì쎣ìì ðLž šœüÎYøÓ‰|¼Y¼¶YÔÑYÕÚ Ú½ðÞñÛ¼Þñœ¡BÿŽ˜‚™”šŠ››™š˜ ‚Z ÿù4íZ�  ïYÿÇ& òYþÆÞñ õY�úçZ˜È&tüZ¬È& ‰[ÄÈ&L“[´Þñ$¥[¬•üÞ¨d¹[ —½ðÛ¼ïêÞñ�7ǤâǦ4ÇŽ£Ç ìY§©¬®¨ªÑ[l×[DÜ[¼æ[Tó[Œ×\<Þ\ÕŠ  þƵ� æ\û€�”ôäÕf¡¢ "Dó\,ó\ÕŸŸµ�D…]…]ÕŸŸüš]!Ф¤èÌ& Ÿ]û€¥±²¥üÆ]7\É]ÛÜ Ûû€ Üû€ÂÅ Bÿ£ Õ]£ ¥µ�$Ö]î ž½Ô·^Ч§èÌ& ¼^û€¨î¨üÜ^'ß^ÝÞ Ýû€ Þû€¡» Bÿ¦ ã^¦ ¨µ�$ä^î ð»üï` ŠªªèÌ& ô`û€«ù±«üša"�aßà ßû€ àû€Bÿ©  a© «µ�$¡aî À»ÌöaŠ­­èÌ& ûaû€ ,±n—�®�®�®®—‡¨üÒp`dÕpÕá á½ð•üBÿް° êpÿù4«q�ú¥qÄÛ�7½­¤â½­Ž£½­ âp$ßt¯�±�±�±±¯’âü¶zbt¹zÕâ â½ð•üBÿ޳³ Ðzÿù4‘{�ú‹{íÚ�7>�¤â>�Ž£>� ÈzüŸ~W$¥~Õ´´ ñ„üŸ~Ýù ¶µ$«~¯²¶µ¶µT²~í¶µ¿~÷±¶µ¶µLÅ~̶µÑ~ñ¶µlÖ~ûh¶µ$æ~ŽÐ¶µ¶µLí~´ñ„«¤Ö&Ÿ´Ö&�ÉÖ&†ÙÖ&wîÖ&mþÖ&cŽ×&Yž×&Jñ„á¤Ö&Õ´Ö&ÆÉÖ&¼ÙÖ&­îÖ&£þÖ&™Ž×&�ž×&€µ¶·µ¶·µ¶·”ý~$€Õ¶µBÿ´´ µ¶µŒÉÌÕ¶µBÿ´´ ¶¶µÜßDâÕ¶µBÿ´´ ·¶µ$ëŒþ¹º»µ¶·»º¹Œ¤€$§€ÕBÿ¸¸ ¹„Û€Þ€ÕBÿ¸¸ ºÔ‘�D”�ÕBÿ¸¸ »Ü›Œñ�ÆÔ«!ÜÓ�üÍ�#½¾¿µ¶·½¾¿Œ—‚$š‚ÕBÿ¼¼ ½„΂Ñ‚ÕBÿ¼¼ ¾Ô„ƒD‡ƒÕBÿ¼¼ ¿Ä›ü„ò†Õã ãë»ÀÐÀЕüBÿ”ÁŽÂÁ ”‡µÐ! ƒ‡·§4ч´ÀÐ$†‡ÿ›ˇ¬•ü³‰dç‡ ÀÀÐë»�7°Œ¤â®ŒŽ£¬Œdf Œ‡ì‡ Ó«ŒÙ ÌÓ Œí Ló ²ŠÄ½ §Š¬ù Ó«ŒÝ Ì× ®Š´Ç Ó«Œ« Ì¥ ¶Š,ç «Š®ŠŸŠ¢Š“Š–ŠlÆ üŸ &# Low-level API for sampling indicesÁ,Î Ðùæ „ËͶ 4ë ”ËÎÙ™Ù ŒÏâIƒ “Ïò“Dž äÏÌ”dâ"ïÏ©•„ã)úÏ,Þ ��y{l² Ó«Œÿ Ìù t— ü‚xüÉ C@ Randomly sample exactly `N` distinct indices from `0..len`, andÁü‘1‰´&Ç�üÏJG This is implemented via Floyd's algorithm. Time complexity is `O(N^2)`Áüž$! and memory complexity is `O(N)`.ÁÇ�üÏ.+ Returns `None` if (and only if) `N > len`.Ád‰ä ä½ððãBÿŽÑŠÒÑÒ ®ÿù4óñŒt™�úí нðŠ�7ú€¶ù€ –: Ÿ$˜Ð�Õ�Õ�ÕÕЯÞÄ�Óæó"´üôöXÀXX X XdùÓæó"´ÜôÖXÓæó"+XXÓæó"0.,XüÏ&ì© Construct and seed an RNGÁÇ�üËPM This method yields a seeded RNG, using [`rng`] ([`ThreadRng`]) if enabled orÁÌœ [`SysRng`] otherwise.Á¶�tºšˆ"É�<Í�¸üÕ96 let mut rng: rand::rngs::SmallRng = rand::make_rng();Áü�,) # let _ = rand::Rng::next_u32(&mut rng);Á<¼�¸Ä�dÈœž#Õ�üÙGD If [`SysRng`] fails to obtain entropy from the OS. This is unlikelyÁü¡74 outside of early boot or unusual system conditions.ÁÙ�tÝüº$ì�üð$ »$•�ü™# [`SysRng`]: crate::rngs::SysRngÁü½)& [`ThreadRng`]: crate::rngs::ThreadRngÁüç;8 [`ThreadRng#Security`]: crate::rngs::ThreadRng#securityÁÓ…Â$œ©Ü£¶|¿DÖ€½ðBÿŽÞÞÃÌ$ ßG½ð\â ݽðW`üÓ:7 Adapter to support [`std::io::Read`] over a [`TryRng`]ÁŽ�t’šˆ"¡�l¥ ```no_runÁä³ use std::{io, io::Read};Á´Ð use std::fs::File;Áüç(% use rand::{rngs::SysRng, RngReader};Á��l” io::copy(Áü¢)& &mut RngReader(SysRng).take(100),ÁüÌ74 &mut File::create("/tmp/random.bytes").unwrap()Á|„ ).unwrap();Á<”�¸Ó‰|¢¼œL¿ŽááÃÌ$ É�½ð4Ì€‚,î·ðÊzNÇàâ½ð€‚Bÿ|b`½ð€‚Bÿßß à½ðz|,Ôßß½ðüõ.Ó‰|ã¼ÝŽääÃÌ$ ú›ó&4ý€‚åèåü¸C$»åæ 倂 æñ°„÷Bÿã Àã å½ð$Å£ü,Ãå�æ�æ�ææåƒðü»0Ó‰|©¼£ŽèèÃÌ$ À›ó&4À‚é géüòBõçèé 瀂 è€g€gŠ‚gê ûcƒg£üûcØ«q¢1ȡ镘Bÿç ùç é½ð$úœpüµ'CüìKH Generate a random value using the thread-local random number generator.Á¸�ü¼SP This function is shorthand for [rng()].[random()](RngExt::random):Á� �ü” IF - See [`ThreadRng`] for documentation of the generator and securityÁüÞ VS - See [`StandardUniform`] for documentation of supported types and distributionsÁµ!�t¹!šˆ"È!�<Ì!�¸üÔ!! let x = rand::random::();Á´ö!ÅŠ#�"�ü‘"" let y = rand::random::();Á´´" println!("{}", y);ÁË"�üÏ".+ if rand::random() { // generates a booleanÁüþ",) println!("Better lucky than good!");Á,«#…‘<±#�¸¹#�ü½#IF If you're calling `random()` repeatedly, consider using a local `rng`Áü‡$96 handle to save an initialization-check on each usage:ÁÁ$�<Å$�¸üÍ$52 use rand::RngExt; // provides the `random` methodÁƒ%�ü‡%A> let mut rng = rand::rng(); // a local handle to the generatorÁÉ%�ôÍ% let mut v = vec![1, 2, 3];Áì%�Üð% for x in v.iter_mut() {ÁÔŒ& *x = rng.random();Á,§&…‘<­&�¸µ&�ü¹&/í‘#üé&" [`ThreadRng`]: rngs::ThreadRngÁÓæó"´’'ôŒ'4¼'ßËBÿ�ëëàŒ Ã'ÿŒ|è' êßËüÌ*wü‘(1. Return an iterator over [`random()`] variatesÁÃ(�üÇ(" This function is shorthand forÁüê(>; [rng()].[random_iter](RngExt::random_iter)().Á©)�l­)Úð»)�<¿)�¸üÇ)<9 let v: Vec = rand::random_iter().take(5).collect();Á´„* println!("{v:?}");Á<›*�¸Óæó"´©*ô£*\Ó*í�Bÿ�ííàŒ ß*ÿŒ|³+ ìßËüÞ0{üá+^[ Generate a random value in the given range using the thread-local random number generator.ÁÀ,�üÄ,"ƒ'üç,PM [rng()].[random_range](RngExt::random_range)(range).Á¸-�l¼-ÚðÊ-�<Î-�¸üÖ-/, let y: f32 = rand::random_range(0.0..=1e9);Á´†.™ü&�.�ü¡.IF let words: Vec<&str> = "Mary had a little lamb".split(' ').collect();Áüë.=: println!("{}", words[rand::random_range(..words.len())]);Á<©/�¸ü±/LI Note that the second example can also be achieved (without `collect`'ingÁüþ/63 to a `Vec`) using [`seq::IteratorRandom::choose`].ÁÓæó"´»0ôµ0då0ë»ßËBÿ�ïŽðïðàŒ ò0Ê› õ0Ñ‘"ì”1–ë»ßËôº1 îßËë»…jXv=?BDüè4"üý17§¦#µ2�ü¹2"ƒ'üÜ2JG [rng()].[random_bool](RngExt::random_bool)(p).Á§3�l«3Úð¹3�<½3�¸üÅ31. println!("{}", rand::random_bool(1.0 / 3.0));Á<÷3�¸ÿ3�dƒ4œž#�4�Ô”4¿©#Óæó"´µ4ô¯4¶|Ø4\ï4€Bÿ ñ¦Àvü¥<=ü©5H…«#Lò5Ö«#ü5�ü€6Hõ«#üÉ6JǬ#ü”7F›­#üÛ7&ë­#‚8�ü†8Cô¦#üÊ8Dµ®#�9�ü“9"ƒ'ü¶9li [rng()].[random_ratio](RngExt::random_ratio)(numerator, denominator).Á£:�d§:œž#´:�ü¸:7¨¯#ð:�lô:Úð‚;�<†;�¸üŽ;-* println!("{}", rand::random_ratio(2, 3));Á<¼;�¸Ä;�üÈ;#ï©#Óæó"´ò;ôì;¶|•<d¬<€Bÿ òÓ­Ówé­Ówüü@$ü—=8³À#Ð=�üÔ="ƒ'ü÷=?< [rng()].[fill](RngExt::fill)(dest).Á·>�l»>ÚðÉ>�<Í>�¸äÕ>æÄ#ìò> rand::fill(&mut arr[..]);Á<�?�¸˜?�üœ?MJ Note that you can instead use [`random()`] to generate an array of randomÁüê?MJ data, though this is slower for small elements (smaller than the RNG wordÁT¸@ size).ÁÓæó"´É@ôÃ@¶|ì@$ƒA€ê êûúBÿ�ôô —AàŒ ˆA¨ßË$‹A óßË„˜íx&(¤Ì üžfc The [Bernoulli distribution](https://en.wikipedia.org/wiki/Bernoulli_distribution) `Bernoulli(p)`.Á…�ü‰OL This distribution describes a single boolean random variable, which is trueÁüÙ<9 with probability `p` and false with probability `1 - p`.Áü–C@ It is a special case of the Binomial distribution with `n = 1`.ÁÚ�TÞ # PlotÁé�üíGD The following plot shows the Bernoulli distribution with `p = 0.1`,Áìµ `p = 0.5`, and `p = 0.9`.ÁÓ�ü×mj ![Bernoulli distribution](https://raw.githubusercontent.com/rust-random/charts/main/charts/bernoulli.svg)ÁÅ�lÉÚð×�\Û ```rustÁüç/, use rand::distr::{Bernoulli, Distribution};Á— �ü› )& let d = Bernoulli::new(0.3).unwrap();ÁüÅ '$ let v = d.sample(&mut rand::rng());Áüí 74 println!("{} is from a Bernoulli distribution", v);Á<¥ �¸­ �|± ÌèÁ �üÅ FC This `Bernoulli` distribution uses 64 bits from the RNG (a `u64`),ÁüŒ FC so only probabilities that are multiples of 2-64 can beÁ„Ó represented.ÁL× ‚¹‚¶ÝÅó†ÙöT¨ ,¨  õõoŠoŠoŠk‚¹oŠk‚¹ù†ùoŠoŠ… …‚¹‚¹Bÿøí ø ùoŠ ô l‚¹ ‹m‚¹ü gü ‹ ‹†‡ˆ †‚¹ ‡€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡ˆ•˜Bÿûú û ü ‹œ ‹#�n‚¹#�n‚¹ÿù±ÿ#�#�‰Š ‰‚¹ Š‚¹Bÿþ� þ ÿ#�î #�¼âü„0- Error type returned from [`Bernoulli::new`].Átëó¹¦íÕÎQP�‚‚”œ¼€ `p < 0` or `p > 1`.Á&€€ó¹:<€€ó¹0�0�0�oó¹0�oó¹…†…0�0�‹ ‹ó¹ó¹Bÿ„¾„ …0� Åpó¹n�q󹈠gˆn�n�Œ�Ž Œó¹ �€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡Ž•˜Bÿ‡Ë‡ ˆn�œn��ró¹�ró¹‹ù±‹���� �ó¹ �ó¹BÿŠÒŠ ‹�î ���só¹�Î���������‘ ‘ó¹BÿŒÝŒ ���Äã!ü…'$ An iterator over a [`Distribution`]Á­�ü±HE This iterator yields random values of type `T` with distribution `D`Áüú(% from a random generator of type `R`.Á£ �ü§ B? Construct this `struct` using [`Distribution::sample_iter`] orÁüê KH [`RngExt::sample_iter`]. It is also used by [`RngExt::random_iter`] andÁܶ! [`crate::random_iter`].Á$î!€�Ž��‘��‘¹› ó!Ê› ö!Û› ù!¢»‡é£=›5xN’“”2479<>D‚",‚"ŽŽå»4�"�"ŽŽë»üœ"%<œ"ŽŽ¥¼ï�t€–Ž—�˜—˜–¹›ëÊ›éÛ›çŸgå»ó!Ÿgë»ö!Ÿgñ»ù!¢»™ g™;>BEILï�ï��žŸ �¢» ž€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡Ÿ•˜Bÿ•Û!• ™å»ë»ñ»ï�œï�ÔŠ)üÒ'<9 A [`Distribution`] which maps sampled values to type `S`Á�(�ü“(A> This `struct` is created by the [`Distribution::map`] method.ÁüÕ(# See its documentation for more.Á•)€›‚œ���žžœ›�¹› ™)�  œ)Û› Ÿ)»— ¢)”¼-$Ê3.ð¿ÐŸ ¡:<?ADFIKD«),«)ššå»<¹)$¹)ššÛ¼üÆ).<Æ)šššÅl¢u€£‚¤�¥�¦£¥¦¤¹›� Û› »— ö´'™)ŸgÛ¼œ)˜µ'Ÿ)Ÿgå¼¢)”¼§ g§jmqtx{‚l¢l¢¢£¤ ¢”¼ £€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡¤•˜Bÿ¢‚)¢ §å»Û¼ñ»å¼l¢œl¢¼� ü°NK A distribution to sample floating point numbers uniformly in the half-openÁüÿ2/ interval `(0, 1]`, i.e. including 1 but not 0.Á²�ü¶JG All values that can be generated are of the form `n * ε/2`. For `f32`Áü�MJ the 24 most significant random bits of a `u32` are used and for `f64` theÁüÏIF 53 most significant bits of a `u64` are used. The conversion uses theÁÔ™ multiplicative method.Á´�ü¸IF See also: [`StandardUniform`] which samples from `[0, 1)`, [`Open01`]Áü‚ LI which samples from `(0, 1)` and [`Uniform`] which samples from arbitraryÁ\Ï  ranges.ÁÛ �lß Úð<í �¸¬õ ³Áü‹ " use rand::distr::OpenClosed01;Á® �ü² 41 let val: f32 = rand::rng().sample(OpenClosed01);Áüç )& println!("f32 from (0, 1): {}", val);Á<‘ �¸™ �ü� 63 [`StandardUniform`]: crate::distr::StandardUniformÁüÔ $! [`Open01`]: crate::distr::Open01Áüù /, [`Uniform`]: crate::distr::uniform::UniformÁdš €½œ–Ã×RQŠ2©U*¨¨€½‰©‰©‰©v€½‰©v€½¬†¬‰©‰©¬ ¬€½€½Bÿ«² « ¬‰© ¹ w€½Ç©x€½¯ g¯Ç©Ç©­®¯ ­€½ ®€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡¯•˜Bÿ®¿ ® ¯Ç©œÇ©pªy€½±÷±pªpª€½Bÿ°° ±Œïü© IF A distribution to sample floating point numbers uniformly in the openÁüó :7 interval `(0, 1)`, i.e. not including either endpoint.Á®�ü²OL All values that can be generated are of the form `n * ε + ε/2`. For `f32`Áü‚OL the 23 most significant random bits of an `u32` are used, for `f64` 52 fromÁüÒ;8 an `u64`. The conversion uses a transmute-based method.ÁŽ�ü’OL See also: [`StandardUniform`] which samples from `[0, 1)`, [`OpenClosed01`]ÁüâLI which samples from `(0, 1]` and [`Uniform`] which samples from arbitraryÁ\¯²Â'»�l¿Úð<Í�¸¬Õ³Áäë use rand::distr::Open01;Áˆ�üŒ.+ let val: f32 = rand::rng().sample(Open01);Áü»)ðÃ'<å�¸í�üñ6¼Ä'ü¨0- [`OpenClosed01`]: crate::distr::OpenClosed01ÁüÙ/ªÅ'4úÙ½|õï!ØJ‚ܳª*²²Ù½©ª©ª©ªzÙ½©ªzÙ½¶†¶©ª©ª° °Ù½Ù½Bÿµ!’µ ¶©ª "™{Ù½çª|Ù½¹ g¹çªçª±²³ ±Ù½ ²€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡³•˜Bÿ¸#Ÿ¸ ¹çªœçª�«}Ù½»÷»�«�«Ù½Bÿºº »¸%�½¾UV¾0%µ%º¼¼ø%í7À%ðBÿ¼¼ ¾άŽÚجø%ö*º¾À%Àø%¯50%²´µ ´º¾ µ½ðBÿ¿ŽÁÁ%Ê¿ÿù0%Â�ú%¼ À½ð %Ë�7È®%¹ø%ú$'€½Ã%Ãø%°%50%³%¶· ¶€½ ·½ðBÿÂŽÄÄ%Ë%Âÿù0%Ã%�ú%½% ýð %Ì%�7M±%º%ø%Ü+!Ù½Æ%Æø%Œ,50%�,¸¹ ¸Ù½ ¹½ðBÿÅŽÇÇ%§,Åÿù0%Ÿ,�ú%™, ƽð %¨,�7ɳ%–,¸&� ÉÊUVÊ0&µ&ºÈÈø&í7À&ðBÿÈÈ Ê“µŽÚ�µø&ö* º¾Ì%Ìø&¯50&²º» ºº¾ »½ðBÿËŽÍÍ&ÊËÿù0&Â�ú&¼ ̽ð &Ë�7o·&¹ø&ú$' €½Ï%Ïø&°%50&³%¼½ ¼€½ ½½ðBÿÎŽÐÐ&Ë%Îÿù0&Ã%�ú&½% Ͻð &Ì%�7÷¹&º%ø&Ü+! Ù½Ò%Òø&Œ,50&�,¾¿ ¾Ù½ ¿½ðBÿÑŽÓÓ&§,Ñÿù0&Ÿ,�ú&™, Ò½ð &¨,�7‹¼&–,ø'õ* º¾Õ%Õø'Ä50'ÇÊË Êº¾ ˽ðBÿÔŽÖÖ'ßÔÿù0'×�ú'Ñ Õ½ð 'à�7ÍÂ'Îø(õ* º¾Ø%Øø(Ä50(ÇÌÍ Ìº¾ ͽðBÿ׎ÙÙ(ß×ÿù0(×�ú(Ñ Ø½ð (à�7™Ã(Îø)õ* º¾Û%Ûø)Ä50)ÇÎÏ Îº¾ ϽðBÿÚŽÜÜ)ßÚÿù0)×�ú)Ñ Û½ð )à�7\Ä)Îø*õ* º¾Þ%Þø*Ä50*ÇÐÑ Ðº¾ ѽðBÿÝŽßß*ßÝÿù0*×�ú*Ñ Þ½ð *à�7Å*Îø+õ*º¾á%áø+Ä50+ÇÒÓ Òº¾ Ó½ðBÿàŽââ+ßàÿù0+×�ú+Ñ á½ð +à�7ëÅ+Îø,¯*º¾ä%äø,è50,ëÔÕ Ôº¾ Õ½ð¹ÀBÿãŽåå,ƒãÿù0,û�ú,õ ä½ð ,„�7�Ç,òø-¯*º¾ç%çø-è50-ëÖ× Öº¾ ×½ðøÀBÿæŽèè-ƒæÿù0-û�ú-õ ç½ð -„�7IÉ-òø.¯*º¾ê%êø.è50.ëØÙ غ¾ Ù½ð·ÁBÿéŽëë.ƒéÿù0.û�ú.õ ê½ð .„�7Ë.òø/¯*º¾í%íø/è50/ëÚÛ Úº¾ Û½ðöÁBÿìŽîî/ƒìÿù0/û�ú/õ í½ð /„�7»Ì/òø0¯*º¾ð%ðø0è500ëÜÝ Üº¾ ݽðµÂBÿïŽññ0ƒïÿù00û�ú0õ ð½ð 0„�7tÎ0òø1¯*º¾ó%óø1è501ëÞß Þº¾ ß½ðôÂBÿòŽôô1ƒòÿù01û�ú1õ ó½ð 1„�76Ð1òø2¯*º¾ö%öø2è502ëàá ຾ á½ð³ÃBÿõŽ÷÷2ƒõÿù02û�ú2õ ö½ð 2„�7øÑ2òø3¯*º¾ù%ùø3è503ëâã ⺾ ã½ðòÃBÿøŽúú3ƒøÿù03û�ú3õ ù½ð 3„�7ºÓ3òø4¯*º¾ü%üø4è504ëäå 亾 å½ð±ÄBÿûŽýý4ƒûÿù04û�ú4õ ü½ð 4„�7|Õ4òø5¯*º¾ÿ%ÿø5è505ëæç 溾 ç½ððÄBÿþŽ€ € 5ƒþÿù05û�ú5õ ÿ½ð 5„�7>×5ò¼›ü HE Sample a `u8`, uniformly distributed over ASCII letters and numbers:Á¬é a-z, A-Z and 0-9.Áÿ�lƒÚð‘�<•�¸¬�³Áü³" use rand::distr::Alphanumeric;ÁÖ�ôÚÑÁüùSP let chars: String = (0..7).map(|_| rng.sample(Alphanumeric) as char).collect();ÁüÍ (% println!("Random chars: {}", chars);Á<ö �¸þ �ü‚ FC The [`SampleString`] trait provides an easier method of generatingÁüÉ >; a random [`String`], and offers more efficient allocation:Á<ˆ �¸ü� 2/ use rand::distr::{Alphanumeric, SampleString};Áüà B? let string = Alphanumeric.sample_string(&mut rand::rng(), 16);Áü† *' println!("Random string: {}", string);Á<± �¸¹ �|½  # PasswordsÁÍ �üÑ OL Users sometimes ask whether it is safe to use a string of random charactersÁü¡ NK as a password. In principle, all RNGs in Rand implementing `CryptoRng` areÁüð LI suitable as a source of randomness for generating passwords (if they areÁü½HE properly seeded), but it is more conservative to only use randomnessÁü†HE directly from the operating system via the `getrandom` crate, or theÁüÏ/, corresponding bindings of a crypto library.Áÿ�üƒMJ When generating passwords or keys, it is important to consider the threatÁüÑLI model and in some cases the memorability of the password. This is out ofÁüžFC scope of the Rand project, and therefore we defer to the followingÁ|å references:Áõ�üù_\ - [Wikipedia article on Password Strength](https://en.wikipedia.org/wiki/Password_strength)ÁüÙ[X - [Diceware for generating memorable passwords](https://en.wikipedia.org/wiki/Diceware)Ád¦®Æ³ÖºV¯¢„Z‚ H*� � ®ÆƒÛ~®Æ„  g„ ƒÛƒÛìíî ì®Æ í€g€gŠ‚gê ûcƒg£üûcØ«q¢1ȡBÿƒ 6¾ƒ „ ƒÛœƒÛ/Ü/Ü/Ü®Æ/ܮƇ †‡ /Ü/Üï ï®Æ®ÆBÿ† 7ņ ‡ /Ü 8Ì€®Æ|Ü�®ÆŠ ÷Š |Ü|Ü®ÆBÿ‰ ‰ Š ¬ìüµ85 Sample a [`u8`], uniformly distributed over letters:Á„î a-z and A-Z.Áÿ�lƒÚð‘�ü•OL You're able to generate random Alphabetic characters via mapping or via theÁüå30 [`SampleString::sample_string`] method like so:Á™�<��¸¬¥³Áü»0- use rand::distr::{Alphabetic, SampleString};Áì�¬ð // Manual mappingÁô†ÑÁü¥QN let chars: String = (0..7).map(|_| rng.sample(Alphabetic) as char).collect();Áü÷(Òú' �ü¤,) // Using [`SampleString::sample_string`]ÁüÑ@= let string = Alphabetic.sample_string(&mut rand::rng(), 16);Áü’*Êý'<½�¸Å�|É–þ'Ù�üÝ(% Refer to [`Alphanumeric#Passwords`].ÁT÷‡Ç…enÅ üÃŒ C*‹ ‹ ‡Ç£Ü‚‡ÇŽ  gŽ £Ü£Üðñò ð‡Ç ñ€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡ò•˜Bÿ� :�� Ž £Üœ£ÜOÝOÝO݃‡ÇO݃‡Ç‘ †‘ OÝOÝó ó‡Ç‡ÇBÿ� ;–� ‘ OÝ <�„‡ÇœÝ…‡Ç” ÷” œÝœÝ‡ÇBÿ“ “ ” øD“GQ‰º¾– %– øDÔHA0D×H…† …º¾ †½ðBÿ• Ž— — DïH• ÿù0DçH�úDáH – ½ð DðH�7ÕøDÞHøF“G‰‹ý™ ™ þÆÂÈ ÔO#º¾ÂȰF…Hº¾š %š &(øFÔHA0F×H‡ˆ ‡º¾ ˆë»ÀÈBÿ˜ Ž› › FïH˜ ·§0FçHÿ›FáH š ÂÈë» FðH�7ÒùFÞHøH“G‰�ý� þž � ž î—(þÆ×È ÖOÿ—(°H…H#º¾×Ⱥ¾Ÿ %Ÿ PS;=øHÔHA0H×H‰Š ‰º¾ Š»µÒÈBÿœ Ž    HïHœ ‘‡0HçH¢‡HáH Ÿ ÂÈ×È»µ HðH�7+ûHÞHøJ“G‰�ý¢ þ£ ÿ¤ £ ¤ ¢ î—(a’š(DþÆïÈ ØOÿ—(°J…H¬š( #º¾ïȺ¾¥ %¥ ª­•˜PRøJÔHA0J×H‹Œ ‹º¾ Œ�ºçÈBÿ¡ ަ ¦ JïH¡ °š0JçHÁšJáH ¥ ÂÈ×ÈïÈ�º JðH�7äüJÞHøL“G‰‘ý¨ þ© ÿª €« ª ¨ « © î—(Þ’š(Áæœ(tþÆŠÉ ÚOÿ—(°L…H¬š( †�(#º¾ŠÉ º¾¬ %¬ 47"ÚÝegøLÔHA0L×H�Ž �º¾ ޵ÉÿÈBÿ§ Ž­ ­ LïH§ €¢0LçH‘¢LáH ¬ ÂÈ×ÈïÈŠÉµÉ LðH�7ÿLÞHøN“G‰“ý¯ þ° ÿ± €² �³ ³ ± ¯ ° ²  î—(‹’š(næœ(!êŸ(¤þÆ¨É ÜOÿ—(°N…H¬š( †�(� (#º¾¨É&º¾´ %´ îñÙÜ”—"z|øNÔHA0N×H�� �º¾ �À€šÉBÿ® ޵ µ NïH® ÿÆÀ€0NçH„À€NáH ´ ÂÈ×ÈïȊɨÉÀ€ NðH�7ƒNÞHøP“G‰•ý· þ¸ ÿ¹ €º �» ‚¼ · » ¼ º ¸ ¹  î—(z’š(]æœ(êŸ(“ž£(æþÆÉÉ ÞOÿ—(°P…H¬š( †�(� (Ê£(#º¾ÉÉ,º¾½ %½ êíÕØ�“vy�‘øPÔHA0P×H‘’ ‘º¾ ’Ú…¸ÉBÿ¶ ޾ ¾ PïH¶ ÿÆÚ…0PçH„Ú…PáH ½ ÂÈ×ÈïȊɨÉÉÉÚ… PðH�7lPÞHøR“G‰—ýÀ þÁ ÿ €à �Ä ‚Å ƒÆ  À Ä Å à Á Æ î—(™ ’š(|æœ(/êŸ(²ž£(”§(þÆíÉ àOÿ—(°R…H¬š( †�(� (Ê£(Ƨ(!#º¾íÉ2º¾Ç %Ç     ¼¿GJ¢¥»¾¤¦øRÔHA0R×H“” “º¾ ”Ú‹ÙÉBÿ¿ ŽÈ È RïH¿ ÿÆÚ‹0RçH„Ú‹RáH Ç ÂÈ×ÈïȊɨÉÉÉíÉÚ‹ RðH�7»RÞHøT“G‰™ýÊ þË ÿÌ €Í �Î ‚Ï ƒÐ „Ñ Ï Ë Î Ê Ñ Í Ð Ì î—(è ’š(Ë æœ(~ êŸ(ž£(T”§(eº«(FþÆ”Ê âOÿ—(°T…H¬š( †�(� (Ê£(Ƨ(!ò«('#º¾”Ê8º¾Ò %Ò r u ] `   £¦þ¹»øTÔHA0T×H•– •º¾ –À’ýÉBÿÉ ŽÓ Ó TïHÉ ÿÆÀ’0TçH„À’TáH Ò ÂÈ×ÈïȊɨÉÉÉíÉ”ÊÀ’ TðH�7p TÞHøV“G‰› ýÕ þÖ ÿ× €Ø �Ù ‚Ú ƒÛ „Ü …Ý  Ú Ö Ý Ù Õ Ü Ø Û × î—(g’š(J æœ(ý êŸ(€ ž£(Ó”§(享(Å�°(vþÆ¾Ê äOÿ—(°V…H¬š( †�(� (Ê£(Ƨ(!ò«('ΰ(-#º¾¾Ê>º¾Þ %Þ þé ì ¤ § / 2 Š � £¦Œ�EHÎÐøVÔHA0V×H—˜ —º¾ ˜Œš¤ÊBÿÔ Žß ß VïHÔ ÿÆŒš0VçH„ŒšVáH Þ ÂÈ×ÈïȊɨÉÉÉíɔʾʌš VðH�7‹VÞHøX“G‰� ýá þâ ÿã €ä �å ‚æ ƒç „è …é †ê  å á è ä ç ã ê æ â é î—(’š(ùæœ(¬êŸ(/ ž£(‚ ”§(“ º«(t�°(%–µ(¦þÆëÊ æOÿ—(°X…H¬š( †�(� (Ê£(Ƨ(!ò«('ΰ(-Úµ(3#º¾ëÊDº¾ë %ë º½¥¨`cë î F I _ b HKŠ�ãåøXÔHA0X×H™š ™º¾ š¾¢ÎÊBÿà Žì ì XïHà ÿƾ¢0XçH„¾¢XáH ë ÂÈ×ÈïȊɨÉÉÉíɔʾÊëʾ¢ XðH�7 XÞHøZ“G‰Ÿ ýî þï ÿð €ñ �ò ‚ó ƒô „õ …ö †÷ ‡ø  ð ÷ ó ï ö ò î õ ñ ø ô î—(õ’š(Øæœ(‹êŸ(ž£(a”§(r º«(S �°(–µ(…̺(ÖþÆ›Ë èOÿ—(°Z…H¬š( †�(� (Ê£(Ƨ(!ò«('ΰ(-Úµ(3–»(9#º¾›ËJº¾ù %ù ¦©‘”LO×Ú25K N 4 7 íðvyÏÒøúøZÔHA0Z×H›œ ›º¾ œÖ«ûÊBÿí Žú ú ZïHí ÿÆÖ«0ZçH„Ö«ZáH ù ÂÈ×ÈïȊɨÉÉÉíɔʾÊëÊ›ËÖ« ZðH�7óZÞHø\“G‰¡ ýü þý ÿþ €ÿ �€ ‚� ƒ‚ „ƒ …„ †… ‡† ˆ‡  † ‚ þ … � ý „ € ü ‡ ƒ ÿ î—(’š(çæœ(šêŸ(ž£(p”§(�º«(b �°( –µ(”̺(å²À(þÆÎË êOÿ—(°\…H¬š( †�(� (Ê£(Ƨ(!ò«('ΰ(-Úµ(3–»(9‚Á(?#º¾ÎËPº¾ˆ %ˆ ÂÅ­°hkóöNQgjPS  ’ • ëî ø\ÔHA0\×H�ž �º¾ žÔµ«ËBÿû މ ‰ \ïHû ÿÆÔµ0\çH„Ôµ\áH ˆ ÂÈ×ÈïȊɨÉÉÉíɔʾÊëÊ›ËÎËÔµ \ðH�7@\ÞHè]µ‹ Œ ¾¿Œ X]á0]æŠ Š �Êø]¦% ]©¾BÿŠ Š Œ ¡$®«$è^µŽ � ¾¿� X^á0^æ� � §Íø^¦% ^©¾Bÿ� � � 8&®B&è_µ‘ ’ ¾¿’ X_á0_æ� � ¼Ðø_¦% _©¾Bÿ� � ’ Í'®×'è`µ ” • ¾¿• X`á0`æ“ “ ÑÓø`¦% `©¾Bÿ“ “ • b)®l)èaô!— ˜ ¾¿˜ Xa 0a¥– – •Ýøaå% aè¾Bÿ– – ˜ &.˜0.D0Pa£»øb™""› œ ¾¿œ XbÇ"0bÌ"š š „åøb�#' b“#¾Bÿš š œ 2®2ØcžE#ž Ÿ   ¡ ¢ £ ¤ ¥ ÇÊÄÅÆÈÉË  ¢ £ ¡ ¥ ¤ HcÈE cÍE� � HcæE cëE� � øc£F$0c¦FBÿ� �   4î !4øc G$0c£GBÿ� � ¡ ‘4î ›4ØcžHPc¡HBÿ� � ¢ ‡5øc–I+8c™IÇBÿ� � £ 6î 6øc›J2xcžJ¬Õ(Bÿ� � ¤ Y7‰ïb7øcüK'hcÿKÊBÿ� � ¥ Ÿü7Àc¬P#ØjžE$¨ © ª « ¬ ­ ® ¯ ÇÊÄÅÆÈÉË« ­ ® ¬ ª ¯ HjÈE jÍE§ § HjæE jëE§ § øj£F$0j¦FBÿ§ § ª a8î k8øj G$0j£GBÿ§ § « Û8î å8ØjžHPj¡HBÿ§ § ¬ Õ9øj–I+8j™IÇBÿ§ § ­ T:î ^:øj›J2xjžJ Ú(Bÿ§ § ® ’;‰ï›;øjüK'hjÿKÊBÿ§ § ¯ Ÿ)<Àj¬P$Ä™üÂ:7 A distribution to uniformly sample elements of a sliceÁý�ü�NK Like [`IndexedRandom::choose`], this uniformly samples elements of a sliceÁüÐNK without modification of the slice (so called "sampling with replacement").ÁüŸNK This distribution object may be a little faster for repeated sampling (butÁüî)& slower for small numbers of samples).Á˜�|œ ## ExamplesÁ¬�ü°:7 Since this is a distribution, [`Rng::sample_iter`] andÁüë;8 [`Distribution::sample_iter`] may be used, for example:Á<§�¸ü¯30 use rand::distr::{Distribution, slice::Choose};Áã�üç+( let vowels = ['a', 'e', 'i', 'o', 'u'];Áü“ 41 let vowels_dist = Choose::new(&vowels).unwrap();ÁÈ �üÌ " // build a string of 10 vowelsÁüï *' let vowel_string: String = vowels_distÁüš &# .sample_iter(&mut rand::rng())ÁŒÁ  .take(10)ÁœÓ ÒŽç �üë ! println!("{}", vowel_string);Áü� '$ assert_eq!(vowel_string.len(), 10);Áüµ ?< assert!(vowel_string.chars().all(|c| vowels.contains(&c)));Á<õ �¸ý �ü� DA For a single sample, [`IndexedRandom::choose`] may be preferred:Á<Æ �¸üÎ !ð•%ð �üô +¤à(ô  ÑÁ¿ �üà 52 println!("{}", vowels.choose(&mut rng).unwrap());Á<ù �¸��ü…@= [`IndexedRandom::choose`]: crate::seq::IndexedRandom::chooseÁüÆ41 [`Rng::sample_iter`]: crate::RngExt::sample_iterÁ%4¤ú$² �³ ² ³ „… ¯•»ú$t¸ÍÍ^4=™@ôÈ×´ µ ¶ «795,¸Ù± ± §çœÌ,ÌÙ± ± ­ÚÌå\åÙ± ± Ûú/=¬ú$¸ �¹ ¸ ¹ „…ÇŸg•»q¯Íͺ  gº ¸ºíï/=/=£¤¥ £ÍÍ ¤€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡¥•˜Bÿ· q„· º ú$•»/=œ/=@?­ú$¼ �½ ½ ¼ „…ë…•»r¯Í; †¾ Ýà@?@?¦ ¦ÍÍÍÍBÿ» r‹» ¾ ú$•»@? s’®ú$À �Á À Á „…¶ù •»s¯ÍÍ� Ôׄ€´þ Error: empty sliceÁ•�ü™HE This error is returned when [`Choose::new`] is given an empty slice.Á&,‹ÏμÂ'÷jâC°à ª)  ÏÎŽJ¯ÏÎÅ  gÅ ŽJŽJª«¬ ªÏÎ «€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡¬•˜BÿÄ tëÄ Å ŽJœŽJ:K:K:K°ÏÎ:K°ÏÎÈ †È :K:K­ ­ÏÎÏÎBÿÇ uòÇ È :K vù±ÏÎÔÖüˆJG The back-end implementing [`UniformSampler`] for floating-point types.ÁÓ�ü×OL Unless you are implementing [`UniformSampler`] for your own type, this typeÁü§96 should not be used directly, use [`Uniform`] instead.Áá�Ôå # Implementation notesÁ€�ü„MJ `UniformFloat` implementations convert RNG output to a float in the rangeÁüÒNK `[1, 2)` via transmutation, map this to `[0, 1)`, then scale and translateÁü¡ NK to the desired range. Values produced this way have what equals 23 bits ofÁüð 30 random digits for an `f32` and 52 for an `f64`.Á¤ �ܨ  # Bias and range errorsÁÄ �üÈ MJ Bias may be expected within the least-significant bit of the significand.Áü– MJ It is not guaranteed that exclusive limits of a range are respected; i.e.Áüä KH when sampling the range `[a, b)` it is not guaranteed that `b` is neverÁd°  sampled.Á½ �üÁ  [`new`]: UniformSampler::newÁüâ 41 [`new_inclusive`]: UniformSampler::new_inclusiveÁü— 6¼Ä'üÎ  [`Uniform`]: super::UniformÁ(dá”Ë Ë µÐ! î†Ðu�ÜM¿@ÏÌ Í  "4÷÷ôÊ Ê ÀÐDƒ,ƒôÊ Ê ÀÐÆ\³”Ï Ï µÐ!‰œ¼"yî†ÐÐ †Ð £¥Æ\Æ\µ µ†Ð†ÐBÿÎ y÷ Î Ð ÀÐÆ\ zþ ´”Ò Ò µÐ!/ù ÀÐzî†ÐGJ^µ”Ô Ô µÐ!zŸgÀÐ{î†ÐÕ  gÕ � ^^¶·¸ ¶†Ð ·€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡¸•˜BÿÓ {„Ó Õ ÀÐ^œ^{`¶”× × µÐ!‰÷±ÀÐÀÐ|î†Ð¦©{`¶”Ù Ù µÐ!ÙÀ�)C†ÐÚ ù±Ú òõ{`{`¹º ¹†Ð º†ÐBÿØ |‹Ø Ú ÀÐ{`î {`°}»)‰ÑÜ ø}ž;X}¡ô‰ÑBÿÛ Û Ü »kJcˆÞTcÆk(}ÆÐ}Ý)Þ ò`}†8}‹Ý Ý ‰Ñø}Õ))‰Ñà á ä ç é í ôõøûý�ä í é ç á 0}�}’ß ß ø}¨´}«ßÉØÊŒÔBÿß ñ'â û'ã ã â ß �¯!(}£�ßÉô‰Ñ¨}‹¾¯!(}Ö�ØÊ«†)¨}¾ á ßÉØÊ˜ÕîiªÕùi}¯}³ø}Ë"¾h}Î"ßÉØÊŒÔBÿß ñ'å û'æ æ å ß �¯!(}Ð# †)¨}¸#¾¯!(}ƒ$Ɔ)¨}ë# ä ßÉØÊ˜ÕqªÕ&q}Ü"}à"ø}÷)90}ú)»¼ »‰Ñ ¼½ð«†)Bÿß Žè è }’*ß ÿù0}Š*�ú}„* ç ½ð }“*�7Ât}�*ø}ç0ßh}ê0½ƒì‰ì ½½ðÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´Òw«†)îàBÿß Žê ñ'ë û'ì ë ì ê }­1ß ÿù0}�1�ú}û0ó´!(}�2�ƒì«†)¨}õ1šµ!(}À2�‰ì«†)¨}¨2 é ½ðƒì‰ì˜Õ4vªÕ?v�7Jv}ø0}‰1}�1ø}È3é¸}Ë3¾ƒì‰ì ¾½ð¿Š)Bÿß Žî ñ'ï û'ð ï î ð }˜4ß ÿù0}ì3�ú}æ3ó´!(}ø4ó‹)¨}à4šµ!(}«5‘Œ)¨}“5 í ½ðƒì‰ì˜Õ›{ªÕ¦{�7±{}ã3}ô3}ø3°‚»*×Ñò ø‚ž;X‚¡ô×ÑBÿñ ñ ò »kˆÞŠÆk(‚ÆЂÝ*ô ò`‚†8‚‹ó ó ×Ñø‚Õ)*×Ñö ÷ ú ý ÿ ƒ ôõøûý�ú ƒ ÿ ý ÷ 0‚�‚’õ õ ø‚¨´‚«ßÉØÊëŒBÿõ ñ'ø û'ù ø ù õ �¯!(‚£�ßÉô×Ѩ‚‹¾¯!(‚Ö�ØÊ¦’)¨‚¾ ÷ ßÉØÊ˜ÕN†ªÕZ†‚¯‚³ø‚Ë"¾h‚Î"ßÉØÊëŒBÿõ ñ'û û'ü û ü õ �¯!(‚Ð#›’)¨‚¸#¾¯!(‚ƒ$Ã’)¨‚ë# ú ßÉØÊ˜Õ£�ªÕ¯�‚Ü"‚à"ø‚÷)90‚ú)¿À ¿×Ñ À½ð¦’)Bÿõ Žþ þ ‚’*õ ÿù0‚Š*�ú‚„* ý ½ð ‚“*�7x‘‚�*ø‚ç0ßh‚ê0Áƒì‰ì Á½ðÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´Òw¦’)îàBÿõ Ž€ ñ'� û'‚ � ‚ € ‚­1õ ÿù0‚�1�ú‚û0ó´!(‚�2�ƒì¦’)¨‚õ1šµ!(‚À2�‰ì¦’)¨‚¨2 ÿ ½ðƒì‰ì˜Õà’ªÕì’�7ø’‚ø0‚‰1‚�1ø‚È3鸂Ë3ƒì‰ì ½ðЖ)Bÿõ Ž„ ñ'… û'† † „ … ‚˜4õ ÿù0‚ì3�ú‚æ3ó´!(‚ø4ˆ˜)¨‚à4šµ!(‚«5¨˜)¨‚“5 ƒ ½ðƒì‰ì˜ÕŒ˜ªÕ˜˜�7¤˜‚ã3‚ô3‚ø3IJüœC@ The back-end implementing [`UniformSampler`] for integer types.Áà�üäOÿò(ü´9Øó(î�Ôò¦ô(��ü‘JG For simplicity, we use the same generic struct `UniformInt` for allÁüÜPM integer types `X`. This gives us only one field type, `X`; to store unsignedÁü­ PM values of this size, we take use the fact that these conversions are no-ops.Áþ �ü‚ LI For a closed range, the number of possible numbers we should generate isÁüÏ NK `range = (high - low + 1)`. To avoid bias, we must ensure that the size ofÁüž LI our sample space, `zone`, is a multiple of `range`; other values must beÁüë 52 rejected (by replacing with a new random sample).Á¡ �ü¥ LI As a special case, we use `range = 0` to represent the full range of theÁüò ?< result type (i.e. for `new_inclusive($ty::MIN, $ty::MAX)`).Á² �ü¶ JG The optimum `zone` is the largest product of `range` which fits in ourÁü�PM (unsigned) target type. We calculate this by calculating how many numbers weÁüÒVS must reject: `reject = (MAX + 1) % range = (MAX - range + 1) % range`. Any (large)Áü©MJ product of `range` will suffice, thus in `sample_single` we multiply by aÁü÷GD power of 2 via bit-shifting (faster but may cause more rejections).Á¿�üÃNK The smallest integer PRNGs generate is `u32`. For 8- and 16-bit outputs weÁü’MJ use `u32` for our `zone` and samples (because it's not slower and becauseÁüàOL it reduces the chance of having to reject a sample). In this case we cannotÁü°JG store `zone` in the target type since it is too large, however we knowÁüû*' `ints_to_reject < range <= $uty::MAX`.Á¦�üªLI An alternative to using a modulus is widening multiply: After a wideningÁü÷OL multiply by `range`, the result is in the high word. Then comparing the lowÁüÇ?< word against `zone` makes sure our distribution is uniform.Á‡�T‹ # BiasÁ–�üšNK Unless the `unbiased` feature flag is used, outputs may have a small bias.ÁüéAã†!ü«MJ 56 (`i8` and `u8`), 48 (`i16` and `u16`), 96 (`i32` and `u32`), 64 (`i64`Áüù(% and `u64`), 128 (`i128` and `u128`).Á¢�ü¦ðú(+T½”ˆ ˆ µÐ! 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“í0�7üv“Û0ø“¥5žh“¨5ðƒì‰ì ð½ðÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´Òw÷•*îàBÿº ŽÅ ñ'Æ û'Ç Å Æ Ç “œ6º ÿù0“¿5�ú“¹5ó´!(“Š7�ƒì÷•*¨“ò6šµ!(“½7�‰ì÷•*¨“¥7 Ä ½ðƒì‰ì˜ÕÛzªÕçz�7óz“¶5“Ç5“Ë5ø“š<¨ø“ï9/ž†!“«:�ø“»:Aã†!ø“‰;@®‡!Ó͈! “à;°“ß;ø“Ö;!¸“�<ñƒì‰ì ñ½ð±š*Bÿº ŽÉ ñ'Ê û'Ë Ê Ë É “›=º ÿù0“¾<�ú“¸<ó´!(“‰>é›*¨“ñ=šµ!(“¼>‰œ*¨“¤> È ½ðƒì‰ì˜Õ䃪Õðƒ�7üƒ“µ<“Æ<“Ê< ””4ƒÙÍ ø”™”§ò òƒÙBÿÌ ”«Ì Í  ”¬ДÓ4Ï ò`”ü8”� Î Î ƒÙø”¯ '4ƒÙÑ Ò Õ Ø Ú Þ ôõøûý�Ò Õ Þ Ú Ø 0”è"”í"Ð Ð ø”ý#´”€$ßÉØÊ¡’ BÿÐ ñ'Ó û'Ô Ó Ô Ð �¯!(”ø$�ßÉôƒÙ¨”à$¾¯!(”«%�ØÊŠ£*¨”“% Ò ßÉØÊ˜Õ‰ªÕ‰”„$”ˆ$ø”Ò(¾h”Õ(ßÉØÊ¡’ BÿÐ ñ'Ö û'× × Ö Ð �¯!(”×)ÿ¢*¨”¿)¾¯!(”Š*§£*¨”ò) Õ ßÉØÊ˜Õ8ŽªÕDŽ”ã(”ç(ø”Ñ09ø”÷/7Üõ 0”Ô0óô óƒÙ ô½ðŠ£*BÿÐ ŽÙ Ù ”ì0Ð ÿù0”ä0�ú”Þ0 Ø ½ð ”í0�7*’”Û0ø”¥5žh”¨5õƒì‰ì õ½ðÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´ÒwŠ£*îàBÿÐ ŽÛ ñ'Ü û'Ý Ü Û Ý ”œ6Ð ÿù0”¿5�ú”¹5ó´!(”Š7�ƒìŠ£*¨”ò6šµ!(”½7�‰ìŠ£*¨”¥7 Ú ½ðƒì‰ì˜Õ –ªÕ–�7%–”¶5”Ç5”Ë5ø”š<¨ø”ï9/ž†!”«:�ø”»:Aã†!ø”‰;@®‡!Ó͈! ”à;°”ß;ø”Ö;!¸”�<öƒì‰ì ö½ðħ*BÿÐ Žß ñ'à û'á à á ß ”›=Ð ÿù0”¾<�ú”¸<ó´!(”‰>ü¨*¨”ñ=šµ!(”¼>œ©*¨”¤> Þ ½ðƒì‰ì˜ÕŸªÕ*Ÿ�76Ÿ”µ<”Æ<”Ê< •”5ÝÙã ø•™•§÷ ÷ÝÙBÿâ •«â ã  •¬ЕÓ5å ò`•ü8•� ä ä ÝÙø•¯ '5ÝÙç è ë î ð ô ôõøûý�è ë ô î ð 0•è"•í"æ æ ø•ý#´•€$ßÉØÊãÈ Bÿæ ñ'é û'ê é ê æ �¯!(•ø$�ßÉôÝÙ¨•à$¾¯!(•«%�ØÊ�°*¨•“% è ßÉØÊ˜ÕF¤ªÕR¤•„$•ˆ$ø•Ò(¾h•Õ(ßÉØÊãÈ Bÿæ ñ'ì û'í í ì æ �¯!(•×)’°*¨•¿)¾¯!(•Š*º°*¨•ò) ë ßÉØÊ˜Õ¤©ªÕ°©•ã(•ç(ø•Ñ09ø•÷/7Üõ 0•Ô0øù øÝÙ ù½ð�°*Bÿæ Žï ï •ì0æ ÿù0•ä0�ú•Þ0 î ½ð •í0�7M­•Û0ø•¥5žh•¨5úƒì‰ì ú½ðÀœÜÄœ¯ÅœóƜǜ€Èœó‘¥_¿´Òw�°*îàBÿæ Žñ ñ'ò û'ó ñ ò ó •œ6æ ÿù0•¿5�ú•¹5ó´!(•Š7�ƒì�°*¨•ò6šµ!(•½7�‰ì�°*¨•¥7 ð ½ðƒì‰ì˜Õ±ªÕ(±�74±•¶5•Ç5•Ë5ø•š<¨ø•ï9/ž†!•«:�ø•»:Aã†!ø•‰;@®‡!Ó͈! •à;°•ß;ø•Ö;!¸•�<ûƒì‰ì û½ð×´*Bÿæ Žõ ñ'ö û'÷ õ ö ÷ •›=æ ÿù0•¾<�ú•¸<ó´!(•‰>�¶*¨•ñ=šµ!(•¼>¯¶*¨•¤> ô ½ðƒì‰ì˜ÕǹªÕÓ¹�7ß¹•µ<•Æ<•Ê<¼ºŒüÃ=: The back-end implementing [`UniformSampler`] for `usize`.Á�„�Ô…„¦ô( „�ü¤„LI Sampling a `usize` value is usually used in relation to the length of anÁüñ„MJ array or other memory structure, thus it is reasonable to assume that theÁü¿…KH vast majority of use-cases will have a maximum size under [`u32::MAX`].Áü‹†LI In part to optimise for this use-case, but mostly to ensure that resultsÁü؆PM are portable across 32-bit and 64-bit architectures (as far as is possible),Áü©‡?< this implementation will use 32-bit sampling when possible.ÁÆŠÜó‡ÆÔ«!Ü�ˆüò‡:üé‡E6dÅŒ­Úï±”uÕ7ù ú û ü TûŒûŒ…ø ø dÒ�,Ò�…ø ø l«Ž4«Ž…ø ø dø�ÆÔ«!Ü‹�ü…�#4ø�…ø ø  ? ? ?Â­Ú ?­Úÿ †ÿ  ? ?ü ü­Ú­ÚBÿþ –¸ˆþ ÿ  ? —¿ˆÃ­Ú"½Ä­Ú‚  g‚ "½"½ýþÿ ý­Ú þ€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡ÿ•˜Bÿ� ˜ň� ‚ "½œ"½ïÀÅ­ÚïÀÅ­Ú… ù±… ïÀïÀ€� €­Ú �­ÚBÿ„ ™̈„ … ïÀî ïÀ¦ÁÆ­Ú‡ · ¦Á¦Á¦Á¦Á‚ ‚­ÚBÿ† š׈† ‡ ¦Á´¡ üð< 9 The back-end implementing [`UniformSampler`] for `char`.Á­ �ü±O ÿò(ü�9 Øó(» �ü¿N K This differs from integer range sampling since the range `0xD800..=0xDFFF`ÁüŽL I are used for surrogate pairs in UCS and UTF-16, and consequently are notÁüÛN K valid Unicode code points. We must therefore avoid sampling values in thisÁTª  range.Á:\¬ ìÛ;cuêQX¬‰ ÄŒ <Œ «ˆ ˆ ©ØÆçÆçÆçÇìÛÆçÇìÛŒ †Œ ÆçÆç‡ ‡ìÛìÛBÿ‹ ž¾ ‹ Œ Æç ŸÅ ÈìÛrèÉìÛ�  g� rèrèˆ‰Š ˆìÛ ‰€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡Š•˜BÿŽ  Ë Ž � rèœrèáéÊìÛáéÊìÛ’ ù±’ áéá鋌 ‹ìÛ ŒìÛBÿ‘ ¡Ò ‘ ’ áéî áéYêËìÛ” Δ YêYêYêYê� �ìÛBÿ“ ¢Ý “ ” YêÔ½$ ü�"@ = The back-end implementing [`UniformSampler`] for `Duration`.ÁÂ" �üÆ"P M Unless you are implementing [`UniformSampler`] for your own types, this typeÁü—#9 Øó(;|È$ ¯Ýi�í§}䬈– — ÌÞ$ $Þ$ «• • ¸Þ\ý$ 4ý$ «• • bbb̯Ýb̯ݚ †š bb“ “¯Ý¯ÝBÿ™ £Ú# ™ š b ¤á# ͯÝFίÝ�  g� FF”•– ”¯Ý •€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡–•˜Bÿœ ¥ç# œ � FœF™ ϯݙ ϯݠ ù±  ™ ™ —˜ —¯Ý ˜¯ÝBÿŸ ¦î# Ÿ   ™ î ™ + Яݢ ΢ + + + + ™ ™¯ÝBÿ¡ §ù# ¡ ¢ + Äù% <œþ% «¸ÞoHTAµC|ú¤ § © ¥ ¦ ¨ ª « ¬ ,˜& <«£ £ ¸ÞL¨& $¨& «£ £ œ»& ,»& «£ £ ¾¿4Û& <«£ £ ¸Þœì& ,ì& «£ £ €— ,Œ' <«£ £ ¸Þlœ' Dœ' «£ £ t³' L³' «£ £ ”Ë' $Ë' «£ £ €— p Ѹޮ  g® p p š›œ š¸Þ ›€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡œ•˜Bÿ­ ¨–% ­ ® p œp  ©�% Ò¸Þ¶¶¶Ó¸Þ¶Ó¸Þ² †² ¶¶� �¸Þ¸ÞBÿ± ª£% ± ² ¶0Ô¸Þ0Ô¸Þµ ù±µ 00žŸ ž¸Þ Ÿ¸ÞBÿ´ «ª% ´ µ 0î 0µÕ¸Þ· η µµµµ   ¸ÞBÿ¶ ¬µ% ¶ · µtÃ" üÓ!B ? Error type returned from [`Uniform::new`] and `new_inclusive`.Á=,Ì" îà܆¹zJ–}͹ º » ¼ º ¼ T“# üØ"6 3 `low > high`, or equal in case of exclusive range.Á=F¸ ¸ îàZ\¸ ¸ îàLõ# ü£#M J Input or range `high - low` is non-finite. Not relevant to integer types.Á=]¸ ¸ îàqs¸ ¸ îàOOOÖîàOÖîà¿ †¿ OO£ £îàîàBÿ¾ ­Ÿ" ¾ ¿ O ®¦" ×îànOØîà  g nOnO¤¥¦ ¤îà ¥€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡¦•˜BÿÁ ¯¬" Á  nOœnOƒPÙîàƒPÙîàÅ ù±Å ƒPƒP§¨ §îà ¨îàBÿÄ °³" Ä Å ƒPî ƒPmQÚîàÇ ÎÇ mQmQmQmQ© ©îàBÿÆ ±¾" Æ Ç mQàü¦'/ , Sample values uniformly between two bounds.ÁÖ' �”Ú'  # ConstructionÁí' �üñ'G D [`Uniform::new`] and [`Uniform::new_inclusive`] construct a uniformÁü¹(O L distribution sampling from the given `low` and `high` limits. `Uniform` mayÁü‰)R O also be constructed via [`TryFrom`] as in `Uniform::try_from(1..=6).unwrap()`.ÁÜ) �üà)P M Constructors may do extra work up front to allow faster sampling of multipleÁü±*I F values. Where only a single sample is required it is suggested to useÁüû*H E [`Rng::random_range`] or one of the `sample_single` methods instead.ÁÄ+ �üÈ+H E When sampling from a constant range, many calculations can happen atÁü‘,N K compile-time and all methods should be fast; for floating-point ranges andÁüà,O L the full range of integer types, this should have comparable performance toÁü°-A > the [`StandardUniform`](super::StandardUniform) distribution.Áò- �ôö-  # Provided implementationsÁ•. �ü™.Q N - `char` ([`UniformChar`]): samples a range over the implementation for `u32`Áüë.O L - `f32`, `f64` ([`UniformFloat`]): samples approximately uniformly within aÁü»/P M range; bias may be present in the least-significant bit of the significandÁüŒ0H E and the limits of the input range may be sampled even when an openÁüÕ0  (exclusive) range is usedÁüõ0J G - Integer types ([`UniformInt`]) may show a small bias relative to theÁüÀ1N K expected uniform distribution of output. In the worst case, bias affectsÁü�2P M 1 in `2^n` samples where n is 56 (`i8` and `u8`), 48 (`i16` and `u16`), 96Áüà2G D (`i32` and `u32`), 64 (`i64` and `u64`), 128 (`i128` and `u128`).Áü¨32 / The `unbiased` feature flag fixes this bias.ÁüÛ3F C - `usize` ([`UniformUsize`]) is handled specially, using the `u32`Áü¢4P M implementation where possible to enable portable results across 32-bit andÁüó4  64-bit CPU architectures.Áü“5O L - `Duration` ([`UniformDuration`]): samples a range over the implementationÁÄã5  for `u32` or `u64`Áüü5K H - SIMD types (requires [`simd_support`] feature) like x86's [`__m128i`]ÁüÈ6G D and `std::simd`'s [`u32x4`], [`f32x4`] and [`mask32x4`] types areÁü�7I F effectively arrays of integer or floating-point types. Each lane isÁüÚ7O L sampled independently from its own range, potentially with more efficientÁüª8G D random-bit-usage than would be achieved with sequential sampling.Áò8 �lö8 Úð„9 �<ˆ9 �¸ü�9- š“¾9 �üÂ98 5 let between = Uniform::try_from(10..10000).unwrap();Áôû9 ÑÁ¤š:  let mut sum = 0;Á´¯:  for _ in 0..1000 {ÁüÆ:( % sum += between.sample(&mut rng);Á,ï: …‘Äõ:  println!("{}", sum);Á<Ž; �¸–; �üš;@ = For a single sample, [`Rng::random_range`] may be preferred:ÁÛ; �<ß; �¸¬ç; ³Áý; �ô�< ÑÁü <, ) println!("{}", rng.random_range(0..10));Á<Í< �¸Õ< �ÌÙ<  [`new`]: Uniform::newÁüó<- * [`new_inclusive`]: Uniform::new_inclusiveÁü¡=/ , [`Rng::random_range`]: RngExt::random_rangeÁüÑ=L I [`__m128i`]: https://doc.rust-lang.org/core/arch/x86/struct.__m128i.htmlÁüž>  [`u32x4`]: std::simd::u32x4Áü¾>  [`f32x4`]: std::simd::f32x4ÁüÞ>% " [`mask32x4`]: std::simd::mask32x4Áü„?H E [`simd_support`]: https://github.com/rust-random/rand#crate-featuresÁ><ûA ”Ê Ê µÐ! ƒB ÆÐ!l†B ‹â{�EÏZ¥É Ë Ĥ ‹âBÿàWóĤ ‹âBÿÈ È è­ moT•B óÈ È Ä¤ ÷QÛ”Í Í µÐ!¸œ¼"²ƒB ÆÐ!À…Ĥ ÷Q‹âÎ †Î éë÷Q÷Q­ ­‹â‹âBÿÌ ²Ö? Ì Î ÀÐ÷Q ³Ý? ܔРРµÐ!wæþ(³ƒB ÆÐ!€ù Ĥ F‹â� ÑRÝ”Ò Ò µÐ!бÿ(´ƒB ÆÐ!ÙŸgĤ ÑR‹âÓ  gÓ ÑRÑR®¯° ®‹â ¯€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡°•˜BÿÑ ´ã? Ñ Ó ÀÐÑRœÑRtÞ”Õ Õ µÐ!ðÀ�)µƒB ÆÐ!ù÷±Ĥ Ĥ t‹â tÞ”× × µÐ!PÀ�)`ÆÐ!U«‹+t‹âØ ù±Ø x{tt±² ±‹â ²‹âBÿÖ µê? Ö Ø ÀÐtî t¶Tß”Ú Ú µÐ!ºµ)¶ƒB ÆÐ!'ÌĤ ¶T‹âÛ ÎÛ QT¶T¶T¶T¶T³ ³‹âBÿÙ ¶õ? Ù Û ÀжTø·‰…$ ?‚æÝ ß ˜šß Ý ø·Ò…I h·Õ… Ä‚æ Ä½ð‡… BÿÜ ŽÞ Þ ·ÿ… Ü ÿù0·ì… �ú·æ… Ý ½ð6r�7Cr·ã… зŸ‡ @·¢‡ Å Å‚æBÿÜ ·«‡ Ü ß  ·¬‡ ø·û‡- ?½æá ã ˜šã á ø·͈I h·Ј Æ½æ Æ½ð‡… Bÿà Žâ â ·úˆ à ÿù0·çˆ �ú·áˆ á ½ðÌs�7Ùs·Þˆ з¤Š @·§Š Ç Ç½æBÿà ·°Š à ã  ·±Š ø¸‰…$ @øæå ç ˜šç å ø¸Ò…I h¸Õ… Èøæ ȽðÞ¿ Bÿä Žæ æ ¸ÿ… ä ÿù0¸ì… �ú¸æ… å ½ðAu�7Nu¸ã… иŸ‡ @¸¢‡ É ÉøæBÿä ¸«‡ ä ç  ¸¬‡ ø¸û‡- @³çé ë ˜šé ë ø¸͈I h¸Ј ʳç ʽðÞ¿ Bÿè Žê ê ¸úˆ è ÿù0¸çˆ �ú¸áˆ é ½ðÙv�7æv¸Þˆ и¤Š @¸§Š Ë Ë³çBÿè ¸°Š è ë  ¸±Š ø¹‰…$ Aîçí ï ˜šï í ø¹Ò…I h¹Õ… Ìîç ̽ðùõ Bÿì Žî î ¹ÿ… ì ÿù0¹ì… �ú¹æ… í ½ð@x�7Mx¹ã… йŸ‡ @¹¢‡ Í ÍîçBÿì ¹«‡ ì ï  ¹¬‡ ø¹û‡- A©èñ ó ˜šó ñ ø¹͈I h¹Ј Ωè νðùõ Bÿð Žò ò ¹úˆ ð ÿù0¹çˆ �ú¹áˆ ñ ½ðÜy�7éy¹Þˆ й¤Š @¹§Š Ï Ï©èBÿð ¹°Š ð ó  ¹±Š øº‰…$ Bäèõ ÷ ˜šõ ÷ øºÒ…I hºÕ… Ðäè н𫬠Bÿô Žö ö ºÿ… ô ÿù0ºì… �úºæ… õ ½ðG{�7T{ºã… кŸ‡ @º¢‡ Ñ ÑäèBÿô º«‡ ô ÷  º¬‡ øºû‡- BŸéù û ˜šû ù øº͈I hºЈ ÒŸé ҽ𫬠Bÿø Žú ú ºúˆ ø ÿù0ºçˆ �úºáˆ ù ½ðë|�7ø|ºÞˆ к¤Š @º§Š Ó ÓŸéBÿø º°Š ø û  º±Š ø»‰…$ CÚéý ÿ ˜šÿ ý ø»Ò…I h»Õ… ÔÚé Ô½ðºâ Bÿü Žþ þ »ÿ… ü ÿù0»ì… �ú»æ… ý ½ðn~�7{~»ã… лŸ‡ @»¢‡ Õ ÕÚéBÿü »«‡ ü ÿ  »¬‡ ø»û‡- C•ê�ƒ˜š�ƒø»͈I h»Ј Ö•ê Ö½ðºâ Bÿ€Ž‚‚»úˆ €ÿù0»çˆ �ú»áˆ �½ð"€�7/€»Þˆ л¤Š @»§Š × ×•êBÿ€»°Š € ƒ »±Š ø¼‰…$ DÐê…‡˜š‡…ø¼Ò…I h¼Õ… ØÐê Ø½ð�º Bÿ„ކ†¼ÿ… „ÿù0¼ì… �ú¼æ… …½ð���7ª�¼ã… мŸ‡ @¼¢‡ Ù ÙÐêBÿ„¼«‡ „ ‡ ¼¬‡ ø¼û‡- D‹ë‰‹˜š‹‰ø¼͈I h¼Ј Ú‹ë Ú½ð�º BÿˆŽŠŠ¼úˆ ˆÿù0¼çˆ �ú¼áˆ ‰½ðQƒ�7^ƒ¼Þˆ м¤Š @¼§Š Û Û‹ëBÿˆ¼°Š ˆ ‹ ¼±Š üŒ7 ü¾= : A distribution using weighted sampling of discrete items.Áü �ü€K H Sampling a `WeightedIndex` distribution returns the index of a randomlyÁüÌH E selected element from the iterator used when the `WeightedIndex` wasÁü•N K created. The chance of a given element being picked is proportional to theÁüäH E weight of the element. The weights can use any type `X` for which anÁü­O L implementation of [`Uniform`] exists. The implementation guarantees thatÁüýI F elements with zero weight are never picked, even when the weights areÁÜÇ  floating point numbers.Áã �Œç  # PerformanceÁù �üý H E Time complexity of sampling from `WeightedIndex` is `O(log N)` whereÁüÆ !  `N` is the number of weights.Áüè P •¤"ü¹ K ï¤"… �ü‰ L I A `WeightedIndex` contains a `Vec` and a [`Uniform`] and so itsÁüÖ O L size is the sum of the size of those objects, possibly plus some alignment.Á¦ �üª L I Creating a `WeightedIndex` will allocate enough space to hold `N - 1`Áü÷ K H weights of type `X`, where `N` is the number of weights. However, sinceÁüÃK H `Vec` doesn't guarantee a particular growth strategy, additional memoryÁü�J G might be allocated but not used. Since the `WeightedIndex` object alsoÁüÚR O contains an instance of `X::Sampler`, this might cause additional allocations,Áü­K H though for primitive types, [`Uniform`] doesn't allocate any memory.Áù �üýA > Sampling from `WeightedIndex` will result in a single call toÁü¿P M `Uniform::sample` (method of the [`Distribution`] trait), which typicallyÁü�G D will request a single value from the underlying [`Rng`], though theÁüØG D exact number depends on the implementation of `Uniform::sample`.Á  �l¤ Úð² �<¶ �¸̾ £€ üØ- ÚÉ"† �üŠ"  let choices = ['a', 'b', 'c'];Áü­  let weights = [2, 1, 1];ÁüÎ5 ÂÊ"ô„ ÑÁ¬£  for _ in 0..100 {Áü¹T Q // 50% chance to print 'a', 25% chance to print 'b', 25% chance to print 'c'ÁüŽ7 4 println!("{}", choices[dist.sample(&mut rng)]);Á,Æ …‘Ì �üÐ5 2 let items = [('a', 0.0), ('b', 3.0), ('c', 7.0)];Áü†M J let dist2 = WeightedIndex::new(items.iter().map(|item| item.1)).unwrap();Á¬Ô êº+üêS P // 0% chance to print 'a', 30% chance to print 'b', 70% chance to print 'c'Áü¾8 5 println!("{}", items[dist2.sample(&mut rng)].0);Á,÷ …‘<ý �¸… �ü‰) & [`Uniform`]: crate::distr::UniformÁ¼³ çáüË^ Ð¥"El— ”��µÐ! ¥ ÆÐ!l¨ áª"T¸ Æëý{|uœ{‰gŽ��24ÔÊ ”Ê ¨ŒŒ³‰|ê dê ¨ŒŒÀÐüÿ œÿ ¨ŒŒĤ …à”’’µÐ!¸±ÿ(½¥ ÆÐ!Àáª"¾‹‰+…Æë“ g“çé……ÜÝÞ ÜÆë Ý€g€gŠ‚gê ûcƒg£üûcØ«q¢1ȡޕ˜Bÿ‘½³ ‘ “ÀÐ…œ…;‡á”••µÐ!Òœ¼"¾¥ ÆÐ!Ûáª"Úñ†+;‡Æë–†–;‡;‡ß ߯ëÆëBÿ”¾º ” –ÀÐ;‡Ï‹â”˜˜µÐ!’À�)¿¥ ÆÐ!›áª"š«‹+Ï‹Æë¹¼Ï‹â”ššµÐ!ìÀ�)ZÆÐ!ñáª"ð«‹+Ï‹Æë›ù±›Ï‹Ï‹àá àÆë áÆëBÿ™¿Á ™ ›ÀÐÏ‹î Ï‹�Áë ã�žá➀ÁŒ  Á’ œœøÁ® <�Á± ö÷ ö ÷óÕBÿœÁÄ œ ž ÁÉ ¬\�Ãë å ¡á⡀Ì  Ã’ ŸŸøÃ® <�ñ øù ø ùóÕBÿŸÃÄ Ÿ ¡ ÃÉ ¬© �Åë 磤á⤀Ō  Å’ ¢¢øÅ® <�ű úû ú ûóÕBÿ¢ÅÄ ¢ ¤ ÅÉ ¬ø�Çë 馧á⧀nj  Ç’ ¥¥øÇ® <�DZ üý ü ýóÕBÿ¥ÇÄ ¥ § ÇÉ ¬K�Éë 멪á⪀Ɍ  É’ ¨¨øÉ® <�ɱ þÿ þ ÿóÕBÿ¨ÉÄ ¨ ª ÉÉ ¬¦�Êë 쬭á⭀ʌ  Ê’ ««øÊ® <�ʱ €� € �óÕBÿ«ÊÄ « ­ ÊÉ ¬`�Ìë í¯°áⰀ̌  Ì’ ®®øÌ® <�̱ ‚ƒ ‚ ƒóÕBÿ®ÌÄ ® ° ÌÉ ¬��Îë ï²³áⳀΌ  Î’ ±±øÎ® <�α „… „ …óÕBÿ±ÎÄ ± ³ ÎÉ ¬£�Ðë ñµ¶áⶀЌ  Ð’ ´´øÐ® <�б †‡ † ‡óÕBÿ´ÐÄ ´ ¶ ÐÉ ¬›"�Òë ó¸¹áâ¹€ÒŒ  Ò’ ··øÒ® <�Ò± ˆ‰ ˆ ‰óÕBÿ·ÒÄ · ¹ ÒÉ ¬R%�Ôë õ»¼áâ¼€ÔŒ  Ô’ ººøÔ® <�Ô± Š‹ Š ‹óÕBÿºÔÄ º ¼ ÔÉ ¬(�Õë ö¾¿áâ¿€ÕŒ  Õ’ ½½øÕ® <�Õ± Œ� Œ �óÕBÿ½ÕÄ ½ ¿ ÕÉ ¬ê*�ÖôHÁÂáâ€֕ Ö›ÀÀøÖº<�Ö½Ž� Ž �óÕBÿÀÖÐÀ  ÖÕ¬,�×ôIÄÅáâŀו ×›ÃÃø×º<�×½�‘ � ‘óÕBÿÃ×Ðà Š×Õ¬ù,t÷ÌÈ Invalid weight errorsÁâ�üæ<9 This type represents errors from [`WeightedIndex::new`],Áü£GD [`WeightedIndex::update_weights`] and other weighted distributions.Á:ŒåJ,€Çîrì÷WußþÇÈÉÊËÌÍÎÈÊÌÎdÕüŒDA The input weight sequence is empty, too long, or wrongly orderedÁJTÆÆÇîhjÆÆÇîl¼üèOL A weight is negative, too large for the distribution, or not a valid numberÁJ_ÆÆÇîsuÆÆÇîœòüÐ>; Not enough non-zero weights are available to sample valuesÁ“�ü›JG When attempting to sample a single value this implies that all weightsÁüêIF are zero. When attempting to sample `amount` values this implies thatÁü¸52 less than `amount` weights are greater than zero.ÁJ@ÆÆÇîUXÆÆÇîDÁüŒ0- Overflow when calculating the sum of weightsÁJ@ÆÆÇîTVÆÆÇî3-÷ÇîРgÐ3-3-’“” ’Çî “€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡”•˜BÿÏØôÏ Ð3-œ3-•.•.•.øÇî•.øÇîÓ†Ó•.•.• •ÇîÇîBÿÒÙûÒ Ó•. Ú‚ùÇîñ.úÇîñ.úÇî×ù±×ñ.ñ.–— –Çî —ÇîBÿÖÛˆÖ ×ñ.î ñ.Û/ûÇîÙÎÙÛ/Û/Û/Û/˜ ˜ÇîBÿØÜ“Ø ÙÛ/Ô½Güá$%" The Standard Uniform distributionÁ‡%�ü‹%SP This [`Distribution`] is the *standard* parameterization of [`Uniform`]. BoundsÁüß%.+ are selected according to the output type.ÁŽ&�ü’&FC Assuming the provided `Rng` is well-behaved, these implementationsÁüÙ&@= generate values with the following ranges and distributions:Áš'�üž'C@ * Integers (`i8`, `i32`, `u64`, etc.) are uniformly distributedÁüâ'OL over the whole range of the type (thus each possible value may be sampledÁô²( with equal probability).ÁüÑ(NK * `char` is uniformly distributed over all Unicode scalar values, i.e. allÁü )DA code points in the range `0...0x10_FFFF`, except for the rangeÁüå)B? `0xD800...0xDFFF` (the surrogate code points). This includesÁü¨*&# unassigned/reserved code points.ÁüÏ*UR For some uses, the [`Alphanumeric`] or [`Alphabetic`] distribution will be moreÁ”¥+ appropriate.Áü¸+B? * `bool` samples `false` or `true`, each with probability 0.5.Áüû+MJ * Floating point types (`f32` and `f64`) are uniformly distributed in theÁüÉ,[X half-open range `[0, 1)`. See also the [notes below](#floating-point-implementation).Áü¥-NK * Wrapping integers ([`Wrapping`]), besides the type identical to theirÁôô- normal integer variants.Áü“.LI * Non-zero integers ([`NonZeroU8`]), which are like their normal integerÁüà.&# variants but cannot sample zero.Á‡/�ü‹/PM The `StandardUniform` distribution also supports generation of the followingÁüÜ/;8 compound types where all component types are supported:Á˜0�üœ0JG * Tuples (up to 12 elements): each element is sampled sequentially andÁüç0OL independently (thus, assuming a well-behaved RNG, there is no correlationÁÄ·1 between elements).ÁüÐ1EB * Arrays `[T; n]` where `T` is supported. Each element is sampledÁü–2JG sequentially and independently. Note that for small `T` this usuallyÁüá2PM results in the RNG discarding random bits; see also [`RngExt::fill`] whichÁü²3KH offers a more efficient approach to filling an array of integer typesÁ¼þ3 with random data.Áü–4KH * SIMD types (requires [`simd_support`] feature) like x86's [`__m128i`]Áüâ4GÛù*üª5I¬ú*üô5MJ sampled independently, potentially with more efficient random-bit-usageÁüÂ6NK (and a different resulting value) than would be achieved with sequentialÁü‘7/, sampling (as with the array types above).ÁÁ7�ìÅ7 ## Custom implementationsÁã7�üç7VS The [`StandardUniform`] distribution may be implemented for user types as follows:Á¾8�<Â8�¸ÔÊ8 # #![allow(dead_code)]Áäå8í…#ü‚952 use rand::distr::{Distribution, StandardUniform};Á¸9�”¼9 struct MyF32 {Á|Ï9 x: f32,Á,ß9…‘å9�üé92/ impl Distribution for StandardUniform {Áüœ:A> fn sample(&self, rng: &mut R) -> MyF32 {ÁüÞ:%" MyF32 { x: rng.random() }ÁL„;‰† ,Ž;…‘<”;�¸œ;�¤ ; ## Example usageÁ<µ;�¸̽;£€ ü×;%" use rand::distr::StandardUniform;Áý;�ü�<74 let val: f32 = rand::rng().sample(StandardUniform);Áü¹<)& println!("f32 from [0, 1): {}", val);Á<ã<�¸ë<�üï<# # Floating point implementationÁü“=WT The floating point implementations for `StandardUniform` generate a random value inÁüë=@= the half-open interval `[0, 1)`, i.e. including 0 but not 1.Á¬>�ü°>Jݾ'üû>M±¿'üÉ?IˆÀ'ü“@FC multiplicative method: `(rng.gen::<$uty>() >> N) as $ty * (ε/2)`.ÁÚ@�üÞ@LI See also: [`Open01`] which samples from `(0, 1)`, [`OpenClosed01`] whichÁü«AOL samples from `(0, 1]` and `Rng::random_range(0..1)` which also samples fromÁüûAOL `[0, 1)`. Note that `Open01` uses transmute-based methods which yield 1 bitÁüËBPM less precision but may perform faster on some architectures (on modern IntelÁüœC;8 CPUs all methods have approximately equal performance).ÁØC�üÜC! 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Both are also implemented by the [rand_xoshiro] crate.Á� �ì”  ## Seeding (construction)Á² �ü¶ H E This generator implements the [`SeedableRng`] trait. All methods areÁüÿ N K suitable for seeding, but note that, even with a fixed seed, output is notÁüÎ !  [portable]. Some suggestions:Áð �üô K H 1. To automatically seed with a unique seed, use [`rand::make_rng()`]:Á\À  ```ÁüÌ!  use rand::rngs::SmallRng;Áüî1 . let mut rng: SmallRng = rand::make_rng();Áü 0 - # let _ = rand::Rng::next_u32(&mut rng);Á\Ñ й,üÝN K 2. To use a deterministic integral seed, use `seed_from_u64`. This uses aÁü¬J G hash function internally to yield a (typically) good seed from anyÁt÷ input.Á\† й,ü’2 / # use rand::{SeedableRng, rngs::SmallRng};ÁüÅ- * let rng = SmallRng::seed_from_u64(1);Áüó  # let _: SmallRng = rng;Á\” й,ü P M 3. To seed deterministically from text or other input, use [`rand_seeder`].Áñ �üõ( % See also [Seeding RNGs] in the book.Áž �Œ¢  ## GenerationÁ´ �ü¸> ; The generator implements [`Rng`] and thus also [`RngExt`].Áü÷5 æý#­ �ü±D A [portable]: https://rust-random.github.io/book/crate-reprod.htmlÁüöI F [Seeding RNGs]: https://rust-random.github.io/book/guide-seeding.htmlÁüÀI Ô‚$üŠI F [Quality]: https://rust-random.github.io/book/guide-rngs.html#qualityÁüÔ# [`StdRng`]: crate::rngs::StdRngÁüø1 . [rand_pcg]: https://crates.io/crates/rand_pcgÁüª9 6 [rand_xoshiro]: https://crates.io/crates/rand_xoshiroÁüäD A [`rand_seeder`]: https://docs.rs/rand_seeder/latest/rand_seeder/ÁÜ©  [`Rng`]: rand_core::RngÁìÅ ¦ƒ$üã) & [`rand::make_rng()`]: crate::make_rngÁQD¿ ÜõÓ¡|�õ+à<›œÚ÷ÜõBÿpÎ7³Ú÷ÜõBÿšš ›È ³ššÚ÷¼Üõž†žÏ ÏÜõÜõBÿ�¤– � žÙ½Üõ  g ÙÙÐÑÒ ÐÜõ Ñ€g€gŠ‚gê ûcƒg£üûcØ«q¢1ȡҕ˜BÿŸ¥� Ÿ  ÙœÙL¾ÜõL¾Üõ£ù±£LLÓÔ ÓÜõ ÔÜõBÿ¢¦¤ ¢ £Lî L0¿Üõ¥Î¥0000Õ ÕÜõBÿ¤§¯ ¤ ¥0ì×üð+( A xoshiro128++ random number generator.Áœ�ü NK The xoshiro128++ algorithm is not suitable for cryptographic purposes, butÁüï:7 is very fast and has excellent statistical properties.Áª�ü®JG The algorithm used here is translated from [the `xoshiro128plusplus.c`ÁüùNK reference source code](http://xoshiro.di.unimi.it/xoshiro128plusplus.c) byÁüÈ(% David Blackman and Sebastiano Vigna.ÁR”âÝö1ㇽ�§\û ûĦ¦ Á „P ÀÝöª gªP P ÚÛÜ ÚÝö Û€g€gŠ‚gê ûcƒg£üûcØ«q¢1ȡܕ˜Bÿ©¨ú© ªP œP BÆÚ÷¸ g¸>B>Båæç åÚ÷ æ€g€gŠ‚gê ûcƒg£üûcØ«q¢1ȡ畘Bÿ·¯ú· ¸>Bœ>B,ÇÚ÷º†º,,è èÚ÷Ú÷Bÿ¹°�¹ º,UÈÚ÷UÈÚ÷½ù±½UUéê éÚ÷ êÚ÷Bÿ¼±ˆ¼ ½Uî UÎDÉÚ÷¿Î¿ÎDÎDÎDÎDë ëÚ÷Bÿ¾²“¾ ¿ÎD’ Òåå+Úüñ0- A strong, fast (amortized), non-portable RNGÁ¢�ü¦JG This is the "standard" RNG, a generator with the following properties:Áñ�üõJ‚°,üÀ,Ö°,üíB? (For a portable version, use the [chacha20] crate directly.)Áü°LI - [CSPRNG]: statistically good quality of randomness and [unpredictable]ÁüýKH - Fast ([amortized](https://en.wikipedia.org/wiki/Amortized_analysis)):ÁüÉNK the RNG is fast for bulk generation, but the cost of method calls is notÁü˜2/ consistent due to usage of an output buffer.ÁË�üÏPM The current algorithm used is the ChaCha block cipher with 12 rounds. PleaseÁü  MJ see this relevant [rand issue] for the discussion. This may change as newÁüî B? evidence of cipher security and performance becomes available.Á± �ìµ è¶,Ó �ü× PM This generator implements the [`SeedableRng`] trait. Any method may be used,Áü¨ MJ but note that `seed_from_u64` is not suitable for usage where security isÁüö PM important. Also note that, even with a fixed seed, output is not [portable].ÁÇ �üË HE Using a fresh seed **direct from the OS** is the most secure option:Á<” �¸üœ 63 # use rand::{SeedableRng, rngs::{StdRng, SysRng}};ÁüÓ 96 let rng = StdRng::try_from_rng(&mut SysRng).unwrap();ÁÔ� # let _: StdRng = rng;Á<¨�¸°�ü´>; Seeding via [`rand::make_rng()`] or [`rand::rng()`] may beÁ\ó faster:Á<ÿ�¸ì‡ # use rand::rngs::StdRng;Áü¥+( let mut rng: StdRng = rand::make_rng();ÁüÑ,Ùé&<þ�¸†�üŠPM Any [`SeedableRng`] method may be used, but note that `seed_from_u64` is notÁüÛMJ suitable where security is required. See also [Seeding RNGs] in the book.Á©�Œ­¯¿,¿�üÃ>Ö¿,ü‚5æý#¸�ü¼D¸À,ü�I†Á,üËPM [unpredictable]: https://rust-random.github.io/book/guide-rngs.html#securityÁüœIÔ‚$üæwt [CSPRNG]: https://rust-random.github.io/book/guide-gen.html#cryptographically-secure-pseudo-random-number-generatorÁüÞ1. [chacha20]: https://crates.io/crates/chacha20Áü�@= [rand issue]: https://github.com/rust-random/rand/issues/932ÁÜѲÄ,ìí¦ƒ$ü‹)äÄ,üµ [`rand::rng()`]: crate::rngÁV4€×ø±EÄÔ1WóäÃÄÝÍ×øBÿØã7ïÝÍ×øBÿ ÇïÂÂÝÍ©fÌ×øÆ gÆ©f©fðñò ð×ø ñ€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡ò•˜BÿŶÞÅ Æ©fœ©fhÍ×øhÍ×øÉù±Éhhóô ó×ø ô×øBÿÈ·åÈ Éhî hŠhÎ×øËÎËŠhŠhŠhŠhõ õ×øBÿʸðÊ ËŠh¤ì'ü³-* A reference to the thread-local generatorÁá�üåLI This type is a reference to a lazily-initialized thread-local generator.Áü²HE An instance can be obtained via [`rand::rng()`][crate::rng()] or viaÁìû [`ThreadRng::default()`].Áü™JG The handle cannot be passed between threads (is not `Send` or `Sync`).Áä�tèüº$÷�üûIF Security must be considered relative to a threat model and validationÁüÅJG requirements. The Rand project can provide no guarantee of fitness forÁü�@= purpose. The design criteria for `ThreadRng` are as follows:ÁÑ�üÕGD - Automatic seeding via [`SysRng`] and after every 64 kB of output.Áü�WT Limitation: there is no automatic reseeding on process fork (see [below](#fork)).ÁüõRO - A rigorously analyzed, unpredictable (cryptographic) pseudo-random generatorÁüÈ`] (see [the book on security](https://rust-random.github.io/book/guide-rngs.html#security)).Áü©=: The currently selected algorithm is ChaCha (12-rounds).Áüç(% See also [`StdRng`] documentation.Áü�C@ - Not to leak internal state through [`Debug`] or serializationÁ´Ô implementations.ÁüëIF - No further protections exist to in-memory state. In particular, theÁüµNK implementation is not required to zero memory on exit (of the process orÁü„/, thread). (This may change in the future.)Áü´GD - Be fast enough for general-purpose usage. Note in particular thatÁüüIF `ThreadRng` is designed to be a "fast, reasonably secure generator"ÁüÆ=: (where "reasonably secure" implies the above criteria).Á„ �üˆ KH We leave it to the user to determine whether this generator meets theirÁüÔ >; security requirements. For an alternative, see [`SysRng`].Á“!�Ô—! # Forks and interruptsÁ²!�ü¶!KH `ThreadRng` is not automatically reseeded on fork. It is recommended toÁü‚"PM explicitly call [`ThreadRng::reseed`] immediately after a fork, for example:ÁlÓ" ```ignoreÁ”á" fn do_fork() {Áüô"*' let pid = unsafe { libc::fork() };Á¬Ÿ# if pid == 0 {Áüµ#30 // Reseed ThreadRng in child processes:Áüé#! rand::rng().reseed();ÁL‹$‰† ,•$…‘<›$�¸£$�ü§$OL Methods on `ThreadRng` are not reentrant-safe and thus should not be calledÁü÷$OL from an interrupt (e.g. a fork handler) unless it can be guaranteed that noÁüÇ%@= other method on the same `ThreadRng` is currently executing.Áˆ&�dŒ&œž#™&�ü�&IF Implementations of [`TryRng`] and [`Rng`] panic in case of [`SysRng`]Áüç&/, failure during reseeding (highly unlikely).Á—'�ü›'#ºÂ,Ü¿'²Ä,XL÷'Œú•€º´P¢qÍü¯(,¯(€ÌÌäçItÑŒúφÏItItþ þŒúŒúBÿνä'Î ÏItùÁÇg.atâ.€åìùÂÔ&eÙÂ×e€äçBÿ Ñ,ž0Ñ�Ò�Ò�ÒÒÑÒþ¯$¸ÓUÿHwÐçÓÓÐçѦeÐ�Ô�Ô�ÔÔÐõïù®Oe¹Âµe €�g�gStorageÁ�g�ûf‘gƒûf§~Ÿ½[l(ÚäçÃÿÿÿÿÿÿÑ‚!eÐ�Ö�Ö�ÖÖЉðùŠ"Ne¹Â‘"e €�g�g»�-�g�ûf‘gƒûf§~Ÿ½[l(ÚäçÃÿÿÿÿÿÿüΉ4üŠˆ-* An iterator over multiple slice elements.Á¸ˆ�켈 This struct is created byÁüÚˆHE [`IndexedRandom::sample`](trait.IndexedRandom.html#tymethod.sample).ÁÓ«Œ©‰Ì£‰_tÙ‰ú$Ù�Ú�ÛÛÚÙÙ‘&4ï‰Û› ü‰ë‘&ø‰û‘&ÿ‰ë‘&d‰ŠŸû›«j‚N©òïÜÝÞè‰ ì‰ÙXZÙM,‰ŠêØØ ú$îûü›Š&D›ŠêØØ¥¼üÇŠ <ÇŠêØØˆ€qâú$à�á�âàáâÙ‘&Û›ŸgîûØì‰ë‘& ˜µ'Øü‰û‘&)Ÿûã gãàehà $»¼½ »Ÿû ¼€g€gŠ‚gê ûcƒg£üûcØ«q¢1È¡½•˜BÿߨƉß ãú$îûñ»ÛœãŒ• Äí A vector of indices.Á†�üŠ30 Multiple internal representations are possible.Á`šœ•üÄž®K/~í�åæèéæç�ý•üBÿéê‡þ•üBÿ†øt­ 4³ `«øää æÃøÇø�ý•üBÿä䯜-DÄ ää�ýÅøÆÔ«!ÜÙ üÓ #tû 4� `ÿøää éùù‡þ•üBÿääÓ�-D’ ää‡þÚã•üì†ìúþÁ Á•ü•üBÿëÙÇë ìLsä•üî gî“—ÂÃÄ Â•ü Àg€gŠ‚gê ûcƒg£üûcØ«q¢1ȡĕ˜BÿíÚÎí î<œDÌÙ"ü£"$! 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